In order that the measured intensities get properly corrected for matrix effects we need to know the composition of the sample (and the standard).
For standards this is easy because of course we already know the composition of the standard (or it wouldn't be a standard!). So based on the "published" standard composition from the Standard.mdb database we calculate the physics relative to the theoretical pure element. This is called the standard k-factor and is calculated as seen here for each element.
(https://smf.probesoftware.com/oldpics/i40.tinypic.com/314qxjp.jpg)
If the standard is a pure element, then the concentration is 1.0 and the matrix correction is 1.0 and therefore the std k-factor is 1.0. In any case the std k-factor is included in the calculation of the unknown concentration by iteratively determining the unknown composition starting with the "1st approximation" where the ratio of intensities (Iunk/Istd) is assumed to be equal to the ratio of the concentrations (Cunk/Cstd) and calculated as seen here:
(https://smf.probesoftware.com/oldpics/i42.tinypic.com/24qnv3s.jpg)
What does all this mean? It means that we need to know the correct composition of the unknown in order to correctly calculate the concentration of each measured element. Therefore, if some elements are *not* measured, for example, geologists often (but not always) assumed formula stoichiometry for including oxygen in the matrix correction. Obviously in the case of variable oxidation states, e.g., FeO vs. Fe2O3, replacement of stoichiometric oxygen by halogens, and glasses containing significant H2O, there is some ambiguity in the matrix chemistry which can significantly affect the matrix correction for measured elements as seen in these posts:
http://smf.probesoftware.com/index.php?topic=62.msg235#msg235
http://smf.probesoftware.com/index.php?topic=81.msg292#msg292
In practice we can sometimes "get away" with a simplification of the matrix assumption, for a quite amazing example we might try measuring only U, Th, Pb (and Y and La for the interference correction on Pb Ma) and assuming CePO4 by difference in the matrix correction of the mineral monazite. Surprisingly this assumption works to an extent that is quite impressive, though obviously one cannot assume that this simplification of the matrix composition is accurate enough without careful testing both ways.
However, it is not uncommon that if the element in question does not cause an interference and is not especially critical in the matrix correction (run a model in CalcZAF and check the absorption correction!), we can simply specify the element as an "unanalyzed" element. In CalcZAF and Probe for EPMA this means that the element does not have an x-ray line specified as shown here in the Elements/Cations dialog from the Analyze! or Acquire! windows:
(https://smf.probesoftware.com/oldpics/i43.tinypic.com/zwcf4h.jpg)
Once the element is entered as an "unanalyzed" element, we can use the Specified Concentrations (or Calculation Options) dialog from the Analyze! window to enter element concentrations by "specification" as seen here:
(https://smf.probesoftware.com/oldpics/i41.tinypic.com/11m4a5z.jpg)
This dialog, seen below, has many options for entering elements that are unanalyzed, or even measured by another technique:
(https://smf.probesoftware.com/oldpics/i42.tinypic.com/2yplov9.jpg)
The simplest method is to click on a row in the element grid containing a specified (or unanalyzed) element and enter the specified concentration in elemental or oxide weight percent. One can also specify by formula, by standard composition (useful when analyzing a standard as an unknown), by text file input (see User's Reference manual for details), or by the (one time) analysis of another sample or by the analysis of a sample just prior to the analysis of the currently selected sample. Whew!
Other options for matrix specification are available in the Calculation Options dialog from the Analyze! window which we turn to next.
From the Analyze! window we can also select the Calculation Options dialog and then we see this:
(https://smf.probesoftware.com/oldpics/i43.tinypic.com/2ii72at.jpg)
Note that in this example we have selected calculate oxygen by formula stoichiometry (the oxygen stoichiometry can be changed in the Elements/Cations dialog), element by difference is Ce and calculate P by stoichiometry to the stoichiometrc oxygen.
This allows us to specify the formula CePO4 by difference from the measured elements expressed as oxides without measuring Ce or P or O.
There are many variations on this method, for example in carbonates we might specify oxygen by stoichiometry and carbon by stoichiometry (0.333 to 1) to the stoichiometric (calculated) oxygen to obtain CO3 by stoichiometry to the measured cations (usually Ca, Mg, Fe, Mn, etc).
Here's an example of a monazite calculation that I've done where Ce2O3 was calculated by difference and P2O5 was calculated by stoichiometry to the calculated (stoichiometric) oxygen using the settings in the Calculation Options dialog shown in the previous post:
Un 8 Allaz-3
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 50.0 Beam Size = 5
(Magnification (analytical) = 40000), Beam Mode = Analog Spot
(Magnification (default) = 400, Magnification (imaging) = 800)
Image Shift (X,Y): .00, .00
Number of Data Lines: 9 Number of 'Good' Data Lines: 9
First/Last Date-Time: 10/30/2013 12:04:35 PM to 10/30/2013 01:02:35 PM
WARNING- Using Exponential Off-Peak correction for th ma
Average Total Oxygen: 27.194 Average Total Weight%: 100.000
Average Calculated Oxygen: 27.194 Average Atomic Number: 39.773
Average Excess Oxygen: .000 Average Atomic Weight: 39.299
Average ZAF Iteration: 11.00 Average Quant Iterate: 3.00
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element Ce is Calculated by Difference from 100%
Element P is Calculated .25 Atoms Relative To 1.0 Atom of Oxygen
Un 8 Allaz-3, Results in Elemental Weight Percents
ELEM: U Th Pb Y La Ce P O
TYPE: ANAL ANAL ANAL ANAL ANAL DIFF STOI CALC
BGDS: LIN EXP LIN LIN LIN
TIME: 200.00 200.00 200.00 120.00 120.00
BEAM: 49.82 49.82 49.82 49.82 49.82
ELEM: U Th Pb Y La Ce P O SUM
219 .472 3.341 .567 1.826 9.508 43.870 13.179 27.237 100.000
220 .446 3.334 .524 1.638 9.721 43.952 13.169 27.216 100.000
221 .237 3.150 .424 1.054 9.937 44.893 13.142 27.162 100.000
222 .510 3.582 .581 1.695 9.716 43.555 13.161 27.200 100.000
223 .445 3.923 .599 1.587 9.413 43.725 13.144 27.165 100.000
224 .512 3.290 .558 1.789 9.884 43.557 13.177 27.234 100.000
225 .515 3.329 .573 1.865 9.354 43.944 13.180 27.240 100.000
226 .125 4.790 .400 1.349 8.802 44.278 13.126 27.129 100.000
227 .446 3.816 .595 1.555 9.514 43.764 13.145 27.167 100.000
AVER: .412 3.617 .536 1.595 9.539 43.949 13.158 27.194 100.000
SDEV: .137 .509 .074 .257 .342 .418 .019 .040 .000
SERR: .046 .170 .025 .086 .114 .139 .006 .013
%RSD: 33.28 14.08 13.75 16.13 3.59 .95 .15 .15
STDS: 15 18 386 1016 836 0 0 0
STKF: .8725 .8707 .6861 .4480 .6591 .0000 .0000 .0000
STCT: 137.33 44.30 140.31 38.76 33.08 .00 .00 .00
UNKF: .0035 .0302 .0041 .0116 .0829 .0000 .0000 .0000
UNCT: .55 1.54 .84 1.00 4.16 .00 .00 .00
UNBG: .77 .26 .54 .13 .19 .00 .00 .00
ZCOR: 1.1794 1.1961 1.3069 1.3748 1.1510 .0000 .0000 .0000
KRAW: .0040 .0347 .0060 .0259 .1257 .0000 .0000 .0000
PKBG: 1.71 6.87 2.56 8.82 23.27 .00 .00 .00
INT%: -14.77 ---- -2.38 ---- ---- ---- ---- ----
Un 8 Allaz-3, Results in Oxide Weight Percents
ELEM: UO2 ThO2 PbO Y2O3 La2O3 Ce2O3 P2O5 O SUM
219 .536 3.802 .611 2.319 11.151 51.384 30.198 .000 100.000
220 .506 3.794 .564 2.080 11.401 51.480 30.175 .000 100.000
221 .268 3.585 .457 1.339 11.654 52.582 30.115 .000 100.000
222 .578 4.076 .626 2.153 11.395 51.015 30.157 .000 100.000
223 .504 4.464 .645 2.015 11.040 51.214 30.118 .000 100.000
224 .580 3.744 .601 2.272 11.591 51.018 30.194 .000 100.000
225 .584 3.788 .617 2.368 10.970 51.471 30.201 .000 100.000
226 .142 5.451 .431 1.713 10.323 51.863 30.078 .000 100.000
227 .505 4.342 .641 1.974 11.157 51.260 30.120 .000 100.000
AVER: .467 4.116 .577 2.026 11.187 51.476 30.151 .000 100.000
SDEV: .156 .580 .079 .327 .401 .490 .045 .000 .000
SERR: .052 .193 .026 .109 .134 .163 .015 .000
%RSD: 33.28 14.08 13.75 16.13 3.59 .95 .15 375.00
STDS: 15 18 386 1016 836 0 0 0
Un 8 Allaz-3, Results in Millions of Years Ago, EPMA Age (from U, Th, Pb)
U WT% Th WT% Pb WT% U PPM Th PPM Pb PPM Age[My] Calc Pb %Pb(Th) %Pb(U)
219 .472289 3.34109 .567045 4722.89 33410.9 5670.45 2323.00 5670.27 64.3415 35.6635
220 .446398 3.33429 .523589 4463.98 33342.9 5235.90 2208.20 5236.10 65.9074 34.0874
221 .236642 3.15039 .424494 2366.42 31503.9 4244.94 2226.00 4245.02 77.4650 22.5299
222 .509558 3.58221 .581436 5095.58 35822.1 5814.36 2231.20 5814.52 64.4655 35.5293
223 .444676 3.92270 .598909 4446.76 39227.0 5989.09 2258.10 5989.38 69.4054 30.5896
224 .511685 3.28988 .557768 5116.85 32898.8 5577.68 2252.20 5577.78 62.3314 37.6634
225 .515049 3.32893 .572963 5150.49 33289.3 5729.63 2285.30 5729.68 62.3537 37.6412
226 .124814 4.79049 .399875 1248.14 47904.9 3998.75 1650.30 3998.89 91.3724 8.62120
227 .445556 3.81612 .594983 4455.56 38161.2 5949.83 2281.40 5949.84 68.7099 31.2850
AVER: .411852 3.61734 .535674 4118.52 36173.4 5356.74 2190.63 5356.83 69.5947 30.4012
SDEV: .137073 .509306 .073673 1370.73 5093.06 736.728 205.618 736.721 9.41884 9.41990
Here's another one: turquoise, which has the ideal formula CuAl6(PO4)4(OH)8 4(H2O). The Calculation Options dialog looks like this:
(https://smf.probesoftware.com/oldpics/i39.tinypic.com/s480ma.jpg)
Since the ratio of H to Al is 16 to 6, that is 2.666 and this gives the following results
Un 5 Turquoise matrix3
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 30.0 Beam Size = 20
(Magnification (analytical) = 40000), Beam Mode = Analog Spot
(Magnification (default) = 400, Magnification (imaging) = 2797)
Image Shift (X,Y): .00, .00
Number of Data Lines: 9 Number of 'Good' Data Lines: 6
First/Last Date-Time: 11/20/2013 03:51:02 PM to 11/20/2013 04:22:23 PM
WARNING- Using Exponential Off-Peak correction for p ka
WARNING- Using Slope-Lo Off-Peak correction for ba la
WARNING- Using Exponential Off-Peak correction for si ka
WARNING- Using Time Dependent Intensity (TDI) Element Correction
Average Total Oxygen: 55.067 Average Total Weight%: 99.890
Average Calculated Oxygen: 55.067 Average Atomic Number: 11.402
Average Excess Oxygen: .000 Average Atomic Weight: 14.468
Average Charge Balance: .005 Fe+ Atomic Charge: 2.000
Average ZAF Iteration: 3.00 Average Quant Iterate: 3.00
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element H is Calculated 2.666 Atoms Relative To 1.0 Atom of Al
Un 5 Turquoise matrix3, Results in Elemental Weight Percents
ELEM: Na P Ca Al K Fe Cu S Ba Si H O
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL RELA CALC
BGDS: LIN EXP LIN LIN LIN LIN LIN LIN S-Lo EXP
TIME: 60.00 60.00 60.00 60.00 60.00 60.00 60.00 60.00 60.00 60.00
BEAM: 30.02 30.02 30.02 30.02 30.02 30.02 30.02 30.02 30.02 30.02
ELEM: Na P Ca Al K Fe Cu S Ba Si H O SUM
137 .007 13.984 .007 21.165 .061 .259 6.374 .240 .084 .015 2.108 54.469 98.775
140 -.005 14.102 .008 21.078 .067 .289 6.501 .241 .066 .016 2.099 54.612 99.074
141 .004 14.246 .006 21.467 .061 .271 6.770 .234 .062 .019 2.138 55.355 100.633
142 -.001 14.404 .005 21.356 .081 .238 6.673 .216 .039 .013 2.127 55.515 100.664
143 -.009 14.583 .003 21.192 .065 .268 6.559 .221 .053 .018 2.111 55.700 100.764
144 .001 14.177 .012 21.088 .069 .301 6.644 .227 .042 .019 2.100 54.749 99.429
AVER: -.001 14.250 .007 21.224 .067 .271 6.587 .230 .058 .017 2.114 55.067 99.890
SDEV: .006 .216 .003 .155 .007 .022 .140 .010 .017 .002 .015 .520 .898
SERR: .002 .088 .001 .063 .003 .009 .057 .004 .007 .001 .006 .212
%RSD: -834.06 1.51 44.38 .73 10.91 8.26 2.12 4.53 29.36 14.98 .73 .94
STDS: 336 285 285 336 336 395 1124 327 835 336 0 0
STKF: .0735 .1599 .3596 .1331 .0409 .6779 .2439 .2207 .7430 .1500 .0000 .0000
STCT: 72.02 276.07 585.58 256.36 29.05 479.39 154.24 192.18 272.78 259.24 .00 .00
UNKF: .0000 .1087 .0001 .1545 .0006 .0023 .0517 .0018 .0004 .0001 .0000 .0000
UNCT: .00 187.63 .10 297.46 .41 1.62 32.68 1.56 .15 .20 .00 .00
UNBG: .33 1.28 .88 .82 .36 .67 1.22 .18 .87 .83 .00 .00
ZCOR: 2.0716 1.3112 1.1184 1.3741 1.1633 1.1845 1.2744 1.2824 1.3769 1.4007 .0000 .0000
KRAW: .0000 .6797 .0002 1.1603 .0141 .0034 .2119 .0081 .0006 .0008 .0000 .0000
PKBG: .99 147.55 1.12 366.70 2.15 3.42 27.70 9.80 1.18 1.25 .00 .00
INT%: -.43 ---- ---- .00 ---- ---- ---- ---- -51.65 ---- ---- ----
TDI%: -.916 -1.846 .068 ---- 2.184 -5.326 ---- ---- ---- ---- ---- ----
DEV%: 5.1 .4 3.9 ---- 3.9 2.6 ---- ---- ---- ---- ---- ----
TDIF: LINEAR QUADRA LINEAR ---- LINEAR LINEAR ---- ---- ---- ---- ---- ----
TDIT: 75.00 76.17 75.33 ---- 77.00 75.83 ---- ---- ---- ---- ---- ----
TDII: .332 188. .974 ---- .778 2.24 ---- ---- ---- ---- ---- ----
Un 5 Turquoise matrix3, Results in Oxide Weight Percents
ELEM: Na PO4 Ca Al K Fe Cu SO4 Ba Si H4O3 O SUM
137 .007 42.880 .007 21.165 .061 .259 6.374 .718 .084 .015 27.203 .000 98.775
140 -.005 43.241 .008 21.078 .067 .289 6.501 .722 .066 .016 27.091 .000 99.074
141 .004 43.682 .006 21.467 .061 .271 6.770 .701 .062 .019 27.591 .000 100.633
142 -.001 44.168 .005 21.356 .081 .238 6.673 .646 .039 .013 27.448 .000 100.664
143 -.009 44.716 .003 21.192 .065 .268 6.559 .661 .053 .018 27.237 .000 100.764
144 .001 43.471 .012 21.088 .069 .301 6.644 .679 .042 .019 27.104 .000 99.429
AVER: -.001 43.693 .007 21.224 .067 .271 6.587 .688 .058 .017 27.279 .000 99.890
SDEV: .006 .661 .003 .155 .007 .022 .140 .031 .017 .002 .200 .000 .898
SERR: .002 .270 .001 .063 .003 .009 .057 .013 .007 .001 .081 .000
%RSD: -834.06 1.51 44.38 .73 10.91 8.26 2.12 4.53 29.36 14.98 .73 451.66
STDS: 336 285 285 336 336 395 1124 327 835 336 0 0
Un 5 Turquoise matrix3, Results Based on 6 Atoms of al
ELEM: Na P Ca Al K Fe Cu S Ba Si H O SUM
137 .002 3.453 .001 6.000 .012 .035 .767 .057 .005 .004 15.996 26.039 52.373
140 -.002 3.497 .002 6.000 .013 .040 .786 .058 .004 .004 15.996 26.215 52.613
141 .001 3.469 .001 6.000 .012 .037 .803 .055 .003 .005 15.996 26.091 52.474
142 .000 3.525 .001 6.000 .016 .032 .796 .051 .002 .003 15.996 26.302 52.725
143 -.003 3.597 .001 6.000 .013 .037 .788 .053 .003 .005 15.996 26.595 53.083
144 .000 3.514 .002 6.000 .013 .041 .803 .054 .002 .005 15.996 26.269 52.701
AVER: .000 3.509 .001 6.000 .013 .037 .791 .055 .003 .005 15.996 26.252 52.661
SDEV: .002 .051 .001 .000 .001 .003 .014 .003 .001 .001 .000 .196 .247
SERR: .001 .021 .000 .000 .001 .001 .006 .001 .000 .000 .000 .080
%RSD: -823.52 1.45 44.83 .00 10.82 8.72 1.71 4.80 29.50 14.99 .00 .75
I have no idea if it is correct, but the total looks good! :D
In the previous turquoise sample, the Time Dependent Intensity (TDI) acquisition was very important as seen here for phosphorus:
(https://smf.probesoftware.com/oldpics/i42.tinypic.com/14we48.jpg)
See additional info on TDI here:
http://smf.probesoftware.com/index.php?topic=116.0
Here's an example of a carbonate calculated by measuring only the cations. Oxygen is calculated by stoichiometry and carbon is calculated by stoichiometry to the calculated (stoichiometric) oxygen:
(https://smf.probesoftware.com/oldpics/i41.tinypic.com/xnrv9k.jpg)
St 135 Set 1 Calcite (analyzed)
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 30.0 Beam Size = 2
(Magnification (analytical) = 4000), Beam Mode = Analog Spot
(Magnification (default) = 3200, Magnification (imaging) = 100)
Image Shift (X,Y): .00, .00
Pre Acquire String : PB OFF
Post Acquire String : PB ON
Locality: unknown
XRF (UCB), ICP-MS (Washington Univ, D. Kremser)
Element XRF-EDS ICP-MS (ppm)
Sr 150 165
Mn 130 166
Fe n.d. 4
Mg n.d. 21
Number of Data Lines: 4 Number of 'Good' Data Lines: 4
First/Last Date-Time: 06/15/2008 10:14:18 AM to 06/15/2008 10:16:05 AM
Average Total Oxygen: 47.916 Average Total Weight%: 100.001
Average Calculated Oxygen: 47.918 Average Atomic Number: 12.575
Average Excess Oxygen: -.002 Average Atomic Weight: 20.031
Average ZAF Iteration: 7.00 Average Quant Iterate: 2.00
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element C is Calculated .333 Atoms Relative To 1.0 Atom of Oxygen
St 135 Set 1 Calcite (analyzed), Results in Elemental Weight Percents
ELEM: Ca Mn Fe Mg P C O
TYPE: ANAL ANAL ANAL ANAL ANAL STOI CALC
BGDS: LIN LIN LIN LIN LIN
TIME: 10.00 10.00 10.00 10.00 10.00
BEAM: 30.00 30.00 30.00 30.00 30.00
ELEM: Ca Mn Fe Mg P C O SUM
1 40.363 -.007 -.046 .000 -.011 11.959 47.943 100.202
2 40.049 .003 .038 -.002 .014 11.978 47.926 100.007
3 40.167 -.006 .016 -.021 .029 11.973 47.959 100.118
4 39.837 .046 .011 -.031 -.015 11.995 47.834 99.676
AVER: 40.104 .009 .005 -.013 .004 11.976 47.916 100.001
SDEV: .220 .025 .036 .015 .021 .015 .056 .231
SERR: .110 .012 .018 .007 .011 .007 .028
%RSD: .55 271.48 732.18 -109.50 492.43 .12 .12
PUBL: 40.031 n.a. n.a. n.a. n.a. 12.000 47.952 99.983
%VAR: .18 --- --- --- --- -.20 -.08
DIFF: .073 --- --- --- --- -.024 -.036
STDS: 138 140 145 139 285 0 0
STKF: .3789 .3969 .4258 .1957 .1599 .0000 .0000
STCT: 3769.3 3961.2 4241.7 1936.5 1599.3 .0 .0
UNKF: .3796 .0001 .0000 -.0001 .0000 .0000 .0000
UNCT: 3775.8 .7 .4 -.8 .4 .0 .0
UNBG: 37.5 30.7 38.3 15.3 21.4 .0 .0
ZCOR: 1.0566 1.2363 1.2120 1.6542 1.1569 .0000 .0000
KRAW: 1.0017 .0002 .0001 -.0004 .0002 .0000 .0000
PKBG: 101.97 1.03 1.01 .95 1.02 .00 .00
St 135 Set 1 Calcite (analyzed), Results Based on Sum of 2 Cations
ELEM: Ca Mn Fe Mg P C O SUM
1 1.006 .000 -.001 .000 .000 .995 2.994 4.994
2 1.000 .000 .001 .000 .000 .998 2.999 4.999
3 1.003 .000 .000 -.001 .001 .997 2.998 4.998
4 .998 .001 .000 -.001 .000 1.003 3.002 5.002
AVER: 1.002 .000 .000 -.001 .000 .998 2.998 4.998
SDEV: .004 .000 .001 .001 .001 .003 .003 .003
SERR: .002 .000 .000 .000 .000 .002 .002
%RSD: .35 271.04 727.41 -109.60 493.78 .33 .10
You can also specify an element by stoichiometry to a measured element (1 C to 1 Ca), oxygen by stoichiometric calculation and an element by stoichiometry to calculated oxygen (.333 C to 1 O) as seen here:
(https://smf.probesoftware.com/oldpics/i43.tinypic.com/2dvo7tl.jpg)
St 138 Set 1 Calcite (Harvard #97189)
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 30.0 Beam Size = 2
(Magnification (analytical) = 4000), Beam Mode = Analog Spot
(Magnification (default) = 3200, Magnification (imaging) = 100)
Image Shift (X,Y): .00, .00
Pre Acquire String : PB OFF
Post Acquire String : PB ON
Specimen from Harvard Mineralogical Museum (Carl Francis)
Locality: Oberdorf, Austria
EPMA (UCB): MnO=0.01, FeO=0.00, MgO=0.00
See Garrels, et al., 1980 AJS 258, 402-418
Number of Data Lines: 4 Number of 'Good' Data Lines: 4
First/Last Date-Time: 06/15/2008 10:16:54 AM to 06/15/2008 10:18:38 AM
Average Total Oxygen: 47.949 Average Total Weight%: 99.995
Average Calculated Oxygen: 47.951 Average Atomic Number: 12.568
Average Excess Oxygen: -.002 Average Atomic Weight: 20.021
Average ZAF Iteration: 2.00 Average Quant Iterate: 2.00
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element C is Calculated .333 Atoms Relative To 1.0 Atom of Oxygen
Element C is Calculated 1 Atoms Relative To 1.0 Atom of Ca
St 138 Set 1 Calcite (Harvard #97189), Results in Elemental Weight Percents
ELEM: Ca Mn Fe Mg P C O
TYPE: ANAL ANAL ANAL ANAL ANAL STOI CALC
BGDS: LIN LIN LIN LIN LIN
TIME: 10.00 10.00 10.00 10.00 10.00
BEAM: 30.00 30.00 30.00 30.00 30.00
ELEM: Ca Mn Fe Mg P C O SUM
5 39.853 .062 -.005 -.019 .010 11.943 47.742 99.584
6 40.366 .010 -.005 -.035 .044 12.097 48.375 100.852
7 39.844 -.034 .034 -.035 -.026 11.940 47.658 99.380
8 40.085 .043 -.012 .018 -.003 12.013 48.021 100.165
AVER: 40.037 .020 .003 -.018 .006 11.998 47.949 99.995
SDEV: .246 .042 .021 .025 .029 .074 .324 .661
SERR: .123 .021 .010 .012 .015 .037 .162
%RSD: .61 209.49 721.04 -138.86 473.91 .61 .68
PUBL: 40.038 .008 .000 .000 n.a. 12.000 47.954 100.000
%VAR: (.00) 150.10 .00 .00 --- -.02 -.01
DIFF: (.00) .012 .000 .000 --- -.002 -.005
STDS: 138 140 145 139 285 0 0
STKF: .3789 .3969 .4258 .1957 .1599 .0000 .0000
STCT: 3769.3 3961.2 4241.7 1936.5 1599.3 .0 .0
UNKF: .3789 .0002 .0000 -.0001 .0001 .0000 .0000
UNCT: 3769.3 1.6 .2 -1.1 .5 .0 .0
UNBG: 40.0 31.0 38.8 16.1 22.2 .0 .0
ZCOR: 1.0566 1.2363 1.2120 1.6542 1.1570 .0000 .0000
KRAW: 1.0000 .0004 .0001 -.0005 .0003 .0000 .0000
PKBG: 95.31 1.06 1.01 .94 1.03 .00 .00
St 138 Set 1 Calcite (Harvard #97189), Results Based on 1 Atoms of c
ELEM: Ca Mn Fe Mg P C O SUM
5 1.000 .001 .000 -.001 .000 1.000 3.001 5.001
6 1.000 .000 .000 -.001 .001 1.000 3.002 5.002
7 1.000 -.001 .001 -.001 -.001 1.000 2.996 4.994
8 1.000 .001 .000 .001 .000 1.000 3.001 5.002
AVER: 1.000 .000 .000 -.001 .000 1.000 3.000 5.000
SDEV: .000 .001 .000 .001 .001 .000 .003 .004
SERR: .000 .000 .000 .001 .000 .000 .001
%RSD: .00 210.32 711.86 -138.67 480.74 .00 .09
So let's calculate oxygen by stoichiometry and do carbon 0.333 C to calculated O. So on a complex carbonate it looks like this:
St 143 Set 1 Kutnahorite (Harvard #85670)
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 30.0 Beam Size = 2
(Magnification (analytical) = 4000), Beam Mode = Analog Spot
(Magnification (default) = 3200, Magnification (imaging) = 100)
Image Shift (X,Y): .00, .00
Pre Acquire String : PB OFF
Post Acquire String : PB ON
Specimen from Harvard Mineralogical Museum (Carl Francis)
Locality: Franklin, NJ
See Garrels, et al., 1980 AJS 258, 402-418
Also J. V. Smith, Am. Jour. Sci. 1960
Number of Data Lines: 4 Number of 'Good' Data Lines: 4
First/Last Date-Time: 06/15/2008 10:27:04 AM to 06/15/2008 10:28:50 AM
Average Total Oxygen: 45.509 Average Total Weight%: 100.231
Average Calculated Oxygen: 45.512 Average Atomic Number: 13.971
Average Excess Oxygen: -.003 Average Atomic Weight: 21.131
Average ZAF Iteration: 7.00 Average Quant Iterate: 2.00
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element C is Calculated .333 Atoms Relative To 1.0 Atom of Oxygen
St 143 Set 1 Kutnahorite (Harvard #85670), Results in Elemental Weight Percents
ELEM: Ca Mn Fe Mg P C O
TYPE: ANAL ANAL ANAL ANAL ANAL STOI CALC
BGDS: LIN LIN LIN LIN LIN
TIME: 10.00 10.00 10.00 10.00 10.00
BEAM: 30.00 30.00 30.00 30.00 30.00
ELEM: Ca Mn Fe Mg P C O SUM
21 19.734 22.026 .382 1.385 .021 11.333 45.532 100.412
22 19.850 21.699 .401 1.377 .016 11.354 45.532 100.229
23 19.615 21.856 .321 1.278 -.008 11.366 45.396 99.824
24 19.767 21.962 .363 1.423 .032 11.338 45.574 100.460
AVER: 19.741 21.886 .367 1.365 .015 11.348 45.509 100.231
SDEV: .097 .143 .034 .062 .017 .015 .077 .289
SERR: .049 .071 .017 .031 .009 .007 .039
%RSD: .49 .65 9.30 4.53 112.08 .13 .17
PUBL: 19.612 21.925 .389 1.333 .000 11.408 45.594 100.261
%VAR: .66 -.18 -5.70 2.43 .00 -.53 -.19
DIFF: .129 -.039 -.022 .032 .000 -.060 -.085
STDS: 138 140 145 139 285 0 0
STKF: .3789 .3969 .4258 .1957 .1599 .0000 .0000
STCT: 3769.3 3961.2 4241.7 1936.5 1599.3 .0 .0
UNKF: .1930 .1843 .0031 .0077 .0001 .0000 .0000
UNCT: 1919.6 1839.4 31.3 75.8 1.3 .0 .0
UNBG: 31.1 43.3 42.8 14.2 22.8 .0 .0
ZCOR: 1.0230 1.1875 1.1669 1.7823 1.1895 .0000 .0000
KRAW: .5093 .4644 .0074 .0392 .0008 .0000 .0000
PKBG: 62.65 43.58 1.74 6.38 1.06 .00 .00
St 143 Set 1 Kutnahorite (Harvard #85670), Results in Oxide Weight Percents
ELEM: CaO MnO FeO MgO P2O5 CO2 O SUM
21 27.611 28.440 .492 2.297 .048 41.527 -.003 100.412
22 27.774 28.019 .516 2.283 .038 41.603 -.003 100.229
23 27.446 28.221 .413 2.119 -.019 41.647 -.003 99.824
24 27.658 28.359 .467 2.359 .073 41.546 -.003 100.460
AVER: 27.622 28.260 .472 2.264 .035 41.581 -.003 100.231
SDEV: .136 .184 .044 .103 .039 .055 .000 .289
SERR: .068 .092 .022 .051 .020 .027 .000
%RSD: .49 .65 9.30 4.53 112.08 .13 -.06
PUBL: 27.441 28.310 .500 2.211 .000 41.801 -.003 100.261
%VAR: .66 -.18 -5.70 2.43 .00 -.53 -.03
DIFF: .181 -.051 -.029 .054 .000 -.221 .000
STDS: 138 140 145 139 285 0 0
St 143 Set 1 Kutnahorite (Harvard #85670), Results Based on 1 Atoms of c
ELEM: Ca Mn Fe Mg P C O SUM
21 .522 .425 .007 .060 .001 1.000 3.016 5.031
22 .524 .418 .008 .060 .001 1.000 3.010 5.020
23 .517 .420 .006 .056 .000 1.000 2.998 4.997
24 .522 .423 .007 .062 .001 1.000 3.017 5.033
AVER: .521 .422 .007 .059 .001 1.000 3.011 5.020
SDEV: .003 .003 .001 .003 .001 .000 .009 .016
SERR: .001 .002 .000 .001 .000 .000 .004
%RSD: .56 .75 9.36 4.64 112.00 .00 .29
Is there any way that I can calculate more than one element as an atomic ratio to another element?
I know the composition of my base glass quite well and I know that the molar ratios stay the same. Since this stuff is loaded with alkali I would like not to have to do more than one element per spectrometer. Even "fixing" and element as a constant would due because the elements in question are in low abundances and are light elements.
Quote from: BenH on February 04, 2015, 01:59:53 PM
Is there any way that I can calculate more than one element as an atomic ratio to another element?
I know the composition of my base glass quite well and I know that the molar ratios stay the same. Since this stuff is loaded with alkali I would like not to have to do more than one element per spectrometer. Even "fixing" and element as a constant would due because the elements in question are in low abundances and are light elements.
Not specifically. But once the atomic ratios are calculated every element has a stoichiometry to every other element.
Also, the previous post shows how to do oxygen by stoichiometry plus another element relative to another.
I'm probably missing what you are really asking. Can you provide an example?
john
John,
Ideally I would like to be able to 'add a compound by difference'. In this case Li2B4O7
Initially I thought I could do this for simple compounds by doing this:
(https://smf.probesoftware.com/oldpics/i58.tinypic.com/10emow1.jpg)
However, in this situation it seems the element is added by difference, but the element by stoichiometry to it, is not added. It seems this could be possible if you checked for 'elements stoichiometric to element by difference' before adding both (or perhaps more?) to the matrix???
Quote from: Gseward on February 04, 2015, 04:44:46 PM
Ideally I would like to be able to 'add a compound by difference'. In this case Li2B4O7
Initially I thought I could do this for simple compounds by doing this:
[snip]
However, in this situation it seems the element is added by difference, but the element by stoichiometry to it, is not added. It seems this could be possible if you checked for 'elements stoichiometric to element by difference' before adding both (or perhaps more?) to the matrix???
It is a good suggestion, but difficult to implement in code and keep all the other existing specification method working. It gets complicated... A lot of it has to do with the order that things are calculated (as you correctly point out!).
But I did get something to kinda of work along the lines you need, here using this specification:
(https://smf.probesoftware.com/oldpics/i60.tinypic.com/21jdvk5.jpg)
Here is the output:
ELEM: Ti Fe Al Mn Mg Si Ca O Li B
TYPE: ANAL ANAL ANAL ANAL ANAL SPEC SPEC CALC STOI RELA
BGDS: EXP LIN AVG LIN LIN
TIME: 1200.00 1200.00 1200.00 1200.00 1200.00
BEAM: 100.09 100.09 100.09 100.09 100.09
ELEM: Ti Fe Al Mn Mg Si Ca O Li B SUM
142 .00152 .01969 .00020 .01182 .03467 .00000 .00000 64.8992 8.03761 25.0453 98.0500
143 .00117 .02084 .00070 .01177 .03541 .00000 .00000 64.8992 8.03748 25.0449 98.0515
144 .00151 .02067 .00028 .01170 .03578 .00000 .00000 64.8993 8.03748 25.0449 98.0515
AVER: .00140 .02040 .00039 .01176 .03529 .000 .000 64.899 8.038 25.045 98.0510
SDEV: .00020 .00062 .00027 .00006 .00056 .000 .000 .000 .000 .000 .00088
SERR: .00012 .00036 .00015 .00004 .00032 .00000 .00000 .00001 .00004 .00013
%RSD: 14.4836 3.03898 68.0015 .53620 1.59054 .00000 .00000 .00003 .00088 .00087
STDS: 22 395 336 140 12 0 0 0 0 0
STKF: .5616 .6862 .1159 .4052 .4215 .0000 .0000 .0000 .0000 .0000
STCT: 1894.84 1019.49 330.27 164.35 978.80 .00 .00 .00 .00 .00
UNKF: .0000 .0002 .0000 .0001 .0002 .0000 .0000 .0000 .0000 .0000
UNCT: .04 .26 .01 .04 .46 .00 .00 .00 .00 .00
UNBG: 3.08 1.43 1.28 .31 .70 .00 .00 .00 .00 .00
ZCOR: 1.1405 1.1652 1.4834 1.1816 1.8006 .0000 .0000 .0000 .0000 .0000
KRAW: .00002 .00026 .00002 .00025 .00046 .00000 .00000 .00000 .00000 .00000
PKBG: 1.01348 1.18203 1.00592 1.12886 1.64704 .00000 .00000 .00000 .00000 .00000
BLNK#: ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
BLNKL: ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
BLNKV: ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
Un 3, Results in Atomic Percents
ELEM: Ti Fe Al Mn Mg Si Ca O Li B SUM
142 .00042 .00468 .00010 .00286 .01894 .00000 .00000 53.8443 15.3762 30.7525 100.000
143 .00032 .00495 .00035 .00284 .01934 .00000 .00000 53.8443 15.3760 30.7520 100.000
144 .00042 .00491 .00014 .00283 .01954 .00000 .00000 53.8442 15.3760 30.7520 100.000
AVER: .00039 .00485 .00019 .00284 .01927 .000 .000 53.844 15.376 30.752 100.000
SDEV: .00006 .00015 .00013 .00002 .00031 .000 .000 .000 .000 .000 .00000
SERR: .00003 .00009 .00008 .00001 .00018 .00000 .00000 .00002 .00009 .00017
%RSD: 14.4836 3.03890 68.0015 .53628 1.59046 .00000 .00000 .00006 .00096 .00096
Yes, the unnormalized total is a little low, but probably good enough for the matrix correction!
Maybe this would work for Ben's situation also?
Of course one can also just simply specify the concentrations explicitly from the Specified Concentrations button in Analyze!
John,
Thanks for the reply. I think in a situation where the measured elements are in low concentration, your suggestion would work. But as you say, in the situation where the measured elements are only trace, one can simply add the matrix from the Specified Concentrations menu.
When the measured elements are a more significant contribution (and thus they have stoich O also), adding the Li relative to the calculated oxygen might become problematic. For my situation I can add approximately the correct amount of Li2B4O7 as a specified concentration, and probably get close enough, but obviously the specified concentration is not involved in any iterations.
Cheers,
Gareth
I have glasses that we are ion exchanging. That means that the glass is immersed in a molten salt bath and alkalis exchange at the surface one for one. The base glass composition is well known. I don't really need to analyze the 3 minor elements in the sample. So I do 2 light minor elements by mole ratio to a measured element. I do Li by difference.
I need a way to do more than one element by mole ratio to a measured major element. Is there a way to do that? If not, is that something that can be modified without burning the building down?
Quote from: BenH on February 05, 2015, 08:48:40 AM
I have glasses that we are ion exchanging. That means that the glass is immersed in a molten salt bath and alkalis exchange at the surface one for one. The base glass composition is well known. I don't really need to analyze the 3 minor elements in the sample. So I do 2 light minor elements by mole ratio to a measured element. I do Li by difference.
I need a way to do more than one element by mole ratio to a measured major element. Is there a way to do that? If not, is that something that can be modified without burning the building down?
I think I should add a formula by difference option to the Calculation Options which would take care of this situation nicely. I'll do that ASAP and let you know when it is ready to download...
In the meantime you can specify fixed concentrations as a formula in the Specified Concentrations dialog as seen here:
(https://smf.probesoftware.com/oldpics/i60.tinypic.com/suvdpi.jpg)
The totals may not be perfect if your measured minor elements are significant, but it might be good enough for the matrix correction of the minor elements.
Ok, the requested formula by difference feature has been added to both the ZAF, Phi-rho-z and alpha factor methods (not yet for the multi-standard calibration curve method), as described here:
http://smf.probesoftware.com/index.php?topic=42.msg2568#msg2568
Many thanks John. I think this will be a useful feature.
Gareth
The formula by difference feature is nice because the software will automatically add the elements in the formula that you aren't analyzing for. However, for the element by difference, by stoichiometry, etc., I will admit that it is not entirely obvious how to add these unanalyzed elements to the element drop down lists as seen here.
(https://smf.probesoftware.com/oldpics/i60.tinypic.com/2sbu5i0.jpg)
The secret tip is that one should add all elements (WDS, EDS, and unanalyzed elements) from the Elements/Cations dialog, by simply clicking on an empty element row as seen here:
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/2mh6hd4.jpg)
and then adding the desired unanalyzed elements *without* an x-ray line as seen here:
(https://smf.probesoftware.com/oldpics/i62.tinypic.com/11hs7f7.jpg)
There is something in the way PfE calculates C in carbonates that I do not understand.
From the 2013 example of kutnohorite at: http://smf.probesoftware.com/index.php?topic=92.msg523#msg523
and ignoring the P content (as its abundance is very low):
Wt% element (from PfE):
Ca Mn Fe Mg C O SUM
#21 19.734 22.026 0.382 1.385 11.333 45.532 100.392
#22 19.850 21.699 0.401 1.377 11.354 45.532 100.213
#23 19.615 21.856 0.321 1.278 11.366 45.396 99.832
#24 19.767 21.962 0.363 1.423 11.338 45.574 100.427
I calculate the molar proportions using the atomic weights from Wieser and Berglund (2009) Pure Appl. Chem. 81, 2131-2156. For the general formula MCO3, the stoichiometric proportion of C should exactly equal the sum of the divalent cations. Similarly, oxygen should be present at exactly three times the proportion of C (or M).
Molar proportions from above data Calculated values
Ca Mn Fe Mg C O C = sum M2+ O = 3*(sum M2+)
0.4924 0.4009 0.0068 0.0570 0.9436 2.8459 0.9571 2.8714
0.4953 0.3950 0.0072 0.0567 0.9453 2.8459 0.9541 2.8623
0.4894 0.3978 0.0057 0.0526 0.9463 2.8374 0.9456 2.8367
0.4932 0.3998 0.0065 0.0585 0.9440 2.8485 0.9580 2.8741
The molar proportions that I calculate by stoichiometry on the basis of the divalent cations do not match those reported by PfE in the example reported. Consequently, the weight proportions of C and O, and sums, that I calculate are:
Calculated by stoichiometry for the formula MCO3:
wt% C wt% O new sum
11.50 45.94 100.96
11.46 45.79 100.58
11.36 45.39 99.81
11.51 45.98 101.00
Calculated formula proportions:
Ca Mn Fe Mg C O sum
#21 0.514 0.419 0.007 0.060 1.000 3.000 5.000
#22 0.519 0.414 0.008 0.059 1.000 3.000 5.000
#23 0.518 0.421 0.006 0.056 1.000 3.000 5.000
#24 0.515 0.417 0.007 0.061 1.000 3.000 5.000
It is not clear to me what the PfE software is doing, and why the molar proportions that it reports do not exactly match the formula MCO3. From PfE:
Ca Mn Fe Mg C O SUM
#21 0.522 0.425 0.007 0.060 1.000 3.016 5.030
#22 0.524 0.418 0.008 0.060 1.000 3.010 5.020
#23 0.517 0.420 0.006 0.056 1.000 2.998 4.997
#24 0.522 0.423 0.007 0.062 1.000 3.017 5.031
I have a few hundred carbonate analyses acquired with PfE - except where the analytical total is exceedingly close to 100.00, the CO2 contents reported by PfE do not match stoichiometric values. PfE appears to systematically overestimate the proportion of CO2 for analyses that have low totals, and to underestimate in the case of high totals, in comparison to stoichiometric calculations. A graph of these data follows as a PDF attachment.
Edit by John: Link to post fixed
Quote from: AndrewLocock on June 25, 2015, 10:16:40 AM
From the 2013 example of kutnohorite at: http://smf.probesoftware.com/index.php?topic=92.msg523#msg523
and ignoring the P content (as its abundance is very low):
Wt% element (from PfE):
Ca Mn Fe Mg C O SUM
#21 19.734 22.026 0.382 1.385 11.333 45.532 100.392
#22 19.850 21.699 0.401 1.377 11.354 45.532 100.213
#23 19.615 21.856 0.321 1.278 11.366 45.396 99.832
#24 19.767 21.962 0.363 1.423 11.338 45.574 100.427
Hi Andrew,
Interesting, it will be fun to figure this out! I can't find the original Kutnahorite data anyway, so let's start with another Kutnahorite example that I can find the data for!
The first thing I might note is that you have to be aware of the various ways to calculate elemnts by stoichiometry. For example in the calcite example posted previously I specified carbon by ratio to Ca 1 : 1, and that makes sense for calcite since the other cations are traces.
But for Kutnahorite and any other mixed cation carbonate, we'll instead want to specify carbon relative something else. In these non-pure calcite samples we'll want to specify carbon by stoichiometry to calculated oxygen, for example 0.333 C to 1 O (because that is CO3) as seen here.
St 143 Set 1 Kutnahorite (Harvard #85670)
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 30.0 Beam Size = 2
Specimen from Harvard Mineralogical Museum (Carl Francis)
Locality: Franklin, NJ
See Garrels, et al., 1980 AJS 258, 402-418
Also J. V. Smith, Am. Jour. Sci. 1960
Number of Data Lines: 4 Number of 'Good' Data Lines: 4
First/Last Date-Time: 06/15/2008 10:27:04 AM to 06/15/2008 10:28:50 AM
Average Total Oxygen: .000 Average Total Weight%: 100.343
Average Calculated Oxygen: .000 Average Atomic Number: 13.960
Average Excess Oxygen: .000 Average Atomic Weight: 21.115
Average ZAF Iteration: 3.00 Average Quant Iterate: 2.00
Element C is Calculated .333 Atoms Relative To 1.0 Atom of O
St 143 Set 1 Kutnahorite (Harvard #85670), Results in Elemental Weight Percents
ELEM: Ca Mn Fe Mg P C O SUM
9 19.709 22.027 .382 1.385 .021 11.398 45.594 100.515
10 19.825 21.700 .401 1.376 .016 11.398 45.594 100.310
11 19.592 21.858 .321 1.278 -.008 11.398 45.594 100.032
12 19.742 21.963 .363 1.422 .032 11.398 45.594 100.514
AVER: 19.717 21.887 .367 1.365 .015 11.398 45.594 100.343
SDEV: .096 .143 .034 .062 .017 .000 .000 .228
SERR: .048 .071 .017 .031 .009 .000 .000
%RSD: .49 .65 9.30 4.52 112.08 .00 .00
PUBL: 19.612 21.925 .389 1.333 n.a. 11.408 45.594 100.261
%VAR: .53 -.17 -5.69 2.41 --- -.09 .00
DIFF: .105 -.038 -.022 .032 --- -.010 .000
STDS: 138 140 145 139 285 --- ---
STKF: .3789 .3969 .4258 .1957 .1601 --- ---
STCT: 125.64 132.04 141.39 64.55 53.31 --- ---
UNKF: .1930 .1843 .0031 .0077 .0001 --- ---
UNCT: 63.99 61.31 1.04 2.53 .04 --- ---
UNBG: 1.04 1.44 1.43 .47 .76 --- ---
ZCOR: 1.0217 1.1875 1.1671 1.7819 1.1889 --- ---
KRAW: .5093 .4644 .0074 .0392 .0008 --- ---
PKBG: 62.65 43.58 1.74 6.38 1.06 --- ---
St 143 Set 1 Kutnahorite (Harvard #85670), Results Based on 1 Atoms of c
ELEM: Ca Mn Fe Mg P C O SUM
9 .518 .423 .007 .060 .001 1.000 3.003 5.012
10 .521 .416 .008 .060 .001 1.000 3.003 5.008
11 .515 .419 .006 .055 .000 1.000 3.003 4.999
12 .519 .421 .007 .062 .001 1.000 3.003 5.013
AVER: .518 .420 .007 .059 .001 1.000 3.003 5.008
SDEV: .003 .003 .001 .003 .001 .000 .000 .007
SERR: .001 .001 .000 .001 .000 .000 .000
%RSD: .49 .65 9.30 4.52 112.08 .00 .00
I'll admit that 1.000 to 3.003 isn't *exactly* 3, but it's very much within the iteration tolerance. Yes, it is a 0.1% relative error but the carbon and oxygen concentrations are just there for the matrix correction and this level of error will have almost no effect on the matrix correction calculation. I suspect the reason for this is just the matrix iteration which is adjusting the concentrations as the matrix iteration proceeds.
I'm not quite sure why you think there is a problem if you are calculating carbon relative to calculated oxygen, but here is the code I'm using to calculate things:
' Add in elements calculated relative to stoichiometric element (in0%)
For i% = 1 To zaf.in1%
If zaf.il%(i%) = 9 Then
zaf.krat!(i%) = (zaf.krat!(zaf.in0%) / zaf.atwts!(zaf.in0%)) * sample(1).StoichiometryRatio! * zaf.atwts!(i%)
zaf.krat!(zaf.in0%) = zaf.krat!(zaf.in0%) + zaf.krat!(i%) * zaf.p1!(i%)
zaf.ksum! = zaf.ksum! + zaf.krat!(i%) + zaf.krat!(i%) * zaf.p1!(i%)
End If
Next i%
End If
Where zaf.in0% is the stoichiometric oxygen channel and .p1 is calculated as seen here:
' Calculate oxide-elemental conversion factors
For i% = 1 To zaf.in1%
If zaf.atwts!(i%) = 0# Then GoTo ZAFSetZAFBadAtomicWeight
zaf.p1(i%) = p2!(i%) * AllAtomicWts!(8) / zaf.atwts!(i%)
Next i%
And .p2 is calculated as seen here:
p2!(i%) = 0#
If sample(1).OxideOrElemental% = 1 Or sample(1).numoxd%(i%) <> 0 Then
If sample(1).numcat%(i%) < 1 Then GoTo ZAFSetZAFNoCations
p2!(i%) = CSng(sample(1).numoxd%(i%)) / CSng(sample(1).numcat%(i%))
End If
Quote from: AndrewLocock on June 25, 2015, 10:16:40 AM
I have a few hundred carbonate analyses acquired with PfE - except where the analytical total is exceedingly close to 100.00, the CO2 contents reported by PfE do not match stoichiometric values. PfE appears to systematically overestimate the proportion of CO2 for analyses that have low totals, and to underestimate in the case of high totals, in comparison to stoichiometric calculations. A graph of these data follows as a PDF attachment.
Ok, that is interesting. So I took the above analyses and edited the raw intensities to force a low total on the first data point, but the carbon-oxygen ratio is still 1 to 3 or very close to that as seen here:
St 143 Set 1 Kutnahorite (Harvard #85670)
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 30.0 Beam Size = 2
(Magnification (analytical) = 4000), Beam Mode = Analog Spot
(Magnification (default) = 3200, Magnification (imaging) = 100)
Image Shift (X,Y): -2.00, 3.00
Pre Acquire String : PB OFF
Post Acquire String : PB ON
Specimen from Harvard Mineralogical Museum (Carl Francis)
Locality: Franklin, NJ
See Garrels, et al., 1980 AJS 258, 402-418
Also J. V. Smith, Am. Jour. Sci. 1960
Number of Data Lines: 4 Number of 'Good' Data Lines: 4
First/Last Date-Time: 06/15/2008 10:27:04 AM to 06/15/2008 10:28:50 AM
Average Total Oxygen: .000 Average Total Weight%: 97.017
Average Calculated Oxygen: .000 Average Atomic Number: 13.729
Average Excess Oxygen: .000 Average Atomic Weight: 20.759
Average ZAF Iteration: 3.00 Average Quant Iterate: 2.00
Element C is Calculated .333 Atoms Relative To 1.0 Atom of O
St 143 Set 1 Kutnahorite (Harvard #85670), Results in Elemental Weight Percents
ELEM: Ca Mn Fe Mg P C O
TYPE: ANAL ANAL ANAL ANAL ANAL RELA SPEC
BGDS: LIN LIN LIN LIN LIN
TIME: 10.00 10.00 10.00 10.00 10.00 --- ---
BEAM: 30.00 30.00 30.00 30.00 30.00 --- ---
ELEM: Ca Mn Fe Mg P C O SUM
9 6.442 21.973 .382 1.404 .021 11.398 45.594 87.213
10 19.825 21.700 .401 1.376 .016 11.398 45.594 100.310
11 19.592 21.858 .321 1.278 -.008 11.398 45.594 100.032
12 19.742 21.963 .363 1.422 .032 11.398 45.594 100.514
AVER: 16.400 21.873 .367 1.370 .015 11.398 45.594 97.017
SDEV: 6.640 .127 .034 .064 .017 .000 .000 6.539
SERR: 3.320 .063 .017 .032 .009 .000 .000
%RSD: 40.49 .58 9.30 4.71 111.79 .00 .00
PUBL: 19.612 21.925 .389 1.333 n.a. 11.408 45.594 100.261
%VAR: -16.38 -.23 -5.69 2.77 --- -.09 .00
DIFF: -3.212 -.052 -.022 .037 --- -.010 .000
STDS: 138 140 145 139 285 --- ---
STKF: .3789 .3969 .4258 .1957 .1601 --- ---
STCT: 125.64 132.04 141.39 64.55 53.31 --- ---
UNKF: .1605 .1843 .0031 .0077 .0001 --- ---
UNCT: 53.23 61.31 1.04 2.53 .04 --- ---
UNBG: 1.04 1.44 1.43 .47 .76 --- ---
ZCOR: 1.0213 1.1867 1.1670 1.7881 1.1926 --- ---
KRAW: .4237 .4644 .0074 .0392 .0008 --- ---
PKBG: 52.46 43.58 1.74 6.38 1.06 --- ---
St 143 Set 1 Kutnahorite (Harvard #85670), Results Based on 1 Atoms of c
ELEM: Ca Mn Fe Mg P C O SUM
9 .169 .421 .007 .061 .001 1.000 3.003 4.663
10 .521 .416 .008 .060 .001 1.000 3.003 5.008
11 .515 .419 .006 .055 .000 1.000 3.003 4.999
12 .519 .421 .007 .062 .001 1.000 3.003 5.013
AVER: .431 .420 .007 .059 .001 1.000 3.003 4.921
SDEV: .175 .002 .001 .003 .001 .000 .000 .172
SERR: .087 .001 .000 .001 .000 .000 .000
%RSD: 40.49 .58 9.30 4.71 111.79 .00 .00
I attached the data file I used to get these results below.
What am I missing?
john
Hi John,
I had a quick look at the new data in your post.
Why are the elemental weight percents of carbon and oxygen
identical for all four analyses?
In the case of a low total, for which the stoichiometric formula MCO3 is maintained, the C and oxygen values should be similarly low.
It puzzles me that the C and O wt% for the low analysis have the
same mass fractions as for the other analyses.
QuoteELEM: Ca Mn Fe Mg P C O SUM
9 6.442 21.973 .382 1.404 .021 11.398 45.594 87.213
By my calculation (again ignoring phosphorus), for the following mass fractions:
Ca Mn Fe Mg
6.442 21.973 0.382 1.404
the mass fractions of C and O for the formula MCO3 should be:
wt% C wt% O new sum
7.51 30.01
67.72This will yield the formula Ca 0.257; Mn 0.640; Fe 0.011; Mg 0.092; C 1.000; O 3.000; Sum 5.000; which is charge balanced.
In contrast, the formula listed for this low analysis has a charge imbalance of about -0.67 pfu:
Quote143 Set 1 Kutnahorite (Harvard #85670), Results Based on 1 Atoms of c
ELEM: Ca Mn Fe Mg P C O SUM
9 .169 .421 .007 .061 .001 1.000 3.003 4.663
I have attached the Excel file of analyses to which my previous post referred. This includes all 267 analytical points, rather than just the best 226 shown in the graph attached to the previous post.
Thanks for looking into this - I am certainly missing something.
Cheers,
Andrew
Quote from: AndrewLocock on June 25, 2015, 12:51:57 PM
Why are the elemental weight percents of carbon and oxygen identical for all four analyses?
Ooops! It's because I forgot to specify that the program calculate oxygen by stoichiometry for this kutnahorite sample! The default method for specifying unanalyzed elements for standards is to just load the missing specified elements from the standard database!
Ok, so if I now properly specify calculate oxygen by stoichiometry (as opposed to just loading it from the standard database) I now get this result:
St 143 Set 1 Kutnahorite (Harvard #85670)
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 30.0 Beam Size = 2
Specimen from Harvard Mineralogical Museum (Carl Francis)
Locality: Franklin, NJ
See Garrels, et al., 1980 AJS 258, 402-418
Also J. V. Smith, Am. Jour. Sci. 1960
Number of Data Lines: 4 Number of 'Good' Data Lines: 4
First/Last Date-Time: 06/15/2008 10:27:04 AM to 06/15/2008 10:28:50 AM
Average Total Oxygen: 45.503 Average Total Weight%: 100.200
Average Calculated Oxygen: 45.506 Average Atomic Number: 13.969
Average Excess Oxygen: -.003 Average Atomic Weight: 21.128
Average ZAF Iteration: 7.00 Average Quant Iterate: 2.00
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element C is Calculated .333 Atoms Relative To 1.0 Atom of Oxygen
St 143 Set 1 Kutnahorite (Harvard #85670), Results in Elemental Weight Percents
ELEM: Ca Mn Fe Mg P C O SUM
9 19.706 22.024 .382 1.385 .021 11.335 45.527 100.381
10 19.823 21.698 .401 1.377 .016 11.356 45.527 100.198
11 19.588 21.855 .321 1.278 -.008 11.368 45.391 99.793
12 19.740 21.961 .363 1.423 .032 11.341 45.569 100.428
AVER: 19.714 21.884 .367 1.365 .015 11.350 45.503 100.200
SDEV: .097 .143 .034 .062 .017 .015 .077 .289
SERR: .049 .071 .017 .031 .009 .007 .039
%RSD: .49 .65 9.30 4.53 112.08 .13 .17
PUBL: 19.612 21.925 .389 1.333 n.a. 11.408 45.594 100.261
%VAR: .52 -.18 -5.70 2.43 --- -.51 -.20
DIFF: .102 -.041 -.022 .032 --- -.058 -.091
STDS: 138 140 145 139 285 --- ---
STKF: .3789 .3969 .4258 .1957 .1601 --- ---
STCT: 125.64 132.04 141.39 64.55 53.31 --- ---
UNKF: .1930 .1843 .0031 .0077 .0001 --- ---
UNCT: 63.99 61.31 1.04 2.53 .04 --- ---
UNBG: 1.04 1.44 1.43 .47 .76 --- ---
ZCOR: 1.0216 1.1873 1.1669 1.7822 1.1889 --- ---
KRAW: .5093 .4644 .0074 .0392 .0008 --- ---
PKBG: 62.65 43.58 1.74 6.38 1.06 --- ---
St 143 Set 1 Kutnahorite (Harvard #85670), Results Based on 1 Atoms of c
ELEM: Ca Mn Fe Mg P C O SUM
9 .521 .425 .007 .060 .001 1.000 3.015 5.029
10 .523 .418 .008 .060 .001 1.000 3.010 5.018
11 .516 .420 .006 .056 .000 1.000 2.997 4.995
12 .522 .423 .007 .062 .001 1.000 3.016 5.031
AVER: .521 .422 .007 .059 .001 1.000 3.010 5.019
SDEV: .003 .003 .001 .003 .001 .000 .009 .016
SERR: .001 .002 .000 .001 .000 .000 .004
%RSD: .56 .75 9.36 4.64 112.00 .00 .29
Ok, now let's try forcing a bad total on the first line again as seen here:
St 143 Set 1 Kutnahorite (Harvard #85670)
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 30.0 Beam Size = 2
Specimen from Harvard Mineralogical Museum (Carl Francis)
Locality: Franklin, NJ
See Garrels, et al., 1980 AJS 258, 402-418
Also J. V. Smith, Am. Jour. Sci. 1960
Number of Data Lines: 4 Number of 'Good' Data Lines: 4
First/Last Date-Time: 06/15/2008 10:27:04 AM to 06/15/2008 10:28:50 AM
Average Total Oxygen: 45.029 Average Total Weight%: 96.717
Average Calculated Oxygen: 45.032 Average Atomic Number: 13.740
Average Excess Oxygen: -.003 Average Atomic Weight: 20.750
Average ZAF Iteration: 7.00 Average Quant Iterate: 2.00
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element C is Calculated .333 Atoms Relative To 1.0 Atom of Oxygen
St 143 Set 1 Kutnahorite (Harvard #85670), Results in Elemental Weight Percents
ELEM: Ca Mn Fe Mg P C O SUM
9 6.438 21.969 .382 1.399 .021 12.613 43.628 86.451
10 19.823 21.698 .401 1.377 .016 11.356 45.527 100.198
11 19.588 21.855 .321 1.278 -.008 11.368 45.391 99.793
12 19.740 21.961 .363 1.423 .032 11.341 45.569 100.428
AVER: 16.397 21.871 .367 1.369 .015 11.670 45.029 96.717
SDEV: 6.640 .127 .034 .064 .017 .629 .937 6.849
SERR: 3.320 .063 .017 .032 .009 .315 .468
%RSD: 40.50 .58 9.30 4.65 111.82 5.39 2.08
PUBL: 19.612 21.925 .389 1.333 n.a. 11.408 45.594 100.261
%VAR: -16.39 -.25 -5.70 2.70 --- 2.29 -1.24
DIFF: -3.215 -.054 -.022 .036 --- .262 -.565
STDS: 138 140 145 139 285 --- ---
STKF: .3789 .3969 .4258 .1957 .1601 --- ---
STCT: 125.64 132.04 141.39 64.55 53.31 --- ---
UNKF: .1605 .1843 .0031 .0077 .0001 --- ---
UNCT: 53.23 61.31 1.04 2.53 .04 --- ---
UNBG: 1.04 1.44 1.43 .47 .76 --- ---
ZCOR: 1.0211 1.1866 1.1669 1.7868 1.1922 --- ---
KRAW: .4237 .4644 .0074 .0392 .0008 --- ---
PKBG: 52.46 43.58 1.74 6.38 1.06 --- ---
St 143 Set 1 Kutnahorite (Harvard #85670), Results Based on 1 Atoms of c
ELEM: Ca Mn Fe Mg P C O SUM
9 .153 .381 .007 .055 .001 1.000 2.597 4.192
10 .523 .418 .008 .060 .001 1.000 3.010 5.018
11 .516 .420 .006 .056 .000 1.000 2.997 4.995
12 .522 .423 .007 .062 .001 1.000 3.016 5.031
AVER: .429 .411 .007 .058 .001 1.000 2.905 4.809
SDEV: .184 .020 .001 .003 .001 .000 .206 .412
SERR: .092 .010 .000 .002 .000 .000 .103
%RSD: 42.88 4.86 9.50 5.94 114.34 .00 7.08
Now that makes more sense, the total (and calculated oxygen) is low because of the missing Ca. Remember, this calculation for matrix effects of unanalyzed elements is *not* an attempt to perform a charge balance of anything- it is just based on the measured concentrations. If the measured concentrations are "off", the calculation of elements by stoichiometry will also be "off".
Does this help?
john
I would have thought that in the case of a bad (low) total, the oxygen calculated by stoichiometric proportion to the divalent cations would be low.
The carbon, calculated by proportion to that oxygen, should therefore also be low, not high, as in your example.
QuoteSt 143 Set 1 Kutnahorite (Harvard #85670), Results in Elemental Weight Percents
ELEM: Ca Mn Fe Mg P C O SUM
9 6.438 21.969 .382 1.399 .021 12.613 43.628 86.451
10 19.823 21.698 .401 1.377 .016 11.356 45.527 100.198
11 19.588 21.855 .321 1.278 -.008 11.368 45.391 99.793
12 19.740 21.961 .363 1.423 .032 11.341 45.569 100.428
I do agree that including some proportion of C in the correction procedure should improve the results.
However, at present, PfE is generating totals based on CO2 contents that are not in actual exact stoichiometric proportion to the divalent cations.
These analytical totals can therefore be misleading as they are, in fact, erroneous.
As the actual total deviates from 100.00 wt%, PfE is either overestimating C (for low totals), or underestimating C (for high totals).
Such deviations could therefore mask the true character of the analysis.
In the case of carbonates, the user must recalculate the correct stoichiometric CO2 contents based on the divalent metal cations.
I cannot see publishing analyses where C and O were not measured but rather determined by stoichiometric constraints, but that still do not charge balance....
Why does the C content deviate from stoichiometry as a function of total?
Thanks,
Andrew
Quote from: AndrewLocock on June 25, 2015, 03:01:22 PM
I would have thought that in the case of a bad (low) total, the oxygen calculated by stoichiometric proportion to the divalent cations would be low.
The carbon, calculated by proportion to that oxygen, should therefore also be low, not high, as in your example.
QuoteSt 143 Set 1 Kutnahorite (Harvard #85670), Results in Elemental Weight Percents
ELEM: Ca Mn Fe Mg P C O SUM
9 6.438 21.969 .382 1.399 .021 12.613 43.628 86.451
10 19.823 21.698 .401 1.377 .016 11.356 45.527 100.198
11 19.588 21.855 .321 1.278 -.008 11.368 45.391 99.793
12 19.740 21.961 .363 1.423 .032 11.341 45.569 100.428
Hi Andrew,
The carbon is not based on the total, it is based on the calculated oxygen which in turn (with this particular calculation option) is based on the cation concentrations.
And in the line above with a bad total, the calculated oxygen concentration *is* low as expected, because some Ca intensity is missing (I edited it to a lower intensity!).
But because the relative ratio of carbon to oxygen is based on the atomic stochiometry, not the concentration stoichiometry, the relative carbon to oxygen has to be different for concentrations compared to atoms.
As seen here, in the formula atoms, the number of oxygen atoms *is* low compared to the carbon as we would expect:
St 143 Set 1 Kutnahorite (Harvard #85670), Results Based on 1 Atoms of c
ELEM: Ca Mn Fe Mg P C O SUM
9 .153 .381 .007 .055 .001 1.000 2.597 4.192
10 .523 .418 .008 .060 .001 1.000 3.010 5.018
11 .516 .420 .006 .056 .000 1.000 2.997 4.995
12 .522 .423 .007 .062 .001 1.000 3.016 5.031
AVER: .429 .411 .007 .058 .001 1.000 2.905 4.809
SDEV: .184 .020 .001 .003 .001 .000 .206 .412
SERR: .092 .010 .000 .002 .000 .000 .103
%RSD: 42.88 4.86 9.50 5.94 114.34 .00 7.08
This all makes sense to me.
Quote from: AndrewLocock on June 25, 2015, 03:01:22 PM
In the case of carbonates, the user must recalculate the correct stoichiometric CO2 contents based on the divalent metal cations.
I cannot see publishing analyses where C and O were not measured but rather determined by stoichiometric constraints, but that still do not charge balance....
Why does the C content deviate from stoichiometry as a function of total?
Again, the C content deviates from stoichiometry *not* as a function of the total but as a function of the total cations.
When the formula proportions are calculated from the concentrations, everything is normalized to the sum of the atoms as it should be. You cannot get charge balance if the analysis is wrong!
It seems you are asking for an exact C to O of 1 to 3, but that is impossible if the carbon is based on the calculated oxygen and the calculated oxygen is wrong because the analysis is bad.
I'm not a geologist so maybe there's some mineralogical thing you are concerned about, but one can't expect the right stoichiometries if the concentrations are wrong, correct?
Maybe you should just do the formula by difference option and specify CO3 as your formula...?
john
I just got back from travel and don't have time and energy now to read the whole thread. But I do have a comment which perhaps doesn't deal with the exact question, but for me, PfE does carbonates as good as can be done by EPMA.
I have never had a problem with the way PfE does carbonates, BECAUSE a correct analysis is self consistent if and only if
(0) All the existent cations are measured,
(1) the analytical total after all the smoke and mirrors is 99.5 - 100.5 (which it is almost always when things done properly)
AND
(2) The cations sum to 1 (.995-1.005), the Carbon is very close if not dead on 1 and the Oxygen is 3 or very close.
In lieu of doing x-ray diffraction to prove it truly is a carbonate, this seems to me to be as close as one can get to an EPMA analysis of a carbonate mineral without measuring O and C (and I've tried it, and it aint easy, and you do not get good numbers).
Hi John,
I don't mean to be obtuse, but the essence of your argument is not clear to me.
Whether or not an analysis has a good total is independent of the nature of the formula wherein a large portion is calculated by stoichiometry, and not measured.
For ideal calcite, Ca = 40.04 wt%, and the C and O calculated by stoichiometry (for the formula CaCO3) are necessarily: C = 12.00 wt%, O = 47.96 wt%, and sum = 100.00 wt%. The formula is CaCO3.
For a "bad analysis" of calcite, where Ca = 38.41 wt%, the stoichiometric ratio 1 Ca = 1 C = 3 O yields: C = 11.51 wt%, O = 46.00 wt%, and sum 95.92 wt%. The formula is still(!) CaCO3 - after all, Ca is the only thing that we have measured.
If oxygen is calculated by stoichiometry to Ca, and C is calculated by stoichiometry to oxygen, how could it be otherwise?
In PfE, in the "Calculation Options" window, the 2 checked options that I am using are: "Calculate with Stoichiometric Oxygen", and "Stoichiometry To Calculated Oxygen: 0.333 Atoms Of C To 1 Oxygen" (as per screen capture in the attached Word document).
I don't understand the distinction that you make:
QuoteBut because the relative ratio of carbon to oxygen is based on the atomic stochiometry, not the concentration stoichiometry, the relative carbon to oxygen has to be different for concentrations compared to atoms.
The C to O atomic ratio is fixed: 0.333 C to 1 O. The O to Ca ratio is also fixed: 1 to 1.
I appreciate your assistance in helping with my (mis)understanding of what PfE is doing.
Thanks,
Andrew
Quote from: AndrewLocock on June 25, 2015, 04:43:01 PM
I appreciate your assistance in helping with my (mis)understanding of what PfE is doing.
Hi Andrew,
I'm sorry. Likewise I don't understand your point.
It seems clear to me that if total is low due to a missing cation, the normalization to the total atoms will not maintain the 1:3 ratio of carbon to oxygen, because concentrations are not atoms. It will only be perfect if the analysis is perfect.
I'd be happy to continue the conversation, but maybe you should just use the formula by difference option and specify CO3 by difference. I promise you will get the 1 to 3 carbon to oxygen ratio you seem to require.
I think part of the confusion is that I'm calculating these elements by stoichiometry in weight percent and then normalizing these concentrations to formula atoms...
I have some mineralogical calculations for amphiboles and biotite, but not for other minerals, sorry to say. But if you could write some charge balancing code for carbonates, I'd be pleased to incorporate that into PFE.
john
Hi Andrew & co,
I *might* agree that this can be confusing. Let's take back the example of good and bad analysis you give (I converted the Ca content in CaO):
Wt-% (O norm.), CaO, CO2, Total
Analysis 1, 56.0238, 43.9673, 99.9911
Analysis 2, 53.7431, 42.1774, 95.9205
Norm., Ca, C, Total cation, O
Analysis 1, 1.00000, 1.00000, 2.00000, 3.00000
Analysis 2, 1.00000, 1.00000, 2.00000, 3.00000
Effectively in both case you still have 1 C for 3 O. With this "simple" case of one cation, you will ALWAYS get 1 cation of Ca, 1 of C and one of O. This is because of the normalization process, which specify (in normal situation) a fixed amount of oxygen per cation to balance the charge. Now, if we consider carbonate, we can assume it must have one oxygen atom for each atom of calcium, and add to this one molecule of CO2, but the more logical way to see this problem is NOT to consider just C, or just CO2, but effectively CO3. Of course, at the end, the recalculation effectively reports results as elemental C wt-% or CO2 wt-%. Key is that, through the mineral formula recalculation, the "game" is always to balance the positive charges (= what is measured) with anions that are NOT measured. In most case, we simply compensate all positive charges with O2-, and the amount of O is defined by the fixed oxidation state for each cation. In the case of carbonate, the negative charge is effectively (CO3)2-, which makes even more sense when we look at the crystalline structure of carbonate; they are effectively made of CO3 triangles and not isolate CO2 molecule ;). Hence a ratio of 1/3 carbon for 1 oxygen (or 1 C for 3 O). Of course, one could state that we have one CO2 and one atom of O, but to me it makes more sense to simply consider CO3 "as a single anionic molecule".
The problem of hydrogen is the same! Hydrogen is a cation (that we cannot measure by EMP), but you balance the charges with anion of (OH)-, and you do not consider simply H+, or H2O; again the crystalline structure show H as being OH anion group, not H2O molecule or isolate H cation... For hydrous mineral, you can consider the total positive charges and the total oxygen WITH oxygen from hydroxide group, but you need to "correct" the total amount of oxygen used to balanced the measured cation (i.e., all cations WITHOUT hydrogen). For instance:
Epidote = (Ca2)(Al2Fe3+)(Si2O7)(SiO4)O(OH)
=> 13 oxygens TOTAL = 26 negative charges
......BUT...... There is ONE hydrogen atom (1 positive charge) that is calculated by stoichiometry and charge balance (or by difference - wrong idea here!).
=> actually there are 12.5 oxygen (a number often refer as being ideal for epidote normalization - without taking into account of Fe2+/Fe3+ issue), as the "half-oxygen" is used to balance the charge of the calculated 1 hydrogen atom. However, to my opinion this is wrong to state this, and we should rather consider 13 oxygens INCLUDING one O associated to one H (and correct for this through the normalization process).
BTW, take a look at my website, I have implemented a form to calculate mineral formula, and it does do the trick (well, kind of a black box for user without access to my code) to calculate any H2O or CO2 content based on user input. To make it more "geologically meaningful", I speak about H2O or CO2 groups, but the calculation does include what I describe above...
http://cub.geoloweb.ch/index.php?page=mineral_formula (http://cub.geoloweb.ch/index.php?page=mineral_formula)
Just my $0.02, but I believe, John, you are doing things 200% correctly, although I can understand Karsten's comment about the "user-friendliness" of the input. Maybe I can work with you to implement a solution similar to what I have on my website.
Julien
Edit by John: I'd be pleased to implement any mineral recalculation code in PFE that anyone makes available... it's good to have geologist friends!
All,
I think the point Andrew is trying to make is that, no matter what the the actual cation concentrations are (e.g. in case of a bad measurement or even just some minor variations due to counting statistics), he would expect the ratios always to be 1 total cations : 1 carbon : 3 oxygen ratio, no matter what the actual analytical total is, as C and O are calculated from the cations by stoichiometry. (C indirectly via O.)
If you have a look at the Excel spreadsheet with the data Andrew posted, there are some measurements with somewhat low cation totals which start to deviate from this assumption, but at the most extreme he's got some analyses in there which basically show zero cations (< 1wt% cation totals), probably just resin measurements, but have calculated carbon of 18 wt% and O of 48 wt%. Independent of those obviously being bad measurements which can't be used, what is the exact reason why C and O are so much higher than what would be their values calculated by stoichiometry?
I admit I don't know too much about the inner mathematical workings of matrix corrections myself, but I assume that the low cation totals make the carbon and oxygen concentrations "go wild" in the iteration (e.g. because of reduced absorption) towards much higher values than what would be stoichiometric. I assume there is a good reason why C and O can't be "pinned" to the cation values within the matrix correction?
Cheers,
Karsten
Quote from: Karsten Goemann on June 27, 2015, 07:49:10 PM
I think the point Andrew is trying to make is that, no matter what the the actual cation concentrations are (e.g. in case of a bad measurement or even just some minor variations due to counting statistics), he would expect the ratios always to be 1 total cations : 1 carbon : 3 oxygen ratio, no matter what the actual analytical total is, as C and O are calculated from the cations by stoichiometry. (C indirectly via O.)
If you have a look at the Excel spreadsheet with the data Andrew posted, there are some measurements with somewhat low cation totals which start to deviate from this assumption, but at the most extreme he's got some analyses in there which basically show zero cations (< 1wt% cation totals), probably just resin measurements, but have calculated carbon of 18 wt% and O of 48 wt%. Independent of those obviously being bad measurements which can't be used, what is the exact reason why C and O are so much higher than what would be their values calculated by stoichiometry?
I admit I don't know too much about the inner mathematical workings of matrix corrections myself, but I assume that the low cation totals make the carbon and oxygen concentrations "go wild" in the iteration (e.g. because of reduced absorption) towards much higher values than what would be stoichiometric. I assume there is a good reason why C and O can't be "pinned" to the cation values within the matrix correction?
Hi Karsten,
I have to admit I pretty confused about all this too. But the relative C:O ratio can be "pinned" if the formula (CO3) difference option is specified.
As I said previously, if the amount of carbon is dependent on the amount of calculated oxygen and the calculated oxygen is wrong because the total/analysis is bad, etc, then that C:O ratio will be wrong... it just depends on the calculation option selected.
john
This thread becomes really interesting. And thanks to Karsten, I think to now understand the problem, but I don't have the solution. I maintain that the idea of a 1:3 ratio C to O is required. And effectively, probably all of us do agree with that. Normally, with this assumption, you should get the right CO2 wt-% value with this, AND you should effectively get the amount of C (atoms) equal to the amount of 2+ cation (atoms).
It is *possible* there is an error in Probe for EPMA (John?). I realized this by re-doing all the calculations both by hand and through my website. The complete XL sheet is attached to this thread. Let me know if you find an error in my logic (the spreadsheet contain all the formula employed)...
Let's start with the output from Probe for EPMA mentioned by Andrew:
Ca Mn Fe Mg C O SUM
#21 19.734 22.026 0.382 1.385 11.333 45.532 100.392
#22 19.85 21.699 0.401 1.377 11.354 45.532 100.213
#23 19.615 21.856 0.321 1.278 11.366 45.396 99.832
#24 19.767 21.962 0.363 1.423 11.338 45.574 100.427
I recalculated this in oxide, as I personally prefer to deal with oxide when it comes to oxide / carbonate:
CaO MnO FeO MgO CO2
#21 27.612 28.440 0.491 2.297 41.525
#22 27.774 28.018 0.516 2.283 41.602
#23 27.445 28.221 0.413 2.119 41.646
#24 27.658 28.358 0.467 2.360 41.543
Now... Here is the output that Andrew mention regarding atom per formula unit:
Fe2+ Mg Mn Ca C Total cation O
#21 0.0072 0.0601 0.4229 0.5194 0.9952 2.0048 3.0000
#22 0.0076 0.0597 0.4165 0.5223 0.9969 2.0031 3.0000
#23 0.0061 0.0556 0.4205 0.5173 1.0003 1.9997 3.0000
#24 0.0069 0.0617 0.4214 0.5199 0.9951 2.0049 3.0000
(I did recalculated this through my online tool for mineral formula recalculation forcing a total of 3 oxygens). This is similar to the results from Probe for EPMA. Notice that effectively, the total number of 2+ cation do NOT match the total number of C!!! I believe this is because somehow the wt-% C calculated by Probe for EPMA is slightly wrong (well, hypothesis)!
Here is now the results of oxide wt-% recalculated based on the assumption that the sum of 2+ cations is equal to the number of atom of carbon - or, since we are dealing only with 2+ cation, we can rather state that the sum of the cations is balanced by an equal amount of (CO3)2- molecule.
FeO MgO MnO CaO CO2 Total
#21 0.4910 2.2970 28.4400 27.6120 42.1227 100.9627
#22 0.5160 2.2830 28.0180 27.7740 41.9881 100.5791
#23 0.4130 2.1190 28.2210 27.4450 41.6137 99.8117
#24 0.4670 2.3600 28.3580 27.6580 42.1621 101.0051
Notice the CO2 is now higher, between 41.61 and 42.16% (versus 41.52 and 41.65% from PfE). What I do NOT understand, is that this difference is not consistent! For instance, analysis #24 yield the highest CO2 content through my calculation, whereas analysis #23 yield the highest content with Probe for EPMA. Once the difference in calculated CO2 wt-% is +0.032% (analysis #23), sometime it is strongly negative (PfE underestimate CO2 content by -0.39% [analysis #22] to -0.62% [analysis #24]).
And as a check, here is now the NEW mineral formula recalculation based on this new CO2 wt-% recalculation. Notice that now both the total of 2+ cations do match the number of C-atom:
Fe2+ Mg Mn Ca C O Sum M
#21 0.014 0.119 0.838 1.029 2.000 6.000 2.000
#22 0.015 0.119 0.828 1.038 2.000 6.000 2.000
#23 0.012 0.111 0.841 1.035 2.000 6.000 2.000
#24 0.014 0.122 0.835 1.030 2.000 6.000 2.000
Question to John: HOW do you recalculate the CO2 in weight-%? I guess, you run the C (or CO2) wt-% content through the matrix correction, right? But you also need to perform a conversion in atomic proportion to recalculate the C (or CO2) content, right? Maybe posting (or sending to me by email) your VB code might help me understanding where the error could be... Otherwise, you can also look at my spreadsheet to assess how this should be done?
Julien
Hi Julien,
Thanks for looking at this. This thread is getting way long, but my calculation code is in this post:
http://smf.probesoftware.com/index.php?topic=92.msg2950#msg2950
I'm pleased to fix anything that isn't right but I don't see anything wrong with the existing calculation for carbon by stoichiometry to calculated oxygen. As I said previously, the CO3 by difference option is probably what you guys are looking for if you need to maintain an exact C:O ratio regardless of the analysis quality.
john
CO3 by difference does not maintain stoichiometry with cations. This is also desired.
Quote from: Gseward on June 28, 2015, 08:41:21 AM
CO3 by difference does not maintain stoichiometry with cations. This is also desired.
Hi Gareth,
Yes, it is not a perfect world!
I am about to post something that I hope helps everyone.
john
Quote from: Julien on June 27, 2015, 10:09:29 PM
Question to John: HOW do you recalculate the CO2 in weight-%? I guess, you run the C (or CO2) wt-% content through the matrix correction, right? But you also need to perform a conversion in atomic proportion to recalculate the C (or CO2) content, right? Maybe posting (or sending to me by email) your VB code might help me understanding where the error could be... Otherwise, you can also look at my spreadsheet to assess how this should be done?
Hi Julien,
In addition to the code posted above I can add the following comments:
1. The oxygen calculated by stoichiometry to the measured cations is added to the matrix correction as a concentration. Likewise, the carbon calculated by stoichiometry to oxygen is also added to the matrix correction as the code above shows as a concentration also.
2. This calculation is iterated because as the concentrations of the cations change, due to the (relatively minor) matrix effect of adding oxygen and carbon, the oxygen and carbon by calculation also are changed as they should.
3. Note that all concentrations are normalized to 100% during the matrix iteration to assist in the matrix correction calculation. If this was not done, some measurements would never converge!
4. Once the matrix iteration converges, the concentration are de-normalized to the actual concentration total and the program then hands off the concentrations to the output routines which convert the concentrations to oxides, formula atoms, etc., if specified by the user.
But please realize the original title of this topic. It is about including unanalyzed elements in the matrix correction so the matrix correction is properly calculated! The code we are discussing is *not* an effort to determine the actual oxygen and carbon concentrations, it is merely to aid in the calculation of the matrix physics!
For example, here is the calculation with the oxygen and carbon specified by calculation as we have been discussing (oxygen by cation stoichiometry and carbon calculated by stocihiometry to calculated oxygen):
St 143 Set 1 Kutnahorite (Harvard #85670), Results in Elemental Weight Percents
ELEM: Ca Mn Fe Mg P C O
TYPE: ANAL ANAL ANAL ANAL ANAL STOI CALC
BGDS: LIN LIN LIN LIN LIN
TIME: 10.00 10.00 10.00 10.00 10.00 --- ---
BEAM: 30.00 30.00 30.00 30.00 30.00 --- ---
ELEM: Ca Mn Fe Mg P C O SUM
9 19.706 22.024 .382 1.385 .021 11.335 45.527 100.381
10 19.823 21.698 .401 1.377 .016 11.356 45.527 100.198
11 19.588 21.855 .321 1.278 -.008 11.368 45.391 99.793
12 19.740 21.961 .363 1.423 .032 11.341 45.569 100.428
AVER: 19.714 21.884 .367 1.365 .015 11.350 45.503 100.200
SDEV: .097 .143 .034 .062 .017 .015 .077 .289
SERR: .049 .071 .017 .031 .009 .007 .039
%RSD: .49 .65 9.30 4.53 112.08 .13 .17
PUBL: 19.612 21.925 .389 1.333 n.a. 11.408 45.594 100.261
%VAR: .52 -.18 -5.70 2.43 --- -.51 -.20
DIFF: .102 -.041 -.022 .032 --- -.058 -.091
STDS: 138 140 145 139 285 --- ---
STKF: .3789 .3969 .4258 .1957 .1601 --- ---
STCT: 125.64 132.04 141.39 64.55 53.31 --- ---
UNKF: .1930 .1843 .0031 .0077 .0001 --- ---
UNCT: 63.99 61.31 1.04 2.53 .04 --- ---
UNBG: 1.04 1.44 1.43 .47 .76 --- ---
ZCOR: 1.0216 1.1873 1.1669 1.7822 1.1889 --- ---
KRAW: .5093 .4644 .0074 .0392 .0008 --- ---
PKBG: 62.65 43.58 1.74 6.38 1.06 --- ---
St 143 Set 1 Kutnahorite (Harvard #85670), Results Based on 1 Atoms of c
ELEM: Ca Mn Fe Mg P C O SUM
9 .521 .425 .007 .060 .001 1.000 3.015 5.029
10 .523 .418 .008 .060 .001 1.000 3.010 5.018
11 .516 .420 .006 .056 .000 1.000 2.997 4.995
12 .522 .423 .007 .062 .001 1.000 3.016 5.031
AVER: .521 .422 .007 .059 .001 1.000 3.010 5.019
SDEV: .003 .003 .001 .003 .001 .000 .009 .016
SERR: .001 .002 .000 .001 .000 .000 .004
%RSD: .56 .75 9.36 4.64 112.00 .00 .29
Yes, I agree the carbon to oxygen ratio is off by around 0.3 % as Andrew points out and this *is* as he says because the total is not exactly 100%.
But we are only including carbon and oxygen to help with the matrix correction accuracy! For example:
Here is the same kutnahorite analysis average exported to CalcZAF (you will see in a moment why I do this, but CalcZAF uses exactly the same code as PFE) as we have been doing, that is oxygen by stocihiometry and carbon by stoichiometry to calculated oxygen and again the C:O ratio is off by 0.3% as we saw in PFE:
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Ca ka .50929 .19297 19.714 27.584 10.372 .521 15.00
Mn ka .46436 .18432 21.885 28.258 8.400 .422 15.00
Fe ka .00738 .00314 .367 .472 .139 .007 15.00
Mg ka .03916 .00766 1.365 2.264 1.185 .059 15.00
P ka .00080 .00013 .015 .035 .010 .001 15.00
C 11.350 41.587 19.925 1.000
O .000 .000 .000 .000
O 45.505 ----- 59.970 3.010
TOTAL: 100.201 100.201 100.000 5.019
Now, because I will be removing the carbon and oxygen from the matrix correction in the calculations below, I will normalize to Ca instead of carbon as seen here:
ELEMENT ABSCOR FLUCOR ZEDCOR ZAFCOR STP-POW BKS-COR F(x)u Ec Eo/Ec MACs
Ca ka 1.0023 .9832 1.0366 1.0216 1.0812 .9588 .9607 4.0390 3.7138 153.893
Mn ka 1.0071 .9999 1.1791 1.1873 1.2431 .9486 .9757 6.5390 2.2939 108.543
Fe ka 1.0039 1.0000 1.1624 1.1669 1.2251 .9488 .9808 7.1120 2.1091 89.0408
Mg ka 1.7946 .9992 .9939 1.7822 .9848 1.0092 .4828 1.3050 11.4943 2855.99
P ka 1.1561 .9933 1.0353 1.1889 1.0493 .9867 .7943 2.1460 6.9897 834.429
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Ca ka .50929 .19297 19.714 27.584 10.372 1.000 15.00
Mn ka .46436 .18432 21.885 28.258 8.400 .810 15.00
Fe ka .00738 .00314 .367 .472 .139 .013 15.00
Mg ka .03916 .00766 1.365 2.264 1.185 .114 15.00
P ka .00080 .00013 .015 .035 .010 .001 15.00
C 11.350 41.587 19.925 1.921
O .000 .000 .000 .000
O 45.505 ----- 59.970 5.782
TOTAL: 100.201 100.201 100.000 9.642
Now what if we *did not* include the oxygen and carbon by calculation in the matrix correction physics? Here is what we would get:
ELEMENT ABSCOR FLUCOR ZEDCOR ZAFCOR STP-POW BKS-COR F(x)u Ec Eo/Ec MACs
Ca ka 1.0195 .9767 .9474 .9434 .9345 1.0138 .9445 4.0390 3.7138 87.6428
Mn ka 1.0326 .9998 1.0646 1.0992 1.0791 .9866 .9516 6.5390 2.2939 87.4901
Fe ka 1.0242 1.0000 1.0468 1.0721 1.0645 .9834 .9613 7.1120 2.1091 72.0165
Mg ka 2.0852 .9985 .9141 1.9032 .8450 1.0817 .4155 1.3050 11.4943 1453.98
P ka 1.2480 .9882 .9539 1.1763 .9028 1.0565 .7358 2.1460 6.9897 454.843
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Ca ka .50929 .19297 18.204 ----- 51.063 1.000 15.00
Mn ka .46436 .18432 20.260 ----- 41.459 .812 15.00
Fe ka .00738 .00314 .337 ----- .678 .013 15.00
Mg ka .03916 .00766 1.458 ----- 6.744 .132 15.00
P ka .00080 .00013 .015 ----- .055 .001 15.00
C .000 ----- .000 .000
O .000 ----- .000 .000
TOTAL: 40.275 ----- 100.000 1.958
First note that the matrix corrections are different (see Ca in red). That is to say *wrong* because we did not have carbon and oxygen in the matrix for calculating the proper physics. That is after all the entire point of this topic. Yes, it's small difference for Mn, but it's worth doing.
In the case of Mg, the difference is *not* so small, because this is a low energy element and more affected by the matrix physics. So, the additional of carbon and oxygen to the calculation makes a significant improvement to accuracy of the measured elements, which is the whole point.
So we are adding the oxygen and carbon by stoichiometry to the analysis to improve the matrix correction and it is doing that as expected. Now the C:O ratio gets slightly distorted because of the subsequent formula atom renomalization (carbon and oxygen have different atomic weights) when the total is not exactly 100%.
But since we are only adding oxygen and carbon to correct the physics, that is the nature of this beast! My best advice is, if you want the C:O ratio exactly 3, then you should utilize the CO3 formula by difference option. In either case the difference to the matrix correction physics is negligible.
I have to run off for the day, but I will return later and add some additional thoughts.
Hi John,
Let me emphasize that I agree with John Fournelle that PfE generates the best carbonate analyses. And also, that I agree with you: C and O should be included in the matrix corrections to improve the accuracy of the measured elements.
However, the results that I am obtaining are not in actual stoichiometric proportion; they are just close to it. This is a problem for me (as I like to make a quick judgement of the quality of an analysis by its total), and for my users (relying on the reported CO2 concentrations, or C and O concentrations).
I ran some analyses of a calcite from an unknown locality using the Smithsonian calcite standard (which is published to have 56.10 wt% CaO = 40.09 wt% Ca), at 15 kV, 10 nA, 5 micron beam diameter, with count times of 30 s on peak, 15 s on each background, JEOL 8900R. The mdb file is attached for your interest.
Probe for EPMA has several calculation options. It is instructive to compare them for a given analytical point (my #24):
Calculate as Elemental: gives Ca 37.44, C 0, O 0, total 37.44 wt%.
Calculate with Stoichiometric Oxygen: gives Ca 38.39, C0, O 15.33, total 53.72 wt%.
(Note that Ca and O are in a perfect stoichiometric ratio of 1:1, specifically 0.9579 mol Ca and 0.9579 mol O).
Calculate with Stoichiometric Oxygen; Stoichiometry to Calculated Oxygen 0.3333333 C to 1 O: gives Ca 39.57, C 12.04, O 47.87, total 99.48 wt%. (Note that the elements are not in the stoichiometric proportion of 1:1:3, rather the molar proportions here are 0.9873 Ca, 1.0024 C, and 2.9921 O).
It appears that including O-by-stoichiometry improves the result for Ca, and is reported in stoichiometric proportion. Including both C and O further improves the result for Ca, but is not reported in stoichiometric proportion. It is not clear to me why stoichiometry is maintained in the first case, but not the second.
Perhaps, after the matrix corrections are completed, PfE should recalculate the mass fractions of C and O to be in stoichiometric agreement with the analyzed elements?
I should point out two problems that I observed in analyzing calcite with PfE and using the Stoichiometry to Calculated Oxygen option. Firstly, the C concentration reported by PfE is negatively correlated with the Ca concentration. A series of replicate calcite analyses yields a linear correlation (R^2=1), where low Ca gives high C, and high Ca gives low C. In the worst case, if I radically defocus the sample, and obtain a poor result of Ca 15.42 wt%, the program reports C 15.11 wt% - considerably in excess of what is chemically possible.
Secondly, if I enable the "Use All Matrix Corrections" for analyses calculated with the Stoichiometry to Calculated Oxygen option, all of the results for a given point are reported as virtually identical (differing only in the second decimal point; RSD for Ca circa 0.002%). In contrast, using the Calculate with Stoichiometric Oxygen gives a wide range of results among the different matrix corrections with an RSD for Ca of 2.0%). I cannot see how including C in the matrix corrections should improve their relative agreement by a factor of 1000.
Thanks, Andrew.
Quote from: AndrewLocock on June 28, 2015, 03:42:41 PM
Firstly, the C concentration reported by PfE is negatively correlated with the Ca concentration. A series of replicate calcite analyses yields a linear correlation (R^2=1), where low Ca gives high C, and high Ca gives low C. In the worst case, if I radically defocus the sample, and obtain a poor result of Ca 15.42 wt%, the program reports C 15.11 wt% - considerably in excess of what is chemically possible.
Hi Andrew,
No worries, there's always room for improvement, I just don't see how to get "there" from "here". :-[
I've attached the CalcZAF/PFE matrix correction calculation code below and if you would be willing to look at it, maybe you can see where I'm going "wrong", but I pretty sure it's not a case of right or wrong, just different ways of getting "there".
As I've said already, because (with this particular method of calculating unanalyzed elements) I'm calculating relative concentrations from atom stoichiometries in the matrix correction code, and if subsequently the concentrations are then normalized to formula atoms, *and* if the total is isn't exactly 100%, then the relative atoms of the two elements by stoichiometry will be slightly different when they are normalized. This is inherent in the fact that carbon and oxygen have different atomic weights!
You mentioned that if the beam is defocused and the analysis total is very bad, then the calculated C:O ratio will be very bad also. I am not surprised. In fact I do not see how the C:O could not be be very bad if the total is very bad, at least for this particular method of calculating by C:O by stoichiometry. Not to be flip, but that's just: garbage in/garbage out!
Now, everyone (except Gareth) seems to be ignoring my repeated mentioning of the alternative method for calculating C:O ratios and that is formula by difference. This insures that the C:O ratio stays exactly as specified the same no matter what the cation concentrations are. Why? Because the total is always exactly 100%.
Here is the kutnahorite example I've been using, with the CO3 formula by difference specified for the unanalyzed elements:
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Ca ka .50929 .19297 19.713 ----- 10.399 .521 15.00
Mn ka .46436 .18432 21.883 ----- 8.422 .422 15.00
Fe ka .00738 .00314 .367 ----- .139 .007 15.00
Mg ka .03916 .00766 1.365 ----- 1.188 .060 15.00
P ka .00080 .00013 .015 ----- .010 .001 15.00
C 11.340 ----- 19.961 1.000
O 45.317 ----- 59.882 3.000
TOTAL: 100.000 ----- 100.000 5.010
1.000 to 3.000 so what's not to like?
Now, if you really want to re-nomalize the results to account for charge balancing (which it sounds like you do), then please send me a carbonate mineral charge balancing code and I will happily implement it in PFE. This software, in case you didn't already know, is a community effort to improve the state of microanalysis! Hence this forum, and hence this protracted discussion...
In the meantime please feel free to examine the matrix correction code I've attached below.
john
John, the idea of getting CO2 by difference won't resolve anything and it is NOT good. I doubt you will get the desired 1:1:3 ratio all the time when calculating CO2 by difference. Calculating the CO2 by stoichiometry also permits to check if the analysis is good (i.e., totals close to 100%). We don't ignore this comment, I guess we just don't like the idea ;)
I agree with Andrew: the best way to do it would be to re-normalize and re-calculate the CO2 wt-% (or C and O wt-%) AFTER the last matrix iteration, when results converged. This is not ideal, as, in normal situation, you would need to re-run the matrix correction with the new value for C and O, but, as you mentioned, this minor change would not affect too strongly the other measured cation wt-%. Again, the whole idea is just to get a perfect ratio of one total measured divalent cation, one carbon atom, and three oxygen (1:1:3).
Of course, the other solution (which I personally apply anyway) is to simply perform a mineral formula recalculation separately using a "home-made" XL spreadsheet. You can't imaging how complicated this normalization can be, with some time special conditions (e.g., fill one site with X amount of atom, another site with Y amount, and sometime a same element can be split in two different "sites" and need additional conditions). I'm not sure if you realize how complicated this can be, and so far there is no universal way to normalize all minerals, and there are often numerous ways to perform this type of calculation. For carbonate it is relatively easy, but deal once with amphibole (including F, Cl and unanalyzed OH or O2-) or allanite (REE-epidote, also with OH), and you will loose all your hairs!
Still, if you want to incorporate a carbonate normalization process AND "proper" recalculation of CO2 wt-% by stoichiometry, please, see my previous post and the attached XL sheet.
http://smf.probesoftware.com/index.php?topic=92.msg2967#msg2967 (http://smf.probesoftware.com/index.php?topic=92.msg2967#msg2967)
It does contain the math behind calculating CO2 wt-%. Maybe Andrew can double check my normalization and confirm this is the way to go. Note that I do force the normalization to yield a perfect total of one total divalent cation - if you don't want this option, simply set the "norm. factor" in the spreadsheet to 1.0000.
I can adjust it to calculate C wt-% if you want, or I can even try to translate it in VB. Note that this "simple" example is only considering 2+ cations, and it would need to be adjusted with some cation factor if the analysis include non-divalent cations (to take into account the fact that, for instance, TWO 3+ cation will be balanced by THREE (CO3)2- anion).
J.
Quote from: Julien on June 28, 2015, 09:32:25 PM
Of course, the other solution (which I personally apply anyway) is to simply perform a mineral formula recalculation separately using a "home-made" XL spreadsheet. You can't imaging how complicated this normalization can be, with some time special conditions (e.g., fill one site with X amount of atom, another site with Y amount, and sometime a same element can be split in two different "sites" and need additional conditions). I'm not sure if you realize how complicated this can be, and so far there is no universal way to normalize all minerals, and there are often numerous ways to perform this type of calculation. For carbonate it is relatively easy, but deal once with amphibole (including F, Cl and unanalyzed OH or O2-) or allanite (REE-epidote, also with OH), and you will loose all your hairs!
Hi Julien,
Yes, exactly. We need some sort of carbonate charge balance code that I can incorporate into PFE for mineral processing.
Any such code needs to be written by a geologist/mineralogist. I am not qualified. I will check your Excel code, thanks!
Wait. I need your VBA code... specifically your .xlsm file.
john
Quote from: Julien on June 28, 2015, 09:32:25 PM
John, the idea of getting CO2 by difference won't resolve anything and it is NOT good. I doubt you will get the desired 1:1:3 ratio all the time when calculating CO2 by difference. Calculating the CO2 by stoichiometry also permits to check if the analysis is good (i.e., totals close to 100%). We don't ignore this comment, I guess we just don't like the idea ;)
Hi Julien,
First of all it is CO3 by difference, not CO2. The reason being that the cations must be calculated elementally if CO3 is specified by difference.
Second, I can understand that you would like to see a *real* total that reflects the quality of carbonate measurement- and that is exactly what the carbon by stoichiometry to stoichiometric oxygen calculation method is for! But since you all are insisting on perfect C:O stoichiometry for an imperfect analysis... you *should* use the formula by difference option! Whether you like it or not! ::)
And third, you *can* still look at the "total" to ascertain the carbonate measurement quality, just not the wt% total! :o
Note that the total formula atoms below for the CO3 formula by difference calculation is 5.011. Since we have fixed C:O to 1:3, we simply subtract the 4 CO3 atoms from the total atoms to get the sum of cations, and yes, just as was the case for the stoichiometric carbon to oxygen calculation we have a high total (5.011 - 4 = 1.011), this time for the sum of cations!!!
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Ca ka .50929 .19297 19.741 ----- 10.416 .522 15.00
Mn ka .46436 .18430 21.884 ----- 8.424 .422 15.00
Fe ka .00738 .00314 .367 ----- .139 .007 15.00
Mg ka .03916 .00766 1.365 ----- 1.188 .060 15.00
P ka .00080 .00013 .015 ----- .010 .001 15.00
C 11.334 ----- 19.956 1.000
O 45.294 ----- 59.867 3.000
TOTAL: 100.000 ----- 100.000 5.011
Even a simple mind like mine can do that subtraction in my head!
But send or post me your VBA code, that is, the Excel .xlsm file with the carbonate charge balance calculation macro, and I will implement it into PFE ASAP as a mineral calculation option for carbonates!
john
Quote from: AndrewLocock on June 28, 2015, 03:42:41 PM
Secondly, if I enable the "Use All Matrix Corrections" for analyses calculated with the Stoichiometry to Calculated Oxygen option, all of the results for a given point are reported as virtually identical (differing only in the second decimal point; RSD for Ca circa 0.002%). In contrast, using the Calculate with Stoichiometric Oxygen gives a wide range of results among the different matrix corrections with an RSD for Ca of 2.0%). I cannot see how including C in the matrix corrections should improve their relative agreement by a factor of 1000.
Hi Andrew,
As I have said already, when using the carbon by stoichiometry to stoichiometric oxygen calculation method, the ability to maintain a perfect C:O ratio through the atom normalization depends on totals being close to 100%. This is simply due to the atom normalization math.
I'll try again: the magnitude of the C:O ratio discrepancy when the concentrations are normalized to atoms, depends on the relative ratio of the atomic weights of carbon and oxygen *and* the degree to which the analytical total varies from 100%. This is what all your "discrepancy" vs. (total - 100) plots show.
And if I have to type the word "stoichiometric" again, I don't know what I'm going to do... :'(
Seriously, please read this post to Julien and see if this explanation helps:
http://smf.probesoftware.com/index.php?topic=92.msg2979#msg2979
Hi John,
I will go through your code over he next week or so. As you will appreciate, it is not short(!).
Some points to ponder:
1) If we analyze just Mg in magnesium oxide, and calculate oxygen by stoichiometry, the ratio of Mg to O is 1:1 in PfE, regardless of analytical total. Why?
2) Stoichiometry for the simple carbonate minerals means the ratio of the sum of the divalent cations (Mg+Ca+Sr+Ba+Mn+Fe+Zn etc.) to C to O is 1:1:3, without exception.
3) The widely differing matrix corrections should give different values for any given analysis, regardless of the options selected in PfE.
Question:
My understanding of ZAF corrections is that they are an interative loop.
Is it possible during the ZAF corrections to match the concentration of C to the corresponding correct proportion of O (or more properly divalent cations) for each iteration?
As you mention:
Quote1. The oxygen calculated by stoichiometry to the measured cations is added to the matrix correction as a concentration. Likewise, the carbon calculated by stoichiometry to oxygen is also added to the matrix correction as the code above shows as a concentration also.
2. This calculation is iterated because as the concentrations of the cations change, due to the (relatively minor) matrix effect of adding oxygen and carbon, the oxygen and carbon by calculation also are changed as they should.
Why not change the C and O concentrations accordingly with each iteration of the ZAF corrections?
Thanks for encouraging me to post these queries in the forum, and of course, for your patience as well as the excellent program.
All the best,
Andrew
Quote from: AndrewLocock on June 29, 2015, 04:09:30 PM
Some points to ponder:
1) If we analyze just Mg in magnesium oxide, and calculate oxygen by stoichiometry, the ratio of Mg to O is 1:1 in PfE, regardless of analytical total. Why?
Yes, this makes sense because in this situation there is only one element by stoichiometry. Oh god, I had to type that word- again... :'(
Quote from: AndrewLocock on June 29, 2015, 04:09:30 PM
2) Stoichiometry for the simple carbonate minerals means the ratio of the sum of the divalent cations (Mg+Ca+Sr+Ba+Mn+Fe+Zn etc.) to C to O is 1:1:3, without exception.
Yup. And if you want to force your measurement to fit this constraint we will need a charge balancing code for carbonate minerals. Hopefully Julien's code will provide this once I implement it in PFE
Quote from: AndrewLocock on June 29, 2015, 04:09:30 PM
3) The widely differing matrix corrections should give different values for any given analysis, regardless of the options selected in PfE.
Not sure what your point here is. Everything changes everything.
Quote from: AndrewLocock on June 29, 2015, 04:09:30 PM
Question: My understanding of ZAF corrections is that they are an interative loop.
Is it possible during the ZAF corrections to match the concentration of C to the corresponding correct proportion of O (or more properly divalent cations) for each iteration?
As you mention:
Quote1. The oxygen calculated by stoichiometry to the measured cations is added to the matrix correction as a concentration. Likewise, the carbon calculated by stoichiometry to oxygen is also added to the matrix correction as the code above shows as a concentration also.
2. This calculation is iterated because as the concentrations of the cations change, due to the (relatively minor) matrix effect of adding oxygen and carbon, the oxygen and carbon by calculation also are changed as they should.
Why not change the C and O concentrations accordingly with each iteration of the ZAF corrections?
Well I do that already, but as concentrations that preserve an actual analytical total. Now having said that maybe the next generation of matrix corrections will not be based on concentrations, and that would (I think) solve your problem. I have to agree that when I got into this business I could not understand why everything was in mass concentrations. After all, the microprobe is *not* a balance and it certainly cannot distinguish isotopes! It really doesn't measure mass, just numbers of atoms! But like mineral names, this may be here to stay although no one can think of a good reason for it.
Quote from: AndrewLocock on June 29, 2015, 04:09:30 PM
Thanks for encouraging me to post these queries in the forum, and of course, for your patience as well as the excellent program.
Of course, and thank-you for participating in the forum. It is awesome to have smart people involved with this project. And I need all the help I can get! The truth is I can't change something unless I understand it, and so if I seem pedantic it's just because I really am trying to understand it.
In addition to the code snippets here:
http://smf.probesoftware.com/index.php?topic=92.msg2950#msg2950
and the ZAF matrix correction code I attached to this post here:
http://smf.probesoftware.com/index.php?topic=92.msg2975#msg2975
I'm also posting my code for atom normalization here:
' Calculate formulas
If mode% = 4 Then
If sample(1).FormulaElement$ <> vbNullString Then ' normal formula calculation
ip% = IPOS1(sample(1).LastChan%, sample(1).FormulaElement$, sample(1).Elsyms$())
If ip% = 0 Then GoTo ConvertWeightInvalidFormulaElement
' Check for insufficient formula basis element
If atoms!(ip%) < 0.01 Then
tmsg$ = TypeLoadString$(sample())
tmsg$ = "There is an insufficient concentration of the formula basis element " & sample(1).Elsyup$(ip%) & " (usually caused by a very low intensity of the x-ray), to calculate a formula for sample " & tmsg$ & ". "
tmsg$ = tmsg$ & "Please delete the data point (line " & Format$(sample(1).Linenumber&(row%)) & ") or change the formula basis element." & vbCrLf & vbCrLf
If datarow% = 0 Then
tmsg$ = tmsg$ & "This message will be displayed for 30 seconds, following that the point will be flagged and ignored and the remaining data will be analyzed as usual."
MiscMsgBoxTim FormMSGBOXTIM, "ConvertWeight", tmsg$, 30#
If ierror Then Exit Sub
sample(1).LineStatus(row%) = False ' flag temporarily
sample(1).GoodDataRows% = sample(1).GoodDataRows% - 1
If sample(1).GoodDataRows% < 0 Then sample(1).GoodDataRows% = 0
Else
Call IOWriteLogRichText(tmsg$, vbNullString, Int(LogWindowFontSize%), vbMagenta, Int(FONT_REGULAR%), Int(0))
End If
GoTo 1000:
End If
temp! = sample(1).FormulaRatio! / atoms!(ip%)
For chan% = 1 To sample(1).LastChan%
weights!(chan%) = atoms!(chan%) * temp!
Next chan%
' Calculate sum of cations (normalize sum of cations to formula atoms)
Else
TotalCations! = 0#
For chan% = 1 To sample(1).LastChan%
If sample(1).AtomicCharges!(chan%) > 0# Then TotalCations! = TotalCations! + atoms!(chan%)
Next chan%
If TotalCations! < 0.01 Then
tmsg$ = TypeLoadString$(sample())
tmsg$ = "There is an insufficient concentration of the cation sum (usually caused by a very low total), to calculate a formula for sample " & tmsg$ & ". "
tmsg$ = tmsg$ & "Please delete the data point (line " & Format$(sample(1).Linenumber&(row%)) & ") or change the formula assignment." & vbCrLf & vbCrLf
If datarow% = 0 Then
tmsg$ = tmsg$ & "This message will be displayed for 30 seconds, following that the point will be flagged and ignored and the remaining data will be analyzed as usual."
MiscMsgBoxTim FormMSGBOXTIM, "ConvertWeight", tmsg$, 30#
If ierror Then Exit Sub
sample(1).LineStatus(row%) = False ' flag temporarily
sample(1).GoodDataRows% = sample(1).GoodDataRows% - 1
If sample(1).GoodDataRows% < 0 Then sample(1).GoodDataRows% = 0
Else
Call IOWriteLogRichText(tmsg$, vbNullString, Int(LogWindowFontSize%), vbMagenta, Int(FONT_REGULAR%), Int(0))
End If
GoTo 1000:
End If
' Normalize to total number of cations
temp! = sample(1).FormulaRatio! / TotalCations!
For chan% = 1 To sample(1).LastChan%
weights!(chan%) = atoms!(chan%) * temp!
Next chan%
End If
End If
End If
But if you think that ZAFSmp code is not short, you ain't seen nothing yet. You would just die if you saw the entire code. There is a lot of it to wade through!
Hi John,
I am looking forward to going though your code for this particular issue.
In the interim, I found some readings with reference to the mass dependency of ZAF corrections, as you mention:
QuoteNow having said that maybe the next generation of matrix corrections will not be based on concentrations, and that would (I think) solve your problem. I have to agree that when I got into this business I could not understand why everything was in mass concentrations. After all, the microprobe is *not* a balance and it certainly cannot distinguish isotopes! It really doesn't measure mass, just numbers of atoms! But like mineral names, this may be here to stay although no one can think of a good reason for it.
--------------------------------
From Goldstein et al. (2003):
Scanning Electron Microscopy and X-ray Microanalysis, Third Edition, 2003 by Goldstein, J., Newbury, D.E., Joy, D.C., Lyman, C.E., Echlin, P., Lifshin, E., Sawyer, L., and Michael, J.R.
9.4. The Approach to X-Ray Quantitation: The Need for Matrix Corrections (p. 402).
"As was first noted by Castaing (1951), the primary generated intensities are roughly proportional to the respective mass fractions of the emitting element. If other contributions to x-ray generation are very small, the measured intensity ratios between specimen and standard are roughly equal to the ratios of the mass or weight fractions of the emitting element. "
And from Reed (1993):
Electron Microprobe Analysis, Second Edition, 1993 by Reed, S.J.B.
1.9 Relationship between X-ray intensity and elemental concentration (pp. 10-11).
"The reason that characteristic X-ray intensities are, to a first approximation, proportional to mass concentration (whereas atomic concentration might appear more reasonable) is related to the fact that incident electrons penetrate an approximately constant mass in materials of different composition. This is because these electrons lose their kinetic energy mainly through interactions with orbital electrons of the target atoms, the number of which is approximately proportional to atomic mass.
The consequences of this can be demonstrated as follows. Consider two elements, A and B, the latter being 'heavier' than the former. To determine the concentration of A in a sample containing a mixture of A and B, one compares the intensity of 'A' radiation emitted by the sample with that from pure A. For the sake of simplicity we assume that the sample contains equal numbers of A and B atoms. Fig. 1.7 shows diagrammatically the volumes excited in pure A (
a) and the A-B compound (
b), given that the masses excited are equal, as noted above. The number of atoms excited in pure A is greater than in the compound because of the presence of heavy B atoms in the latter. Consequently the ratio of the numbers of excited A atoms in sample and standard, and hence the X-ray intensity ratio, is less than 0.5 (the atomic concentration of A in the compound).
The following argument shows that this ratio is, in fact, equal to the mass concentration (given the assumptions stated above). If the atomic concentration of A is
nA, then the mass concentration is given by
CA =
nAAA/[
nAAA + (l-
nA)
AB] where
AA and
AB are the atomic weights of A and B respectively. The number of atoms excited in the pure A standard is equal to
Nm/
AA, where
N is Avogadro's number and
m the mass penetrated by the incident electrons. In the case of the compound, the number of A atoms in the excited volume is
nANm /[
nAAA + (l-
nA)
AB]. The X-ray intensity ratio (which is proportional to the ratio of the numbers of excited atoms) is given by this expression divided by
Nm/
AA, which is equal to the expression given above for
CA. In reality the intensity ratio is not exactly equal to the mass concentration, firstly because
Z /A is not constant and secondly because the 'stopping power' of all bound electrons is not the same. This, together with other factors which affect the measured intensities, gives rise to the need for matrix corrections, as described below."
-------------------------------------------------------------------------------------------------
I found this explanation to be useful, and have attached the 2 pages from Reed's book as a PDF (which shows the diagram).
Thanks,
Andrew
Quote from: AndrewLocock on July 06, 2015, 01:33:32 PM
In the interim, I found some readings with reference to the mass dependency of ZAF corrections, as you mention:
QuoteNow having said that maybe the next generation of matrix corrections will not be based on concentrations, and that would (I think) solve your problem. I have to agree that when I got into this business I could not understand why everything was in mass concentrations. After all, the microprobe is *not* a balance and it certainly cannot distinguish isotopes! It really doesn't measure mass, just numbers of atoms! But like mineral names, this may be here to stay although no one can think of a good reason for it.
Hi Andrew,
Well we've come full circle now(!)... actually I am very well aware of these weight vs. atom issues and have published several papers on it (see below). I was mostly just making a funny in the above post!
But since you bring it up, a more physical model for some matrix correction parameters (besides those which are already normalized to mass concentrations, e.g., mass absorption coefficients- hence the term!), is the so called "electron fraction" model as published in our papers. See attached below.
Basically it is a historical accident that chemists started with weight fraction before atomic fraction. This is because atomic weight was discovered before atomic number! Mendeleev's first periodic tables were ordered by atomic weight, *not* atomic number- because atomic number had not been discovered yet. Which was why he got a few things wrong- like the periodic order of Te and I! That is one of the three places in the periodic table where atomic number goes up but atomic weight goes down!
In fact uranium carbide behaves much more like uranium than carbon because uranium has many more electrons (and protons) than carbon, as opposed to the 1:1 atomic ratio you'd think it might relate to as Reed mentions. And because all electron solid interactions (up to 1 meV or so) are *dominated* by electrostatic interactions (electrons and protons), this is what we should be using in our matrix calculations.
But.. the early chemists were committed to weight fraction because they were chemists not physicists! :'(
But again, this really has nothing to do with our discussion. As I said previously: "the magnitude of the C:O ratio discrepancy when the [weight] concentrations are normalized to atoms, depends on the relative ratio of the atomic weights of carbon and oxygen *and* the degree to which the analytical total varies from 100%."
So when one does not have a perfect analytical total and one then re-normalizes the concentrations to atoms, you will always get this discrepancy... because the atomic weights of oxygen and carbon are different!
The only way around this problem, is to take the weight concentrations and perform a charge balance calculation which I will be adding to the PFE code as soon as Julien (or some other geologist) writes it up. I talked to Julien over the weekend and the sticking point now is that Julien's current code is in php and he is very busy right now...
Here is a web page you might find interesting:
http://epmalab.uoregon.edu/BSE.htm
Quote from: Probeman on July 06, 2015, 02:12:12 PM
The only way around this problem, is to take the weight concentrations and perform a charge balance calculation...
Following up on this point, and on the excellent suggestions of Julien Allaz:
Attached is an explicit spreadsheet (Excel, *.xlsx) for recalculation from an analysis (wt%) to a formula (atoms per formula unit, apfu). This is a linear transformation, and so no iteration is needed.
This spreadsheet permits calculation of the formula proportions based on:
1) The number of oxygen (or oxygen equivalent, e.g. 2 F = 1 O),
or2) The number of cations present (including H, C, S as cations),
or3) The total number of atoms.
In addition, if H2O or CO2 has not been measured or input in weight percent, then the number of groups of OH, H2O, and CO2 in the formula can be specified. The spreadsheet will calculate the corresponding weight proportions of H2O and CO2.
Because the spreadsheet is general (can be used for almost any inorganic mineral), the constituents must be entered by the user in the appropriate oxidation states. A worksheet for converting between oxides (e.g. FeO and Fe2O3) or to/from elements is also included.
However, I have not implemented "recalculation of an unanalyzed element based on a fixed apfu" because of the large number of possible elements.
The attached spreadsheet uses a ferroan dolomite analysis as an example, with 2 CO3 groups specified.
The formula results are the same whether calculated on 6 oxygen, 4 cations, or 10 total atoms:
C2Mg0.664Ca1.125Mn(II)0.003Fe(II)0.208O6
The results are rounded to 3 decimal places, and concatenated in the formula in order of increasing atomic number.
For more complex calculations (e.g., garnets, amphiboles etc., where estimation of ferric/ferrous proportions by charge balance or select cation sums is needed), users may need to look at separate programs or spreadsheets dedicated to such tasks.
Andrew
Hi Andrew,
This is very useful stuff. Thank-you.
john
I should mention that Julien Allaz's mineral re-normalization code has been translated from php to VB, so I will be able to implement this in Probe for EPMA at some point "real soon now"...
Here is an updated version of the Excel spreadsheet, which now properly deals with cases where both halogens and hydrogen are present in oxide materials.
As many of you already know, there are two ways to specify unanalyzed elements *by difference* in the Probe for EPMA matrix corrections. Here is a screen shot of the Calculation Options dialog in PFE showing the two "difference" methods:
(https://smf.probesoftware.com/gallery/1_06_07_18_12_40_38.png)
So one could specify OH by difference by selecting the "element by difference" option, then selecting hydrogen as the element by difference, then making sure that the oxygen stoichiometry for hydrogen is changed from the default of 1 cation and 2 oxygens, to 1 hydrogen and 1 oxygen, in the Elements/Cations dialog.
Then the program will calculate OH by difference. The other method is to use the "formula by difference" method where one specifies the unanalyzed elements as a formula, in this example, as OH, and the program adds them in automatically during the matrix calculation. The benefit of including these unanalyzed elements by difference into the matrix correction, is that the presence (or absence) of the unanalyzed elements can affect the concentrations of the analyzed elements. Thus affecting the calculation by difference. This is particularly import for so called "water by difference" measurements as discussed here:
http://smf.probesoftware.com/index.php?topic=922.0
As another example of elements by difference, one might be measuring traces in a matrix and have no need to measure the major elements. Say, traces in quartz or zircon, where one would measure the trace elements and merely specify the matrix elements as SiO2 or ZrSiO4 respectively, as a formula by difference. This is discussed here:
http://smf.probesoftware.com/index.php?topic=42.msg2568#msg2568
This formula by difference methods has worked well for when calculating without stoichiomeric oxygen, but after Gareth Seward and Marisa Acosta reported to us that this formula by difference method was not working correctly when oxygen was being calculated by stoichiomtry, we took a look and *finally* managed to find the problem and fixed the code. This latest version of PFE will fix this issue.
Here is an example of an apatite sample where the students wanted to calculate OH by difference and calculate oxygen by stoichiometry:
Un 52 BMA-062-16fa_g25, Results in Elemental Weight Percents
SPEC: O H
TYPE: FORM FORM
AVER: 38.302 .038
SDEV: .504 .041
ELEM: Ca P S Al Fe As Ba K
BGDS: LIN EXP LIN LIN LIN EXP LIN LIN
TIME: 25.00 8.00 25.00 25.00 30.00 60.00 90.00 90.00
BEAM: 30.06 30.06 30.06 30.06 30.06 99.04 99.04 99.04
ELEM: Ca P S Al Fe As Ba K SUM
384 38.598 18.351 .032 .007 .181 -.076 -.008 .022 100.000
385 38.462 18.005 .019 -.002 .167 -.003 -.001 .013 100.000
386 38.210 18.037 .018 .002 .183 .030 -.007 .010 100.000
387 38.235 17.974 .032 .008 .194 -.010 -.006 .003 100.000
388 38.602 18.336 .037 -.007 .181 .030 -.004 .002 100.000
389 37.771 18.007 .030 .011 .218 .074 .001 .059 100.000
AVER: 38.313 18.118 .028 .003 .187 .007 -.004 .018 100.000
SDEV: .315 .175 .008 .007 .017 .051 .004 .021 .000
SERR: .129 .072 .003 .003 .007 .021 .001 .009
%RSD: .82 .97 28.02 213.60 9.28 676.66 -86.58 116.07
STDS: 285 285 327 336 160 662 835 336
STKF: .3596 .1601 .2210 .1333 .0654 .5052 .7431 .0409
STCT: 738.0 4696.5 1704.0 6059.0 1413.2 583.1 3099.0 588.4
UNKF: .3609 .1598 .0002 .0000 .0016 .0001 .0000 .0002
UNCT: 740.6 4689.7 1.9 1.1 34.1 .1 -.1 2.7
UNBG: 6.8 10.7 2.9 30.0 27.0 12.9 6.5 10.4
ZCOR: 1.0615 1.1335 1.1605 1.3622 1.1852 1.3270 1.4078 .9827
KRAW: 1.0036 .9986 .0011 .0002 .0242 .0001 .0000 .0045
PKBG: 110.25 468.43 1.67 1.04 2.27 1.01 .98 1.26
INT%: ---- ---- ---- ---- ---- ---- ---- ----
TDI%: .046 .488 4.073 1.487 2.693 ---- ---- ----
DEV%: .4 .2 24.6 2.3 1.6 ---- ---- ----
TDIF: LOG-LIN LOG-LIN LOG-LIN LOG-LIN LOG-LIN ---- ---- ----
TDIT: 56.67 37.83 55.50 55.83 57.83 ---- ---- ----
TDII: 747. 4700. 4.56 31.2 61.7 ---- ---- ----
TDIL: 6.62 8.46 1.52 3.44 4.12 ---- ---- ----
ELEM: Mn Na Sr F Sm Nd Cl Y
BGDS: LIN LIN LIN LIN LIN LIN LIN LIN
TIME: 60.00 90.00 60.00 60.00 60.00 90.00 40.00 90.00
BEAM: 99.04 99.04 99.04 99.04 99.04 99.04 99.04 99.04
ELEM: Mn Na Sr F Sm Nd Cl Y SUM
384 .302 .115 .050 2.828 .067 .102 .125 .337 100.000
385 .294 .118 .049 3.490 .027 .115 .132 .297 100.000
386 .332 .102 .043 3.229 .024 .085 .147 .257 100.000
387 .361 .102 .057 3.950 .047 .055 .092 .229 100.000
388 .309 .119 .041 3.970 .022 .091 .115 .295 100.000
389 .313 .124 .042 4.081 .007 .126 .133 .370 100.000
AVER: .318 .113 .047 3.591 .032 .096 .124 .298 100.000
SDEV: .024 .009 .006 .497 .021 .025 .019 .051 .000
SERR: .010 .004 .003 .203 .009 .010 .008 .021
%RSD: 7.63 8.01 13.19 13.84 65.51 26.11 15.42 17.23
STDS: 25 336 251 835 1011 1009 285 1016
STKF: .7341 .0735 .4267 .1715 .5260 .5221 .0602 .4481
STCT: 4303.0 1786.2 3853.8 561.2 1133.9 3358.0 836.0 1076.4
UNKF: .0026 .0005 .0004 .0071 .0002 .0007 .0011 .0026
UNCT: 15.4 12.7 3.6 23.1 .5 4.4 15.1 6.2
UNBG: 5.8 10.3 5.5 2.3 4.8 11.8 9.0 2.5
ZCOR: 1.2109 2.1625 1.1789 5.0816 1.4239 1.3990 1.1400 1.1620
KRAW: .0036 .0071 .0009 .0412 .0004 .0013 .0181 .0057
PKBG: 3.67 2.24 1.66 11.03 1.10 1.37 2.68 3.45
INT%: ---- ---- ---- -21.28 -6.97 -.95 -.31 ----
TDI%: ---- ---- ---- ---- ---- ---- ---- ----
DEV%: ---- ---- ---- ---- ---- ---- ---- ----
TDIF: ---- ---- ---- ---- ---- ---- ---- ----
TDIT: ---- ---- ---- ---- ---- ---- ---- ----
TDII: ---- ---- ---- ---- ---- ---- ---- ----
TDIL: ---- ---- ---- ---- ---- ---- ---- ----
ELEM: Eu Gd Mg La Ce Si
BGDS: AVG LIN LIN LIN LIN LIN
TIME: 60.00 60.00 90.00 60.00 60.00 60.00
BEAM: 99.04 99.04 99.04 99.04 99.04 99.04
ELEM: Eu Gd Mg La Ce Si SUM
384 .029 .041 .045 .025 .133 .099 100.000
385 -.005 .057 .044 .015 .112 .090 100.000
386 -.008 .047 .039 .017 .097 .075 100.000
387 .015 .029 .036 .005 .079 .058 100.000
388 .024 .051 .041 .016 .129 .094 100.000
389 .016 .056 .124 .023 .176 .295 100.000
AVER: .012 .047 .055 .017 .121 .118 100.000
SDEV: .015 .011 .034 .007 .033 .088 .000
SERR: .006 .004 .014 .003 .014 .036
%RSD: 130.06 22.47 61.89 42.93 27.58 73.94
STDS: 1004 1005 160 1007 1001 160
STKF: .5289 .5281 .0776 .5143 .5111 .1621
STCT: 1239.6 4995.6 3016.8 11742.1 3550.7 5699.0
UNKF: .0001 .0003 .0003 .0001 .0009 .0010
UNCT: .2 3.0 13.4 2.7 6.0 35.8
UNBG: 5.6 22.3 19.3 63.8 25.3 5.8
ZCOR: 1.4453 1.4722 1.5909 1.3981 1.3935 1.1629
KRAW: .0002 .0006 .0044 .0002 .0017 .0063
PKBG: 1.04 1.14 1.69 1.04 1.24 7.09
INT%: 11.30 -17.82 ---- -5.08 -.03 ----
TDI%: ---- ---- ---- ---- ---- ----
DEV%: ---- ---- ---- ---- ---- ----
TDIF: ---- ---- ---- ---- ---- ----
TDIT: ---- ---- ---- ---- ---- ----
TDII: ---- ---- ---- ---- ---- ----
TDIL: ---- ---- ---- ---- ---- ----
Un 52 BMA-062-16fa_g25, Results in Oxide Weight Percents
SPEC: O HO
TYPE: FORM FORM
AVER: -1.540 .638
SDEV: .207 .685
ELEM: CaO P2O5 SO3 Al2O3 FeO As2O3 BaO K2O SUM
384 54.007 42.049 .081 .014 .232 -.100 -.008 .026 100.000
385 53.816 41.256 .048 -.004 .215 -.004 -.001 .016 100.000
386 53.464 41.330 .044 .005 .235 .040 -.008 .013 100.000
387 53.498 41.185 .081 .015 .249 -.014 -.007 .004 100.000
388 54.011 42.014 .093 -.013 .233 .040 -.004 .003 100.000
389 52.849 41.262 .075 .020 .280 .097 .001 .071 100.000
AVER: 53.608 41.516 .070 .006 .241 .010 -.005 .022 100.000
SDEV: .441 .402 .020 .013 .022 .067 .004 .025 .000
SERR: .180 .164 .008 .005 .009 .027 .002 .010
%RSD: .82 .97 28.02 213.60 9.28 676.66 -86.58 116.07
STDS: 285 285 327 336 160 662 835 336
ELEM: MnO Na2O SrO F Sm2O3 Nd2O3 Cl Y2O3 SUM
384 .390 .155 .059 2.828 .077 .119 .125 .429 100.000
385 .380 .158 .057 3.490 .031 .134 .132 .377 100.000
386 .429 .138 .051 3.229 .028 .100 .147 .327 100.000
387 .466 .138 .068 3.950 .054 .064 .092 .291 100.000
388 .398 .161 .048 3.970 .025 .106 .115 .374 100.000
389 .404 .167 .050 4.081 .008 .147 .133 .470 100.000
AVER: .411 .153 .055 3.591 .037 .112 .124 .378 100.000
SDEV: .031 .012 .007 .497 .025 .029 .019 .065 .000
SERR: .013 .005 .003 .203 .010 .012 .008 .027
%RSD: 7.63 8.01 13.19 13.84 65.51 26.11 15.42 17.23
STDS: 25 336 251 835 1011 1009 285 1016
ELEM: Eu2O3 Gd2O3 MgO La2O3 Ce2O3 SiO2 SUM
384 .033 .047 .075 .029 .155 .213 100.000
385 -.006 .066 .073 .017 .131 .192 100.000
386 -.010 .054 .065 .020 .114 .160 100.000
387 .018 .034 .059 .005 .093 .124 100.000
388 .028 .059 .069 .019 .151 .202 100.000
389 .019 .064 .205 .027 .206 .630 100.000
AVER: .014 .054 .091 .020 .142 .254 100.000
SDEV: .018 .012 .056 .008 .039 .187 .000
SERR: .007 .005 .023 .003 .016 .077
%RSD: 130.06 22.47 61.89 42.93 27.58 73.94
STDS: 1004 1005 160 1007 1001 160
Notice that the oxygen concentration in the oxide output is negative. This is because the program is also performing the correction for the halogen equivalent for oxygen in the matrix calculation! Pretty cool!
If you'd like to learn more about the halogen equivalence for stoichiometric oxygen calculation feature see this post:
http://smf.probesoftware.com/index.php?topic=8.msg1127#msg1127
How does one delete previously-added unanalyzed elements from the list of elements?
Sometimes, one might want to try adding an unanalyzed element to set of analyses, as a test.
However, one may not want to keep such elements.
It would be nice to easily delete them, if one doesn't want them.
Thanks,
Andrew
Quote from: AndrewLocock on September 28, 2018, 09:10:25 AM
How does one delete previously-added unanalyzed elements from the list of elements?
Sometimes, one might want to try adding an unanalyzed element to set of analyses, as a test.
However, one may not want to keep such elements.
It would be nice to easily delete them, if one doesn't want them.
Hi Andrew,
It gets complicated because it's difficult to know what an element might be utilized for, so to be safe we only allow elements to be deleted from the Acquire! Elements/Cations dialog. Sorry.
john
This topic is entitled "Specifying Unanalyzed Elements For a Proper Matrix Correction", but it could just as well have been titled "Including unanalyzed elements for proper quantification of analyzed elements".
I recently responded to a question on the JEOL Listserver about how to add the carbonate molecule to a carbonate analysis using the JEOL software. I don't know the JEOL software, but then it was suggested performing the calculation off-line perhaps using Excel. This is *not* a good idea as most of you know, because the matrix correction will be significantly wrong and the quantification of the analyzed elements will be significantly wrong.
If the total of the elements in the matrix correction is significantly under 100%, the matrix correction physics will be significantly wrong in most cases. For example carbonates.
Here is an analysis of a standard dolomite where because the software knows that it is a standard, it can automatically specify the unanalyzed elements to get a correct quantification for the elements that were acquired:
St 141 Set 1 Dolomite (Harvard #105064), Results in Elemental Weight Percents
ELEM: Ca Mn P Mg Fe C O
TYPE: ANAL ANAL ANAL ANAL ANAL SPEC SPEC
BGDS: LIN LIN LIN LIN LIN
TIME: 10.00 10.00 10.00 10.00 10.00 --- ---
BEAM: 30.01 30.01 30.01 30.01 30.01 --- ---
ELEM: Ca Mn P Mg Fe C O SUM
43 21.796 .081 -.040 13.417 .145 12.986 52.021 100.406
44 21.698 .036 .025 13.332 .145 12.986 52.021 100.243
45 21.876 .105 .024 13.396 .168 12.986 52.021 100.576
46 22.000 .068 -.014 13.224 .145 12.986 52.021 100.430
AVER: 21.843 .073 -.001 13.342 .151 12.986 52.021 100.414
SDEV: .128 .029 .032 .087 .011 .000 .000 .136
SERR: .064 .014 .016 .043 .006 .000 .000
%RSD: .58 39.60-2300.07 .65 7.43 .00 .00
PUBL: 21.841 .015 n.a. 13.195 .062 12.986 52.021 100.120
%VAR: .01 383.93 --- 1.12 143.23 .00 .00
DIFF: .001 .058 --- .147 .089 .000 .000
STDS: 138 140 285 139 145 --- ---
STKF: .3789 .3969 .1600 .1957 .4258 --- ---
STCT: 128.18 134.89 56.49 65.78 142.56 --- ---
UNKF: .2030 .0006 .0000 .0853 .0012 --- ---
UNCT: 68.66 .20 .00 28.69 .42 --- ---
UNBG: .14 .77 1.00 .06 .49 --- ---
ZCOR: 1.0763 1.2369 1.2287 1.5634 1.2161 --- ---
KRAW: .5356 .0015 -.0001 .4362 .0029 --- ---
PKBG: 484.48 1.27 1.00 473.26 1.85 --- ---
Note that carbon and oxygen were automatically loaded from the standard database into Probe for EPMA, because the software knows that it is a standard. But what if this was an unknown carbonate? Here is the same material (dolomite standard), but this time acquired as an unknown:
Un 6 Dolomite (Harvard #105064), Results in Elemental Weight Percents
ELEM: Ca Mn P Mg Fe C
TYPE: ANAL ANAL ANAL ANAL ANAL SPEC
BGDS: LIN LIN LIN LIN LIN
TIME: 10.00 10.00 10.00 10.00 10.00 ---
BEAM: 29.99 29.99 29.99 29.99 29.99 ---
ELEM: Ca Mn P Mg Fe C SUM
47 21.220 .033 -.006 11.758 .135 .000 33.140
48 21.136 .021 .010 11.939 .150 .000 33.258
49 21.296 .055 .013 12.068 .164 .000 33.596
50 21.292 .080 .067 12.059 .128 .000 33.626
51 21.237 .066 .026 11.925 .117 .000 33.371
52 21.278 .090 .017 11.796 .156 .000 33.337
53 20.925 .121 .084 11.887 .161 .000 33.178
AVER: 21.198 .067 .030 11.919 .145 .000 33.358
SDEV: .132 .034 .033 .119 .018 .000 .191
SERR: .050 .013 .012 .045 .007 .000
%RSD: .62 51.24 108.72 1.00 12.32 .00
STDS: 138 140 285 139 145 ---
STKF: .3789 .3969 .1600 .1957 .4258 ---
STCT: 128.18 134.89 56.49 65.78 142.56 ---
UNKF: .2047 .0006 .0002 .0852 .0012 ---
UNCT: 69.26 .19 .08 28.63 .41 ---
UNBG: .13 .78 .97 .05 .51 ---
ZCOR: 1.0354 1.2003 1.2679 1.3995 1.1694 ---
KRAW: .5403 .0014 .0015 .4353 .0029 ---
PKBG: 529.78 1.25 1.09 606.24 1.81 ---
First note the very low total (~33 wt.%). Because the software does not know that this is a carbonate, it cannot automatically specify the unanalyzed carbon and oxygen. And note that although Ca (Ka) isn't so affected (21.2 wt.% in the unknown vs. 21.8 wt.% in the standard), the Mg (Ka) is very much affected (11.9 wt.% in the unknown vs. 13.3 wt.% in the standard!).
Observe the differences in the magnitude of the matrix corrections for Ca (Ka) and Mg (Ka), in the line labeled ZCOR, and you will understand why.
So how to add in the missing carbonate molecule? For the JEOL software Pete McSwiggen's suggestion is good because I assume that the JEOL software is including the specified unanalyzed elements in the matrix correction.
In Probe for EPMA one can do the same thing by first adding carbon as a unanalyzed element in the Elements/Cations dialog, then simply checking the Calculate with Stoichiometric Oxygen option, and finally specify 0.333 atoms of carbon per oxygen molecule as seen here:
(https://smf.probesoftware.com/gallery/395_12_10_18_3_31_34.png)
Once that is done, the analysis proceeds as follows:
Un 6 Dolomite (Harvard #105064), Results in Elemental Weight Percents
ELEM: Ca Mn P Mg Fe C O
TYPE: ANAL ANAL ANAL ANAL ANAL STOI CALC
BGDS: LIN LIN LIN LIN LIN
TIME: 10.00 10.00 10.00 10.00 10.00 --- ---
BEAM: 29.99 29.99 29.99 29.99 29.99 --- ---
ELEM: Ca Mn P Mg Fe C O SUM
47 22.060 .034 -.006 13.130 .141 12.959 52.019 100.336
48 21.965 .022 .010 13.349 .156 12.955 52.136 100.594
49 22.130 .057 .012 13.486 .171 12.925 52.228 101.008
50 22.123 .082 .065 13.482 .133 12.929 52.298 101.113
51 22.071 .068 .025 13.327 .122 12.945 52.160 100.719
52 22.122 .092 .016 13.162 .162 12.942 52.071 100.567
53 21.748 .125 .081 13.286 .167 12.970 52.172 100.549
AVER: 22.031 .069 .029 13.318 .150 12.946 52.155 100.698
SDEV: .137 .035 .032 .140 .019 .016 .093 .274
SERR: .052 .013 .012 .053 .007 .006 .035
%RSD: .62 51.26 108.66 1.05 12.33 .13 .18
STDS: 138 140 285 139 145 --- ---
STKF: .3789 .3969 .1600 .1957 .4258 --- ---
STCT: 128.18 134.89 56.49 65.78 142.56 --- ---
UNKF: .2047 .0006 .0002 .0852 .0012 --- ---
UNCT: 69.26 .19 .08 28.63 .41 --- ---
UNBG: .13 .78 .97 .05 .51 --- ---
ZCOR: 1.0761 1.2369 1.2276 1.5637 1.2160 --- ---
KRAW: .5403 .0014 .0015 .4353 .0029 --- ---
PKBG: 529.78 1.25 1.09 606.24 1.81 --- ---
Note that now the concentrations and matrix corrections for Ca and Mg are correct.
By the way, the same calculation options will work for any carbonate such as calcite, magnesite, siderite, etc.
Since I mentioned the effect of not including water by difference as it affects the matrix correction in my JEOL Listserver post, I will "show my work" as to how the various unanalyzed elements affects the analyzed elements, as they are added to the matrix correction of a hydrous glass. For a publication reference see this paper:
https://link.springer.com/article/10.1007%2Fs00445-005-0003-z
In this example I selected an experimental glass from Withers, which nominally contains 4.9 wt.% H2O, but FTIR showed 5.06 wt%. Here is the analysis of this glass as an unknown with nothing but the analyzed elements:
Un 17 Withers-N5, Results in Elemental Weight Percents
ELEM: Na K Cl Ba F Ti Fe Mn Ca Si Al Mg O H O
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL SPEC SPEC
BGDS: MAN LIN LIN LIN LIN LOW MAN LIN MAN MAN MAN MAN EXP
TIME: 60.00 20.00 10.00 20.00 40.00 10.00 40.00 10.00 20.00 20.00 20.00 60.00 --- --- ---
BEAM: 9.98 9.98 9.98 9.98 9.98 9.98 9.98 9.98 9.98 9.98 9.98 9.98 --- --- ---
ELEM: Na K Cl Ba F Ti Fe Mn Ca Si Al Mg O-D H O SUM
574 1.206 3.594 .218 .029 .046 .106 2.963 .058 .154 30.812 4.487 -.010 --- .000 .000 43.664
575 1.187 3.590 .221 .016 .045 .122 2.951 .076 .140 30.681 4.454 -.014 --- .000 .000 43.469
576 1.163 3.469 .192 .032 .054 .135 2.960 .080 .121 30.677 4.413 -.019 --- .000 .000 43.275
577 1.171 3.500 .276 .040 .059 .096 2.993 .056 .109 30.817 4.512 -.020 --- .000 .000 43.610
578 1.225 3.549 .276 -.013 .045 .071 3.001 .078 .108 30.727 4.451 -.012 --- .000 .000 43.505
579 1.218 3.559 .255 -.077 .038 .122 3.019 .079 .123 30.718 4.502 -.015 --- .000 .000 43.541
580 1.143 3.579 .238 .015 .048 .100 2.954 .052 .124 30.733 4.422 -.020 --- .000 .000 43.387
581 1.235 3.438 .264 -.019 .065 .116 2.933 .048 .144 30.823 4.443 -.015 --- .000 .000 43.475
582 1.170 3.501 .175 -.025 .043 .132 3.028 .049 .112 30.879 4.462 -.012 --- .000 .000 43.514
583 1.160 3.556 .233 -.061 .018 .145 2.995 .030 .136 30.874 4.465 -.017 --- .000 .000 43.534
584 1.183 3.491 .227 .004 .018 .122 2.956 .061 .125 30.945 4.416 -.017 --- .000 .000 43.532
585 1.148 3.503 .204 .029 .038 .119 2.978 .059 .153 30.943 4.465 -.015 --- .000 .000 43.623
AVER: 1.184 3.527 .232 -.002 .043 .115 2.978 .060 .129 30.802 4.458 -.016 --- .000 .000 43.511
SDEV: .031 .051 .032 .038 .014 .020 .029 .015 .016 .095 .032 .003 --- .000 .000 .105
SERR: .009 .015 .009 .011 .004 .006 .009 .004 .005 .028 .009 .001 --- .000 .000
%RSD: 2.59 1.43 13.87-1520.63 33.07 17.23 .99 25.47 12.47 .31 .72 -21.27 --- .00 .00
STDS: 336 374 285 835 835 22 395 25 358 162 336 12 --- --- ---
STKF: .0735 .1132 .0602 .7431 .1715 .5547 .6779 .7341 .1693 .2018 .1333 .4736 --- --- ---
STCT: 2447.9 2423.7 839.3 8520.6 2398.7 6097.6 14136.8 13590.2 2247.6 34290.6 23223.7 24410.3 --- --- ---
UNKF: .0082 .0301 .0017 .0000 .0002 .0010 .0258 .0005 .0011 .2710 .0411 -.0001 --- --- ---
UNCT: 274.6 645.2 24.2 -.2 2.7 10.8 538.5 9.5 15.2 46037.3 7157.6 -6.4 --- --- ---
UNBG: 16.0 12.6 5.0 29.0 3.8 5.8 30.1 16.1 5.4 173.0 135.8 23.3 --- --- ---
ZCOR: 1.4355 1.1708 1.3315 1.3476 2.1906 1.1747 1.1530 1.1748 1.1290 1.1368 1.0853 1.2443 --- --- ---
KRAW: .1122 .2662 .0289 .0000 .0011 .0018 .0381 .0007 .0068 1.3426 .3082 -.0003 --- --- ---
PKBG: 18.14 52.35 6.39 1.00 1.77 3.03 18.90 1.61 3.79 267.17 53.70 .72 --- --- ---
INT%: ---- ---- ---- -3.80 ---- -.02 ---- ---- ---- ---- ---- ---- --- --- ---
If we calculate the above elemental analysis as oxide formulas (but still without oxygen included in the matrix correction), we get the following results:
Un 17 Withers-N5, Results in Oxide Weight Percents
ELEM: Na2O K2O Cl BaO F TiO2 FeO MnO CaO SiO2 Al2O3 MgO O-D H2O O SUM
574 1.625 4.330 .218 .033 .046 .177 3.812 .075 .216 65.918 8.479 -.016 --- .000 .000 84.911
575 1.600 4.324 .221 .018 .045 .203 3.797 .098 .196 65.639 8.415 -.024 --- .000 .000 84.533
576 1.568 4.179 .192 .035 .054 .225 3.808 .103 .169 65.629 8.338 -.032 --- .000 .000 84.267
577 1.578 4.216 .276 .045 .059 .161 3.851 .072 .153 65.928 8.526 -.033 --- .000 .000 84.831
578 1.651 4.276 .276 -.015 .045 .118 3.861 .100 .152 65.736 8.410 -.020 --- .000 .000 84.588
579 1.642 4.287 .255 -.086 .038 .204 3.884 .102 .171 65.716 8.507 -.025 --- .000 .000 84.696
580 1.540 4.311 .238 .017 .048 .166 3.800 .068 .173 65.749 8.356 -.034 --- .000 .000 84.432
581 1.665 4.141 .264 -.021 .065 .193 3.773 .062 .202 65.942 8.395 -.025 --- .000 .000 84.656
582 1.577 4.217 .175 -.028 .043 .220 3.895 .063 .157 66.061 8.431 -.020 --- .000 .000 84.792
583 1.564 4.283 .233 -.068 .018 .241 3.853 .039 .190 66.051 8.437 -.028 --- .000 .000 84.813
584 1.595 4.205 .227 .004 .018 .204 3.803 .079 .175 66.202 8.344 -.027 --- .000 .000 84.829
585 1.547 4.220 .204 .032 .038 .198 3.831 .076 .214 66.199 8.436 -.024 --- .000 .000 84.971
AVER: 1.596 4.249 .232 -.003 .043 .192 3.831 .078 .181 65.897 8.423 -.026 --- .000 .000 84.693
SDEV: .041 .061 .032 .042 .014 .033 .038 .020 .023 .204 .060 .005 --- .000 .000 .207
SERR: .012 .018 .009 .012 .004 .010 .011 .006 .007 .059 .017 .002 --- .000 .000
%RSD: 2.59 1.43 13.87-1520.63 33.07 17.23 .99 25.47 12.47 .31 .72 -21.27 --- .00 .00
STDS: 336 374 285 835 835 22 395 25 358 162 336 12 --- --- ---
Note that total is much better, but the SiO2 concentration is only 65.9 wt.%. Now we will recalculate the glass but this time include stoichiometric oxygen in the matrix correction:
Un 17 Withers-N5, Results in Oxide Weight Percents
ELEM: Na2O K2O Cl BaO F TiO2 FeO MnO CaO SiO2 Al2O3 MgO O-D H2O O SUM
574 2.177 4.249 .205 .033 .085 .179 3.990 .077 .225 70.085 9.983 .016 --- .000 .000 91.303
575 2.144 4.244 .207 .018 .083 .206 3.974 .101 .205 69.801 9.909 .008 --- .000 .000 90.901
576 2.102 4.100 .180 .036 .099 .227 3.986 .107 .179 69.809 9.823 -.002 --- .000 .000 90.646
577 2.115 4.136 .258 .045 .109 .162 4.031 .074 .163 70.096 10.042 -.004 --- .000 .000 91.230
578 2.211 4.195 .258 -.015 .082 .119 4.041 .103 .161 69.906 9.904 .012 --- .000 .000 90.978
579 2.200 4.206 .239 -.087 .069 .206 4.064 .105 .181 69.881 10.022 .007 --- .000 .000 91.093
580 2.067 4.230 .223 .017 .087 .168 3.978 .070 .182 69.960 9.850 -.004 --- .000 .000 90.828
581 2.234 4.061 .248 -.021 .120 .195 3.949 .064 .211 70.160 9.897 .007 --- .000 .000 91.123
582 2.116 4.137 .164 -.028 .079 .222 4.076 .065 .166 70.273 9.939 .012 --- .000 .000 91.222
583 2.100 4.202 .218 -.068 .033 .244 4.032 .040 .198 70.295 9.953 .003 --- .000 .000 91.248
584 2.141 4.125 .213 .004 .033 .206 3.981 .082 .184 70.459 9.840 .003 --- .000 .000 91.271
585 2.076 4.141 .191 .032 .070 .200 4.010 .079 .223 70.423 9.943 .007 --- .000 .000 91.394
AVER: 2.140 4.169 .217 -.003 .079 .194 4.009 .080 .190 70.096 9.925 .005 --- .000 .000 91.103
SDEV: .055 .060 .030 .042 .026 .034 .039 .021 .022 .230 .069 .006 --- .000 .000 .223
SERR: .016 .017 .009 .012 .008 .010 .011 .006 .006 .066 .020 .002 --- .000 .000
%RSD: 2.55 1.44 13.88-1522.79 33.11 17.23 .98 25.47 11.70 .33 .70 120.12 --- .00 .00
STDS: 336 374 285 835 835 22 395 25 358 162 336 12 --- --- ---
Please note that by including the stoichiometric oxygen in the matrix correction the SiO2 concentration went from 65.9 wt.% to 70.09 wt.%. This is because oxygen absorbs Si Ka more than Si. So without stoichiometric oxygen in the matrix correction, the matrix is anomalously high in Si, which again, does not absorb Si Ka as much as oxygen, so the matrix correction for Si is underestimated.
But we still have a total of only 91.1 wt.%, so one might be forgiven to estimate the water by difference as 8.9 wt.%. But one would be wrong because we haven't provided a correction for the ion migration of Na and the effect on the other elements. The TDI correction for Na in this glass is around 100% as seen here in this plot of log intensity vs. time:
(https://smf.probesoftware.com/gallery/395_13_10_18_2_49_45.png)
So turning on the TDI correction we obtain these analyses:
Un 17 Withers-N5, Results in Oxide Weight Percents
ELEM: Na2O K2O Cl BaO F TiO2 FeO MnO CaO SiO2 Al2O3 MgO O-D H2O O SUM
574 4.117 4.182 .204 .033 .084 .179 3.989 .077 .224 69.392 10.084 .018 --- .000 .000 92.582
575 4.842 4.291 .207 .018 .082 .206 3.973 .101 .205 70.089 10.042 .010 --- .000 .000 94.065
576 4.255 3.997 .180 .036 .097 .227 3.985 .107 .179 69.839 9.930 -.001 --- .000 .000 92.831
577 4.575 4.261 .258 .045 .108 .162 4.029 .074 .163 69.847 10.167 -.002 --- .000 .000 93.688
578 4.550 4.211 .258 -.015 .081 .119 4.039 .103 .161 69.530 10.023 .013 --- .000 .000 93.073
579 4.687 4.256 .239 -.087 .068 .206 4.062 .105 .181 69.813 10.148 .008 --- .000 .000 93.685
580 4.257 4.207 .223 .017 .086 .168 3.976 .070 .182 69.621 9.960 -.003 --- .000 .000 92.765
581 4.968 4.191 .247 -.021 .118 .195 3.947 .064 .210 70.217 10.033 .008 --- .000 .000 94.177
582 4.447 4.237 .164 -.028 .079 .222 4.074 .065 .166 70.473 10.054 .013 --- .000 .000 93.966
583 4.547 4.070 .218 -.068 .032 .244 4.030 .040 .198 69.777 10.078 .004 --- .000 .000 93.170
584 4.524 4.049 .212 .004 .032 .206 3.979 .082 .184 70.249 9.959 .005 --- .000 .000 93.486
585 3.984 4.322 .191 .032 .069 .200 4.008 .078 .223 70.019 10.041 .008 --- .000 .000 93.176
AVER: 4.479 4.190 .217 -.003 .078 .194 4.008 .080 .190 69.905 10.043 .007 --- .000 .000 93.389
SDEV: .288 .101 .030 .042 .026 .033 .039 .020 .022 .317 .072 .006 --- .000 .000 .534
SERR: .083 .029 .009 .012 .007 .010 .011 .006 .006 .091 .021 .002 --- .000 .000
%RSD: 6.43 2.40 13.86-1523.55 33.08 17.23 .98 25.47 11.70 .45 .71 95.57 --- .00 .00
STDS: 336 374 285 835 835 22 395 25 358 162 336 12 --- --- ---
Note that the Na concentration went from around 2.2 wt% to 4.4 wt.%, but the Si dropped slightly because the TDI effect on Si is usually an increase in intensity as the Na intensity drops due to ion migration under the electron beam.
Now based on our totals of around 93.4 wt.%, our water by difference estimate would be around 6.6 wt.%, but that isn't very close to the FTIR H2O measurement of 5.06 wt.%. So what's going on? Well we have not yet included the water by difference into the matrix correction. Once we do that we obtain these results:
Un 17 Withers-N5, Results in Oxide Weight Percents
ELEM: Na2O K2O Cl BaO F TiO2 FeO MnO CaO SiO2 Al2O3 MgO O-D H2O O SUM
574 4.191 4.211 .205 .033 .086 .180 4.037 .078 .227 70.047 10.230 .020 --- 6.454 .000 100.000
575 4.912 4.315 .207 .018 .084 .207 4.012 .102 .207 70.615 10.157 .011 --- 5.152 .000 100.000
576 4.329 4.024 .181 .036 .100 .229 4.032 .108 .181 70.477 10.069 .001 --- 6.233 .000 100.000
577 4.646 4.286 .259 .046 .110 .164 4.071 .075 .165 70.405 10.292 -.001 --- 5.483 .000 100.000
578 4.627 4.239 .259 -.015 .083 .120 4.085 .104 .163 70.140 10.158 .015 --- 6.022 .000 100.000
579 4.760 4.281 .240 -.088 .070 .207 4.104 .106 .182 70.371 10.272 .010 --- 5.485 .000 100.000
580 4.333 4.236 .224 .018 .088 .169 4.024 .070 .184 70.264 10.101 -.001 --- 6.290 .000 100.000
581 5.040 4.214 .248 -.021 .120 .196 3.985 .064 .212 70.735 10.146 .010 --- 5.052 .000 100.000
582 4.513 4.261 .164 -.028 .080 .224 4.114 .065 .168 71.014 10.173 .015 --- 5.237 .000 100.000
583 4.624 4.096 .218 -.069 .033 .246 4.075 .040 .200 70.382 10.213 .006 --- 5.936 .000 100.000
584 4.597 4.074 .213 .004 .033 .207 4.022 .083 .186 70.832 10.085 .007 --- 5.658 .000 100.000
585 4.050 4.350 .191 .033 .071 .202 4.053 .079 .225 70.631 10.176 .010 --- 5.929 .000 100.000
AVER: 4.552 4.216 .217 -.003 .080 .196 4.051 .081 .192 70.493 10.173 .009 --- 5.744 .000 100.000
SDEV: .288 .100 .030 .043 .026 .034 .039 .021 .022 .284 .070 .007 --- .469 .000 .000
SERR: .083 .029 .009 .012 .008 .010 .011 .006 .006 .082 .020 .002 --- .135 .000
%RSD: 6.33 2.38 13.86-1528.18 33.05 17.22 .97 25.48 11.66 .40 .69 76.35 --- 8.16 .00
STDS: 336 374 285 835 835 22 395 25 358 162 336 12 --- --- ---
Note that our SiO2 concentration went up slightly because we added additional oxygen (from H2O) into the matrix calculation, and so now our water by difference is around 5.7 wt.% which is quite close to our FTIR value of 5.06 wt.%. If we had included other trace elements in the analysis, we would get even closer.
So, the lesson is, always include all the unanalyzed elements into the matrix correction, or you will have significant errors in the analyzed elements. Excel is great, but it doesn't know physics! Please let me know if anyone has any questions.
Does it make a difference if one includes oxygen as a specified element in the Elements/Cations menu of the Acquire! window prior to acquisition vs. simply selecting "Calculate with stoichiometric oxygen" under Calculation Options during the analysis step (following acquisition)?
I realize the output to the log may vary, but do the final concentrations saved from the Output menu differ? If so, is there any way to add "specified" oxygen as an element to a sample set that was initially acquired without it?
Cheers!
Quote from: pvburger on March 08, 2019, 11:03:41 AM
Does it make a difference if one includes oxygen as a specified element in the Elements/Cations menu of the Acquire! window prior to acquisition vs. simply selecting "Calculate with stoichiometric oxygen" under Calculation Options during the analysis step (following acquisition)?
I realize the output to the log may vary, but do the final concentrations saved from the Output menu differ? If so, is there any way to add "specified" oxygen as an element to a sample set that was initially acquired without it?
Cheers!
Hi Paul,
This is a really good question because it relates to an important point about how stoichiometric oxygen is handled along with "excess oxygen" in Probe for EPMA (and CalcZAF for that matter).
Basically, stoichiometric oxygen or oxygen by stoichiometry are unrelated to acquisition because in either case they are "unanalyzed" or "specified" elements. So you can specify them prior to acquisition or after acquisition of the "analyzed" elements.
If you check the "Use Stoichiometric Oxygen" option in the Calculation Options dialog, the software will automatically add oxygen to your matrix and include it in the matrix corrections.
But sometimes, we will want to specify some additional or "excess" oxygen as part of our analysis. For example your Fe is specified as FeO, but you are measuring a magnetite specimen. There is some discussion here on this:
https://smf.probesoftware.com/index.php?topic=223.msg1002#msg1002
But the bottom line is that yes, you can have oxygen calculated by stoichiometry, *and* you can add oxygen as a "specified" element for dealing with excess or oxygen deficits. Oxygen as an unanalyzed element is added, just as you would with any other unanalyzed elements, from the Elements/Cations dialog, but leaving the x-ray line blank.
Now all of this changes when you have oxygen as an analyzed element! When oxygen is being analyzed for (and when the oxidation state of Fe is uncertain this is actually a very good idea), the software will automatically subtract the stoichiometric oxygen from the measured oxygen to obtain the so called "excess" oxygen. This post describes that situation:
https://smf.probesoftware.com/index.php?topic=197.msg888#msg888
This can get complicated but play around with your samples, and if you can, try analyzing some standards as unknowns, e.g., magnetite, and it should become clear. But feel free to post some examples of what you are trying to accomplish if you have any questions at all.
Most of us understand the effects of "unanalyzed" elements in the matrix correction and how it is important to include these elements either by specification, difference or by stoichiometry to other analyzed elements, in order to obtain an accurate matrix correction.
For example the issue of unanalyzed water in hydrous glasses, where one gets a results with a total of say 95% and one might be forgiven to think that, OK, I've got 5 wt% H2O there because 100 - 95 = 5 in Excel. But that would be wrong because Excel doesn't know anything about matrix correction physics. In fact what we see when we specify water by difference is described in this and other posts in this topic:
https://smf.probesoftware.com/index.php?topic=92.msg7701#msg7701
Basically adding oxygen (and hydrogen) to our glass matrix correction results in a significant change in the concentration of other elements. In a generic example of a silicate glass, the Si (and other element) concentrations increases significantly. Why is this? Because it turns out that Si Ka is not well absorbed by Si atoms, but they are well absorbed by oxygen atoms! Once the matrix correction "knows" about the extra oxygen (water), the absorption correction increases correspondingly.
So in our generic example of a 95% total in a hydrous glass, once we add H2O by difference and include it in the matrix correction, because the Si (and other elements) increase by about 1%, we instead obtain about 4% H2O by difference. This effect was described in the Roman et al. paper referenced here:
https://smf.probesoftware.com/index.php?topic=61.msg4303#msg4303
Now this makes some intuitive sense to me because Si Ka is a fairly low energy emission line and therefore fairly well absorbed by other elements, but I never expected this to be the case for Fe Ka at 6.4 keV!
Here's an example for a magnetite sample where the Fe is expressed, as we usually do in EPMA, as FeO:
Un 96 7138_PPO-2_Mgt4_HO-1, Results in Elemental Weight Percents
ELEM: Fe Mg Si Ti V Mn Cr Al O
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL CALC
BGDS: MAN MAN MAN MAN EXP LIN MAN MAN
TIME: 40.00 120.00 40.00 80.00 30.00 30.00 80.00 120.00 ---
BEAM: 45.93 45.93 45.93 45.93 45.93 45.93 45.93 45.93 ---
ELEM: Fe Mg Si Ti V Mn Cr Al O SUM
146 60.944 1.463 .058 5.329 .265 .422 .375 1.542 23.842 94.240
AVER: 60.944 1.463 .058 5.329 .265 .422 .375 1.542 23.842 94.240
SDEV: .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
SERR: .000 .000 .000 .000 .000 .000 .000 .000 .000
%RSD: .00 .00 .00 .00 .00 .00 .00 .00 .00
STDS: 396 396 14 22 23 25 396 396 ---
STKF: .1836 .0330 .4101 .5547 .6328 .7341 .3060 .0469 ---
STCT: 1119.3 3499.0 4307.2 9290.4 8344.6 14435.6 1338.8 1992.0 ---
UNKF: .5710 .0066 .0004 .0548 .0028 .0040 .0043 .0088 ---
UNCT: 3481.1 701.1 4.3 917.6 37.1 77.9 18.9 373.9 ---
UNBG: 12.2 47.8 2.8 32.9 15.3 29.2 6.1 29.4 ---
ZCOR: 1.0674 2.2108 1.4127 .9728 .9416 1.0658 .8682 1.7520 ---
KRAW: 3.1102 .2004 .0010 .0988 .0044 .0054 .0141 .1877 ---
PKBG: 286.31 15.65 2.55 28.88 3.43 3.67 4.10 13.70 ---
INT%: .00 ---- ---- ---- -15.76 ---- -1.38 ---- ---
As one can see our Fe concentration is 60.944 and our total is 94.240. So we're missing about 5% of something and that something of course is mostly the excess oxygen in the Fe2O3 molecule in magnetite. Now how much of an effect can this ~5% missing oxygen have on our Fe concentration? What would you guess? I wouldn't have guessed this much:
Un 96 7138_PPO-2_Mgt4_HO-1, Results in Elemental Weight Percents
ELEM: Fe Mg Si Ti V Mn Cr Al O
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL DIFF
BGDS: MAN MAN MAN MAN EXP LIN MAN MAN
TIME: 40.00 120.00 40.00 80.00 30.00 30.00 80.00 120.00 ---
BEAM: 45.93 45.93 45.93 45.93 45.93 45.93 45.93 45.93 ---
ELEM: Fe Mg Si Ti V Mn Cr Al O SUM
146 61.421 1.451 .057 5.379 .267 .425 .383 1.532 29.085 100.000
AVER: 61.421 1.451 .057 5.379 .267 .425 .383 1.532 29.085 100.000
SDEV: .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
SERR: .000 .000 .000 .000 .000 .000 .000 .000 .000
%RSD: .00 .00 .00 .00 .00 .00 .00 .00 .00
STDS: 396 396 14 22 23 25 396 396 ---
STKF: .1836 .0330 .4101 .5547 .6328 .7341 .3060 .0469 ---
STCT: 1119.3 3499.0 4307.2 9290.4 8344.6 14435.6 1338.8 1992.0 ---
UNKF: .5710 .0066 .0004 .0548 .0028 .0040 .0044 .0088 ---
UNCT: 3481.6 701.6 4.3 918.5 37.1 77.9 19.1 374.1 ---
UNBG: 11.8 47.3 2.8 32.0 15.3 29.2 5.9 29.2 ---
ZCOR: 1.0756 2.1904 1.4061 .9808 .9506 1.0740 .8773 1.7396 ---
KRAW: 3.1106 .2005 .0010 .0989 .0044 .0054 .0143 .1878 ---
PKBG: 296.98 15.83 2.54 29.68 3.43 3.67 4.25 13.80 ---
INT%: .00 ---- ---- ---- -15.75 ---- -1.36 ---- ---
Holy cow! Our Fe concentration went from 60.944 to 61.421 which is almost 0.5 wt% absolute. And note how the ZCOR (matrix correction) for Fe Ka went from 1.0674 to 1.0756. But even more mind blowing is to compare the *other* elements we measured: Mg, Ti, Al, etc. What happened to them? Well they went slightly *down* in concentration! Why? Because they are more absorbed by Fe than by O. It just goes to show you that one cannot intuit physics, you have to just run the darn calculation.
Of course we really should calculate the excess oxygen in our magnetites/ilmenites using a ferric/ferrous calculation (and more on that later), but the oxygen by difference calculation demonstrates that once we obtain our ferric/ferrous ratio, we really need to calculate the excess oxygen from that and specify it in Probe for EPMA, to obtain a more accurate Fe concentration for our mineral thermodynamic calculations.
Now, I'm no geologist but perhaps one should then recalculate our ferric/ferrous ratios, this time using our improved Fe concentration. Again, more on this later...
I'm no geologist but I think this is a cool trick to deal with missing OH in (some/all?) amphiboles.
So here is a tremolite (asbestos) analysis I did recently for the CDC:
Un 13 AZ asbestos gr6, Results in Oxide Weight Percents
ELEM: Na2O SiO2 K2O Al2O3 FeO MgO CaO Cl TiO2 F MnO ZnO O HO SUM
642 -.016 57.171 .112 .186 3.613 22.006 12.782 .004 -.044 -.063 .185 .028 .000 .000 95.963
643 .006 57.423 .086 .203 3.307 22.143 12.787 .000 -.031 .049 .215 .009 .000 .000 96.199
644 .008 57.522 .078 .182 3.437 22.184 12.780 .004 -.015 -.027 .178 .026 .000 .000 96.358
645 .060 57.454 .073 .163 3.168 22.240 12.908 .003 .012 -.071 .175 .029 .000 .000 96.213
646 .088 57.484 .079 .053 3.012 22.158 13.087 -.003 -.036 -.047 .138 -.041 .000 .000 95.972
AVER: .029 57.411 .086 .157 3.307 22.146 12.869 .002 -.023 -.032 .178 .010 .000 .000 96.141
SDEV: .043 .139 .016 .060 .233 .086 .134 .003 .022 .049 .028 .030 .000 .000 .170
SERR: .019 .062 .007 .027 .104 .039 .060 .001 .010 .022 .012 .013 .000 .000
%RSD: 146.89 .24 18.18 38.14 7.04 .39 1.04 159.31 -97.92 -151.68 15.48 295.57 223.61 .00
STDS: 336 162 374 336 162 162 162 285 22 835 25 660 --- ---
Note that the total is quite low due to the missing OH molecule. Now looking up the formula for tremolite we see this: Ca2Mg5Si8O22(OH)2. So there are 2 OH molecules for every 8 Si atoms or 0.25 hydroxyls for every Si atom.
Next we add hydrogen as an unanalyzed elements in the Elements/Cations dialog like this, being sure to specify 1 hydrogen and 1 oxygen, to obtain the hydroxyl molecule:
(https://smf.probesoftware.com/gallery/395_11_07_19_12_34_09.png)
Next we go into the Calculation Options dialog and specify oxygen by stoichiometry, and .25 hydrogens (as hydroxyl), to 1 Si atom as seen here:
(https://smf.probesoftware.com/gallery/395_11_07_19_12_34_22.png)
Now when we calculate the composition we get:
Un 13 AZ asbestos gr6, Results in Oxide Weight Percents
ELEM: Na2O SiO2 K2O Al2O3 FeO MgO CaO Cl TiO2 F MnO ZnO O HO SUM
642 -.014 57.329 .112 .187 3.634 22.208 12.820 .004 -.044 -.065 .186 .028 .000 4.057 100.442
643 .009 57.587 .086 .204 3.326 22.349 12.826 .000 -.032 .050 .216 .009 .000 4.075 100.705
644 .011 57.682 .078 .183 3.456 22.389 12.819 .004 -.015 -.028 .179 .026 .000 4.082 100.866
645 .063 57.613 .073 .164 3.186 22.446 12.946 .003 .012 -.073 .176 .029 .000 4.077 100.717
646 .091 57.650 .079 .054 3.030 22.366 13.126 -.003 -.036 -.048 .139 -.042 .000 4.080 100.486
AVER: .032 57.572 .086 .158 3.326 22.352 12.908 .002 -.023 -.033 .179 .010 .000 4.074 100.643
SDEV: .043 .141 .016 .060 .234 .088 .134 .003 .022 .049 .028 .030 .000 .010 .176
SERR: .019 .063 .007 .027 .105 .039 .060 .001 .010 .022 .012 .013 .000 .004
%RSD: 136.72 .24 18.19 38.03 7.03 .39 1.04 159.31 -97.92 -151.40 15.48 295.57 -651.92 .24
STDS: 336 162 374 336 162 162 162 285 22 835 25 660 --- ---
Not only is our total now very close to 100%, but note how the Si and Mg compositions have changed, because now the matrix effect of that 4 wt% OH was included in the matrix calculations.
Quote from: Probeman on July 11, 2019, 12:39:23 PM
I'm no geologist but I think this is a cool trick to deal with missing OH in (some/all?) amphiboles.
So here is a tremolite (asbestos) analysis I did recently for the CDC:
Un 13 AZ asbestos gr6, Results in Oxide Weight Percents
ELEM: Na2O SiO2 K2O Al2O3 FeO MgO CaO Cl TiO2 F MnO ZnO O HO SUM
642 -.016 57.171 .112 .186 3.613 22.006 12.782 .004 -.044 -.063 .185 .028 .000 .000 95.963
643 .006 57.423 .086 .203 3.307 22.143 12.787 .000 -.031 .049 .215 .009 .000 .000 96.199
644 .008 57.522 .078 .182 3.437 22.184 12.780 .004 -.015 -.027 .178 .026 .000 .000 96.358
645 .060 57.454 .073 .163 3.168 22.240 12.908 .003 .012 -.071 .175 .029 .000 .000 96.213
646 .088 57.484 .079 .053 3.012 22.158 13.087 -.003 -.036 -.047 .138 -.041 .000 .000 95.972
AVER: .029 57.411 .086 .157 3.307 22.146 12.869 .002 -.023 -.032 .178 .010 .000 .000 96.141
SDEV: .043 .139 .016 .060 .233 .086 .134 .003 .022 .049 .028 .030 .000 .000 .170
SERR: .019 .062 .007 .027 .104 .039 .060 .001 .010 .022 .012 .013 .000 .000
%RSD: 146.89 .24 18.18 38.14 7.04 .39 1.04 159.31 -97.92 -151.68 15.48 295.57 223.61 .00
STDS: 336 162 374 336 162 162 162 285 22 835 25 660 --- ---
Note that the total is quite low due to the missing OH molecule. Now looking up the formula for tremolite we see this: Ca2Mg5Si8O22(OH)2. So there are 2 OH molecules for every 8 Si atoms or 0.25 hydroxyls for every Si atom.
Next we add hydrogen as an unanalyzed elements in the Elements/Cations dialog like this, being sure to specify 1 hydrogen and 1 oxygen, to obtain the hydroxyl molecule:
(https://smf.probesoftware.com/gallery/395_11_07_19_12_34_09.png)
Next we go into the Calculation Options dialog and specify oxygen by stoichiometry, and .25 hydrogens (as hydroxyl), to 1 Si atom as seen here:
(https://smf.probesoftware.com/gallery/395_11_07_19_12_34_22.png)
Now when we calculate the composition we get:
Un 13 AZ asbestos gr6, Results in Oxide Weight Percents
ELEM: Na2O SiO2 K2O Al2O3 FeO MgO CaO Cl TiO2 F MnO ZnO O HO SUM
642 -.014 57.329 .112 .187 3.634 22.208 12.820 .004 -.044 -.065 .186 .028 .000 4.057 100.442
643 .009 57.587 .086 .204 3.326 22.349 12.826 .000 -.032 .050 .216 .009 .000 4.075 100.705
644 .011 57.682 .078 .183 3.456 22.389 12.819 .004 -.015 -.028 .179 .026 .000 4.082 100.866
645 .063 57.613 .073 .164 3.186 22.446 12.946 .003 .012 -.073 .176 .029 .000 4.077 100.717
646 .091 57.650 .079 .054 3.030 22.366 13.126 -.003 -.036 -.048 .139 -.042 .000 4.080 100.486
AVER: .032 57.572 .086 .158 3.326 22.352 12.908 .002 -.023 -.033 .179 .010 .000 4.074 100.643
SDEV: .043 .141 .016 .060 .234 .088 .134 .003 .022 .049 .028 .030 .000 .010 .176
SERR: .019 .063 .007 .027 .105 .039 .060 .001 .010 .022 .012 .013 .000 .004
%RSD: 136.72 .24 18.19 38.03 7.03 .39 1.04 159.31 -97.92 -151.40 15.48 295.57 -651.92 .24
STDS: 336 162 374 336 162 162 162 285 22 835 25 660 --- ---
Not only is our total now very close to 100%, but note how the Si and Mg compositions have changed, because now the matrix effect of that 4 wt% OH was included in the matrix calculations.
Hi John,
This is not correct. Amphiboles generally have around 2 wt% H2O assuming that no F-, Cl-, or O2- substitutes for OH-. For charge balance, you should have specified 2 hydrogens per oxygen. Also, note that Al3+ can substitute for Si4+ on the tetrahedral sites, and so it is not sound practice to specify a given number of OH- per Si4+.
Brian
Hello,
The general idea of calculating the hydroxyl content in advance of the matrix corrections is a good one, but I should draw your attention to some problems with the discussion immediately above.
1) The concentrations of the elements should be expressed as neutral oxides.
Thus, the method should report percent-by-weight of H2O, not the hydroxyl moiety.
For both of the average tremolite compositions discussed, the amount of H2O(!) should be 2.19 wt%.
This corresponds to two hydroxyl units per formula unit in each of these cases:
(K0.016) (Ca1.923Mn0.021Fe0.019Na0.008)Σ1.971 (Mg4.605Fe0.367Al0.026Zn0.002)Σ5 (Si8.006)Σ8.006 O22 (OH)2
(K0.016) (Ca1.921Fe0.037Mn0.021Na0.008)Σ1.987 (Mg4.627Fe0.349Al0.021Zn0.002)Σ4.999 (Si7.995Al0.005)Σ8 O22 (OH)2
The final totals are thus 98.4 to 98.8 wt%.
2) Many (most) amphibole species do not have exactly 8 Si per formula unit.
One could instead use the ratio of H to oxygen for those amphiboles that are assumed to have only hydroxyl present (no oxo-substitution, and no significant F or Cl present).
The ratio would be 2 H for 24 oxygen, or 0.0833333 H for 1 O.
3) A minor point, but in my view, negative values of the measured elements should be automatically set to zero, prior to averaging.
Best regards,
Andrew
As I said, I'm no geologist, so please explain why the formula for tremolite is given as Ca2Mg5Si8O22(OH)2
http://www.webmineral.com/data/Tremolite.shtml#.XSeiNP57laQ
I only assumed Si might be a valid element to ratio hydrogen to because there's almost no Al in this composition. Maybe this only works for tremolite?
My main point was just to show the matrix effect of including OH or H2O, on the other measured elements. What is your suggestion for adding in the missing hydroxyl or water to improve the matrix correction accuracy? Just specify 2% H2O?
Hello,
Although end-member tremolite has the formula: □Ca2(Mg5)(Si8)O22(OH)2, where □ indicates a vacancy on the A-site of amphibole, other amphiboles have substitutions for Si (and for hydroxyl).
Thus, end-member kaersutite has the formula: NaCa2(Mg3TiAl)(Si6Al2)O22O2.
Similarly, end-member pargasite has the formula: NaCa2(Mg4Al)(Si6Al2)O22(OH)2.
For the hydroxyl group of amphiboles, if Cl and F are assumed to be absent, one could specify 2 hydroxyl groups.
In both end-member tremolite and end-member pargasite, the ratio of H to O would therefore be 2 to 24, or 0.083333:1.
It is critical that the output in weight percent be expressed as neutral oxides, that is, H2O.
End-member ideal tremolite has the following oxide weight percent composition:
SiO2 59.17, MgO 24.81, CaO 13.81, H2O 2.22 wt%, sum 100.01 (all rounded to 2 decimal places).
End-member ideal pargasite has the following oxide weight percent composition:
SiO2 43.13, Al2O3 18.30, MgO 19.29, CaO 13.42, Na2O 3.71, H2O 2.16 wt%, sum 100.01 (all rounded to 2 decimal places).
Because Si varies considerably (in principle from 5 atoms per formula unit in sadanagaite to 8 in tremolite), it is not a good choice as a basis for H calculation. Oxygen should be better (assuming no oxo-substitution).
All the best,
Andrew
I'm completely confused now. Some of that oxygen in the formula isn't associated with the cations. If I just specify hydrogen elementally relative to the calculated oxygen, it won't add in the additional oxygen in hydroxl or water. Correct?
So what *exactly* would you do in the Calculation Options dialog?
If I specify .08333 hydrogens to calculated oxygen I get:
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element H is Calculated .08333 Atoms Relative To 1.0 Atom of Oxygen
Using Conductive Coating Correction For Electron Absorption and X-Ray Transmission:
Sample Coating=C, Density=2.1 gm/cm3, Thickness=200 angstroms, Sin(Thickness)=311.145 angstroms
Un 13 AZ asbestos gr6, Results in Elemental Weight Percents
ELEM: Na Si K Al Fe Mg Ca Cl Ti F Mn Zn O H
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL CALC STOI
BGDS: MAN MAN LIN MAN MAN MAN MAN LIN LIN LIN LIN LIN
TIME: 40.00 40.00 20.00 40.00 40.00 165.00 150.00 120.00 30.00 120.00 30.00 30.00 --- ---
BEAM: 29.92 29.92 29.92 29.92 29.92 29.92 29.92 29.92 29.92 29.92 29.92 29.92 --- ---
ELEM: Na Si K Al Fe Mg Ca Cl Ti F Mn Zn O H SUM
642 -.010 26.802 .093 .099 2.825 13.397 9.163 .004 -.026 -.065 .144 .022 47.925 .250 100.624
643 .006 26.921 .071 .108 2.586 13.481 9.167 .000 -.019 .050 .168 .007 48.069 .250 100.866
644 .008 26.967 .065 .097 2.687 13.505 9.162 .004 -.009 -.028 .138 .021 48.156 .250 101.025
645 .047 26.935 .061 .087 2.477 13.540 9.253 .003 .007 -.073 .136 .023 48.138 .250 100.885
646 .067 26.952 .066 .028 2.355 13.492 9.382 -.003 -.022 -.048 .107 -.033 48.059 .251 100.655
AVER: .024 26.915 .071 .084 2.586 13.483 9.226 .002 -.014 -.033 .139 .008 48.070 .250 100.811
SDEV: .032 .066 .013 .032 .182 .053 .096 .003 .013 .049 .021 .024 .091 .000 .169
SERR: .014 .029 .006 .014 .081 .024 .043 .001 .006 .022 .010 .011 .041 .000
%RSD: 136.38 .24 18.19 38.02 7.03 .39 1.04 159.31 -97.92 -151.40 15.48 295.56 .19 .10
STDS: 336 162 374 336 162 162 162 285 22 835 25 660 --- ---
STKF: .0735 .2018 .1132 .1332 .0950 .0568 .1027 .0602 .5547 .1715 .7341 .4865 --- ---
STCT: 58.60 246.04 197.64 255.36 19.35 72.74 178.88 61.41 44.86 13.54 136.63 66.08 --- ---
UNKF: .0001 .2126 .0006 .0006 .0215 .0926 .0838 .0000 -.0001 -.0001 .0011 .0001 --- ---
UNCT: .10 259.20 1.11 1.10 4.38 118.69 146.07 .01 -.01 -.01 .21 .01 --- ---
UNBG: .30 .20 .95 .80 .22 .52 .99 .37 .06 .05 .15 .36 --- ---
ZCOR: 1.9014 1.2659 1.1175 1.4587 1.2014 1.4554 1.1004 1.2304 1.2048 4.1651 1.2217 1.2664 --- ---
KRAW: .0017 1.0535 .0056 .0043 .2265 1.6316 .8165 .0002 -.0002 -.0005 .0015 .0001 --- ---
PKBG: 1.34 1319.20 2.18 2.37 20.95 228.69 149.12 1.04 .86 .90 2.43 1.03 --- ---
INT%: ---- ---- ---- ---- -.01 ---- ---- ---- ---- 76.60 ---- ---- --- ---
TDI%: 2.963 .033 -2.002 -3.947 -.711 .000 .000 .000 .000 .000 .000 .000 --- ---
DEV%: .2 .1 18.6 23.1 3.4 .0 .0 .0 .0 .0 .0 .0 --- ---
TDIF: HYP-EXP LOG-LIN LOG-LIN LOG-LIN LOG-LIN ---- ---- ---- ---- ---- ---- ---- --- ---
TDIT: 111.80 112.60 78.00 111.00 115.40 .00 .00 .00 .00 .00 .00 .00 --- ---
TDII: .369 259. 2.01 1.84 4.57 ---- ---- ---- ---- ---- ---- ---- --- ---
TDIL: -.996 5.56 .697 .611 1.52 ---- ---- ---- ---- ---- ---- ---- --- ---
Un 13 AZ asbestos gr6, Results in Oxide Weight Percents
ELEM: Na2O SiO2 K2O Al2O3 FeO MgO CaO Cl TiO2 F MnO ZnO O HO SUM
642 -.014 57.339 .112 .187 3.634 22.216 12.821 .004 -.044 -.065 .186 .028 .000 4.219 100.624
643 .009 57.593 .086 .204 3.327 22.356 12.827 .000 -.032 .050 .216 .009 .000 4.221 100.866
644 .011 57.691 .078 .183 3.457 22.396 12.820 .004 -.015 -.028 .179 .026 .000 4.222 101.025
645 .063 57.623 .073 .164 3.187 22.454 12.947 .003 .012 -.073 .176 .029 .000 4.226 100.885
646 .091 57.660 .079 .054 3.030 22.373 13.128 -.003 -.036 -.048 .139 -.042 .000 4.229 100.655
AVER: .032 57.581 .086 .158 3.327 22.359 12.909 .002 -.023 -.033 .179 .010 .000 4.223 100.811
SDEV: .043 .140 .016 .060 .234 .088 .134 .003 .022 .049 .028 .030 .000 .004 .169
SERR: .019 .063 .007 .027 .105 .039 .060 .001 .010 .022 .012 .013 .000 .002
%RSD: 136.38 .24 18.19 38.02 7.03 .39 1.04 159.31 -97.92 -151.40 15.48 295.56 418.33 .10
STDS: 336 162 374 336 162 162 162 285 22 835 25 660 --- ---
Quote from: Probeman on July 11, 2019, 02:25:03 PM
I'm completely confused now. Some of that oxygen in the formula isn't associated with the cations. If I just specify hydrogen elementally relative to the calculated oxygen, it won't add in the additional oxygen in hydroxl or water. Correct?
So what *exactly* would you do in the Calculation Options dialog?
Sorry to cause confusion.
The program actually does better than you might expect!
Let me explain with the example of apophyllite, ideal formula: KCa4Si8O20(OH)·8H2O
The ratio of hydrogen to oxygen in this formula is 17 to 29, or about 0.58621:1.
From the Handbook of Mineralogy entry for hydroxyapophyllite, the ideal oxide weight percents are:
SiO2 53.10, CaO 24.78, K2O 5.20, H2O 16.92 wt%, sum 100.00.
I ran some apophyllite analyses last year.
The measured oxides were: Na2O, SiO2, K2O, Al2O3, CaO, MgO, and BaO.
In the Calculation Options window, I selected:
Stoichiometry to Calculated Oxygen
0.58621 Atoms of
H to 1 Oxygen
(This is shown in the attached MS-Word document entitled "apophyllite example.docx").
The results (also in the attached MS-Word document) are:
Na2O SiO2 K2O Al2O3 CaO MgO BaO H2O Total
Average: 0.03 52.98 4.81 0.02 24.52 0.01 0.00 16.98 99.36
Thus, the program has calculated the presence of 16.98 wt% H2O.
If I calculate the formula proportions (on the basis of 8 Si+Al), I get:
Si7.998 Al0.002 Ca3.966 Na0.010 K0.926 H17.101, with 28.98 O by charge balance.
(Remember, the ideal is Si8, Ca4, K1, H17, O29).
I consider this to be pretty good initial results for a hydroxylated- and hydrated-mineral.
The take-home message is that Probe-for-EPMA can calculate the appropriate content of H2O.Just try it!
(I have equally good results for analcime, NaAlSi2O6·H2O).
Best regards,
Andrew
I should also note that the major element composition of that apophyllite without any calculated OH & H2O was:
SiO2 51.23, K2O 4.65 CaO 23.79, sum 79.67 wt%.
Thus, the calculated OH & H2O content made significant changes (about 3% relative) in these major elements during the data reduction process.
The major element results:
SiO2 K2O CaO H2O
Average: 52.98 4.81 24.52 16.98
Cheers,
Andrew
Quote from: AndrewLocock on July 11, 2019, 03:01:04 PM
Sorry to cause confusion.
The program actually does better than you might expect!
Let me explain with the example of apophyllite, ideal formula: KCa4Si8O20(OH)·8H2O
The ratio of hydrogen to oxygen in this formula is 17 to 29, or about 0.58621:1.
From the Handbook of Mineralogy entry for hydroxyapophyllite, the ideal oxide weight percents are:
SiO2 53.10, CaO 24.78, K2O 5.20, H2O 16.92 wt%, sum 100.00.
I ran some apophyllite analyses last year.
The measured oxides were: Na2O, SiO2, K2O, Al2O3, CaO, MgO, and BaO.
In the Calculation Options window, I selected:
Stoichiometry to Calculated Oxygen 0.58621 Atoms of H to 1 Oxygen
(This is shown in the attached MS-Word document entitled "apophyllite example.docx").
The results (also in the attached MS-Word document) are:
Na2O SiO2 K2O Al2O3 CaO MgO BaO H2O Total
Average: 0.03 52.98 4.81 0.02 24.52 0.01 0.00 16.98 99.36
Thus, the program has calculated the presence of 16.98 wt% H2O.
If I calculate the formula proportions (on the basis of 8 Si+Al), I get:
Si7.998 Al0.002 Ca3.966 Na0.010 K0.926 H17.101, with 28.98 O by charge balance.
(Remember, the ideal is Si8, Ca4, K1, H17, O29).
I consider this to be pretty good initial results for a hydroxylated- and hydrated-mineral.
The take-home message is that Probe-for-EPMA can calculate the appropriate content of H2O.
Just try it!
(I have equally good results for analcime, NaAlSi2O6·H2O).
Best regards,
Andrew
Hi Andrew,
OK, wow, that makes more sense. So if I specify 0.08333 hydrogens to each oxygen (and specifying hydrogen oxide as H2O), I get this:
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element H is Calculated .08333 Atoms Relative To 1.0 Atom of Oxygen
Using Conductive Coating Correction For Electron Absorption and X-Ray Transmission:
Sample Coating=C, Density=2.1 gm/cm3, Thickness=200 angstroms, Sin(Thickness)=311.145 angstroms
Un 13 AZ asbestos gr6, Results in Elemental Weight Percents
ELEM: Na Si K Al Fe Mg Ca Cl Ti F Mn Zn O H
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL CALC STOI
BGDS: MAN MAN LIN MAN MAN MAN MAN LIN LIN LIN LIN LIN
TIME: 40.00 40.00 20.00 40.00 40.00 165.00 150.00 120.00 30.00 120.00 30.00 30.00 --- ---
BEAM: 29.92 29.92 29.92 29.92 29.92 29.92 29.92 29.92 29.92 29.92 29.92 29.92 --- ---
ELEM: Na Si K Al Fe Mg Ca Cl Ti F Mn Zn O H SUM
642 -.011 26.791 .093 .099 2.822 13.344 9.163 .004 -.026 -.064 .144 .022 45.847 .244 98.472
643 .006 26.909 .071 .108 2.583 13.427 9.167 .000 -.019 .050 .167 .007 45.989 .245 98.711
644 .007 26.955 .065 .097 2.684 13.452 9.162 .004 -.009 -.028 .138 .021 46.076 .245 98.870
645 .046 26.923 .061 .087 2.474 13.486 9.253 .003 .007 -.072 .136 .023 46.055 .245 98.728
646 .066 26.940 .066 .028 2.353 13.437 9.382 -.003 -.022 -.048 .107 -.033 45.974 .245 98.494
AVER: .023 26.904 .071 .084 2.583 13.429 9.225 .002 -.014 -.032 .139 .008 45.988 .245 98.655
SDEV: .032 .065 .013 .032 .182 .053 .096 .003 .013 .049 .021 .024 .090 .000 .169
SERR: .014 .029 .006 .014 .081 .024 .043 .001 .006 .022 .010 .011 .040 .000
%RSD: 140.42 .24 18.19 38.06 7.04 .39 1.04 159.31 -97.92 -151.40 15.48 295.57 .20 .10
STDS: 336 162 374 336 162 162 162 285 22 835 25 660 --- ---
STKF: .0735 .2018 .1132 .1332 .0950 .0568 .1027 .0602 .5547 .1715 .7341 .4865 --- ---
STCT: 58.60 246.04 197.64 255.36 19.35 72.74 178.88 61.41 44.86 13.54 136.63 66.08 --- ---
UNKF: .0001 .2126 .0006 .0006 .0215 .0926 .0838 .0000 -.0001 -.0001 .0011 .0001 --- ---
UNCT: .10 259.20 1.11 1.10 4.38 118.68 146.06 .01 -.01 -.01 .21 .01 --- ---
UNBG: .30 .20 .95 .81 .22 .53 .99 .37 .06 .05 .15 .36 --- ---
ZCOR: 1.8912 1.2654 1.1175 1.4576 1.2006 1.4496 1.1004 1.2318 1.2048 4.1235 1.2210 1.2653 --- ---
KRAW: .0016 1.0535 .0056 .0043 .2264 1.6315 .8165 .0002 -.0002 -.0005 .0015 .0001 --- ---
PKBG: 1.32 1312.38 2.18 2.37 20.78 226.62 148.12 1.04 .86 .90 2.43 1.03 --- ---
INT%: ---- ---- ---- ---- -.01 ---- ---- ---- ---- 76.60 ---- ---- --- ---
TDI%: 2.963 .033 -2.002 -3.947 -.711 .000 .000 .000 .000 .000 .000 .000 --- ---
DEV%: .2 .1 18.6 23.1 3.4 .0 .0 .0 .0 .0 .0 .0 --- ---
TDIF: HYP-EXP LOG-LIN LOG-LIN LOG-LIN LOG-LIN ---- ---- ---- ---- ---- ---- ---- --- ---
TDIT: 111.80 112.60 78.00 111.00 115.40 .00 .00 .00 .00 .00 .00 .00 --- ---
TDII: .369 259. 2.01 1.84 4.57 ---- ---- ---- ---- ---- ---- ---- --- ---
TDIL: -.996 5.56 .697 .611 1.52 ---- ---- ---- ---- ---- ---- ---- --- ---
Un 13 AZ asbestos gr6, Results in Oxide Weight Percents
ELEM: Na2O SiO2 K2O Al2O3 FeO MgO CaO Cl TiO2 F MnO ZnO O H2O SUM
642 -.015 57.315 .112 .186 3.631 22.128 12.821 .004 -.044 -.064 .186 .028 .000 2.184 98.472
643 .008 57.568 .086 .204 3.323 22.266 12.826 .000 -.032 .050 .216 .009 .000 2.186 98.711
644 .010 57.667 .078 .183 3.453 22.307 12.819 .004 -.015 -.028 .179 .026 .000 2.186 98.870
645 .062 57.598 .073 .164 3.183 22.364 12.947 .003 .012 -.072 .176 .029 .000 2.188 98.728
646 .089 57.634 .079 .053 3.027 22.283 13.127 -.003 -.036 -.048 .139 -.042 .000 2.190 98.494
AVER: .031 57.556 .086 .158 3.323 22.270 12.908 .002 -.023 -.032 .179 .010 .000 2.187 98.655
SDEV: .043 .140 .016 .060 .234 .087 .134 .003 .022 .049 .028 .030 .000 .002 .169
SERR: .019 .063 .007 .027 .105 .039 .060 .001 .010 .022 .012 .013 .000 .001
%RSD: 140.42 .24 18.19 38.06 7.04 .39 1.04 159.31 -97.92 -151.40 15.48 295.57 69.72 .10
STDS: 336 162 374 336 162 162 162 285 22 835 25 660 --- ---
And as you and Brian said, the total is a little low, probably out of focus. Looking at another sample I get this:
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element H is Calculated .08333 Atoms Relative To 1.0 Atom of Oxygen
Using Conductive Coating Correction For Electron Absorption and X-Ray Transmission:
Sample Coating=C, Density=2.1 gm/cm3, Thickness=200 angstroms, Sin(Thickness)=311.145 angstroms
Un 3 AZ asbestos gr1, Results in Elemental Weight Percents
ELEM: Na Si K Al Fe Mg Ca Cl Ti F Mn Zn O H
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL CALC STOI
BGDS: MAN MAN LIN MAN MAN MAN MAN LIN LIN LIN LIN LIN
TIME: 40.00 40.00 20.00 40.00 40.00 165.00 150.00 120.00 30.00 120.00 30.00 30.00 --- ---
BEAM: 29.90 29.90 29.90 29.90 29.90 29.90 29.90 29.90 29.90 29.90 29.90 29.90 --- ---
ELEM: Na Si K Al Fe Mg Ca Cl Ti F Mn Zn O H SUM
138 .008 26.996 .051 .014 2.275 13.729 9.586 .004 .026 -.031 .082 .025 46.289 .245 99.298
139 .008 27.285 .040 .033 2.379 13.658 9.453 .006 .008 .040 .133 -.028 46.554 .245 99.813
140 .030 27.073 .065 .050 2.282 13.667 9.501 .002 .013 -.032 .080 -.048 46.323 .245 99.251
141 .055 27.055 .032 .055 2.533 13.677 9.358 .000 .011 .009 .136 -.010 46.350 .245 99.505
142 .037 27.221 .028 .016 2.592 13.659 9.399 .004 .014 .005 .107 .017 46.519 .245 99.861
143 .059 27.190 .059 .042 2.310 13.713 9.476 .004 -.002 .004 .101 .037 46.501 .245 99.740
144 .082 27.189 .043 .080 2.457 13.619 9.446 -.001 -.019 -.052 .028 .004 46.468 .245 99.589
AVER: .040 27.144 .045 .041 2.404 13.674 9.460 .003 .007 -.008 .095 .000 46.429 .245 99.580
SDEV: .027 .104 .014 .023 .126 .037 .073 .002 .014 .031 .037 .030 .106 .000 .242
SERR: .010 .039 .005 .009 .048 .014 .028 .001 .005 .012 .014 .011 .040 .000
%RSD: 68.48 .38 30.26 56.41 5.25 .27 .78 93.90 205.40 -385.54 38.60-8861.00 .23 .08
STDS: 336 162 374 336 162 162 162 285 22 835 25 660 --- ---
STKF: .0735 .2018 .1132 .1332 .0950 .0568 .1027 .0602 .5547 .1715 .7341 .4865 --- ---
STCT: 55.79 246.63 196.50 255.38 19.50 71.86 178.02 66.46 44.04 14.00 136.85 66.47 --- ---
UNKF: .0002 .2145 .0004 .0003 .0200 .0945 .0860 .0000 .0001 .0000 .0008 .0000 --- ---
UNCT: .16 262.18 .70 .55 4.11 119.57 149.02 .02 .00 .00 .15 .00 --- ---
UNBG: .30 .21 .96 .82 .22 .54 1.01 .36 .05 .05 .17 .38 --- ---
ZCOR: 1.8837 1.2652 1.1173 1.4579 1.2011 1.4474 1.1006 1.2318 1.2033 4.1276 1.2215 1.2656 --- ---
KRAW: .0029 1.0631 .0036 .0021 .2106 1.6638 .8371 .0003 .0001 -.0001 .0011 .0000 --- ---
PKBG: 1.53 1227.91 1.74 1.67 20.07 223.49 149.16 1.07 1.12 .98 1.91 1.00 --- ---
INT%: ---- ---- ---- ---- -.01 ---- ---- ---- ---- -129.12 ---- ---- --- ---
TDI%: 7.889 .289 -4.914 1.125 .386 .000 .000 .000 .000 .000 .000 .000 --- ---
DEV%: .2 .1 29.7 56.7 3.6 .0 .0 .0 .0 .0 .0 .0 --- ---
TDIF: HYP-EXP LOG-LIN LOG-LIN LOG-LIN LOG-LIN ---- ---- ---- ---- ---- ---- ---- --- ---
TDIT: 116.14 116.14 81.43 114.71 120.57 .00 .00 .00 .00 .00 .00 .00 --- ---
TDII: .435 262. 1.58 1.33 4.32 ---- ---- ---- ---- ---- ---- ---- --- ---
TDIL: -.832 5.57 .460 .286 1.46 ---- ---- ---- ---- ---- ---- ---- --- ---
Un 3 AZ asbestos gr1, Results in Oxide Weight Percents
ELEM: Na2O SiO2 K2O Al2O3 FeO MgO CaO Cl TiO2 F MnO ZnO O H2O SUM
138 .011 57.754 .061 .026 2.927 22.766 13.413 .004 .043 -.031 .106 .031 .000 2.187 99.298
139 .011 58.372 .048 .062 3.061 22.648 13.227 .006 .013 .040 .172 -.035 .000 2.188 99.813
140 .041 57.919 .078 .095 2.936 22.664 13.294 .002 .021 -.032 .103 -.060 .000 2.190 99.251
141 .074 57.880 .039 .105 3.258 22.681 13.094 .000 .018 .009 .176 -.013 .000 2.185 99.505
142 .049 58.235 .033 .030 3.335 22.651 13.151 .004 .023 .005 .139 .021 .000 2.185 99.861
143 .079 58.170 .071 .079 2.971 22.741 13.259 .004 -.004 .004 .131 .046 .000 2.187 99.740
144 .110 58.167 .052 .152 3.161 22.585 13.216 -.001 -.032 -.052 .037 .005 .000 2.189 99.589
AVER: .054 58.071 .055 .078 3.093 22.676 13.236 .003 .012 -.008 .123 .000 .000 2.187 99.580
SDEV: .037 .222 .017 .044 .162 .061 .103 .002 .024 .031 .048 .038 .000 .002 .242
SERR: .014 .084 .006 .017 .061 .023 .039 .001 .009 .012 .018 .014 .000 .001
%RSD: 68.48 .38 30.26 56.41 5.25 .27 .78 93.90 205.40 -385.54 38.60-8860.99 .00 .08
STDS: 336 162 374 336 162 162 162 285 22 835 25 660 --- ---
Which is much better. Dang, geology is complicated compared to physics!
Now I'm almost afraid to ask, but can you tell me why the tremolite formula is stated as Ca2(Mg5)(Si8)O22(OH)2 when Ca2(Mg5)(Si8)O23(H2O) is chemically the same? Which to me makes more sense considering how hydrogen (oxide) needs to be treated.
Quote from: Probeman on July 11, 2019, 04:28:46 PM
Now I'm almost afraid to ask, but can you tell me why the tremolite formula is stated as Ca2(Mg5)(Si8)O22(OH)2 when Ca2(Mg5)(Si8)O23(H2O) is chemically the same? Which to me makes more sense considering how hydrogen (oxide) needs to be treated.
It has to do with how the hydrogen is present in the crystal structure.
In the case of hydroxyl, the hydrogen is located at about 0.9 to 1 angstrom away from an oxygen atom.
In the case of an H2O molecule ("water molecule"), two hydrogen atoms are located about 0.9 to 1 angstrom away from a single oxygen atom.
The H2O molecule is not linear, so in a crystal structure the central oxygen also tends to be attracted to a cation.
And, the hydrogen atoms of this H2O group may be weakly attracted to other oxygen atoms (usually within 2 to 3 angstroms distance) - this is the so-called "hydrogen bonding", for which the best example is ice.
Although it is possible to express a formula in different ways, e.g., Mg(OH)2 could be expressed as MgO·H2O, it is best to use the formula the reflects what is present in the crystal structure (or glass). In the example of apophyllite KCa4Si8O20(OH)·8H2O, both hydroxyl and H2O are present. And in tremolite, hydroxyl groups are present, but H2O groups are not.
Finally, in a chemical analysis that is expressed at neutral oxides, the hydrogen content should be expressed as H2O, regardless of how it is present in the crystal structure or glass.
Cheers,
Andrew
Quote from: AndrewLocock on July 12, 2019, 07:42:53 AM
Quote from: Probeman on July 11, 2019, 04:28:46 PM
Now I'm almost afraid to ask, but can you tell me why the tremolite formula is stated as Ca2(Mg5)(Si8)O22(OH)2 when Ca2(Mg5)(Si8)O23(H2O) is chemically the same? Which to me makes more sense considering how hydrogen (oxide) needs to be treated.
It has to do with how the hydrogen is present in the crystal structure.
In the case of hydroxyl, the hydrogen is located at about 0.9 to 1 angstrom away from an oxygen atom.
In the case of an H2O molecule ("water molecule"), two hydrogen atoms are located about 0.9 to 1 angstrom away from a single oxygen atom.
The H2O molecule is not linear, so in a crystal structure the central oxygen also tends to be attracted to a cation.
And, the hydrogen atoms of this H2O group may be weakly attracted to other oxygen atoms (usually within 2 to 3 angstroms distance) - this is the so-called "hydrogen bonding", for which the best example is ice.
Although it is possible to express a formula in different ways, e.g., Mg(OH)2 could be expressed as MgO·H2O, it is best to use the formula the reflects what is present in the crystal structure (or glass). In the example of apophyllite KCa4Si8O20(OH)·8H2O, both hydroxyl and H2O are present. And in tremolite, hydroxyl groups are present, but H2O groups are not.
Finally, in a chemical analysis that is expressed at neutral oxides, the hydrogen content should be expressed as H2O, regardless of how it is present in the crystal structure or glass.
Cheers,
Andrew
Hi Andrew,
Thank-you. This sort of makes sense, even to a non-geologist like me! ;D
Quote from: Probeman on July 02, 2019, 11:09:46 AM
Most of us understand the effects of "unanalyzed" elements in the matrix correction and how it is important to include these elements either by specification, difference or by stoichiometry to other analyzed elements, in order to obtain an accurate matrix correction.
For example the issue of unanalyzed water in hydrous glasses, where one gets a results with a total of say 95% and one might be forgiven to think that, OK, I've got 5 wt% H2O there because 100 - 95 = 5 in Excel. But that would be wrong because Excel doesn't know anything about matrix correction physics. In fact what we see when we specify water by difference is described in this and other posts in this topic:
https://smf.probesoftware.com/index.php?topic=92.msg7701#msg7701
Basically adding oxygen (and hydrogen) to our glass matrix correction results in a significant change in the concentration of other elements. In a generic example of a silicate glass, the Si (and other element) concentrations increases significantly. Why is this? Because it turns out that Si Ka is not well absorbed by Si atoms, but they are well absorbed by oxygen atoms! Once the matrix correction "knows" about the extra oxygen (water), the absorption correction increases correspondingly.
So in our generic example of a 95% total in a hydrous glass, once we add H2O by difference and include it in the matrix correction, because the Si (and other elements) increase by about 1%, we instead obtain about 4% H2O by difference. This effect was described in the Roman et al. paper referenced here:
https://smf.probesoftware.com/index.php?topic=61.msg4303#msg4303
Now this makes some intuitive sense to me because Si Ka is a fairly low energy emission line and therefore fairly well absorbed by other elements, but I never expected this to be the case for Fe Ka at 6.4 keV!
Here's an example for a magnetite sample where the Fe is expressed, as we usually do in EPMA, as FeO:
Un 96 7138_PPO-2_Mgt4_HO-1, Results in Elemental Weight Percents
ELEM: Fe Mg Si Ti V Mn Cr Al O
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL CALC
BGDS: MAN MAN MAN MAN EXP LIN MAN MAN
TIME: 40.00 120.00 40.00 80.00 30.00 30.00 80.00 120.00 ---
BEAM: 45.93 45.93 45.93 45.93 45.93 45.93 45.93 45.93 ---
ELEM: Fe Mg Si Ti V Mn Cr Al O SUM
146 60.944 1.463 .058 5.329 .265 .422 .375 1.542 23.842 94.240
AVER: 60.944 1.463 .058 5.329 .265 .422 .375 1.542 23.842 94.240
SDEV: .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
SERR: .000 .000 .000 .000 .000 .000 .000 .000 .000
%RSD: .00 .00 .00 .00 .00 .00 .00 .00 .00
STDS: 396 396 14 22 23 25 396 396 ---
STKF: .1836 .0330 .4101 .5547 .6328 .7341 .3060 .0469 ---
STCT: 1119.3 3499.0 4307.2 9290.4 8344.6 14435.6 1338.8 1992.0 ---
UNKF: .5710 .0066 .0004 .0548 .0028 .0040 .0043 .0088 ---
UNCT: 3481.1 701.1 4.3 917.6 37.1 77.9 18.9 373.9 ---
UNBG: 12.2 47.8 2.8 32.9 15.3 29.2 6.1 29.4 ---
ZCOR: 1.0674 2.2108 1.4127 .9728 .9416 1.0658 .8682 1.7520 ---
KRAW: 3.1102 .2004 .0010 .0988 .0044 .0054 .0141 .1877 ---
PKBG: 286.31 15.65 2.55 28.88 3.43 3.67 4.10 13.70 ---
INT%: .00 ---- ---- ---- -15.76 ---- -1.38 ---- ---
As one can see our Fe concentration is 60.944 and our total is 94.240. So we're missing about 5% of something and that something of course is mostly the excess oxygen in the Fe2O3 molecule in magnetite. Now how much of an effect can this ~5% missing oxygen have on our Fe concentration? What would you guess? I wouldn't have guessed this much:
Un 96 7138_PPO-2_Mgt4_HO-1, Results in Elemental Weight Percents
ELEM: Fe Mg Si Ti V Mn Cr Al O
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL DIFF
BGDS: MAN MAN MAN MAN EXP LIN MAN MAN
TIME: 40.00 120.00 40.00 80.00 30.00 30.00 80.00 120.00 ---
BEAM: 45.93 45.93 45.93 45.93 45.93 45.93 45.93 45.93 ---
ELEM: Fe Mg Si Ti V Mn Cr Al O SUM
146 61.421 1.451 .057 5.379 .267 .425 .383 1.532 29.085 100.000
AVER: 61.421 1.451 .057 5.379 .267 .425 .383 1.532 29.085 100.000
SDEV: .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
SERR: .000 .000 .000 .000 .000 .000 .000 .000 .000
%RSD: .00 .00 .00 .00 .00 .00 .00 .00 .00
STDS: 396 396 14 22 23 25 396 396 ---
STKF: .1836 .0330 .4101 .5547 .6328 .7341 .3060 .0469 ---
STCT: 1119.3 3499.0 4307.2 9290.4 8344.6 14435.6 1338.8 1992.0 ---
UNKF: .5710 .0066 .0004 .0548 .0028 .0040 .0044 .0088 ---
UNCT: 3481.6 701.6 4.3 918.5 37.1 77.9 19.1 374.1 ---
UNBG: 11.8 47.3 2.8 32.0 15.3 29.2 5.9 29.2 ---
ZCOR: 1.0756 2.1904 1.4061 .9808 .9506 1.0740 .8773 1.7396 ---
KRAW: 3.1106 .2005 .0010 .0989 .0044 .0054 .0143 .1878 ---
PKBG: 296.98 15.83 2.54 29.68 3.43 3.67 4.25 13.80 ---
INT%: .00 ---- ---- ---- -15.75 ---- -1.36 ---- ---
Holy cow! Our Fe concentration went from 60.944 to 61.421 which is almost 0.5 wt% absolute. And note how the ZCOR (matrix correction) for Fe Ka went from 1.0674 to 1.0756. But even more mind blowing is to compare the *other* elements we measured: Mg, Ti, Al, etc. What happened to them? Well they went slightly *down* in concentration! Why? Because they are more absorbed by Fe than by O. It just goes to show you that one cannot intuit physics, you have to just run the darn calculation.
Of course we really should calculate the excess oxygen in our magnetites/ilmenites using a ferric/ferrous calculation (and more on that later), but the oxygen by difference calculation demonstrates that once we obtain our ferric/ferrous ratio, we really need to calculate the excess oxygen from that and specify it in Probe for EPMA, to obtain a more accurate Fe concentration for our mineral thermodynamic calculations.
Now, I'm no geologist but perhaps one should then recalculate our ferric/ferrous ratios, this time using our improved Fe concentration. Again, more on this later...
The idea of calculating excess oxygen and including that excess oxygen into the matrix correction physics is a very appealing idea. Based on the preliminary calculations quoted above, it appears that the effect of excess oxygen could, at least in some cases, affect the accuracy of various geological thermometers/barometers. Simply because the addition of excess oxygen in the matrix calculations causes some element concentrations to increase, while other elements will show a decrease in concentrations.
So we've chatted with a few geologists about adding such a calculation for ferric/ferrous ratios into Probe for EPMA, it seems that there needs to be a separate calculation (normalization) for each (non-hydrous) mineral species, e.g., magnetite/ilmenite, garnet, etc., etc.
There also seems to be some various approaches to this ferric/ferrous calculation, apparently optimized for different mineral species. That is, Gihorso, Droop, Stormer, etc.
Geologists: what are your thoughts on this? What mineral species should we perform these ferric/ferrous excess oxygen calculations for, and what method should we utilize? We'd like to get a consensus from the geological community before starting work on the coding.
Hello,
The general principles of charge-balanced formulas are best laid out by Droop (1987) Min. Mag. 51, Issue 361, pp. 431-435.
A given mineral is assumed to have a set number of cation positions for a set number of oxygen atoms, with iron being the only element with variable valence state. The proportion of ferric iron is calculated to reach the ideal number of cations and of oxygen atoms.
It is important to realize the effects of propagation-of-uncertainty on the calculation of structural formulas.
This is outlined by Giaramita and Day (1990) Am. Min. 75, pp. 170-182.
As an example, below is solid-solution in the spinel group of magnetite - ulvospinel - spinel.
For the weight-percent oxides, we will assume some reasonable standard deviations, as might be found in a set of electron microprobe analyses:
MgO Al2O3 TiO2 FeOtot sum wt% 4.86 12.30 9.64 69.34 96.14 sd 0.25 0.45 0.35 0.60 n/a RSD 5.1% 3.7% 3.6% 0.9% n/a |
The resulting formula, calculated for 3 cations and 4 oxygen, is:
Mg Al Ti Fe2+ Fe3+ O cations average 0.250 0.500 0.250 1.000 1.000 4.000 3.000
std dev 0.012 0.016 0.009 0.016 0.021 0.000 0.000
RSD 4.8% 3.2% 3.4% 1.6% 2.1% 0.0% 0.0% |
Although the starting relative uncertainty in FeO was 0.9%, the propagated relative uncertainty is considerably higher; for Fe2+ it is 1.6% and for Fe3+ it is 2.1%.
The example of augite based on the analysis and uncertainties given by Giaramita and Day (1990) follows:
oxide Na2O MgO Al2O3 SiO2 CaO TiO2 Cr2O3 MnO FeOtot sum
mean 1.20 16.59 8.04 50.16 15.97 0.84 0.15 0.15 6.18 99.28
std dev 0.04 0.14 0.08 0.23 0.15 0.05 0.05 0.04 0.16 0.37
RSD 3.3% 0.8% 1.0% 0.5% 0.9% 6.0% 33.1% 27.1% 2.6% 0.4% |
The resulting formula, calculated for 4 cations and 6 oxygen, is:
element Na Mg Al Si Ca Ti Cr Mn Fe2+ Fe3+ O cations
average 0.085 0.901 0.345 1.826 0.623 0.023 0.004 0.005 0.152 0.036 6.000 4.000
std dev 0.003 0.007 0.003 0.007 0.005 0.001 0.001 0.001 0.014 0.015 0.000 0.000
RSD 3.3% 0.7% 1.0% 0.4% 0.8% 6.0% 33.1% 27.1% 9.2% 40.2% 0.0% 0.0%
|
Although the starting relative uncertainty in FeO was 2.6%, the propagated relative uncertainty is (very) considerably higher; for Fe2+ it is 9.2% and for Fe3+ it is 40.2% (in part, because of the small absolute amount of ferric iron).
These latter relative uncertainties would apply to the recalculated weight-percent FeO and Fe2O3.
Cheers,
Andrew
Hi Andrew,
Thanks for responding. OK, so you think the Droop method is the way to go forward on this recalculation. Let's see if anyone else objects, but that decision is fine by me. I assume you already have written code that performs these calculations?
On the uncertainties issue, thanks for the info but let's not get ahead of ourselves. You said:
QuoteA given mineral is assumed to have a set number of cation positions for a set number of oxygen atoms, with iron being the only element with variable valence state. The proportion of ferric iron is calculated to reach the ideal number of cations and of oxygen atoms.
So let's discuss how the user will specify this "given mineral" in the software interface. Will the user select a mineral species from a drop down list, or will they specify a "a set number of cation positions for a set number of oxygen atoms". How does your code expect this specification?
Quote from: John Donovan on July 24, 2019, 09:26:43 AM
So let's discuss how the user will specify this "given mineral" in the software interface. Will the user select a mineral species from a drop down list, or will they specify a "a set number of cation positions for a set number of oxygen atoms". How does your code expect this specification?
Hello,
Attached is an example Excel spreadsheet of how this charge-balance calculation could work.
In this spreadsheet, the user inputs the desired
# of cations,
# of oxygen, and the
weight-percentages of nine common oxides: Na2O MgO Al2O3 SiO2 CaO TiO2 Cr2O3 MnO FeO
totalThe spreadsheet calculates:
- the sum of these oxides
- the molar amounts of the elements, including oxygen, assuming only ferrous iron
- the atomic proportions of the elements, including oxygen, assuming only ferrous iron, based on the input # of cations
- the charge-balanced proportions of the elements, based on the input # of cations and # of oxygen
The atomic ratio of ferric iron to total iron (Fe3+/ΣFe) is given, as are the recalculated weight percentages of FeO and Fe2O3, along with a revised sum of the oxides.
There are 6 analyses in this example file:
1) The augite from Giaramita and Day (1990), based on 4 cations and 6 oxygen.
2) The augite from Giaramita and Day (1990), based on 8 cations and 12 oxygen.
3) A magnetite-spinel-ulvospinel solid solution, based on 3 cations and 4 oxygen.
4) The garnet from Knowles (1987), based on 8 cations and 12 oxygen.
5) A mostly grossular garnet (#5) from Table 58 of volume 1A of the second edition of Deer, Howie and Zussman.
6) A mostly almandine garnet (#12) from Table 55 of volume 1A of the second edition of Deer, Howie and Zussman.
For the augite examples, the proportions of ferric iron are identical, as the ratios of cations to oxygen are identical.
The magnetite etc. solid solution is a hypothetical (fictive) composition, and so the total is exactly 100.00%.
For the garnet of Knowles (1987), charge balance is achieved with 0.59 wt% Fe2O3, and the final sum is 100.57 wt%.
For the mostly grossular garnet, all of the iron is recalculated as ferric iron, and exact charge balance is still not achieved; the oxygen remains as 11.973 atoms per 8 cations.
For the mostly almandine garnet, all of the iron remains as ferrous iron, and exact charge balance is still not achieved; the oxygen remains as 12.085 atoms per 8 cations.
In these latter two cases, the compositions do NOT achieve charge balance (indeed, they cannot). This is probably because of errors and uncertainties in the analyses.
The key formula in this Excel spreadsheet is the calculation of the proportion of ferric iron, which is handled with a nested IF formula:
IF(AI3<B3,IF(2*(B3-AI3)<=AH3,2*(B3-AI3),AH3),0)
If (the atomic proportion of oxygen is Less Than the input # of oxygen,
If (two times (the input # of oxygen Minus the atomic proportion of oxygen) is Less Than or Equal To the atomic proportion of ferrous iron,
then Calculate two times (the input # of oxygen Minus the atomic proportion of oxygen),
Otherwise use the atomic proportion of ferrous iron,
Otherwise report zero.
I hope that this spreadsheet and explanation will prove useful.
Regards,
Andrew
Quote from: AndrewLocock on July 24, 2019, 10:56:15 AM
For the mostly grossular garnet, all of the iron is recalculated as ferric iron, and exact charge balance is still not achieved; the oxygen remains as 11.973 atoms per 8 cations.
For the mostly almandine garnet, all of the iron remains as ferrous iron, and exact charge balance is still not achieved; the oxygen remains as 12.085 atoms per 8 cations.
In these latter two cases, the compositions do NOT achieve charge balance (indeed, they cannot). This is probably because of errors and uncertainties in the analyses.
The key formula in this Excel spreadsheet is the calculation of the proportion of ferric iron, which is handled with a nested IF formula:
IF(AI3<B3,IF(2*(B3-AI3)<=AH3,2*(B3-AI3),AH3),0)
If (the atomic proportion of oxygen is Less Than the input # of oxygen,
If (two times (the input # of oxygen Minus the atomic proportion of oxygen) is Less Than or Equal To the atomic proportion of ferrous iron,
then Calculate two times (the input # of oxygen Minus the atomic proportion of oxygen),
Otherwise use the atomic proportion of ferrous iron,
Otherwise report zero.
I hope that this spreadsheet and explanation will prove useful.
Regards,
Andrew
Hi Andrew,
This is a good explanation, thanks. I will start working on this soon, but probably not until after M&M.
It occurs to me, with the two examples you gave that did not achieve charge balance, I wonder if these compositions would achieve charge balance if the additional excess oxygen was added back into the matrix correction physics and the charge balance re-calculated?
This is the approach that I will be taking for this calculation, as I already do with the interference and MAN corrections.
Thanks again.
Quote from: John Donovan on July 24, 2019, 11:42:01 AM
Hi Andrew,
This is a good explanation, thanks. I will start working on this soon, but probably not until after M&M.
It occurs to me, with the two examples you gave that did not achieve charge balance, I wonder if these compositions would achieve charge balance if the additional excess oxygen was added back into the matrix correction physics and the charge balance re-calculated?
This is the approach that I will be taking for this calculation, as I already do with the interference and MAN corrections.
Thanks again.
Hi John,
It is conceivable that such an addition-and-recalculation might improve these analyses, if they had been obtained by electron microprobe analysis, but I think that they were both wet chemical analyses.
There are a few other points of concern with adding the ferric/ferrous recalculation into the matrix corrections:
1) The recalculation assumes that Fe is the ONLY element with variable valence, and that there are NO significant vacancies (cation or anion) in the material. This is mostly applicable to anhydrous oxides.
2) The result generated by the Probe-for-EPMA software during the iteration of the matrix corrections will
probably need to be recalculated by the user after the fact, as it will probably diverge from the ideal during such iterations.
My reasoning is based on the case of carbonate minerals such as calcite, CaCO3, for which the CO2 content is calculated by stoichiometry and added into the iteration loop(s) of the matrix corrections.
In the case of calcite analyses, the final amount of CO2 reported by Probe-for-EPMA is usually NOT in perfect stoichiometric ratio to the divalent cations (it is usually close, but rarely perfect).
It is
definitely preferable to have that CO2 present for the matrix corrections.
However, the user should (must) recalculate elsewhere the final proportion of CO2 to match stoichiometry.
Thus, I suspect that some (slight) divergence from ideality could similarly occur in the ferric/ferrous recalculation during the iterations of the matrix corrections.
Cheers,
Andrew
Quote from: AndrewLocock on July 24, 2019, 12:33:58 PM
Thus, I suspect that some (slight) divergence from ideality could similarly occur in the ferric/ferrous recalculation during the iterations of the matrix corrections.
Yes, indeed. Sometimes reality is not ideal! ;)
Quote from: John Donovan on July 24, 2019, 12:39:48 PM
Quote from: AndrewLocock on July 24, 2019, 12:33:58 PM
Thus, I suspect that some (slight) divergence from ideality could similarly occur in the ferric/ferrous recalculation during the iterations of the matrix corrections.
Yes, indeed. Sometimes reality is not ideal! ;)
Hi John,
Below is a graph of the C vs. Ca formula contents from multiple analyses of the Smithsonian calcite standard.
CO2 was added by stoichiometry (0.33333 C for every 1 O) prior to the matrix corrections.
The amount of C is
perfectly anti-correlated with the amount of Ca.
My interpretation: this is an unfortunate consequence of the analytical uncertainty in Ca coupling with the algorithm loops in Probe-for-EPMA.
If Ca is low, PfE determines C as high. If Ca is high, PfE determines C as low. Of course the ideal is 1:1, CaCO3.
I am pretty sure that the Smithsonian calcite is electrically neutral (charge-balanced!), so the behaviour in this graph is an
artifact of the data reduction process.
Take home message: at present, add CO2 in to get the best data reduction, then recalculate it for stoichiometry.
Cheers,
Andrew
(https://smf.probesoftware.com/gallery/406_24_07_19_12_54_52.jpeg)
(https://smf.probesoftware.com/index.php?action-gallery;sa=view;pic=1404)
Hi Andrew,
Interesting. Is the stoichiometry correlated in any way with the analytical total?
I ask because it seems to me this could also be an artifact of the normalization from weight percent to atoms. When you get a chance please send me the MDB file and I'll look into it.
Quote from: John Donovan on July 24, 2019, 04:04:34 PM
Hi Andrew,
Interesting. Is the stoichiometry correlated in any way with the analytical total?
I ask because it seems to me this could also be an artifact of the normalization from weight percent to atoms.
Hi John,
The data are from back in 2015; I have attached the raw oxide data (CaO and CO2) and the molar proportions that result as an Excel file. There are actually two calcite samples present (which I previously confused, sorry).
The plots of the molar proportions show
negative linear correlations (essentially identical for the two calcites):
(https://smf.probesoftware.com/gallery/406_25_07_19_9_07_47.jpeg)
(https://smf.probesoftware.com/gallery/406_25_07_19_9_16_41.jpeg)
Of course, the molar amount of CO2 should(!) be equal to the molar amount of CaO.
That is, these graphs
should simply show y = x.
If one recalculates the wt% CO2 based on the stoichiometry CaCO3, it has a negative linear correlation with the wt% CO2 initially reported by Probe-for-EPMA:
(https://smf.probesoftware.com/gallery/406_25_07_19_9_47_17.jpeg)
The weight percent CO2 reported by Probe-for-EPMA (after the iterated matrix corrections) is
not in stoichiometric proportion to the CaO content for these calcite analyses.
In answer to your question about correlation with the analytical total, for the two calcites, the initial data reported by Probe-for-EPMA show a negative linear correlation between wt% CO2 and analytical total.
Whereas, when CO2 is calculated by stoichiometry to the CaO content, the wt% CO2 and the subsequent revised totals are positively correlated, in the ratio 2.2742. This is, of course, the ratio found in ideal calcite, CaCO3 (43.97 wt% CO2, 56.03 wt% CaO, total 100.00), where 100/43.97 = 2.2742.
(https://smf.probesoftware.com/gallery/406_25_07_19_10_25_13.jpeg)
I will send you this MDB file separately.
Best regards,
Andrew
Quote from: AndrewLocock on July 25, 2019, 10:42:47 AM
In answer to your question about correlation with the analytical total, for the two calcites, the initial data reported by Probe-for-EPMA show a negative linear correlation between wt% CO2 and analytical total.
Whereas, when CO2 is calculated by stoichiometry to the CaO content, the wt% CO2 and the subsequent revised totals are positively correlated, in the ratio 2.2742. This is, of course, the ratio found in ideal calcite, CaCO3 (43.97 wt% CO2, 56.03 wt% CaO, total 100.00), where 100/43.97 = 2.2742.
(https://smf.probesoftware.com/gallery/406_25_07_19_10_25_13.jpeg)
I will send you this MDB file separately.
Best regards,
Andrew
Hi Andrew,
Yes, this is exactly what I suspected. For those analyses where the totals are not close to 100%, when the concentrations are normalized to 100% for the formula calculations, the CO2 stoichiometry gets "distorted" due to different atomic weights relative to atom proportions.
As evidence for this, please note that for those analyses in the above plot where the analytical totals are close to 100%, the stoichiometric CO2 values are almost exactly equal to the ideal concentration of 43.97 wt% CO2.
I'm really not sure what one can do about this except try to obtain better analytical totals! :P
In principle I guess one could concoct a "correction" for those analyses which don't total close to 100%, but this seems to me to be a little problematic for several reasons.
The good news is that averaging these analyses together should average out this normalization effect. Assuming the average analytical total is close to 100%! :)
Thank-you for your help on this.
Quote from: John Donovan on July 25, 2019, 11:31:36 AM
Hi Andrew,
Yes, this is exactly what I suspected. For those analyses where the totals are not close to 100%, when the concentrations are normalized to 100% for the formula calculations, the CO2 stoichiometry gets "distorted" due to different atomic weights relative to atom proportions.
As evidence for this, please note that for those analyses in the above plot where the analytical totals are close to 100%, the stoichiometric CO2 values are almost exactly equal to the ideal concentration of 43.97 wt% CO2.
I'm really not sure what one can do about this except try to obtain better analytical totals! :P
In principle I guess one could concoct a "correction" for those analyses which don't total close to 100%, but this seems to me to be a little problematic for several reasons.
The good news is that averaging these analyses together should average out this normalization effect. Assuming the average analytical total is close to 100%! :)
Thank-you for your help on this.
Hi John,
I am confused as to why (or how) oxygen is handled vs. how CO2 is handled in Probe-for-EPMA. Both are added in prior to the iterative matrix corrections (yes?). But the behaviour of a simple oxide compound seems different than that of a simple carbonate.
For example, I just measured Mg in periclase (20 points). The results are given as elements in weight percent, with oxygen calculated by stoichiometry in Probe-for-EPMA. The totals are between 99.6 and 100.6 wt%.
A graph of the oxygen wt% vs. analytical total follows the ideal ratio of 2.5191:
(https://smf.probesoftware.com/gallery/406_25_07_19_12_54_18.jpeg)
Probe-for-EPMA can figure out the
exact stoichiometric amount of oxygen in MgO for a series of points with differing amounts of Mg (and therefore differing analytical totals).
Why are the results for the calculation of CO2 in CaCO3 any different?
Or how is it that the CO2 is handled that causes the results to differ from stoichiometry?
Thanks,
Andrew
Hi Andrew,
It's a good question. I'm not quite sure myself but as I said, I think it's because of the normalization to atoms for the CO2 calculation. My code is based on Armstrong's code and it's all on Github so you can check it out yourself.
https://github.com/openmicroanalysis/calczaf
You'll want to look at procedure ZAFSMP in code module ZAF.bas. The calculation for an element in relative atoms to stoichiometric oxygen is calculated in two places, here is the first approximation calculation:
' Add in elements calculated relative to stoichiometric element (in0%)
For i% = 1 To zaf.in1%
If zaf.il%(i%) = 15 Then
zaf.krat!(i%) = (zaf.krat!(zaf.in0%) / zaf.atwts!(zaf.in0%)) * sample(1).StoichiometryRatio! * zaf.atwts!(i%)
zaf.krat!(zaf.in0%) = zaf.krat!(zaf.in0%) + zaf.krat!(i%) * zaf.p1!(i%)
zaf.ksum! = zaf.ksum! + zaf.krat!(i%) + zaf.krat!(i%) * zaf.p1!(i%)
End If
Next i%
End If
The relative element calculation code inside the iteration loop is:
' Calculate element relative to stoichiometric oxygen based on previous iteration calculation of oxygen
If zaf.il%(zaf.in0%) = 0 Then ' if calculating oxygen by stoichiometry
For i% = 1 To zaf.in1%
If zaf.il%(i%) = 15 Then
r1!(i%) = (r1!(zaf.in0%) / zaf.atwts!(zaf.in0%)) * sample(1).StoichiometryRatio! * zaf.atwts!(i%)
zaf.ksum! = zaf.ksum! + r1!(i%)
zaf.krat!(i%) = r1!(i%)
End If
Next i%
The integer "15" is the flag for an element calculated by stocihiometry to stoichiometric oxygen.
krat is the k-ratio
ksum is the k-ratio sum
If you see anything you think we should modify please let me know and send me a test file to try it. Maybe we'll figure this out together!
john
Andrew,
But really I don't think the relative element calculation is the real problem. I suspect that the real problem comes at the end of the iteration loop when it de-normalizes everything to get back to the actual analytical total.
This code is in the same procedure and is after the iteration loop completes to the specified precision:
' Un-Normalize
3400:
For i% = 1 To zaf.in0%
zaf.conc!(i%) = zaf.conc!(i%) * zaf.ksum!
Next i%
What I think is happening is that because the matrix physics and unanalyzed element calculations are all performed in concentration units and during the iteration everything is normalized to total 1.0, when the loop exits, the program takes these concentrations and de-normalizes them for the actual analytical total.
But because the atomic proportion calculations are based on the number of atoms, a divergence from the previously calculated stoichiometry occurs, depending on the difference to a 100% analytical total. Because concentrations scale differently than concentrations.
Does this make any sense to you?
By the way, if you turn on DebugMode you will get a lot more output of the intermediate calculations, maybe more than you want! So maybe use the CalcZAF output menu in the PFE Analyze! window by right clicking the sample, and export a sample to CalcZAF format and perform the Debug calculations there...
I suggest that beam sensitivity is a contributing factor here. For the analysis of calcite, many exhibit differing beam sensitive behavior. During beam damage, CO2 is released and the residual beam volume becomes progressively an oxide residue. Ultimately the analysis would be of Ca oxide after complete CO2 loss.
The calculation of CO2 by stoichiometry is made by associating a carbon with the oxygen calculated from the measured cations in the sample, Ca, Mg, Fe, etc. So if a differential amount of CO2 is lost, then the cation concentration increases, and the calculated CO2 amount also increases. This results in a high total as there is too much CO2 calculated because the analytical volume is a more cation-rich composition.
So when doing conventional analysis, a low total indicates beam damage. When calculating CO2 by stoichiometry a high total indicates the same.
There is also the possibility of organic material in biogenically produced calcite or aragonite. I have analyzed a number of these materials and they exhibit significant beam sensitivity. But the point here is that there are organic materials that could also be in the carbonate. Not knowing what the specific material is, it is also possible that there are small inclusions of quartz or sulfate.
This may not be the whole story here, but that is my take.
Paul
Andrew,
Do you have a nice simple example of this formula normalization issue, but not a beam sensitive sample? In an MDB file?
Paul is correct that sample sensitivity to the beam can be an issue, especially with carbonates, but my intuition is that this (anti)-correlation with the analytical totals is essentially a normalization issue of some kind.
Quote from: Paul Carpenter on July 25, 2019, 02:30:17 PM
I suggest that beam sensitivity is a contributing factor here. For the analysis of calcite, many exhibit differing beam sensitive behavior. During beam damage, CO2 is released and the residual beam volume becomes progressively an oxide residue. Ultimately the analysis would be of Ca oxide after complete CO2 loss.
The calculation of CO2 by stoichiometry is made by associating a carbon with the oxygen calculated from the measured cations in the sample, Ca, Mg, Fe, etc. So if a differential amount of CO2 is lost, then the cation concentration increases, and the calculated CO2 amount also increases. This results in a high total as there is too much CO2 calculated because the analytical volume is a more cation-rich composition.
So when doing conventional analysis, a low total indicates beam damage. When calculating CO2 by stoichiometry a high total indicates the same.
There is also the possibility of organic material in biogenically produced calcite or aragonite. I have analyzed a number of these materials and they exhibit significant beam sensitivity. But the point here is that there are organic materials that could also be in the carbonate. Not knowing what the specific material is, it is also possible that there are small inclusions of quartz or sulfate.
This may not be the whole story here, but that is my take.
Paul
Hi Paul,
I take your point about the considerable beam sensitivity of calcite.
I just examined the Smithsonian siderite reference material, and ran 10 points with a 10-micron defocussed beam at 15 kV and 10 nA, with a count time of 30 s on peak, and 6 time-dependent-intensity (TDI) intervals for the Fe measurement.
The behaviour of Fe as a function of time is shown below:
(https://smf.probesoftware.com/gallery/406_25_07_19_4_52_29.jpeg)
As the Fe signal does not vary significantly with time, I turned off the TDI correction.
(I do not consider this siderite to be beam sensitive under the analytical conditions used here.)
The initial analytical totals range from 99.7 to 100.3 wt%.
However, the molar proportions of CO2 derived from the wt% CO2 reported by Probe-for-EPMA are negatively correlated with the molar proportions of the sum of FeO + MnO:
(https://smf.probesoftware.com/gallery/406_25_07_19_4_54_05.jpeg)
As I cannot attribute this behaviour to the sample, I concur with John that this is probably a result of how the CO2 is handled during the matrix corrections.
I will have to do some work to understand the Basic code provided (I am not a programmer).
But, I suspect that, although the initial amount of CO2 provided at the start of the matrix corrections may be in the correct stoichiometric ratio to the Fe+Mn of this siderite, by the time the iterations converge, this stoichiometric relationship has been altered. As John suggests, this may have to do with exactly how the algorithm proceeds (normalization to help with convergence?).
Best regards,
Andrew
Quote from: John Donovan on July 25, 2019, 04:54:44 PM
Andrew,
Do you have a nice simple example of this formula normalization issue, but not a beam sensitive sample? In an MDB file?
Paul is correct that sample sensitivity to the beam can be an issue, especially with carbonates, but my intuition is that this (anti)-correlation with the analytical totals is essentially a normalization issue of some kind.
Hi John,
Here is the MDB file for 4 lines of 10-point analyses on Smithsonian siderite.
The material does not exhibit beam damage (no significant change of intensity of Fe with time) under the conditions used.
Also attached is the formatted Excel file of the results.
As before, the CO2 wt% results reported by Probe-for-EPMA are close to, but systematically different from, the ideal stoichiometry.
Best regards,
Andrew
Hi Andrew,
Thanks. This will be useful.
Here's another approach in my KISS (keep it simple stupid) philosophy: run Probe for EPMA in simulation mode! Then there's no instrumental or sample issues!
You might already know that you can run PFE in "demo" or "simulation" mode. In PFE's simulation mode one can peak elements, acquire wavescans, acquire standards and if you specify an unknown name that is already a standard in your simulation run, it will utilize the physics for that standard composition as the unknown.
See the attached simulation run below where all I ran was Ca using a pure CaCO3 standard. I then added C as a specified (unanalyzed) element, and specified 0.3333 atoms of carbon for each atom of stoichiometric oxygen.
So here is the CaCO3 standard analyzed as an unknown:
St 136 Set 2 CaCO3, Results in Elemental Weight Percents
ELEM: Ca C O
TYPE: ANAL STOI CALC
BGDS: LIN
TIME: 10.00 --- ---
BEAM: 30.01 --- ---
ELEM: Ca C O SUM
6 39.888 12.010 47.920 99.817
7 39.875 12.011 47.917 99.803
8 40.341 11.970 47.994 100.305
9 40.025 11.997 47.942 99.964
AVER: 40.032 11.997 47.943 99.972
SDEV: .216 .019 .036 .233
SERR: .108 .009 .018
%RSD: .54 .16 .07
PUBL: 40.044 12.000 47.956 100.000
%VAR: (-.03) -.03 -.03
DIFF: (-.01) -.003 -.013
STDS: 136 --- ---
STKF: .3790 --- ---
STCT: 128.04 --- ---
UNKF: .3789 --- ---
UNCT: 128.00 --- ---
UNBG: .17 --- ---
ZCOR: 1.0567 --- ---
KRAW: .9997 --- ---
PKBG: 756.80 --- ---
St 136 Set 2 CaCO3, Results Based on 1 Atoms of ca
ELEM: Ca C O SUM
6 1.000 1.005 3.009 5.014
7 1.000 1.005 3.010 5.015
8 1.000 .990 2.980 4.970
9 1.000 1.000 3.001 5.001
AVER: 1.000 1.000 3.000 5.000 <---- sanity check!
SDEV: .000 .007 .014 .021
SERR: .000 .003 .007
%RSD: .00 .70 .46
Note that the standard intensity varies because we add noise to the simulation, but the average is as expected. Within the precision of the noise. Now here is an analysis of an unknown which was named CaCO3, so the standard composition is automatically utilized for calculating the intensities from the composition (running the matrix correction backwards!):
Un 3 CaCO3, Results in Elemental Weight Percents
ELEM: Ca C O
TYPE: ANAL STOI CALC
BGDS: LIN
TIME: 10.00 --- ---
BEAM: 30.02 --- ---
ELEM: Ca C O SUM
3 39.880 12.010 47.918 99.808
4 39.845 12.013 47.912 99.771
5 39.689 12.027 47.887 99.604
AVER: 39.805 12.017 47.906 99.728 <---- note slightly low total
SDEV: .101 .009 .017 .109
SERR: .059 .005 .010
%RSD: .25 .07 .03
STDS: 136 --- ---
STKF: .3790 --- ---
STCT: 128.28 --- ---
UNKF: .3767 --- ---
UNCT: 127.50 --- ---
UNBG: .15 --- ---
ZCOR: 1.0568 --- ---
KRAW: .9939 --- ---
PKBG: 866.07 --- ---
Un 3 CaCO3, Results Based on 1 Atoms of ca
ELEM: Ca C O SUM
3 1.000 1.005 3.010 5.015
4 1.000 1.006 3.012 5.018
5 1.000 1.011 3.022 5.034
AVER: 1.000 1.007 3.015 5.022 <---- note slightly high C and O formula atoms
SDEV: .000 .003 .007 .010
SERR: .000 .002 .004
%RSD: .00 .33 .22
Note that the totals are a little low (random noise) *and* that the C and O are a little high relative to Ca. Now another unknown, but this time with slightly high totals:
Un 4 CaCO3, Results in Elemental Weight Percents
ELEM: Ca C O
TYPE: ANAL STOI CALC
BGDS: LIN
TIME: 10.00 --- ---
BEAM: 30.00 --- ---
ELEM: Ca C O SUM
10 40.197 11.982 47.970 100.150
11 40.088 11.992 47.952 100.032
AVER: 40.142 11.987 47.961 100.091 <---- note slightly high totals
SDEV: .077 .007 .013 .083
SERR: .055 .005 .009
%RSD: .19 .06 .03
STDS: 136 --- ---
STKF: .3790 --- ---
STCT: 128.00 --- ---
UNKF: .3799 --- ---
UNCT: 128.33 --- ---
UNBG: .16 --- ---
ZCOR: 1.0566 --- ---
KRAW: 1.0025 --- ---
PKBG: 812.48 --- ---
Un 4 CaCO3, Results Based on 1 Atoms of ca
ELEM: Ca C O SUM
10 1.000 .995 2.989 4.984
11 1.000 .998 2.996 4.995
AVER: 1.000 .996 2.993 4.989 <---- note slightly low C and O atoms
SDEV: .000 .002 .005 .007
SERR: .000 .002 .004
%RSD: .00 .25 .17
Now note that the C and O are slightly low when the totals are slightly high.
This is what I've been trying to say all along. That is, I think that the atomic proportionality gets slightly distorted when the normalized composition in the matrix iteration loop is de-normalized after the iteration loop is exited. This is how Armstrong coded this many years ago in his CITZAF/TRYZAF code.
I think we can use this test run to see the effect most clearly since it is such a simple example. Maybe Paul Carpenter also has some ideas on this code as he worked on it with John Armstrong many years ago.
Edit by John: I just realized the output of the CaCO3 standard as an "unknown" had the C and O specified by concentration. That is now fixed, so that C is now specified as 0.3333 atoms for each atom of stoichiometric oxygen as previously stated. The attached MDB file below has been updated to reflect this.
Previously I wondered if the de-normalization of the concentrations to the analytical total after the matrix iteration loop is exited, was affecting the conversion to atoms. But I just checked, and no, that's not the issue:
Un 4 CaCO3, Results in Elemental Weight Percents
ELEM: Ca C O
TYPE: ANAL STOI CALC
BGDS: LIN
TIME: 10.00 --- ---
BEAM: 30.00 --- ---
ELEM: Ca C O SUM
10 40.137 11.964 47.899 100.000
11 40.075 11.988 47.937 100.000
AVER: 40.106 11.976 47.918 100.000
SDEV: .044 .017 .027 .000
SERR: .031 .012 .019
%RSD: .11 .14 .06
STDS: 136 --- ---
STKF: .3790 --- ---
STCT: 128.00 --- ---
UNKF: .3799 --- ---
UNCT: 128.33 --- ---
UNBG: .16 --- ---
ZCOR: 1.0566 --- ---
KRAW: 1.0025 --- ---
PKBG: 812.48 --- ---
Un 4 CaCO3, Results Based on 1 Atoms of ca
ELEM: Ca C O SUM
10 1.000 .995 2.989 4.984
11 1.000 .998 2.996 4.995
AVER: 1.000 .996 2.993 4.989
SDEV: .000 .002 .005 .007
SERR: .000 .002 .004
%RSD: .00 .25 .17
So, with the de-normalization code commented out, the analytical totals are now 100.000, but the atoms for C and O are still low. In fact they are exactly the same numbers as before when they were de-normalized to the actual analytical totals.
I'm beginning to wonder if non-stoichiometric results are unavoidable when one obtains the "wrong" Ca concentration. Afterall, if one measures too high or too low a Ca concentration in a carbonate (for whatever reason!), why would one expect the atom proportions to be calculated correctly?
Hi Andrew,
I again return to this plot of analytical totals versus Ca concentration you posted earlier. With some additional annotations.
(https://smf.probesoftware.com/gallery/1_27_07_19_3_14_34.png)
I'm probably missing something, so please correct me if you see something, but it seems to me that when making a measurement of CaCO3, why would one expect to obtain the exactly correct stoichiometry for CO2, when the Ca measurement is not exactly correct?
We already know the code calculates the correct CO2 when the correct Ca is provided (relative to the standard of course). So if the measured Ca concentration is different than the expected Ca, the matrix correction will be different and the concentration of stoichiometric carbon, based on the calculated oxygen, which is itself based on the measured Ca content, will also be different.
Am I making any sense?
In fact I think the answer is laying right in front of our noses. In Reply#86 look at the ZCOR values for Ca Ka for the standard CaCO3, the slightly high total CaCO3 and the slightly low total CaCO3. I summarize them here:
ZCOR: 1.0567 --- --- <--- close to 100% total
ZCOR: 1.0568 --- --- <--- slightly high total
ZCOR: 1.0566 --- --- <--- slightly low total
In short, different Ca concentrations are calculated for each different case, meaning that different amounts of stoichiometric oxygen are calculated for each composition, and hence different amounts of carbon are calculated for each composition. Only when the correct Ca is measured, does the correct stoichiometric oxygen get calculated, and subsequently only then does the correct carbon by stoichiometry to oxygen get calculated.
What do you think?
Quote from: John Donovan on July 27, 2019, 11:55:34 AM
Hi Andrew,
I again return to this plot of analytical totals versus Ca concentration you posted earlier. With some additional annotations.
(https://smf.probesoftware.com/gallery/1_27_07_19_3_14_34.png)
I'm probably missing something, so please correct me if you see something, but it seems to me that when making a measurement of CaCO3, why would one expect to obtain the exactly correct stoichiometry for CO2, when the Ca measurement is not exactly correct?
We already know the code calculates the correct CO2 when the correct Ca is provided (relative to the standard of course). So if the measured Ca concentration is different than the expected Ca, the matrix correction will be different and the concentration of stoichiometric carbon, based on the calculated oxygen, which is itself based on the measured Ca content, will also be different.
Am I making any sense?
In fact I think the answer is laying right in front of our noses. In Reply#86 look at the ZCOR values for Ca Ka for the standard CaCO3, the slightly high total CaCO3 and the slightly low total CaCO3. I summarize them here:
ZCOR: 1.0567 --- --- <--- close to 100% total
ZCOR: 1.0568 --- --- <--- slightly high total
ZCOR: 1.0566 --- --- <--- slightly low total
In short, different Ca concentrations are calculated for each different case, meaning that different amounts of stoichiometric oxygen are calculated for each composition, and hence different amounts of carbon are calculated for each composition. Only when the correct Ca is measured, does the correct stoichiometric oxygen get calculated, and subsequently only then does the correct carbon by stoichiometry to oxygen get calculated.
What do you think?
Hi John,
Let us look at how Probe-for-EPMA handles a binary oxide, MgO, in comparison to a simple carbonate, siderite (Fe,Mn)CO3.
In the case of MgO, I measured the Mg K-alpha intensity for 20 points, and for the usual reasons, we have uncertainty in the results. The Mg concentrations range from 60.05 to 60.65 wt%, and the analytical totals from about 99.6 to 100.6 wt%.
However, regardless of this analytical uncertainty, for every point, Probe-for-EPMA reports oxygen-by-stoichiometry
in the ideal ratio of 1:1 (with rounding in the fifth decimal place):
(https://smf.probesoftware.com/gallery/406_29_07_19_9_31_50.jpeg)
In the case of siderite, I measured the Fe K-alpha and Mn K-alpha intensities for 40 points, and for the usual reasons, we have uncertainty in the results (but beam damage was not an issue). The (Fe+Mn) concentrations range from 47.9 to 48.6 wt%, and the analytical totals from Probe-for-EPMA are reported between 99.7 and 100.4 wt%.
However, Probe-for-EPMA reports CO2-by-stoichiometry
as a function of concentration!(https://smf.probesoftware.com/gallery/406_29_07_19_10_41_00.jpeg)
Only when the concentration is extremely close to 100.00 wt% is the correct, stoichiometric, amount of CO2 reported.
So, in the case of MgO, regardless of analytical uncertainty, the stoichiometric ratio of 1:1 Mg:O is maintained.
But in the case of a carbonate, such as calcite CaCO3 or siderite (Fe,Mn)CO3, stoichiometry is
not maintained.
Rather, the proportion of CO2 reported by Probe-for-EPMA is a function of concentration.
To follow up on your above post:
"In short, different Ca concentrations are calculated for each different case, meaning that different amounts of stoichiometric oxygen are calculated for each composition, and hence different amounts of carbon are calculated for each composition. Only when the correct Ca is measured, does the correct stoichiometric oxygen get calculated, and subsequently only then does the correct carbon by stoichiometry to oxygen get calculated." Yes, in Probe-for-EPMA, different amounts of Ca result in different amounts of C and O being calculated.
Unfortunately, they are
not calculated in the stoichiometric ratio for CaCO3 where Ca : C : O should be 1:1:3.
The question is why do we see this behaviour?
We need to look into the matrix correction code more closely.
Best regards,
Andrew
Hi Andrew,
I do appreciate what you are saying, but am not seeing a problem with the code.
Here is the calculation for stoichiometric oxygen:
' Calculate amount of stoichiometric oxygen and add to total
r1!(zaf.in0%) = 0#
For i% = 1 To zaf.in1%
r1!(zaf.in0%) = r1!(zaf.in0%) + r1!(i%) * zaf.p1!(i%)
Next i%
zaf.ksum! = zaf.ksum! + r1!(zaf.in0%)
Immediately prior to this in the ZAFSmp code is the calculation for an element relative to stoichiometric oxygen:
For i% = 1 To zaf.in1%
If zaf.il%(i%) = 15 Then
r1!(i%) = (r1!(zaf.in0%) / zaf.atwts!(zaf.in0%)) * sample(1).StoichiometryRatio! * zaf.atwts!(i%)
zaf.ksum! = zaf.ksum! + r1!(i%)
zaf.krat!(i%) = r1!(i%)
End If
Next i%
My point is that if the total is low, then an incorrect amount of Ca is calculated (relative to the standard), hence an incorrect amount of stoichiometric oxygen is calculated, and then there is no reason to expect the correct amount of carbon would be calculated. Again *relative to the standard*. That is the sample Ca concentration will be distorted relative to the standard Ca concentration by the apparent difference in the matrix corrections for the estimated Ca concentrations relative to the standard containing Ca.
Quote from: John Donovan on July 29, 2019, 11:50:17 AM
Hi Andrew,
I do appreciate what you are saying, but am not seeing a problem with the code.
Here is the calculation for stoichiometric oxygen:
' Calculate amount of stoichiometric oxygen and add to total
r1!(zaf.in0%) = 0#
For i% = 1 To zaf.in1%
r1!(zaf.in0%) = r1!(zaf.in0%) + r1!(i%) * zaf.p1!(i%)
Next i%
zaf.ksum! = zaf.ksum! + r1!(zaf.in0%)
Immediately prior to this in the ZAFSmp code is the calculation for an element relative to stoichiometric oxygen:
For i% = 1 To zaf.in1%
If zaf.il%(i%) = 15 Then
r1!(i%) = (r1!(zaf.in0%) / zaf.atwts!(zaf.in0%)) * sample(1).StoichiometryRatio! * zaf.atwts!(i%)
zaf.ksum! = zaf.ksum! + r1!(i%)
zaf.krat!(i%) = r1!(i%)
End If
Next i%
My point is that if the total is low, then an incorrect amount of Ca is calculated (relative to the standard), hence an incorrect amount of stoichiometric oxygen is calculated, and then there is no reason to expect the correct amount of carbon would be calculated. Again *relative to the standard*. That is the sample Ca concentration will be distorted relative to the standard Ca concentration by the apparent difference in the matrix corrections for the estimated Ca concentrations relative to the standard containing Ca[/size].
Hi John,
The problem arises in the atomic (molar) ratio of the elements to each other.
In MgO, the ideal 1:1 ratio is maintained throughout the iterative matrix corrections.
However, in the carbonates, the ratios of C and O to the cation(s) diverge from ideal, as a function of concentration.
Perhaps the key is in the word "iterative".
Although the matrix corrections might
start with the ideal ratios of C to O to cations, they do not
end that way.
(Except when the analysis is fortuitously close to 100%).
The fact that the divergence is
linear as a function of composition should be a clue to what is going on.
Cheers,
Andrew
Hi Andrew,
I see that and I suspect it's because we have essentially a non physical situation when the total is not close to 100%.
I increased the iteration tolerance to 100 times more precision but I still get the same results. Here is the calculation of a line with high totals with some intermediate results output to the log window:
ZAFSmp: Iteration #1
Norm Wt% ca ka c (15) o (14) o (0)UnNorm Sum
UNKRAT: .3804 .0000 .0000
Conc*100 71.4693 .000000 .000000 28.5307 55.360
ZAFSmp: Iteration #2
Norm Wt% ca ka c (15) o (14) o (0)UnNorm Sum
UNKRAT: .3804 .0714 .0000
Conc*100 48.3182 8.84037 .000000 42.8414 80.749
ZAFSmp: Iteration #3
Norm Wt% ca ka c (15) o (14) o (0)UnNorm Sum
UNKRAT: .3804 .1072 .0000
Conc*100 41.9457 11.2737 .000000 46.7806 95.080
ZAFSmp: Iteration #4
Norm Wt% ca ka c (15) o (14) o (0)UnNorm Sum
UNKRAT: .3804 .1170 .0000
Conc*100 40.5185 11.8187 .000000 47.6628 99.035
ZAFSmp: Iteration #5
Norm Wt% ca ka c (15) o (14) o (0)UnNorm Sum
UNKRAT: .3804 .1193 .0000
Conc*100 40.2145 11.9348 .000000 47.8507 99.921
ZAFSmp: Iteration #6
Norm Wt% ca ka c (15) o (14) o (0)UnNorm Sum
UNKRAT: .3804 .1197 .0000
Conc*100 40.1504 11.9593 .000000 47.8903 100.110
ZAFSmp: Iteration #7
Norm Wt% ca ka c (15) o (14) o (0)UnNorm Sum
UNKRAT: .3804 .1198 .0000
Conc*100 40.1369 11.9644 .000000 47.8986 100.150
Un 4 CaCO3
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 30.0 Beam Size = 0
(Magnification (analytical) = 4000), Beam Mode = Analog Spot
(Magnification (default) = 200, Magnification (imaging) = 100)
Image Shift (X,Y): -2.00, 3.00
Formula Based on 1.00 Atoms of Ca Oxygen Calc. by Stoichiometry
Number of Data Lines: 2 Number of 'Good' Data Lines: 1
First/Last Date-Time: 07/26/2019 10:30:56 AM to 07/26/2019 10:31:33 AM
Average Total Oxygen: 47.970 Average Total Weight%: 100.150
Average Calculated Oxygen: 47.970 Average Atomic Number: 12.577
Average Excess Oxygen: .000 Average Atomic Weight: 20.035
Average ZAF Iteration: 7.00 Average Quant Iterate: 2.00
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element C is Calculated .3333 Atoms Relative To 1.0 Atom of Oxygen
Un 4 CaCO3, Results in Elemental Weight Percents
ELEM: Ca C O
TYPE: ANAL STOI CALC
BGDS: LIN
TIME: 10.00 --- ---
BEAM: 30.00 --- ---
ELEM: Ca C O SUM
10 40.197 11.982 47.970 100.150
AVER: 40.197 11.982 47.970 100.150
SDEV: .000 .000 .000 .000
SERR: .000 .000 .000
%RSD: .00 .00 .00
STDS: 136 --- ---
STKF: .3790 --- ---
STCT: 128.00 --- ---
UNKF: .3804 --- ---
UNCT: 128.51 --- ---
UNBG: .16 --- ---
ZCOR: 1.0566 --- ---
KRAW: 1.0039 --- ---
PKBG: 822.90 --- ---
Un 4 CaCO3, Results Based on 1 Atoms of ca
ELEM: Ca C O SUM
10 1.000 .995 2.989 4.984
AVER: 1.000 .995 2.989 4.984
SDEV: .000 .000 .000 .000
SERR: .000 .000 .000
%RSD: .00 .00 .00
If you have any specific suggestions I'm all ears. But I don't think one can get a perfect result with imperfect data.
Quote from: John Donovan on July 29, 2019, 12:48:41 PM
Hi Andrew,
I see that and I suspect it's because we have essentially a non physical situation when the total is not close to 100%.
I increased the iteration tolerance to 100 times more precision but I still get the same results.
....
If you have any specific suggestions I'm all ears. But I don't think one can get a perfect result with imperfect data.
Hi John,
As Probe-for-EPMA treats these situations differently (simple oxygen by stoichiometry vs. additional element by stoichiometry to oxygen), and yields what are actually non-stoichiometric values in the latter case, I have a couple of
non-optimal suggestions.
1) For the carbonates discussed, proceed as above with 0.333333 C for every 1 O, in order to get the best available matrix correction.
Then, after the data are output to Excel, discard the CO2 value reported by Probe-for-EPMA.
Recalculate a new atomic value of CO2 based on ideal stoichiometry to the measured elements; recalculate the wt% CO2; recalculate the analytical total.
This is, in fact, my present procedure for carbonates.
2) Change the code in Probe-for-EPMA to do the same thing after the matrix corrections are completed.
That is, discard the CO2 that resulted from the matrix corrections, and recalculate a new value based on the input stoichiometric ratio and the final values of the measured elements.
However, this may be viewed as not straightforward, and possibly even confusing.
Until we understand why the results for simple oxides do not deviate from stoichiometry, whereas those of the carbonates deviate in a linear fashion, it is hard to justify any other recommendations.
All the best,
Andrew
Hi Andrew,
I'll continue to think about this with Paul Carpenter, but I agree these are non-optimal solutions, for the simple reason that they are non-physical.
Quote from: John Donovan on July 29, 2019, 01:44:25 PM
Hi Andrew,
I'll continue to think about this with Paul Carpenter, but I agree these are non-optimal solutions, for the simple reason that they are non-physical.
Hi John,
My preference is to report stoichiometric proportions for calculated elements.
Calcite should be CaCO3, not Ca C0.995 O2.989.
The latter formula is an artifact of imperfect data, and therefore imperfect matrix corrections.
We
know that there is a problem in the matrix corrections for elements calculated by stoichiometry to oxygen.
If we could treat "CO3" in the same way that we treat "O" in the matrix corrections, we would not have this divergence.
However, C and O are different, so this is not an option (differing backscatter, absorption, fluorescence).
This topic has implications for all of the options in Probe-for-EPMA with respect to elements by difference, elements by stoichiometry to another element, and elements by stoichiometry to oxygen.
That said, I must
emphasize that these very powerful options are still the best way to get superior quality data for such compounds.
Cheers,
Andrew
Quote from: AndrewLocock on July 29, 2019, 02:44:59 PM
We know that there is a problem in the matrix corrections for elements calculated by stoichiometry to oxygen.
Hi Andrew,
But only when an unknown sample is imperfectly measured with respect to an "assumed" perfect standard!
If both your standard and your unknowns had low totals (or both had high totals), you would get an "ideal" stoichiometry for your unknown. That's physics for you. :)
And let's please keep in mind that this non-stoichiometry effect is generally smaller than our nominal 2% accuracy in EPMA. And also that if it's random counting statistics causing this non-stoichiometry, then the analytical averages will be stoichiometric, if the average analytical total is close to 100% (or whatever our Ca standard is supposed to be).
Quote from: John Donovan on July 29, 2019, 03:10:37 PM
Quote from: AndrewLocock on July 29, 2019, 02:44:59 PM
We know that there is a problem in the matrix corrections for elements calculated by stoichiometry to oxygen.
Hi Andrew,
But only when an unknown sample is imperfectly measured with respect to an "assumed" perfect standard!
If both your standard and your unknowns had low totals (or both had high totals), you would get an "ideal" stoichiometry for your unknown. That's physics for you.
And let's please keep in mind that this non-stoichiometry effect is generally smaller than our nominal 2% accuracy in EPMA. And also that if it's random counting statistics causing this non-stoichiometry, then the analytical averages will be stoichiometric, if the average is close to 100%.
Hi John,
There are several reasons why this issue is problematic.
1) It occurs in analyses where an element is specified by stoichiometric ratio to oxygen, but NOT in simple oxides for which oxygen is the only calculated element.
2) The lack of stoichiometry shows a perfect linear correlation with concentrations and thus with analytical totals, whether high or low.
3) The lack of stoichiometry could conceivably mask other, real, problems with the analysis (such as the extent of beam damage). Because of the negative correlation of reported CO2 vs. CaO, the range of analytical totals is artificially minimized by this problem in analyses of calcite.
4) Most seriously, the inattentive user might actually try to publish Ca C0.995 O2.989 as a result for calcite - it is simply not correct.
All measurements are imperfect to some extent, and whether the standard is ideal or not, stoichiometric relationships should hold, unless invalidated by real data (e.g., end-member wustite).
This issue is a good reminder to users of the data to carefully check their results.
All the best,
Andrew
Hi Andrew,
I don't disagree. I'll work on this with Paul Carpenter/John Armstrong and get back to you. In the meantime feel free to look at the code yourself and see if you can see what might be going on. There's a reason the physics code is hosted on GitHub. This code is a community effort after all. :)
Quote from: John Donovan on July 29, 2019, 03:44:53 PM
Hi Andrew,
I don't disagree. I'll work on this with Paul Carpenter/John Armstrong and get back to you. In the meantime feel free to look at the code yourself and see if you can see what might be going on. There's a reason the physics code is hosted on GitHub. This code is a community effort after all. :)
Good news.
Andrew, Paul and I are in contact with John Armstrong and he explains the problem as being a well known (at the time!) issue, which occurs whenever an *unanalyzed* element is being calculated relative to calculated (unanalyzed) oxygen. He put it this way to us: oxygen calculated by stoichiometry is no problem when all other elements are measured. But when another unanalyzed element is introduced and this element is also dependent on the (also) unanalyzed oxygen, the solution is not obvious.
The basic issue being, what oxygen concentration should be utilized for the element relative to total oxygen? The oxygen value used in the last iteration for calculating correction factors is one possibility, and there's also the oxygen value adjusted for the other unanalyzed element...
There were several different methods proposed by various researchers at the time, but no one solution gave a perfect result. In fact all the proposed methods gave good results when the analytical totals were close to 100%, but they also gave increasingly different results as the analytical totals (including the unanalyzed elements) diverged from 100%.
John Armstrong said he would review the code to remember which method he chose at the time, but whatever method was chosen, there may not be a perfect solution to this issue.
Hi John,
Thanks very much for following this up.
I appreciate your efforts, and look forward to any progress, although the issue may prove intractable.
I imagine that some sort of caveat would then be added to Probe for EPMA to ensure that the users are aware of the issue.
I should add, naturally, that all matrix-reduction software that can handle "elements specified by stoichiometry" will be subject to this issue.
One of the many things that I appreciate about Probe for EPMA is the willingness to examine issues in detail.
And of course the many powerful data reduction options.
All the best,
Andrew
During this interesting (and subtle) discussion on carbon stoichiometry to unanalyzed oxygen, I think it is important to not overlook some other benefits to including elements that are not analyzed, into the matrix correction. That is after all, the main purpose of this topic (Specifying Unanalyzed Elements For a Proper Matrix Correction).
In the case of our ideal CaCO3 composition, what is the matrix effect of not including carbon in the matrix correction? Good question! I'm glad I asked! :) Here is the same CaCO3 discussed previously but *without* specifying carbon relative to the calculated oxygen:
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Un 2 CaCO3, Results in Elemental Weight Percents
ELEM: Ca C O SUM
2 38.764 .000 15.475 54.239
AVER: 38.764 .000 15.475 54.239
SDEV: .000 .000 .000 .000
SERR: .000 .000 .000
%RSD: .00 .00 .00
STDS: 136 --- ---
STKF: .3790 --- ---
STCT: 128.65 --- ---
UNKF: .3780 --- ---
UNCT: 128.32 --- ---
UNBG: .18 --- ---
ZCOR: 1.0255 --- ---
KRAW: .9975 --- ---
PKBG: 704.69 --- ---
Un 2 CaCO3, Results Based on 1 Atoms of ca
ELEM: Ca C O SUM
2 1.000 .000 1.000 2.000
AVER: 1.000 .000 1.000 2.000
SDEV: .000 .000 .000 .000
SERR: .000 .000 .000
%RSD: .00 .00 .00
Well clearly the analytical total is crap, and of course the atomic ratios are completely bonkers, but note the concentration of Ca. We are getting around 38.7 wt% Ca, when the ideal Ca content should be around 40 wt%. That a pretty large error, and is completely due to the fact that when carbon is not included in the matrix correction, the correction for Ca Ka is not going to be accurate.
Now let's turn the carbon relative to calculated oxygen calculation back on:
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element C is Calculated .3333 Atoms Relative To 1.0 Atom of Oxygen
Un 2 CaCO3, Results in Elemental Weight Percents
ELEM: Ca C O SUM
2 39.943 12.005 47.928 99.876
AVER: 39.943 12.005 47.928 99.876
SDEV: .000 .000 .000 .000
SERR: .000 .000 .000
%RSD: .00 .00 .00
STDS: 136 --- ---
STKF: .3790 --- ---
STCT: 128.65 --- ---
UNKF: .3780 --- ---
UNCT: 128.32 --- ---
UNBG: .18 --- ---
ZCOR: 1.0567 --- ---
KRAW: .9975 --- ---
PKBG: 704.69 --- ---
Un 2 CaCO3, Results Based on 1 Atoms of ca
ELEM: Ca C O SUM
2 1.000 1.003 3.006 5.009
AVER: 1.000 1.003 3.006 5.009
SDEV: .000 .000 .000 .000
SERR: .000 .000 .000
%RSD: .00 .00 .00
Now our analytical total is much better, and of course our stoichiometry pretty good as well, but even more importantly, our Ca wt% is now 39.94 wt%, very close to the ideal 40 wt%.
Again, this is exactly why we need to include these unanalyzed elements into our physics matrix corrections.
And now for something (almost) completely different! :D
This is a different situation involving (only) the calculation of stoichiometric (unanalyzed) oxygen in the matrix correction. In this example we have compositions in which one or more halogens replace some of the stoichiometric oxygen sites. This can occur primarily chlor-apatites and fluor-phlogopites, though I'm sure there are cases with other minerals (and glasses) with similar halogen replacement situations (oxygen equivalence).
If you've been following the recent (quite long) discussion involving calculating carbon in carbonates as an unanalyzed element relative to calculated stoichiometric oxygen, you might have seen this code snippet:
' Calculate element relative to stoichiometric oxygen based on previous iteration calculation of oxygen
If zaf.il%(zaf.in0%) = 0 Then ' if calculating oxygen by stoichiometry
For i% = 1 To zaf.in1%
If zaf.il%(i%) = 15 Then
r1!(i%) = (r1!(zaf.in0%) / zaf.atwts!(zaf.in0%)) * sample(1).StoichiometryRatio! * zaf.atwts!(i%)
zaf.ksum! = zaf.ksum! + r1!(i%)
zaf.krat!(i%) = r1!(i%)
End If
Next i%
' Calculate amount of stoichiometric oxygen and add to total
r1!(zaf.in0%) = 0#
For i% = 1 To zaf.in1%
r1!(zaf.in0%) = r1!(zaf.in0%) + r1!(i%) * zaf.p1!(i%)
Next i%
' Calculate equivalent oxygen from halogens and subtract from calculated oxygen if flagged
If UseOxygenFromHalogensCorrectionFlag Then r1!(zaf.in0%) = r1!(zaf.in0%) - ConvertHalogensToOxygen(zaf.in1%, sample(1).Elsyms$(), sample(1).DisableQuantFlag%(), r1!())
' Add to sum
zaf.ksum! = zaf.ksum! + r1!(zaf.in0%)
End If
Note the line of code to calculate the halogen effect on stoichiometric oxygen. This is where a correction for halogens (F, Cl, Br and I) replacing stoichiometric oxygen is made. The idea being that if one calculates stoichiometric oxygen as usual, the total will be too high because the halogen is replacing some of the stoichiometric oxygen. So how much of an effect could this be on the matrix? And why do we care?
Well the effect depends on the composition of the mineral and the particular emitting line in question. And we should care because sometimes the matrix effect of *subtracting* this replaced stoiciometric oxygen is large enough to significantly effect the results.
So here is an example involving chlor-apatite, where the halogen correction has *not* been applied:
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Oxygen Equivalent from Halogens (F/Cl/Br/I), Not Subtracted in the Matrix Correction
Un 5 Cl-apatite as unk, Results in Elemental Weight Percents
ELEM: Si F Cl Mg Ca P Al K O SUM
429 .022 -.545 6.825 .035 38.442 17.751 .006 .000 38.323 100.858
430 .010 -.193 6.868 .028 38.363 17.816 .001 .003 38.354 101.251
431 .015 .173 6.766 .045 38.087 17.885 -.001 -.009 38.346 101.308
432 .026 .123 6.706 .032 38.319 17.901 .004 -.018 38.465 101.557
433 .010 .117 6.890 .022 38.150 17.715 -.003 .011 38.133 101.046
AVER: .017 -.065 6.811 .032 38.272 17.814 .002 -.002 38.324 101.204
SDEV: .007 .305 .075 .009 .149 .081 .004 .011 .120 .266
SERR: .003 .136 .034 .004 .067 .036 .002 .005 .054
%RSD: 41.59 -468.63 1.11 26.47 .39 .46 216.37 -452.12 .31
STDS: 160 284 285 12 285 285 160 374 ---
STKF: .1621 .0256 .0602 .4736 .3596 .1601 .0335 .1132 ---
STCT: 1746.9 73.2 2281.7 18768.4 8605.4 3444.2 5316.8 1646.9 ---
UNKF: .0001 -.0001 .0602 .0002 .3575 .1596 .0000 .0000 ---
UNCT: 1.6 -.4 2281.6 8.3 8554.2 3433.5 1.9 -.4 ---
UNBG: 2.7 4.9 17.5 19.2 33.9 7.1 96.3 10.8 ---
ZCOR: 1.1443 5.1792 1.1305 1.5496 1.0706 1.1163 1.3347 1.0079 ---
KRAW: .0009 -.0049 1.0000 .0004 .9940 .9969 .0004 -.0002 ---
PKBG: 1.60 .93 132.03 1.43 253.74 490.50 1.02 .98 ---
INT%: ---- -102.12 ---- ---- ---- ---- ---- ---- ---
As you can see the totals are slightly high because the oxygen has been calculated based on the cations, without consideration of the chlorine oxygen equivalence. In fact for ideal chlor-apatite, the oxygen concentration should be around 36.8 wt%. Now here is the same sample, but with the halogen correction turned on:
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Oxygen Equivalent from Halogens (F/Cl/Br/I), Subtracted in the Matrix Correction
Un 5 Cl-apatite as unk, Results in Elemental Weight Percents
ELEM: Si F Cl Mg Ca P Al K O SUM
429 .022 -.539 6.823 .035 38.429 17.731 .006 .000 36.979 99.486
430 .010 -.187 6.866 .028 38.349 17.794 .001 .003 36.849 99.713
431 .015 .177 6.764 .045 38.071 17.861 -.001 -.009 36.708 99.632
432 .026 .128 6.704 .032 38.304 17.877 .004 -.018 36.861 99.917
433 .010 .122 6.888 .022 38.134 17.691 -.003 .011 36.489 99.365
AVER: .017 -.060 6.809 .032 38.257 17.791 .002 -.002 36.777 99.623
SDEV: .007 .304 .075 .009 .150 .081 .004 .011 .188 .212
SERR: .003 .136 .034 .004 .067 .036 .002 .005 .084
%RSD: 41.59 -509.17 1.11 26.47 .39 .45 216.35 -452.09 .51
STDS: 160 284 285 12 285 285 160 374 ---
STKF: .1621 .0256 .0602 .4736 .3596 .1601 .0335 .1132 ---
STCT: 1746.9 73.2 2281.7 18768.4 8605.4 3444.2 5316.8 1646.9 ---
UNKF: .0001 -.0001 .0602 .0002 .3575 .1596 .0000 .0000 ---
UNCT: 1.6 -.3 2281.6 8.3 8554.2 3433.5 1.9 -.4 ---
UNBG: 2.7 4.9 17.5 19.2 33.9 7.1 96.3 10.8 ---
ZCOR: 1.1424 5.1608 1.1302 1.5466 1.0701 1.1149 1.3325 1.0070 ---
KRAW: .0009 -.0045 1.0000 .0004 .9940 .9969 .0004 -.0002 ---
PKBG: 1.60 .94 132.03 1.43 253.74 490.50 1.02 .98 ---
INT%: ---- -101.99 ---- ---- ---- ---- ---- ---- ---
The calculated oxygen is now 36.77 wt%, which is much closer to the ideal 36.8 wt%. The concentrations of the other elements have also decreased slightly, due to the change in the matrix correction from there being less oxygen than before. And the total is somewhat better, but not a big change in any case.
Now let's next consider fluor-phlogopite...
Continuing our discussion, now what about fluor-phlogopite? We might expect a larger matrix effect for fluorine because it is a lower energy emission line, and also because it is quite heavily absorbed by oxygen in the matrix. So here is an analysis of a fluor-phlogopite *without* the halogen correction:
Un 10 fluor-phlogopite, Results in Elemental Weight Percents
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Oxygen Equivalent from Halogens (F/Cl/Br/I), Not Subtracted in the Matrix Correction
ELEM: Si F Cl Mg Ca P Al K O SUM
495 19.822 9.091 .008 17.459 -.002 -.006 6.612 9.393 41.872 104.250
496 19.990 9.254 .001 17.359 .001 .001 6.576 9.369 41.971 104.521
497 19.814 9.112 .000 17.298 .002 .000 6.604 9.420 41.764 104.014
498 20.136 9.783 .002 17.534 .005 -.004 6.645 9.384 42.312 105.797
499 20.246 9.633 .006 17.372 .006 -.007 6.600 9.305 42.272 105.432
AVER: 20.002 9.375 .003 17.404 .002 -.003 6.608 9.374 42.038 104.803
SDEV: .191 .315 .003 .093 .003 .004 .025 .043 .243 .773
SERR: .085 .141 .002 .041 .001 .002 .011 .019 .109
%RSD: .95 3.36 100.14 .53 130.45 -112.21 .38 .46 .58
STDS: 160 284 285 12 285 285 160 374 ---
STKF: .1621 .0256 .0602 .4736 .3596 .1601 .0335 .1132 ---
STCT: 1749.1 72.8 2270.1 18778.0 8626.5 3449.1 5319.3 1650.6 ---
UNKF: .1501 .0260 .0000 .1230 .0000 .0000 .0446 .0827 ---
UNCT: 1619.3 73.8 1.1 4877.0 .5 -.5 7086.9 1205.7 ---
UNBG: 4.2 4.3 11.1 20.7 17.9 3.5 82.2 9.7 ---
ZCOR: 1.3328 3.6125 1.2142 1.4150 1.1176 1.4038 1.4819 1.1339 ---
KRAW: .9258 1.0143 .0005 .2597 .0001 -.0001 1.3323 .7304 ---
PKBG: 392.05 18.49 1.10 237.07 1.03 .87 87.21 125.86 ---
INT%: ---- .00 ---- ---- ---- ---- ---- ---- ---
First of all we notice the rather high total due to the full stoichiometric oxygen complement being added to the matrix without considering that the fluorine is replacing some of that oxygen. In addition we note that the matrix correction (ZCOR) for fluorine is 3.6125, which is over 360%, so a rather large matrix effect. Meanwhile the ideal fluorine concentration is calculated as being around 9 wt%, while we are getting almost 9.4 wt%.
So now we turn on the halogen correction from the Analytical | Analysis Options dialog as seen here:
(https://smf.probesoftware.com/gallery/395_31_07_19_10_22_11.png)
and now we see the halogen corrected composition for this fluor-phlogopite:
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Oxygen Equivalent from Halogens (F/Cl/Br/I), Subtracted in the Matrix Correction
Un 10 fluor-phlogopite, Results in Elemental Weight Percents
ELEM: Si F Cl Mg Ca P Al K O SUM
495 19.842 8.873 .008 17.303 -.002 -.006 6.604 9.397 38.047 100.064
496 20.009 9.028 .001 17.201 .001 .001 6.568 9.373 38.080 100.261
497 19.833 8.892 .000 17.143 .002 .000 6.596 9.424 37.932 99.821
498 20.157 9.533 .002 17.368 .005 -.004 6.637 9.388 38.205 101.290
499 20.267 9.391 .006 17.208 .006 -.007 6.592 9.309 38.224 100.995
AVER: 20.021 9.143 .003 17.244 .002 -.003 6.599 9.378 38.098 100.486
SDEV: .191 .301 .003 .090 .003 .004 .025 .043 .120 .628
SERR: .086 .135 .002 .040 .001 .002 .011 .019 .054
%RSD: .96 3.29 100.14 .52 130.45 -112.21 .38 .46 .32
STDS: 160 284 285 12 285 285 160 374 ---
STKF: .1621 .0256 .0602 .4736 .3596 .1601 .0335 .1132 ---
STCT: 1749.1 72.8 2270.1 18778.0 8626.5 3449.1 5319.3 1650.6 ---
UNKF: .1501 .0260 .0000 .1230 .0000 .0000 .0446 .0827 ---
UNCT: 1619.3 73.8 1.1 4877.0 .5 -.5 7086.9 1205.7 ---
UNBG: 4.2 4.3 11.1 20.7 17.9 3.5 82.2 9.7 ---
ZCOR: 1.3341 3.5235 1.2166 1.4020 1.1185 1.4112 1.4800 1.1343 ---
KRAW: .9258 1.0143 .0005 .2597 .0001 -.0001 1.3323 .7304 ---
PKBG: 392.05 18.49 1.10 237.07 1.03 .87 87.21 125.86 ---
INT%: ---- .00 ---- ---- ---- ---- ---- ---- ---
The totals are now more reasonable, but even more importantly note that the fluorine ZCOR decreased to 3.5235 and the measured fluorine concentration dropped to ~9.1 wt%, which is much closer to the published value. Basically, in fluor-phlogopite compositions, ones reported fluorine concentrations will be high by around 2 or 3% when this halogen correction to the stoichiometric oxygen is not properly performed.
It is probably obvious, but maybe worth saying again, that this sort of calculation cannot be performed off-line (e.g., in Excel), because the matrix correction needs to be re-calculated based on the new composition and re-applied to the measured intensities.
I haven't explored other halogen containing compositions, but is anyone interested in writing this effect up as a short paper or abstract?
Just FYI, we're just putting the finishing touches on a ferrous/ferric calculation for PFE (and CalcZAF!) that will calculate excess oxygen from ferric iron for minerals using the method of Droop (1987) *and* include it in the matrix correction. This excess oxygen has a surprisingly large effect on the matrix correction physics, even for minerals such as ilmenite/magnetite. I'm just posting this here so we'll have a link for the "interactive help" button in the Calculation Options dialog.
We hope to have a new version of both PFE and CalcZAF uploaded tonight or tomorrow, but first we want to give a big thanks to Andrew Locock, Anette von der Handt, John Fournelle and Emma Bullock, who provided the mineralogical expertise to allow us to implement this.
More details to follow soon but in the meantime the original paper by Droop is attached below
OK, now on to Probe for EPMA. We think the implementation of the ferrous/ferric calculation (from Droop, 1987) is pretty good, but please download the latest version (12.7.1) and let us know what you think. The CalcZAF implementation is described here:
https://smf.probesoftware.com/index.php?topic=691.msg8592#msg8592
So let's take an example of hematite. Calculating all iron as FeO we get these results:
Un 3 Hematite, Results in Elemental Weight Percents
ELEM: Fe O
TYPE: ANAL CALC
BGDS: LIN
TIME: 10.00 ---
BEAM: 30.00 ---
ELEM: Fe O SUM
29 68.992 19.766 88.758
30 69.126 19.805 88.931
31 68.758 19.699 88.457
AVER: 68.959 19.757 88.715
SDEV: .186 .053 .240
SERR: .108 .031
%RSD: .27 .27
STDS: 39 ---
STKF: .6810 ---
STCT: 228.06 ---
UNKF: .6566 ---
UNCT: 219.89 ---
UNBG: .48 ---
ZCOR: 1.0503 ---
KRAW: .9642 ---
PKBG: 456.58 ---
Un 3 Hematite, Results in Oxide Weight Percents
ELEM: FeO O SUM
29 88.758 .000 88.758
30 88.931 .000 88.931
31 88.457 .000 88.457
AVER: 88.715 .000 88.715
SDEV: .240 .000 .240
SERR: .138 .000
%RSD: .27 -91.65
STDS: 39 ---
Note the low totals (~88%) due to the missing ferric oxygen. Now we specify the ferrous/ferric calculation and the mineral cations and oxygen (2 and 3 respectively for hematites) as seen here:
(https://smf.probesoftware.com/gallery/1_19_08_19_4_07_00.png)
and re-calculating we now obtain these results:
Un 3 Hematite, Results in Elemental Weight Percents
ELEM: Fe O
TYPE: ANAL CALC
BGDS: LIN
TIME: 10.00 ---
BEAM: 30.00 ---
ELEM: Fe O SUM
29 70.168 30.155 100.323
30 70.305 30.213 100.518
31 69.930 30.052 99.982
AVER: 70.134 30.140 100.274
SDEV: .190 .081 .271
SERR: .109 .047
%RSD: .27 .27
STDS: 39 ---
STKF: .6810 ---
STCT: 228.06 ---
UNKF: .6566 ---
UNCT: 219.89 ---
UNBG: .48 ---
ZCOR: 1.0682 ---
KRAW: .9642 ---
PKBG: 456.58 ---
Ferrous/Ferric Calculation Results:
Ferric/TotalFe FeO Fe2O3 Oxygen from Fe2O3
29 1.000 .000 100.323 10.052
30 1.000 .000 100.518 10.071
31 1.000 .000 99.982 10.017
AVER: 1.000 .000 100.274 10.047
Un 3 Hematite, Results in Oxide Weight Percents
ELEM: FeO O SUM
29 90.271 10.052 100.323
30 90.447 10.071 100.518
31 89.965 10.017 99.982
AVER: 90.228 10.047 100.274
SDEV: .244 .027 .271
SERR: .141 .016
%RSD: .27 .27
STDS: 39 ---
Our totals are now much better but because we included this excess oxygen in the matrix correction as suggested by Brian Joy, even more impressive is that our Fe went from 68.959 to 70.134 wt%!
We also added this ferrous/ferric output to the User Specified Output options as seen here:
(https://smf.probesoftware.com/gallery/1_19_08_19_4_07_30.png)
so now these results can be output to Excel as usual:
(https://smf.probesoftware.com/gallery/1_19_08_19_4_07_57.png)
Here's a "real world" example of a titanium magnetite with the ferrous/ferric excess oxygen calculation in Probe for EPMA using the method of Droop (1987) to calculate the excess oxygen from ferric iron. This excess oxygen is then added into the matrix correction for improved accuracy. The output below also includes oxides and sum of cations also as specified in the Calculation Options dialog.
Un 30 8400 Mgt Trav In-Out
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 50.0 Beam Size = 0
(Magnification (analytical) = 20000), Beam Mode = Analog Spot
(Magnification (default) = 1000, Magnification (imaging) = 100)
Image Shift (X,Y): -2.00, 3.00
Formula Based on Sum of Cations = 3.00 Oxygen Calc. by Stoichiometry
Number of Data Lines: 6 Number of 'Good' Data Lines: 6
First/Last Date-Time: 07/23/2019 02:12:20 PM to 07/23/2019 02:29:56 PM
Average Total Oxygen: 28.684 Average Total Weight%: 100.294
Average Calculated Oxygen: 28.684 Average Atomic Number: 20.135
Average Excess Oxygen: .000 Average Atomic Weight: 31.696
Average ZAF Iteration: 3.00 Average Quant Iterate: 4.00
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Excess Oxygen From Ferric Iron Calculated and Included in the Matrix Correction
Charge Balance Method of Droop (1987), Total Cations= 3.00, Total Oxygens= 4.00
Un 30 8400 Mgt Trav In-Out, Results in Elemental Weight Percents
ELEM: Fe Mg Si Ti V Mn Cr Al O
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL CALC
BGDS: MAN MAN MAN MAN LIN LIN MAN MAN
TIME: 40.00 140.00 40.00 80.00 30.00 30.00 88.00 141.00 ---
BEAM: 50.32 50.32 50.32 50.32 50.32 50.32 50.32 50.32 ---
ELEM: Fe Mg Si Ti V Mn Cr Al O SUM
72 60.751 1.862 .019 6.903 .309 .403 .054 1.270 28.664 100.234
73 60.644 1.863 .075 6.872 .333 .407 .059 1.258 28.657 100.170
74 60.946 1.871 .021 6.884 .295 .405 .056 1.255 28.732 100.464
75 60.505 1.856 .028 6.918 .323 .420 .056 1.260 28.584 99.950
76 60.954 1.876 .016 6.951 .335 .422 .043 1.251 28.776 100.623
77 60.805 1.858 .023 6.949 .301 .404 .044 1.249 28.693 100.325
AVER: 60.768 1.864 .030 6.913 .316 .410 .052 1.257 28.684 100.294
SDEV: .175 .008 .022 .032 .017 .008 .007 .008 .066 .235
SERR: .071 .003 .009 .013 .007 .003 .003 .003 .027
%RSD: .29 .41 73.90 .47 5.40 2.06 12.65 .61 .23
STDS: 395 12 14 22 23 25 24 396 ---
STKF: .6779 .4736 .4101 .5547 .6328 .7341 .6400 .0469 ---
STCT: 6812.2 53482.2 7089.5 14540.1 13304.5 22081.3 4697.4 3264.8 ---
UNKF: .5649 .0085 .0002 .0703 .0033 .0038 .0006 .0072 ---
UNCT: 5676.3 964.8 3.7 1841.7 69.6 114.7 4.3 503.0 ---
UNBG: 20.5 79.1 5.5 52.0 25.2 49.5 9.6 48.0 ---
ZCOR: 1.0758 2.1821 1.4034 .9839 .9547 1.0761 .8885 1.7401 ---
KRAW: .8333 .0180 .0005 .1267 .0052 .0052 .0009 .1541 ---
PKBG: 277.35 13.19 1.68 36.42 3.77 3.32 1.45 11.48 ---
INT%: .00 ---- ---- ---- -17.39 -.03 -10.90 .00 ---
Ferrous/Ferric Calculation Results:
Ferric/TotalFe FeO Fe2O3 Oxygen from Fe2O3
72 .458 42.390 39.749 3.983
73 .455 42.482 39.494 3.957
74 .460 42.324 40.100 4.018
75 .456 42.333 39.459 3.954
76 .458 42.468 39.953 4.003
77 .458 42.388 39.828 3.990
AVER: .458 42.397 39.764 3.984
Un 30 8400 Mgt Trav In-Out, Results in Oxide Weight Percents
ELEM: FeO MgO SiO2 TiO2 V2O3 MnO Cr2O3 Al2O3 O SUM
72 78.156 3.087 .041 11.515 .454 .520 .079 2.400 3.983 100.234
73 78.019 3.090 .161 11.464 .491 .526 .086 2.377 3.957 100.170
74 78.407 3.103 .044 11.484 .433 .523 .081 2.371 4.018 100.464
75 77.839 3.078 .059 11.539 .476 .542 .082 2.382 3.954 99.950
76 78.418 3.110 .034 11.594 .492 .545 .063 2.363 4.003 100.623
77 78.225 3.080 .050 11.591 .442 .522 .065 2.359 3.990 100.325
AVER: 78.177 3.091 .065 11.531 .465 .530 .076 2.375 3.984 100.294
SDEV: .225 .013 .048 .054 .025 .011 .010 .015 .025 .235
SERR: .092 .005 .020 .022 .010 .004 .004 .006 .010
%RSD: .29 .41 73.90 .47 5.40 2.06 12.65 .61 .64
STDS: 395 12 14 22 23 25 24 396 ---
Un 30 8400 Mgt Trav In-Out, Results Based on Sum of 3 Cations
ELEM: Fe Mg Si Ti V Mn Cr Al O SUM
72 2.381 .168 .001 .315 .013 .016 .002 .103 3.921 6.921
73 2.377 .168 .006 .314 .014 .016 .002 .102 3.921 6.921
74 2.384 .168 .002 .314 .013 .016 .002 .102 3.922 6.922
75 2.378 .168 .002 .317 .014 .017 .002 .103 3.921 6.921
76 2.380 .168 .001 .316 .014 .017 .002 .101 3.922 6.922
77 2.382 .167 .002 .317 .013 .016 .002 .101 3.923 6.923
AVER: 2.380 .168 .002 .316 .014 .016 .002 .102 3.922 6.922
SDEV: .002 .000 .002 .001 .001 .000 .000 .001 .001 .001
SERR: .001 .000 .001 .001 .000 .000 .000 .000 .000
%RSD: .10 .24 73.96 .46 5.41 2.06 12.76 .74 .02
Note that if we did *not* include the calculation of excess oxygen in the matrix correction our oxides and formula would look like this:
Un 30 8400 Mgt Trav In-Out, Results in Oxide Weight Percents
ELEM: FeO MgO SiO2 TiO2 V2O3 MnO Cr2O3 Al2O3 O SUM
72 77.687 3.107 .037 11.434 .451 .517 .074 2.412 .000 95.718
73 77.554 3.109 .158 11.383 .487 .523 .080 2.388 .000 95.684
74 77.933 3.123 .041 11.402 .430 .520 .076 2.383 .000 95.908
75 77.374 3.098 .056 11.458 .472 .539 .076 2.393 .000 95.467
76 77.946 3.130 .031 11.512 .489 .542 .058 2.375 .000 96.083
77 77.755 3.100 .047 11.509 .439 .519 .059 2.371 .000 95.799
AVER: 77.708 3.111 .062 11.450 .461 .527 .071 2.387 .000 95.776
SDEV: .221 .013 .048 .054 .025 .011 .010 .015 .000 .210
SERR: .090 .005 .020 .022 .010 .004 .004 .006 .000
%RSD: .28 .41 78.00 .47 5.41 2.06 13.52 .61 -167.33
STDS: 395 12 14 22 23 25 24 396 ---
Un 30 8400 Mgt Trav In-Out, Results Based on Sum of 3 Cations
ELEM: Fe Mg Si Ti V Mn Cr Al O SUM
72 2.379 .170 .001 .315 .013 .016 .002 .104 3.376 6.376
73 2.375 .170 .006 .313 .014 .016 .002 .103 3.379 6.379
74 2.382 .170 .002 .313 .013 .016 .002 .103 3.374 6.374
75 2.376 .170 .002 .316 .014 .017 .002 .104 3.378 6.378
76 2.378 .170 .001 .316 .014 .017 .002 .102 3.376 6.376
77 2.380 .169 .002 .317 .013 .016 .002 .102 3.377 6.377
AVER: 2.378 .170 .002 .315 .014 .016 .002 .103 3.377 6.377
SDEV: .002 .000 .002 .001 .001 .000 .000 .001 .002 .002
SERR: .001 .000 .001 .001 .000 .000 .000 .000 .001
%RSD: .10 .24 78.05 .46 5.41 2.06 13.63 .74 .06
Of course the oxygen formula is low, but note the effect of this "missing oxygen" on the concentrations of the other elements. E.g., without the excess oxygen in the matrix correction, the Fe and Ti concentrations went down, but the Mg and Al concentrations went up!
Mike Dungan, Andrew Locock and I fixed a problem with some oxide compositions in the ferric/ferric excess oxygen calculation as seen here:
Ferrous/Ferric Calculation Results:
Ferric/TotalFe FeO Fe2O3 Oxygen from Fe2O3
37 .387 44.824 31.498 3.156
38 .387 44.633 31.339 3.140
AVER: .387 44.729 31.419 3.148
Un 6 CH-19_Ox99_Mgt Core-1, Results in Oxide Weight Percents
ELEM: FeO MgO TiO2 V2O3 MnO Cr2O3 Al2O3 SiO2 CaO O SUM
37 73.166 2.152 18.583 .543 .586 .006 1.835 .053 .014 3.156 100.093
38 72.832 2.159 18.500 .553 .574 .002 1.906 .043 .014 3.140 99.723
AVER: 72.999 2.156 18.541 .548 .580 .004 1.870 .048 .014 3.148 99.908
SDEV: .236 .005 .059 .008 .008 .003 .051 .007 .000 .011 .261
SERR: .167 .003 .042 .005 .006 .002 .036 .005 .000 .008
%RSD: .32 .23 .32 1.39 1.45 69.25 2.70 14.77 1.72 .36
STDS: 395 12 22 23 25 24 306 14 306 ---
Un 6 CH-19_Ox99_Mgt Core-1, Results Based on Sum of 3 Cations
ELEM: Fe Mg Ti V Mn Cr Al Si Ca O SUM
37 2.251 .118 .514 .016 .018 .000 .080 .002 .001 4.000 7.000
38 2.248 .119 .514 .016 .018 .000 .083 .002 .001 4.000 7.000
AVER: 2.250 .118 .514 .016 .018 .000 .081 .002 .001 4.000 7.000
SDEV: .002 .001 .000 .000 .000 .000 .002 .000 .000 .000 .000
SERR: .002 .000 .000 .000 .000 .000 .002 .000 .000 .000
%RSD: .10 .46 .09 1.62 1.22 69.07 2.93 14.55 1.49 .00
This change now properly handles oxides such as Al2O3, V2O3, Cr2O3, etc. You can update PFE anytime.
We've recently been working with Julien Allaz to fix the way in which the oxygen-halogen correction is applied to standards in Probe for EPMA as first reported by Ben Wade:
https://smf.probesoftware.com/index.php?topic=1247.msg9305#msg9305
During that time we realized that these recent halogen correction issues for standards (when oxygen is calculated by stoichiometry rather than a fixed concentration), are somewhat similar to the excess oxygen calculation using the Droop method of charge balance (hey- it's all about charge balance!). Again only for standard samples, when oxygen is calculated by stoichiometry (as opposed to added by fixed concentration from the standard database).
Previously, for the excess oxygen from ferric iron calculation, we simply did not allow one to perform this excess oxygen calculation for standards (only for unknown samples). But we realized yesterday that it's the same issue in that a double correction is applied for standards if the excess (or deficit) oxygen is already included in the standard database, and the excess (or deficit) oxygen correction for ferric oxygen (or halogen equivalence) is applied in Probe for EPMA, *and* the oxygen in the standard is calculated by stocihiometry. Whew!
So what we did was enable the calculation of excess oxygen for standards (just as we have had for the halogen correction), so if the standard analysis is using the default fixed oxygen concentration from the standard database, all is well. This can be seen is this output:
Excess Oxygen From Ferric Iron was not Included in the Matrix Correction (because oxygen was not calculated by cation stoichiometry)
St 395 Set 1 Magnetite U.C. #3380, Results in Elemental Weight Percents
ELEM: F Fe Al Mg Mn O
TYPE: ANAL ANAL SPEC SPEC SPEC SPEC
BGDS: LIN LIN
TIME: 20.00 20.00 --- --- --- ---
BEAM: 29.98 29.98 --- --- --- ---
ELEM: F Fe Al Mg Mn O SUM
10 .051 71.844 .201 .072 .054 27.803 100.025
11 .073 72.195 .201 .072 .054 27.803 100.398
12 .026 72.209 .201 .072 .054 27.803 100.365
AVER: .050 72.083 .201 .072 .054 27.803 100.263
SDEV: .023 .207 .000 .000 .000 .000 .207
SERR: .014 .119 .000 .000 .000 .000
%RSD: 46.70 .29 .00 .00 .00 .00
PUBL: n.a. 72.080 .201 .072 .054 27.803 100.210
%VAR: --- (.00) .00 .00 .00 .00
DIFF: --- (.00) .000 .000 .000 .000
STDS: 835 395 --- --- --- ---
STKF: .1715 .6779 --- --- --- ---
STCT: 57.18 228.22 --- --- --- ---
UNKF: .0002 .6779 --- --- --- ---
UNCT: .07 228.22 --- --- --- ---
UNBG: .32 .49 --- --- --- ---
ZCOR: 2.2854 1.0633 --- --- --- ---
KRAW: .0013 1.0000 --- --- --- ---
PKBG: 1.23 466.16 --- --- --- ---
Ferrous/Ferric Calculation Results:
Ferric/TotalFe FeO Fe2O3 Oxygen from Fe2O3
10 .000 .000 .000 .000
11 .000 .000 .000 .000
12 .000 .000 .000 .000
AVER: .000 .000 .000 .000
But in the case where the user changes the standard analysis calculation to calculate oxygen by stoichiometry, the program will now zero out the excess oxygen (just as it now does for the deficit oxygen from halogens), and not perform a double correction as seen here:
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Oxygen Equivalent from Halogens (F/Cl/Br/I) was Subtracted in the Matrix Correction
Excess Oxygen From Ferric Iron Calculated and Included in the Matrix Correction
Charge Balance Method of Droop (1987), Total Cations= 3.00, Total Oxygens= 4.00
St 395 Set 1 Magnetite U.C. #3380, Results in Elemental Weight Percents
ELEM: F Fe Al Mg Mn O
TYPE: ANAL ANAL SPEC SPEC SPEC CALC
BGDS: LIN LIN
TIME: 20.00 20.00 --- --- --- ---
BEAM: 29.98 29.98 --- --- --- ---
ELEM: F Fe Al Mg Mn O SUM
10 .051 71.838 .201 .072 .054 27.742 99.957
11 .073 72.206 .201 .072 .054 27.908 100.514
12 .026 72.215 .201 .072 .054 27.859 100.427
AVER: .050 72.086 .201 .072 .054 27.836 100.299
SDEV: .023 .215 .000 .000 .000 .085 .300
SERR: .014 .124 .000 .000 .000 .049
%RSD: 46.75 .30 .00 .00 .00 .31
PUBL: n.a. 72.080 .201 .072 .054 27.803 100.210
%VAR: --- (.01) .00 .00 .00 .12
DIFF: --- (.01) .000 .000 .000 .033
STDS: 835 395 --- --- --- ---
STKF: .1715 .6779 --- --- --- ---
STCT: 57.18 228.22 --- --- --- ---
UNKF: .0002 .6779 --- --- --- ---
UNCT: .07 228.22 --- --- --- ---
UNBG: .32 .49 --- --- --- ---
ZCOR: 2.2865 1.0633 --- --- --- ---
KRAW: .0013 1.0000 --- --- --- ---
PKBG: 1.23 466.16 --- --- --- ---
Ferrous/Ferric Calculation Results:
Ferric/TotalFe FeO Fe2O3 Oxygen from Fe2O3
10 .674 30.092 69.266 6.940
11 .678 29.937 69.966 7.010
12 .671 30.591 69.252 6.938
AVER: .674 30.207 69.495 6.963
So now, the code for dealing with this is seen here:
If sample(1).Type% = 1 Then
analysis.WtPercents!(chan%) = ConvertTotalToExcessOxygen!(Int(1), sample(), stdsample())
If UseOxygenFromHalogensCorrectionFlag And sample(1).OxideOrElemental% = 1 Then
If analysis.WtPercents!(chan%) < 0# Then analysis.WtPercents!(chan%) = 0# ' zero out oxygen deficit from standard database
End If
If sample(1).FerrousFerricCalculationFlag And sample(1).OxideOrElemental% = 1 Then
If analysis.WtPercents!(chan%) > 0# Then analysis.WtPercents!(chan%) = 0# ' zero out oxygen excess from standard database
End If
' For unknowns, use specified oxygen weight percent
Else
analysis.WtPercents!(chan%) = stdsample(1).ElmPercents!(ip%)
End If
One possible remaining issue is when one has both halogens and ferric iron present in a standard, and one tries to calculate oxygen by stoichiometry, the excess/deficit oxygen might not be handled perfectly. In this case, we would just say, simply use the default to calculate oxygen elementally (fixed concentration from the standard database) and all will be well. But I think it will work, because if both the oxygen-halogen correction *and* the ferric iron calculation correction are turned on, you'll get a zero value for excess/deficit oxygen, so it should all work.
Remember, in all cases, the calculations for unknown samples are handled just fine. This is all pretty complicated we know, but please ask us any questions you may have.
In the meantime, update Probe for EPMA from the Help menu and these options are all available now.
Recently Andrew Locock found a mineral calculation for an unanalyzed elements situation which did not properly apply the oxygen-halogen correction when calculating oxygen by stoichiometry (that is, when not measuring oxygen, or specifying oxygen as a fixed concentration). The following examples were all measured by Andrew on one of his microprobe instruments (yes he has two of them!).
I should also mention that a full paper on the effects of unanalyzed elements in EPMA analysis is being prepared with Aurelien Moy as first author (and Andrew and myself and several others) that will be submitted later this year for publication.
As a quick review of the unanalyzed element problem can be seen is this carbonate example where oxygen is calculated by stoichiometry and carbon is calculated relative to stoichiometric oxygen in the ratio of 0.333 atoms of carbon to one atom of oxygen:
(https://smf.probesoftware.com/gallery/1_27_08_21_7_39_46.png)
One can click on the images to see them better, though I'm not quite sure why he specified 0.33368 atoms of carbon in this example...
Another slightly more complicated example is that of tourmaline where 0.129 atoms of hydrogen are calculated relative to stoichiometric oxygen *and* 0.5 atoms of boron are calculated relative to silicon:
(https://smf.probesoftware.com/gallery/1_27_08_21_7_40_01.png)
Now as for the halogen-oxygen correction, this is applied when oxygen is calculated by stoichiometry and a halogen element (chlorine, fluorine, etc.) is also present and replacing some of the stoichiometric oxygen. In these cases, unless a correction is applied to the stoichiometric oxygen concentration, too much oxygen will be included in the EPMA matrix iteration and the correction of the other elements will be calculated incorrectly.
For chlorine measurements the effect of this excess oxygen is fairly small, but for fluorine, which is heavily absorbed by oxygen, the effect is much larger. There is a separate topic devoted to this topic here, if anyone wants to learn more about these details:
https://smf.probesoftware.com/index.php?topic=1247.0
So back to Andrew's observations. What Andrew found is that when he was *not* measuring fluorine and was calculating oxygen by stoichiometry in some topaz minerals, the halogen-oxygen correction was being applied correctly as seen here:
(https://smf.probesoftware.com/gallery/1_27_08_21_7_45_03.png)
That is, when the unanalyzed fluorine is calculated by stoichiometry to stoichiometric oxygen.
However, he found that when he tried to calculate the fluorine by stoichiometry to aluminum (aluminium to some!), the program did not apply the halogen-oxygen correction as expected. This was because it turned out that the element relative to another element code was located *after* the oxygen by stoichiometry code in the matrix iteration. When we moved the element relative to another element code to *before* the oxygen by stoichiometry code, it all worked as seen here:
(https://smf.probesoftware.com/gallery/1_27_08_21_7_45_18.png)
8)
Any questions?
I have a question: is it an "oxygen-halogen" correction, or a "halogen-oxygen" correction? :D
Quote from: Probeman on August 27, 2021, 09:55:31 AM
I have a question: is it an "oxygen-halogen" correction, or a "halogen-oxygen" correction? :D
"Oxygen equivalent of fluorine" is how it was put by Deer, Howie and Zussman in the Appendix of their book
An Introduction to the Rock-Forming Minerals.
So, more broadly, the oxygen equivalent of the halogen content.
Sorry about the typo in the carbonate example above.
Andrew
Quote from: AndrewLocock on August 27, 2021, 10:21:42 AM
Quote from: Probeman on August 27, 2021, 09:55:31 AM
I have a question: is it an "oxygen-halogen" correction, or a "halogen-oxygen" correction? :D
"Oxygen equivalent of fluorine" is how it was put by Deer, Howie and Zussman in the Appendix of their book
An Introduction to the Rock-Forming Minerals.
So, more broadly, the oxygen equivalent of the halogen content.
Sorry about the typo in the carbonate example above.
Andrew
OK, then I'm going to use "oxygen-halogen" correction, because I can't usually spell "equivalent" or "equivalence"! ;D
I think it's worth demonstrating in some detail exactly how important it is to include these unanalyzed elements in the matrix correction. For example here are the quant results for the above topaz example (data from Locock) with fluorine not included in the matrix iteration:
Un 2 Topaz, Results in Elemental Weight Percents
ELEM: Al Si F O
TYPE: ANAL ANAL SPEC CALC
BGDS: LIN LIN
TIME: 20.00 20.00 --- ---
BEAM: 15.18 15.18 --- ---
ELEM: Al Si F O SUM
6 28.266 15.337 .000 42.617 86.220
7 28.270 15.327 .000 42.608 86.205
8 28.137 15.383 .000 42.555 86.075
9 28.351 15.455 .000 42.827 86.634
10 28.221 15.368 .000 42.611 86.200
AVER: 28.249 15.374 .000 42.644 86.267
SDEV: .078 .051 .000 .106 .213
SERR: .035 .023 .000 .047
%RSD: .28 .33 .00 .25
STDS: 73 73 --- ---
STKF: .2305 .1076 --- ---
STCT: 448.80 238.86 --- ---
UNKF: .2303 .1078 --- ---
UNCT: 448.33 239.45 --- ---
UNBG: 1.83 1.54 --- ---
ZCOR: 1.2268 1.4258 --- ---
KRAW: .9990 1.0025 --- ---
PKBG: 245.93 156.66 --- ---
And here is with the fluorine included:
Un 2 Topaz, Results in Elemental Weight Percents
ELEM: Al Si F O
TYPE: ANAL ANAL STOI CALC
BGDS: LIN LIN
TIME: 20.00 20.00 --- ---
BEAM: 15.18 15.18 --- ---
ELEM: Al Si F O SUM
6 29.308 15.258 20.647 34.758 99.970
7 29.312 15.247 20.645 34.750 99.954
8 29.176 15.304 20.641 34.696 99.817
9 29.393 15.376 20.675 34.957 100.401
10 29.262 15.288 20.647 34.752 99.948
AVER: 29.290 15.294 20.651 34.783 100.018
SDEV: .080 .051 .014 .101 .223
SERR: .036 .023 .006 .045
%RSD: .27 .33 .07 .29
STDS: 73 73 --- ---
STKF: .2305 .1076 --- ---
STCT: 448.80 238.86 --- ---
UNKF: .2303 .1078 --- ---
UNCT: 448.33 239.45 --- ---
UNBG: 1.83 1.54 --- ---
ZCOR: 1.2720 1.4184 --- ---
KRAW: .9990 1.0025 --- ---
PKBG: 245.93 156.66 --- ---
Note that the Al concentration changes by around 1 wt% *absolute* or over 3% relative!
And if we don't specify the oxygen-halogen correction to remove the excess stoichiometric oxygen from the matrix iteration, not only is our total way too high but look at the effect on the Al concentration from including that excess oxygen:
Un 2 Topaz, Results in Elemental Weight Percents
ELEM: Al Si F O
TYPE: ANAL ANAL STOI CALC
BGDS: LIN LIN
TIME: 20.00 20.00 --- ---
BEAM: 15.18 15.18 --- ---
ELEM: Al Si F O SUM
6 29.819 15.136 23.211 43.768 111.934
7 29.823 15.125 23.210 43.760 111.918
8 29.685 15.182 23.209 43.702 111.778
9 29.904 15.254 23.233 43.979 112.369
10 29.772 15.166 23.212 43.761 111.911
AVER: 29.801 15.173 23.215 43.794 111.982
SDEV: .080 .051 .010 .106 .225
SERR: .036 .023 .004 .048
%RSD: .27 .34 .04 .24
STDS: 73 73 --- ---
STKF: .2305 .1076 --- ---
STCT: 448.80 238.86 --- ---
UNKF: .2303 .1078 --- ---
UNCT: 448.33 239.45 --- ---
UNBG: 1.83 1.54 --- ---
ZCOR: 1.2942 1.4071 --- ---
KRAW: .9990 1.0025 --- ---
PKBG: 245.93 156.66 --- ---
Bottom line: whether the element is missing or in excess, it needs to be dealt with the the matrix iteration for accurate results!
In this topic we have been emphasizing the importance of including the concentrations of all unanalyzed (specified) elements to obtain an accurate matrix correction, and therefore hopefully, accurate results:
https://www.cambridge.org/core/journals/microscopy-and-microanalysis/article/epma-matrix-correction-all-elements-must-be-present-for-accuracy-four-examples-with-b-c-o-and-f/759C69631A916EA69913539C22989A31
This is because for major elements the most important parameters for analysis accuracy are the accuracy of the matrix correction *and* the accuracy of the standard compositions. For major elements, the accuracy of the background measurement is usually "in the noise", and usually, little affected by spectral interferences.
But what about trace elements? For trace element accuracy, the accuracy of the matrix corrections and standard compositions are not so critical, as it is the accuracy of the background measurements (and spectral interference correction!) that becomes the dominant factor:
https://smf.probesoftware.com/index.php?topic=928.msg8498#msg8498
We can appreciate this point by assuming typical EPMA matrix correction accuracy of say ~2%. If we are measuring a concentration of say, 1000 PPM (0.1 wt%), then 2% of 1000 PPM is 20 PPM (0.002 wt%). A level of accuracy very likely close to the precision of our measurement. Again, usually "in the noise" of our measurement.
We can demonstrate this more clearly in a different manner by making trace element measurements in a material of known composition, the major (and minor) elements being specified to account for the effect of the matrix effects of the unanalyzed elements. Here is the analysis with *no* (unanalyzed) matrix specified:
Un 33 MA-1058 Rxn-1 (trav), Results in Elemental Weight Percents
ELEM: Zr Nb La Sr Ti Si Ca Al Fe Na K Mg Mn Cr O
TYPE: ANAL ANAL ANAL ANAL ANAL SPEC SPEC SPEC SPEC SPEC SPEC SPEC SPEC SPEC SPEC
BGDS: MULT MULT MULT MULT MULT
TIME: 240.00 240.00 240.00 240.00 240.00 --- --- --- --- --- --- --- --- --- ---
BEAM: 80.06 80.06 80.06 80.06 80.06 --- --- --- --- --- --- --- --- --- ---
ELEM: Zr Nb La Sr Ti Si Ca Al Fe Na K Mg Mn Cr O SUM
472 .030 .001 .004 .009 .391 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .436
473 .024 -.001 .002 .003 .323 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .352
474 .013 .002 -.003 .009 .419 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .439
475 .021 .003 -.001 .001 .282 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .306
476 .011 -.002 -.001 .009 .242 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .259
477 .009 .000 .001 .004 .245 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .259
478 .007 .002 .003 .010 .268 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .290
479 .013 .002 .001 .006 .186 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .207
480 .003 -.002 -.002 .002 .129 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .130
481 .010 -.001 .003 .004 .291 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .308
482 .022 .000 .000 .008 .389 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .420
AVER: .015 .000 .001 .006 .288 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .310
SDEV: .008 .002 .002 .003 .089 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .098
SERR: .003 .000 .001 .001 .027 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
%RSD: 55.52 394.62 422.74 53.43 30.94 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00
STDS: 257 541 1007 251 22 --- --- --- --- --- --- --- --- --- ---
STKF: .4109 .9936 .5384 .4225 .5616 --- --- --- --- --- --- --- --- --- ---
STCT: 52.56 382.07 133.42 50.64 82.83 --- --- --- --- --- --- --- --- --- ---
UNKF: .0001 .0000 .0000 .0000 .0029 --- --- --- --- --- --- --- --- --- ---
UNCT: .02 .00 .00 .01 .42 --- --- --- --- --- --- --- --- --- ---
UNBG: .08 .19 .31 .10 .07 --- --- --- --- --- --- --- --- --- ---
ZCOR: 1.1199 1.0725 1.0567 1.2265 1.0088 --- --- --- --- --- --- --- --- --- ---
KRAW: .0003 .0000 .0000 .0001 .0051 --- --- --- --- --- --- --- --- --- ---
PKBG: 1.22 1.01 1.00 1.06 6.68 --- --- --- --- --- --- --- --- --- ---
Note that the total is around 0.3 wt%, mostly from the Ti measurement, therefore the matrix correction has to assume the matrix is almost pure Ti metal. And even if we calculate this as an oxide matrix, nothing changes except the Ti concentration by about 0.017 wt%:
ELEM: Zr Nb La Sr Ti Si Ca Al Fe Na K Mg Mn Cr O
TYPE: ANAL ANAL ANAL ANAL ANAL SPEC SPEC SPEC SPEC SPEC SPEC SPEC SPEC SPEC CALC
BGDS: MULT MULT MULT MULT MULT
TIME: 240.00 240.00 240.00 240.00 240.00 --- --- --- --- --- --- --- --- --- ---
BEAM: 80.06 80.06 80.06 80.06 80.06 --- --- --- --- --- --- --- --- --- ---
ELEM: Zr Nb La Sr Ti Si Ca Al Fe Na K Mg Mn Cr O SUM
472 .031 .001 .004 .010 .414 .000 .000 .000 .000 .000 .000 .000 .000 .000 .290 .751
473 .025 -.001 .002 .003 .343 .000 .000 .000 .000 .000 .000 .000 .000 .000 .238 .611
474 .013 .002 -.003 .009 .445 .000 .000 .000 .000 .000 .000 .000 .000 .000 .304 .770
475 .022 .003 -.001 .002 .299 .000 .000 .000 .000 .000 .000 .000 .000 .000 .209 .533
476 .012 -.002 -.001 .009 .257 .000 .000 .000 .000 .000 .000 .000 .000 .000 .176 .450
477 .009 .000 .001 .004 .260 .000 .000 .000 .000 .000 .000 .000 .000 .000 .178 .453
478 .008 .002 .003 .010 .285 .000 .000 .000 .000 .000 .000 .000 .000 .000 .196 .503
479 .013 .002 .001 .006 .197 .000 .000 .000 .000 .000 .000 .000 .000 .000 .138 .357
480 .003 -.002 -.003 .002 .137 .000 .000 .000 .000 .000 .000 .000 .000 .000 .092 .231
481 .010 -.001 .003 .004 .310 .000 .000 .000 .000 .000 .000 .000 .000 .000 .211 .538
482 .023 .000 .001 .008 .413 .000 .000 .000 .000 .000 .000 .000 .000 .000 .286 .731
AVER: .015 .000 .001 .006 .305 .000 .000 .000 .000 .000 .000 .000 .000 .000 .211 .539
SDEV: .009 .002 .002 .003 .094 .000 .000 .000 .000 .000 .000 .000 .000 .000 .066 .169
SERR: .003 .000 .001 .001 .028 .000 .000 .000 .000 .000 .000 .000 .000 .000 .020
%RSD: 55.61 394.67 423.76 51.36 30.90 .00 .00 .00 .00 .00 .00 .00 .00 .00 31.18
STDS: 257 541 1007 251 22 --- --- --- --- --- --- --- --- --- ---
STKF: .4109 .9936 .5384 .4225 .5616 --- --- --- --- --- --- --- --- --- ---
STCT: 52.56 382.07 133.42 50.64 82.83 --- --- --- --- --- --- --- --- --- ---
UNKF: .0001 .0000 .0000 .0001 .0029 --- --- --- --- --- --- --- --- --- ---
UNCT: .02 .00 .00 .01 .42 --- --- --- --- --- --- --- --- --- ---
UNBG: .08 .19 .31 .10 .07 --- --- --- --- --- --- --- --- --- ---
ZCOR: 1.1423 1.1009 1.1251 1.2484 1.0712 --- --- --- --- --- --- --- --- --- ---
KRAW: .0003 .0000 .0000 .0001 .0051 --- --- --- --- --- --- --- --- --- ---
PKBG: 1.22 1.01 1.00 1.06 6.68 --- --- --- --- --- --- --- --- --- ---
Which we can see is from the change in the matrix correction for Ti Ka by about 6%. The other trace elements still show no change at all. And what happens if we specify the correct matrix correctly as shown here:
Un 33 MA-1058 Rxn-1 (trav), Results in Elemental Weight Percents
ELEM: Zr Nb La Sr Ti Si Ca Al Fe Na K Mg Mn Cr O
TYPE: ANAL ANAL ANAL ANAL ANAL SPEC SPEC SPEC SPEC SPEC SPEC SPEC SPEC SPEC SPEC
BGDS: MULT MULT MULT MULT MULT
TIME: 240.00 240.00 240.00 240.00 240.00 --- --- --- --- --- --- --- --- --- ---
BEAM: 80.06 80.06 80.06 80.06 80.06 --- --- --- --- --- --- --- --- --- ---
ELEM: Zr Nb La Sr Ti Si Ca Al Fe Na K Mg Mn Cr O SUM
472 .040 .002 .005 .011 .462 23.714 11.392 4.620 4.928 .994 .000 10.125 .108 .089 44.198 100.688
473 .032 -.001 .002 .004 .383 23.714 11.392 4.620 4.928 .994 .000 10.125 .108 .089 44.198 100.589
474 .017 .002 -.004 .011 .497 23.714 11.392 4.620 4.928 .994 .000 10.125 .108 .089 44.198 100.692
475 .028 .004 -.002 .003 .334 23.714 11.392 4.620 4.928 .994 .000 10.125 .108 .089 44.198 100.535
476 .015 -.003 -.001 .010 .287 23.714 11.392 4.620 4.928 .994 .000 10.125 .108 .089 44.198 100.476
477 .012 .000 .001 .005 .291 23.714 11.392 4.620 4.928 .994 .000 10.125 .108 .089 44.198 100.478
478 .010 .002 .003 .012 .319 23.714 11.392 4.620 4.928 .994 .000 10.125 .108 .089 44.198 100.513
479 .017 .002 .001 .007 .220 23.714 11.392 4.620 4.928 .994 .000 10.125 .108 .089 44.198 100.415
480 .004 -.002 -.003 .003 .154 23.714 11.392 4.620 4.928 .994 .000 10.125 .108 .089 44.198 100.324
481 .013 -.001 .004 .005 .347 23.714 11.392 4.620 4.928 .994 .000 10.125 .108 .089 44.198 100.536
482 .030 .000 .001 .009 .462 23.714 11.392 4.620 4.928 .994 .000 10.125 .108 .089 44.198 100.670
AVER: .020 .001 .001 .007 .341 23.714 11.392 4.620 4.928 .994 .000 10.125 .108 .089 44.198 100.538
SDEV: .011 .002 .003 .003 .105 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .116
SERR: .003 .001 .001 .001 .032 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
%RSD: 55.77 394.36 423.62 46.10 30.87 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00
STDS: 257 541 1007 251 22 --- --- --- --- --- --- --- --- --- ---
STKF: .4109 .9936 .5384 .4225 .5616 --- --- --- --- --- --- --- --- --- ---
STCT: 52.56 382.07 133.42 50.64 82.83 --- --- --- --- --- --- --- --- --- ---
UNKF: .0001 .0000 .0000 .0001 .0029 --- --- --- --- --- --- --- --- --- ---
UNCT: .02 .00 .00 .01 .42 --- --- --- --- --- --- --- --- --- ---
UNBG: .08 .19 .31 .10 .07 --- --- --- --- --- --- --- --- --- ---
ZCOR: 1.4847 1.4029 1.2509 1.3181 1.1972 --- --- --- --- --- --- --- --- --- ---
KRAW: .0003 .0000 .0000 .0001 .0051 --- --- --- --- --- --- --- --- --- ---
PKBG: 1.22 1.01 1.00 1.07 6.68 --- --- --- --- --- --- --- --- --- ---
Essentially no change in the trace elements, and only a rather small matrix effect on the Ti concentration. Or does it? Let try another matrix, say MgO:
Un 33 MA-1058 Rxn-1 (trav), Results in Elemental Weight Percents
ELEM: Zr Nb La Sr Ti Si Ca Al Fe Na K Mg Mn Cr O
TYPE: ANAL ANAL ANAL ANAL ANAL SPEC SPEC SPEC SPEC SPEC SPEC SPEC SPEC SPEC SPEC
BGDS: MULT MULT MULT MULT MULT
TIME: 240.00 240.00 240.00 240.00 240.00 --- --- --- --- --- --- --- --- --- ---
BEAM: 80.06 80.06 80.06 80.06 80.06 --- --- --- --- --- --- --- --- --- ---
ELEM: Zr Nb La Sr Ti Si Ca Al Fe Na K Mg Mn Cr O SUM
472 .041 .002 .005 .020 .454 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.522
473 .033 -.001 .002 .011 .377 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.422
474 .018 .002 -.004 .019 .489 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.525
475 .029 .004 -.002 .008 .328 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.368
476 .015 -.003 -.001 .019 .282 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.312
477 .012 .000 .001 .012 .286 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.312
478 .010 .002 .003 .021 .313 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.349
479 .017 .002 .001 .015 .216 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.252
480 .004 -.002 -.003 .009 .151 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.160
481 .014 -.001 .004 .012 .341 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.369
482 .031 .000 .001 .018 .454 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.503
AVER: .020 .001 .001 .015 .336 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.372
SDEV: .011 .002 .003 .005 .104 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .115
SERR: .003 .001 .001 .001 .031 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
%RSD: 55.77 394.38 423.62 31.13 30.87 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00
STDS: 257 541 1007 251 22 --- --- --- --- --- --- --- --- --- ---
STKF: .4109 .9936 .5384 .4225 .5616 --- --- --- --- --- --- --- --- --- ---
STCT: 52.56 382.07 133.42 50.64 82.83 --- --- --- --- --- --- --- --- --- ---
UNKF: .0001 .0000 .0000 .0001 .0029 --- --- --- --- --- --- --- --- --- ---
UNCT: .02 .00 .00 .01 .42 --- --- --- --- --- --- --- --- --- ---
UNBG: .08 .19 .31 .10 .07 --- --- --- --- --- --- --- --- --- ---
ZCOR: 1.5270 1.4383 1.2357 1.7923 1.1773 --- --- --- --- --- --- --- --- --- ---
KRAW: .0003 .0000 .0000 .0002 .0051 --- --- --- --- --- --- --- --- --- ---
PKBG: 1.22 1.01 1.00 1.10 6.68 --- --- --- --- --- --- --- --- --- ---
So we can see that even if we specify the matrix correction completely wrong, for trace elements, at least in this case, there is no significant effect and even for the minor element Ti, we see only a change of 0.025 wt%, or only about 2%.
What's the moral of this story?
1. Matrix corrections and standard composition accuracy is very important for major elements. These items should be your "focus".
2. For trace elements the accuracy of the background correction (and spectral interferences if present) are very important. Matrix corrections and standard composition accuracy, not so much if at all.
3. For minor elements, of course it's a "sliding scale" depending on the peak to background ratio (and the physics details), but if minor element accuracy is important we would want to have accurate background measurements primarily. The accuracy of the standard compositions and matrix correction effects are generally very small for minor elements.
To illustrate this last point here is the sample again calculated using all 10 matrix corrections in Probe for EPMA, where we can see the total variance of the Ti concentrations is quite small:
Summary of All Calculated (averaged) Matrix Corrections:
Un 33 MA-1058 Rxn-1 (trav)
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Elemental Weight Percents:
ELEM: Zr Nb La Sr Ti Si Ca Al Fe Na K Mg Mn Cr O TOTAL
1 .020 .001 .001 .012 .336 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.370 Armstrong/Love Scott (default)
2 .022 .001 .001 .015 .346 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.385 Conventional Philibert/Duncumb-Reed
3 .021 .001 .001 .013 .335 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.370 Heinrich/Duncumb-Reed
4 .022 .001 .001 .015 .337 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.374 Love-Scott I
5 .021 .001 .001 .013 .336 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.372 Love-Scott II
6 .023 .001 .001 .016 .348 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.388 Packwood Phi(pz) (EPQ-91)
7 .021 .001 .001 .014 .334 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.371 Bastin (original) Phi(pz)
8 .022 .001 .001 .015 .342 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.380 Bastin PROZA Phi(pz) (EPQ-91)
9 .022 .001 .001 .015 .341 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.380 Pouchou and Pichoir-Full (PAP)
10 .022 .001 .001 .014 .342 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.380 Pouchou and Pichoir-Simplified (XPP)
AVER: .022 .001 .001 .014 .340 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.377
SDEV: .001 .000 .000 .001 .005 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .007
SERR: .000 .000 .000 .000 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
MIN: .020 .001 .001 .012 .334 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.370
MAX: .023 .001 .001 .016 .348 .000 .000 .000 .000 .000 .000 60.303 .000 .000 39.697 100.388
In fact the Ti variance for all 10 matrix corrections is only 50 PPM
Quote from: John Donovan on August 19, 2019, 12:07:09 PM
Just FYI, we're just putting the finishing touches on a ferrous/ferric calculation for PFE (and CalcZAF!) that will calculate excess oxygen from ferric iron for minerals using the method of Droop (1987) *and* include it in the matrix correction. This excess oxygen has a surprisingly large effect on the matrix correction physics, even for minerals such as ilmenite/magnetite. I'm just posting this here so we'll have a link for the "interactive help" button in the Calculation Options dialog.
We hope to have a new version of both PFE and CalcZAF uploaded tonight or tomorrow, but first we want to give a big thanks to Andrew Locock, Anette von der Handt, John Fournelle and Emma Bullock, who provided the mineralogical expertise to allow us to implement this.
More details to follow soon but in the meantime the original paper by Droop is attached below
I'm wondering if someone much smarter than me on here can help me think through a problem related to Ferrous/Ferric ratios in glass. I have a series of basaltic glasses that were created by a researcher a long time ago under known and controlled fO2 conditions. A subset of each of these glasses were mounted in epoxy for microprobe analysis and a split of each sample was analysed using wet chemical methods to determine the Ferrous/Ferric content. I can't figure out how I can (if I can) use the relatively new Ferrous/Ferric in the software.
Any help would be greatly appreciated!!!
Short answer is you can't for glasses.
The ferric/ferrous excess oxygen calculation is based on charge balance (Droop, 1987) so a formula (number of cations and oxygens) is required for it to work. We even got it to work for most amphibole compositions with a lot of help from Andrew Locock and Aurelien Moy.
But I guess I'm not sure why you want to try this when you already have ferric/ferrous contents from wet chemistry. Just specify the excess oxygen from ferric iron in PFE and it will perform a matrix correction and should give you nicer totals.
The following conversions for Fe2O3, FeO and excess O may be useful to some.
Conversions between FeO and Fe2O3 in wt%:
Fe2O3 = FeO * (159.6882 / [2 * 71.8444]) = FeO * 1.111348
FeO = Fe2O3 * ([2 * 71.8444] / 159.6882) = Fe2O3 * 0.8998085
Conversions for Fe3+-bearing compounds with "excess oxygen":
Fe2O3 wt% = wt% O "excess oxygen"* (molar mass Fe2O3/molar mass O)
Fe2O3 wt% = wt% O "excess oxygen" * (159.6882/15.9994)
Fe2O3 wt% = wt% O "excess oxygen" * 9.980887
Example: hematite, with 89.981 wt% FeOtotal and "excess oxygen" 10.019 wt% O:
Fe2O3 wt% = 10.019 wt% O * 9.980887 = 100.00
FeOfinal = FeOtotal – Fe2O3 * 0.8998085 = 0.
Thus, hematite is 100.00 wt% Fe2O3
Example: magnetite, with 93.09 wt% FeOtotal and "excess oxygen" 6.91 wt% O:
Fe2O3 wt% = 6.91 wt% O * 9.980887 = 68.97
FeOfinal = FeOtotal – Fe2O3 * 0.8998085 = 93.09 – 62.06 = 31.06
Thus, magnetite has 68.97 Fe2O3 and 31.06 FeO, sum 100.00 wt%
Quote from: DavidAdams on August 22, 2022, 05:51:18 PM
Quote from: John Donovan on August 19, 2019, 12:07:09 PM
Just FYI, we're just putting the finishing touches on a ferrous/ferric calculation for PFE (and CalcZAF!) that will calculate excess oxygen from ferric iron for minerals using the method of Droop (1987) *and* include it in the matrix correction. This excess oxygen has a surprisingly large effect on the matrix correction physics, even for minerals such as ilmenite/magnetite. I'm just posting this here so we'll have a link for the "interactive help" button in the Calculation Options dialog.
We hope to have a new version of both PFE and CalcZAF uploaded tonight or tomorrow, but first we want to give a big thanks to Andrew Locock, Anette von der Handt, John Fournelle and Emma Bullock, who provided the mineralogical expertise to allow us to implement this.
More details to follow soon but in the meantime the original paper by Droop is attached below
I'm wondering if someone much smarter than me on here can help me think through a problem related to Ferrous/Ferric ratios in glass. I have a series of basaltic glasses that were created by a researcher a long time ago under known and controlled fO2 conditions. A subset of each of these glasses were mounted in epoxy for microprobe analysis and a split of each sample was analysed using wet chemical methods to determine the Ferrous/Ferric content. I can't figure out how I can (if I can) use the relatively new Ferrous/Ferric in the software.
Any help would be greatly appreciated!!!
Actually I just remembered that there there is a method you might be able to use to determine ferric/ferrous ratios in glasses, but it's non-trivial.
That is the method of water by difference (by analyzing oxygen) first proposed by Barbara Nash at University of Utah. Basically one analyzes for oxygen along with all the cations and then subtracts the oxygen from cations from the analyzed oxygen.
I made a study of this method using the features available in Probe for EPMA (curved backgrounds, Area Peak Factors, empirical mass absorption coefficients, including water in the matrix correction, etc.) on some synthetic glasses from Tony Withers (Universität Bayreuth) and the results are discussed here :
https://smf.probesoftware.com/index.php?topic=922.0
and the details are in the attached pdf at the above link. The point is that in Probe for EPMA one can assign the excess oxygen as water or OH to be included in the matrix correction, or one can simply assume the excess oxygen is due to ferric iron. In all cases some assumptions have to be made.
It was pretty difficult to get enough accuracy with oxygen to obtain an accurate H2O value (but I did analyze them "blind" in the first effort and they came out very close to the FTIR values), and I think it would be even harder to get the excess oxygen from ferric iron, but it might be possible.
Quote from: AndrewLocock on August 23, 2022, 08:17:38 AM
The following conversions for Fe2O3, FeO and excess O may be useful to some.
Conversions between FeO and Fe2O3 in wt%:
Fe2O3 = FeO * (159.6882 / [2 * 71.8444]) = FeO * 1.111348
FeO = Fe2O3 * ([2 * 71.8444] / 159.6882) = Fe2O3 * 0.8998085
Conversions for Fe3+-bearing compounds with "excess oxygen":
Fe2O3 wt% = wt% O "excess oxygen"* (molar mass Fe2O3/molar mass O)
Fe2O3 wt% = wt% O "excess oxygen" * (159.6882/15.9994)
Fe2O3 wt% = wt% O "excess oxygen" * 9.980887
Example: hematite, with 89.981 wt% FeOtotal and "excess oxygen" 10.019 wt% O:
Fe2O3 wt% = 10.019 wt% O * 9.980887 = 100.00
FeOfinal = FeOtotal – Fe2O3 * 0.8998085 = 0.
Thus, hematite is 100.00 wt% Fe2O3
Example: magnetite, with 93.09 wt% FeOtotal and "excess oxygen" 6.91 wt% O:
Fe2O3 wt% = 6.91 wt% O * 9.980887 = 68.97
FeOfinal = FeOtotal – Fe2O3 * 0.8998085 = 93.09 – 62.06 = 31.06
Thus, magnetite has 68.97 Fe2O3 and 31.06 FeO, sum 100.00 wt%
Thanks, Andrew! That's really helpful! :)
Quote from: Probeman on August 22, 2022, 06:59:16 PM
Short answer is you can't for glasses.
The ferric/ferrous excess oxygen calculation is based on charge balance (Droop, 1987) so a formula (number of cations and oxygens) is required for it to work. We even got it to work for most amphibole compositions with a lot of help from Andrew Locock and Aurelien Moy.
But I guess I'm not sure why you want to try this when you already have ferric/ferrous contents from wet chemistry. Just specify the excess oxygen from ferric iron in PFE and it will perform a matrix correction and should give you nicer totals.
I don't know, I just thought there might be an easy way in the software to input a known ratio for oxidation states for all the various elements out there that have been determined by other techniques such as wet chemistry, XANES, EELS, Raman etc. without having to calculated the excess oxygen external to PfE then input that excess oxygen into the software in order to have it calculated the matrix corrections. I suppose that was a silly assumption on my part. Thanks for the clarification about ferrous/ferric calculation option in the software! :)
Quote from: DavidAdams on August 23, 2022, 03:00:19 PM
Quote from: Probeman on August 22, 2022, 06:59:16 PM
Short answer is you can't for glasses.
The ferric/ferrous excess oxygen calculation is based on charge balance (Droop, 1987) so a formula (number of cations and oxygens) is required for it to work. We even got it to work for most amphibole compositions with a lot of help from Andrew Locock and Aurelien Moy.
But I guess I'm not sure why you want to try this when you already have ferric/ferrous contents from wet chemistry. Just specify the excess oxygen from ferric iron in PFE and it will perform a matrix correction and should give you nicer totals.
I don't know, I just thought there might be an easy way in the software to input a known ratio for oxidation states for all the various elements out there that have been determined by other techniques such as wet chemistry, XANES, EELS, Raman etc. without having to calculated the excess oxygen external to PfE then input that excess oxygen into the software in order to have it calculated the matrix corrections. I suppose that was a silly assumption on my part. Thanks for the clarification about ferrous/ferric calculation option in the software! :)
Oh, sorry. I get what you're after now.
Yes, you can specify the Fe:O ratio using any (1 to 99) integers from the Elements/Cations dialog.
So for example, instead of FeO or Fe2O3 or Fe3O4, you could specify Fe4O5 or Fe4O6 or Fe5O7 or whatever.
Quote from: Probeman on August 22, 2022, 06:59:16 PM
Yes, you can specify the Fe:O ratio using any (1 to 99) integers from the Elements/Cations dialog.
So for example, instead of FeO or Fe2O3 or Fe3O4, you could specify Fe4O5 or Fe4O6 or Fe5O7 or whatever.
There are certain limitations to using the integer Fe
xO
y method for specifying the proportions of ferric- and ferrous iron.
For this method, the ratio of x:y ranges from 2:3 up to 1:1, but both x and y must be integers, e.g., Fe
66O
99 and Fe
99O
99.
These correspond to Fe
2O
3 and FeO, respectively.
From inspection of the higher values of y:
The minimum proportion of ferric iron, Fe
3+/ΣFe (other than zero percent), is 2.041%, given by the moiety Fe
98O
99.
The maximum proportion of ferric iron, Fe
3+/ΣFe (other than one hundred percent), is 98.462%, given by the moiety Fe
65O
97.
One may wish to specify a proportion of ferric iron, Fe
3+/ΣFe less than 2.041% (or conceivably more than 98.462 w%).
If the concentration of total iron is known (or can be estimated to a reasonable precision), one can calculate and then specify the "excess oxygen".
If the matrix corrections result in a change in the amount of total iron, the "excess oxygen" can be recalculated, and the process iterated manually.
Cheers,
Andrew
Yes, you are absolutely correct. If the amount of oxygen you are adding is less than a percent or two (relative), your suggestion of specifying the ferric oxygen as excess oxygen works fine.
Either way, they get included in the matrix (and MAN) corrections.
I just wanted to note that one can also use the CalcZAF application for making these sorts of excess oxygen calculations.
So for example see this order of clicks and instructions:
(https://smf.probesoftware.com/gallery/395_27_08_22_1_07_43.png)
1. Note that the default cation ratio for Fe oxide is 1:1 or FeO. That can be modified of course by clicking on the element row.
2. Click the Enter Composition As Formula String button and enter whatever ratio you want from 1 to 99 for the cation and 0 to 99 for oxygen. For example Fe98O99 or very slightly more oxidized than FeO (in CalcZAF you can actually enter any short integer (1 to 32K) for the formula units, unlike PFE). Click OK.
3. Next click the Calculation Options button and check the Display Results as Oxide Formula checkbox. Click OK.
4. Click the Calculate button and you will obtain the following output:
fe98o99, sample 1
Current Mass Absorption Coefficients From:
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Z-LINE X-RAY Z-ABSOR MAC
Fe ka Fe 6.8270e+01
Fe ka O 2.2548e+01
O ka Fe 4.0015e+03
O ka O 1.1999e+03
ELEMENT ABSFAC ZEDFAC FINFAC STP-POW BKS-COR F(x)e
Fe ka 1.0157 4.3900 4.4588 .2087 .9161 .9846
O ka 1.4270 3.9154 5.5873 .2438 .9546 .7008
SAMPLE: 32767, TOA: 40, ITERATIONS: 0, Z-BAR: 21.95976
ELEMENT ABSCOR FLUCOR ZEDCOR ZAFCOR STP-POW BKS-COR F(x)u Ec Eo/Ec MACs
Fe ka .9974 1.0000 1.0534 1.0507 1.0759 .9791 .9871 7.1120 2.1091 58.0072
O ka 1.7001 .9927 .8553 1.4435 .7847 1.0900 .4122 .5317 28.2114 3372.68
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Fe ka .00000 .73813 77.554 99.773 49.746 1.000 15.00
O 22.446 .227 50.254 1.010
TOTAL: 100.000 100.000 100.000 2.010
The Fe is displayed as FeO (99.73%), since that is the currently defined stoichiometry for Fe, but the oxygen (0.227%) is displayed as the *excess" oxygen based on the formula Fe98O99!
Note you have to re-check the Display Results as Oxide Formulas for each new formula entered. Try it out.
Are there any proper correction procedures for situations where the sample mineral is porous? I am thinking of two cases: some serpentine minerals and chert. Obviously, you get low totals. You have the added problem that both phases can have significant water. I get asked very often can you just scale up the analysis to 100 and I constantly tell the users "no". But is there a correction procedure that can be applied? Thanks.
You may want to look into particle analyses by EPMA, specifically the peak-to-background ratio method. This is the usual recommendation to approaching quantitative analysis of porous samples. Otherwise, there are also recommendation to utilize standardless Monte Carlo simulations.
As per the Reed (2005) book: Another possibility is to measure peak-to-background ratios and make use of the fact that the effect of particle geometry on the continuum is similar to that on characteristic X-rays of the same energy (Statham and Pawley, 1977; Small, Newbury and Myklebust, 1979). Concentrations can be derived from peak-to-background ratios measured on the sample compared with ratios measured on standards. In ED spectra it is often necessary to remove the peaks by 'stripping' in order to determine the background, owing to the lack of suitable peak-free regions in the spectrum. The precision of measured peak to-background ratios is governed by the statistical error in the relatively low background intensity: this necessitates longer acquisition times than are customarily used for measuring peaks.
Some more references that may be relevant:
Goldstein, J.I., Newbury, D.E., Michael, J.R., Ritchie, N.W.M., Scott, J.H.J., Joy, D.C. (2018). Analysis of Specimens with Special Geometry: Irregular Bulk Objects and Particles. In: Scanning Electron Microscopy and X-Ray Microanalysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6676-9_23
Newbury, D. E. (2004). Quantitative electron probe microanalysis of rough targets: Testing the peak‐to‐local background method. Scanning: The Journal of Scanning Microscopies, 26(3), 103-114.
Sorbier, L., Rosenberg, E., & Merlet, C. (2004). Microanalysis of porous materials. Microscopy and Microanalysis, 10(6), 745-752.
Sorbier, L., Rosenberg, E., Merlet, C., & Llovet, X. (2000). EPMA of porous media: A Monte Carlo approach. Microchimica Acta, 132, 189-199.
Thanks Anette,
I will take a look at the references you supplied.
Would the analysis still be valid, if the standard were the same mineral and porous, just as the unknown (chert standard and chert unknown), or am I degrading now the analysis, by compromising the standard? The porosity may not be the same in both, but would be closer.
Thanks.
Joe
Quote from: Joe Boesenberg on March 30, 2023, 10:35:17 AM
Are there any proper correction procedures for situations where the sample mineral is porous? I am thinking of two cases: some serpentine minerals and chert. Obviously, you get low totals. You have the added problem that both phases can have significant water. I get asked very often can you just scale up the analysis to 100 and I constantly tell the users "no". But is there a correction procedure that can be applied? Thanks.
Great question. Anette's response is exactly on-point, so I can just mention a few random thoughts about porosity...
Porosity is a complicated subject. In the extreme porosity does not matter in (non-thin film) analysis EPMA as the distance between the atoms does not make a difference for the matrix corrections as long as the incident electrons come to rest inside the sample (interaction volume). And technically, for fully conductive samples where the porosity/voids are "filled" with vacuum, the porosity should also not make any difference.
However, problems with porosity begin to be a problem when the sample is not conductive and/or the voids are able to retain surface charging, and/or the voids are filled with some gas or liquid, and/or the voids are coated with adsorbed water, etc. Then Anette's suggestions are worth applying.
To answer your last question, yes, if we had a standard serpentinite that had the same exact porosity characteristics as our unknown, that could normalize out these effects, but of course that is not usually an option! :)
And regarding water, yes absolutely it should be included in the matrix correction! First to obtain an accurate matrix correction for the other elements which will be affected quite strongly by this "missing" water:
https://smf.probesoftware.com/index.php?topic=92.msg8485;topicseen#msg8485
In fact even a few wt% missing water can affect the matrix correction surprisingly enough as this hydrous glass analysis shows:
https://smf.probesoftware.com/index.php?topic=92.msg8439;topicseen#msg8439
See also:
Roman, D. C., Cashman, K. V., Gardner, C. A., Wallace, P. J., & Donovan, J. J. (2006). Storage and interaction of compositionally heterogeneous magmas from the 1986 eruption of Augustine Volcano, Alaska. Bulletin of Volcanology, 68, 240-254.
I'm adding a description of this specify unanalyzed element concentrations by input text file here so I can refer to it in another post.
A long, long time ago... Heather Lowers at the USGS in Denver asked for a way to input lots of concentrations analyzed from another technique into Probe for EPMA by using a text file which listed the sample names and element concentrations using this button:
(https://smf.probesoftware.com/gallery/1_06_05_23_9_09_44.png)
I've never used it, but apparently they do. Here is the section from the User Reference Manual on this feature:
(https://smf.probesoftware.com/gallery/1_06_05_23_9_10_03.png)
I just wanted to mention the paper published last year by Dungan, Donovan, Locock and Bullock which demonstrates improved accuracy for major elements (especially Fe), when excess oxygen from ferric iron is included in the matrix correction. See attached pdf below which was published last year in American Mineralogist.
See also this post by John Donovan pointing out how to perform these calculations in Probe for EPMA (and CalcZAF) based on a suggestion from Andrew Locock and Anette von der Handt to utilize the method of Droop (1989) for calculating excess oxygen from ferric iron back in 2019:
https://smf.probesoftware.com/index.php?topic=92.msg8593#msg8593
This implementation of this was assisted by Anette von der Handt and Andrew Locock which was extended to amphibole calculations. The idea for including excess oxygen from ferric iron is an old idea, but based on ideas contributed by many other people including John Donovan, Brian Joy, Aurelien Moy and John Fournelle on the need to include all unanalyzed elements into the matrix correction for the most accurate EPMA analyses.
In the case on excess oxygen from ferric iron in Hematite, without incorporating this excess oxygen, the Fe concentrations will be low by around 1 wt% absolute, resulting in not only a low total, but also inaccurate Fe (and Ti in Fe-Ti oxides).
Aurelien Moy will be publishing a technical paper describing the physics of these various matrix effects for various unanalyzed elements situations, including excess oxygen, but also for other elements, e.g., carbon in carbonates, water in hydrous glasses, boron in boro-silicates, etc.
See also these other publications:
Tingle, Tracy N., et al. "The effect of "missing"(unanalyzed) oxygen on quantitative electron probe microanalysis of hydrous silicate and oxide minerals." Geological Society of America Abstracts with Programs. Vol. 28. No. 6. 1996.
Moy, Aurélien, et al. "On the Importance of Including All Elements in the EPMA Matrix Correction." (2023): 855-856.
One of the interesting aspects to Probe for EPMA is that one can calculate the same data in multiple ways, for example, one can acquire data using off-peak backgrounds and calculate the quant results using the off-peak background method.
But one can also take that same data (usually one should first copy the MDB file to another folder just to keep things straight), and then proceed to apply MAN backgrounds to those same measurements by simply ignoring the off-peak intensities as described here:
https://smf.probesoftware.com/index.php?topic=4.msg2255#msg2255
https://smf.probesoftware.com/index.php?topic=987.msg6455#msg6455
One will find that one can attain about 40% better precision than off-peak backgrounds (in 1/2 the acquisition time!) as explained in our 2016 paper (Donovan et al., 2016, Amer. Min.) and also improve accuracy by utilizing a blank correction.
However, one can also calculate the same data using different ways of specifying unanalyzed elements as well. For example one could specify a fixed concentration of an element, or one could specify to calculate an unanalyzed element (or formula) by difference.
Recently Anette von der Handt measured oxygen for some materials using quantitative x-ray mapping and wanted to compare the measured (and calculated excess oxygen) using measured oxygen, with the Droop et al. method for calculating excess oxygen from ferric iron based on charge balance and a mineral formula. I'll post on using the ferric/ferrous method in CalcImage in the CalcImage board in a moment, but let's start with the Droop method for calculating excess oxygen in Probe for EPMA first, because I had to remember how this needs to be done, when oxygen is measured.
So, we've measured oxygen and now we have a result in say a magnetite material:
(https://smf.probesoftware.com/gallery/1_19_04_24_10_59_20.png)
And we're within ~1.3% relative so not too bad (of course using empirical MACs from Pouchou and Bastin!). But now we want to see how this direct measurement result compares to simply calculating our excess oxygen from ferric iron, because, well you know, we had to give up a spectrometer just to measure oxygen! And maybe using the Droop charge balance method we can do just as well, at least maybe for excess oxygen in magnetites...
So we go (after making a copy of our MDB file!) into the Calculation Options dialog in Probe for EPMA and select the Ferrous/Ferric method for our magnetite material and specify oxygen by stoichiometry, and then we get this error:
(https://smf.probesoftware.com/gallery/1_19_04_24_10_33_13.png)
Doh! If we try and quantify with both measured oxygen *and* oxygen calculated by stoichiometry, we will be adding oxygen *twice* into the matrix correction, and that's no good, right?
OK, so what do we do? Well, we need to disable the measured oxygen for quantification from the Elements/Cations dialog as seen here:
(https://smf.probesoftware.com/gallery/1_19_04_24_10_33_36.png)
And now we can go back into Calculation Options and specify our ferric/ferrous formula and oxygen by stoicihiometry. Now when we quantify our magnetite material we obtain this result:
(https://smf.probesoftware.com/gallery/1_19_04_24_10_33_49.png)
Wait, what the heck? We've got our excess oxygen from ferric iron calculated properly (6.88 wt%) but our totals are low by exactly that amount! And that's because although the excess oxygen from ferric iron was calculated and included into the matrix correction, it was not output to the user! And that's because there's no place to print it out since the only oxygen column present is the measured oxygen column which is reserved for the measurement results and we disabled the measured oxygen for quantification.
So what we need to do is, add oxygen as an *unanalyzed* element to our element list as seen here:
(https://smf.probesoftware.com/gallery/1_19_04_24_10_34_02.png)
Remember, an unanalyzed element is simply an element *without* an x-ray line specified. Now let's calculate the concentrations again:
(https://smf.probesoftware.com/gallery/1_19_04_24_10_34_15.png)
Well now, that's pretty neat, isn't it? 8) But it took me a minute to remember all this when looking at Anette's x-ray maps in CalcImage, where she basically wanted to do the same thing but for maps! I'll post more about that in a bit in the CalcImage topic...
Many of you have probably utilized the Formula by Difference feature in the Analyze! window Calculation Options dialog:
https://smf.probesoftware.com/index.php?topic=92.msg7333#msg7333
By utilizing this option one can, for example, measure only the trace elements in a material, and simply specify the matrix for a proper matrix correction as seen here:
Formula RbTiOPO4 is Calculated by Difference from 100%
Un 7 RbTiOPO4, Results in Elemental Weight Percents
ELEM: K Cs Na Ca Mg Rb Ti P O
TYPE: ANAL ANAL ANAL ANAL ANAL FORM FORM FORM FORM
BGDS: LIN EXP EXP LIN LIN
TIME: 400.00 400.00 400.00 400.00 400.00 --- --- --- ---
BEAM: 100.94 100.94 100.94 100.94 100.94 --- --- --- ---
ELEM: K Cs Na Ca Mg Rb Ti P O SUM
360 .015 .013 -.001 .000 -.001 34.970 19.598 12.673 32.732 100.000
361 .016 .012 -.002 .000 -.001 34.971 19.599 12.673 32.732 100.000
362 .016 .015 .002 .000 .000 34.968 19.597 12.672 32.730 100.000
363 .015 .013 -.004 .000 -.002 34.971 19.599 12.673 32.733 100.000
364 .016 .015 .003 .000 .000 34.967 19.597 12.672 32.729 100.000
365 .015 .013 .002 .000 .000 34.969 19.598 12.673 32.731 100.000
366 .016 .012 .001 .000 -.001 34.970 19.598 12.673 32.732 100.000
AVER: .016 .014 .000 .000 -.001 34.969 19.598 12.673 32.731 100.000
SDEV: .000 .001 .003 .000 .001 .001 .001 .001 .001 .000
SERR: .000 .000 .001 .000 .000 .001 .000 .000 .000
%RSD: 2.86 9.44 3950.98 273.41 -74.31 .00 .00 .00 .00
STDS: 374 1125 336 358 358 --- --- --- ---
STKF: .1102 .2652 .0583 .1676 .0644 --- --- --- ---
STCT: 8027.8 14411.6 630.3 6846.5 3948.1 --- --- --- ---
UNKF: .0001 .0001 .0000 .0000 .0000 --- --- --- ---
UNCT: 9.9 6.3 .0 .1 -.2 --- --- --- ---
UNBG: 44.7 162.4 7.8 37.9 23.0 --- --- --- ---
ZCOR: 1.1551 1.1603 2.6809 1.0543 1.8506 --- --- --- ---
KRAW: .0012 .0004 .0000 .0000 -.0001 --- --- --- ---
PKBG: 1.22 1.04 1.00 1.00 .99 --- --- --- ---
As long as no major elements interfere with any of the trace elements, this is a great way to avoid having to analyze the major elements if one is only interested in the trace elements. Because for the quantitative interference correction one must measure both the interfered element and the interfering element...
And yes, the average measured Ca was 1.4 PPM +/- 3.9 PPM so the values all appear to be zeros with only 3 decimal places displayed! Here is the same analysis with maximum digits option selected (in Analytical | Analysis Options):
Formula RbTiOPO4 is Calculated by Difference from 100%
Un 7 RbTiOPO4, Results in Elemental Weight Percents
ELEM: K Cs Na Ca Mg Rb Ti P O
TYPE: ANAL ANAL ANAL ANAL ANAL FORM FORM FORM FORM
BGDS: LIN EXP EXP LIN LIN
TIME: 400.00 400.00 400.00 400.00 400.00 --- --- --- ---
BEAM: 100.94 100.94 100.94 100.94 100.94 --- --- --- ---
ELEM: K Cs Na Ca Mg Rb Ti P O SUM
360 .01541 .01330 -.00090 .00026 -.00102 34.9699 19.5982 12.6730 32.7319 100.000
361 .01556 .01219 -.00214 .00046 -.00090 34.9706 19.5986 12.6732 32.7325 100.000
362 .01607 .01545 .00166 -.00049 -.00014 34.9680 19.5971 12.6723 32.7301 100.000
363 .01548 .01346 -.00391 .00018 -.00161 34.9711 19.5989 12.6734 32.7330 100.000
364 .01612 .01493 .00333 .00042 -.00011 34.9672 19.5967 12.6720 32.7294 100.000
365 .01512 .01320 .00186 .00047 -.00038 34.9688 19.5976 12.6726 32.7308 100.000
366 .01635 .01206 .00054 -.00031 -.00102 34.9697 19.5981 12.6729 32.7317 100.000
AVER: .01573 .01351 .00006 .00014 -.00074 34.969 19.598 12.673 32.731 100.000
SDEV: .00045 .00128 .00253 .00039 .00055 .001 .001 .001 .001 .00001
SERR: .00017 .00048 .00095 .00015 .00021 .00053 .00030 .00019 .00049
%RSD: 2.86351 9.44152 3950.98 273.411 -74.309 .00399 .00399 .00399 .00399
STDS: 374 1125 336 358 358 --- --- --- ---
STKF: .1102 .2652 .0583 .1676 .0644 --- --- --- ---
STCT: 8027.8 14411.6 630.3 6846.5 3948.1 --- --- --- ---
UNKF: .0001 .0001 .0000 .0000 .0000 --- --- --- ---
UNCT: 9.9 6.3 .0 .1 -.2 --- --- --- ---
UNBG: 44.7 162.4 7.8 37.9 23.0 --- --- --- ---
ZCOR: 1.1551 1.1603 2.6809 1.0543 1.8506 --- --- --- ---
KRAW: .00124 .00044 .00000 .00001 -.00006 --- --- --- ---
PKBG: 1.22201 1.03897 1.00041 1.00145 .98934 --- --- --- ---
But it is important to consider whether one is calculating the analyzed elements as elemental concentrations or oxide concentrations! If one is calculating the measured elements in say a carbonate, as elemental then one should specify the complete formula by difference (CO3) as shown here:
(https://smf.probesoftware.com/gallery/1_27_08_24_11_52_51.png)
This yields the following results for a carbonate where only Ca was measured:
Formula CO3 is Calculated by Difference from 100%
Un 6 CaCO3, Results in Elemental Weight Percents
ELEM: Ca O C
TYPE: ANAL FORM FORM
BGDS: LIN
TIME: 10.00 --- ---
BEAM: 30.00 --- ---
ELEM: Ca O C SUM
12 40.312 47.742 11.946 100.000
13 39.892 48.078 12.030 100.000
14 39.981 48.007 12.013 100.000
15 40.036 47.962 12.002 100.000
AVER: 40.055 47.947 11.998 100.000
SDEV: .181 .145 .036 .000
SERR: .091 .072 .018
%RSD: .45 .30 .30
STDS: 136 --- ---
STKF: .3790 --- ---
STCT: 121.34 --- ---
UNKF: .3791 --- ---
UNCT: 121.38 --- ---
UNBG: .16 --- ---
ZCOR: 1.0567 --- ---
KRAW: 1.0003 --- ---
PKBG: 793.20 --- ---
Un 6 CaCO3, Results in Atomic Percents
ELEM: Ca O C SUM
12 20.179 59.866 19.955 100.000
13 19.899 60.076 20.025 100.000
14 19.958 60.031 20.010 100.000
15 19.995 60.004 20.001 100.000
AVER: 20.008 59.994 19.998 100.000
SDEV: .121 .091 .030 .000
SERR: .060 .045 .015
%RSD: .60 .15 .15
However, if one wants to calculate the analyzed elements as oxides, for example, Ca as an oxide, then one should not enter CO3 as the formula by difference, but instead enter CO2 as the formula by difference since the oxygen for the Ca has already been accounted for. For example:
(https://smf.probesoftware.com/gallery/1_27_08_24_11_53_08.png)
Now when the results are calculated we obtain (essentially) the same results:
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Formula CO2 is Calculated by Difference from 100%
Un 6 CaCO3, Results in Elemental Weight Percents
ELEM: Ca O C
TYPE: ANAL FORM FORM
BGDS: LIN
TIME: 10.00 --- ---
BEAM: 30.00 --- ---
ELEM: Ca O C SUM
12 40.312 47.791 11.898 100.000
13 39.892 48.050 12.058 100.000
14 39.981 47.995 12.024 100.000
15 40.036 47.961 12.003 100.000
AVER: 40.055 47.949 11.996 100.000
SDEV: .181 .112 .069 .000
SERR: .091 .056 .035
%RSD: .45 .23 .58
STDS: 136 --- ---
STKF: .3790 --- ---
STCT: 121.34 --- ---
UNKF: .3791 --- ---
UNCT: 121.38 --- ---
UNBG: .16 --- ---
ZCOR: 1.0567 --- ---
KRAW: 1.0003 --- ---
PKBG: 793.20 --- ---
Un 6 CaCO3, Results in Atomic Percents
ELEM: Ca O C SUM
12 20.183 59.939 19.878 100.000
13 19.897 60.034 20.069 100.000
14 19.957 60.014 20.029 100.000
15 19.995 60.002 20.003 100.000
AVER: 20.008 59.997 19.995 100.000
SDEV: .124 .041 .082 .000
SERR: .062 .021 .041
%RSD: .62 .07 .41
Be sure to update to the latest Probe for EPMA using the Help menu as usual!