Some of you have already seen John Armstrong's excellent presentation of Si-Ir alloy data he and Paul Carpenter acquired for JPL when John and Paul were still at Cal Tech. It is a wonderful example of why we need more than one matrix correction method.
Basically the presentation starts by John explaining how JPL was sure that the alloy in question was either Si50Ir50 (atomic) or Si55Ir45 (atomic), but they didn't know which phase it was. So John proceeds to show his measurements, which when calculated using his default matrix corrections (Armstrong/Reed/CITZMU) gave this result:
(https://smf.probesoftware.com/oldpics/i59.tinypic.com/2sbtqvq.jpg)
So, it must be the Si55Ir45 phase right? Maybe...
But let's run the other matrix corrections to be sure by checking the Use All Matrix Corrections box as seen here:
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/33y4cgm.jpg)
Then we obtain these results after clicking the Calculate button as seen here:
(https://smf.probesoftware.com/oldpics/i58.tinypic.com/2yjy49y.jpg)
Please note that matrix correction #1, the one we showed above does give the Si55Ir45 composition, but now look at the very next matrix correction, a traditional one going back to Philibert, which gives a 50:50 atomic ratio- also one of the "expected" compositions!
So which one is right? Well we could start playing the game where we evaluate the ability of these different matrix corrections to give the right answer for this particular system, and yes, the atomic number correction is significant, so perhaps the more "primitive", Philibert correction is more suspect, but in the end John and Paul were able to utilize a SiIr alloy of known composition as a primary standard and the Si55Ir45 (atomic) composition is the correct composition, but using pure element standards the choice seems arbitrary based on the results above.
This is just one more reason why the professional analyst needs to rely on more than a single matrix correction- for the simple reason that they have all been "optimized" to particular empirical data sets and therefore work better on some compositions than others.
In the meantime let's look at the original Armstrong/Reed correction which gave us the Si55Ir45 (atomic) composition using the Heinrich/CitZAF MACs as originally implemented by John as seen here again:
SAMPLE: 1, ITERATIONS: 4, Z-BAR: 67.40733
ELEMENT ABSCOR FLUCOR ZEDCOR ZAFCOR STP-POW BKS-COR F(x)u Ec Eo/Ec MACs
Ir la .9907 1.0000 1.0824 1.0723 1.1287 .9589 .9548 11.2150 1.7833 124.108
Si ka 1.6859 .9886 .7791 1.2986 .5819 1.3389 .5095 1.8390 10.8755 1456.45
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Ir la .79090 .79090 84.806 ----- 44.860 .449 20.00
Si ka .11730 .11730 15.232 ----- 55.140 .551 20.00
TOTAL: 100.038 ----- 100.000 1.000
Let's try a different set of MACs, the Henke MACs for example as seen here:
SAMPLE: 1, ITERATIONS: 3, Z-BAR: 67.89716
ELEMENT ABSCOR FLUCOR ZEDCOR ZAFCOR STP-POW BKS-COR F(x)u Ec Eo/Ec MACs
Ir la .9911 1.0000 1.0780 1.0684 1.1220 .9608 .9544 11.2150 1.7833 123.152
Si ka 1.5841 .9880 .7773 1.2166 .5782 1.3444 .5368 1.8390 10.8755 1302.59
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Ir la .79090 .79090 84.498 ----- 46.387 .464 20.00
Si ka .11730 .11730 14.271 ----- 53.613 .536 20.00
TOTAL: 98.769 ----- 100.000 1.000
Somewhat more ambiguous to say the least. Let's run all the matrix corrections again but with the same (Henke) mass absorption coefficients:
Summary of All Calculated (averaged) Matrix Corrections:
#1 approx. Ir45Si55 (atomic) based on Ir3Si5 standard
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Elemental Weight Percents:
ELEM: Ir Si TOTAL
1 84.498 14.271 98.769 Armstrong/Love Scott (default)
2 86.704 11.747 98.451 Conventional Philibert/Duncumb-Reed
3 84.857 12.874 97.731 Heinrich/Duncumb-Reed
4 84.334 12.785 97.119 Love-Scott I
5 84.324 12.798 97.122 Love-Scott II
6 84.203 11.044 95.247 Packwood Phi(pz) (EPQ-91)
7 86.125 13.959 100.084 Bastin (original) Phi(pz)
8 84.607 13.656 98.263 Bastin PROZA Phi(pz) (EPQ-91)
9 84.525 12.801 97.326 Pouchou and Pichoir-Full (Original)
10 84.289 12.599 96.888 Pouchou and Pichoir-Simplified (XPP)
AVER: 84.847 12.853 97.700
SDEV: .858 .969 1.299
SERR: .271 .306
MIN: 84.203 11.044 95.247
MAX: 86.704 14.271 100.084
Atomic Percents:
ELEM: Ir Si TOTAL
1 46.387 53.613 100.000 Armstrong/Love Scott (default)
2 51.891 48.109 100.000 Conventional Philibert/Duncumb-Reed
3 49.063 50.937 100.000 Heinrich/Duncumb-Reed
4 49.082 50.918 100.000 Love-Scott I
5 49.053 50.947 100.000 Love-Scott II
6 52.699 47.301 100.000 Packwood Phi(pz) (EPQ-91)
7 47.413 52.587 100.000 Bastin (original) Phi(pz)
8 47.516 52.485 100.000 Bastin PROZA Phi(pz) (EPQ-91)
9 49.107 50.893 100.000 Pouchou and Pichoir-Full (Original)
10 49.435 50.565 100.000 Pouchou and Pichoir-Simplified (XPP)
AVER: 49.164 50.836 100.000
SDEV: 1.930 1.930 .000
SERR: .610 .610
MIN: 46.387 47.301 100.000
MAX: 52.699 53.613 100.000
Pretty hard to tell what the correct answer is! So, what can we do next? Well I then ran Penepma 2012 for around 10 days and modeled 11 binary compositions in the Si-Ir system and here are some results for Si Ka at 20 keV:
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/2n8yi6x.jpg)
The weight percents of Si and k-ratio (also in percent) are shown circled in red. Here is the Ir La line at 20 keV:
(https://smf.probesoftware.com/oldpics/i62.tinypic.com/11ufdat.jpg)
Currently I haven't yet provided a way to automatically insert these Penepma Monte-Carlo calculations into the matrix.mdb database (though it is on the "to do list"), but next we'll look at utilizing the Penfluor/Fanal Si-Ir binary which contains a full Monte-Carlo calculation for the primary intensity and an analytical expression for the fluorescence.
OK, let's start again with the Armstrong/Reed/CITZMU phi-rho-z calculation of the SiIr alloy where we obtain what ostensibly appears to be Si55Ir45 (atomic):
#1 approx. Ir45Si55 (atomic) based on Ir3Si5 standard
SAMPLE: 1, ITERATIONS: 4, Z-BAR: 67.40733
ELEMENT ABSCOR FLUCOR ZEDCOR ZAFCOR STP-POW BKS-COR F(x)u Ec Eo/Ec MACs
Ir la .9907 1.0000 1.0824 1.0723 1.1287 .9589 .9548 11.2150 1.7833 124.108
Si ka 1.6859 .9886 .7791 1.2986 .5819 1.3389 .5095 1.8390 10.8755 1456.45
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Ir la .79090 .79090 84.806 ----- 44.860 .449 20.00
Si ka .11730 .11730 15.232 ----- 55.140 .551 20.00
TOTAL: 100.038 ----- 100.000 1.000
Now we switch to alpha factor polynomial fitting using the Analytical | ZAF, Phi-Rho-Z, Alpha Factor, Calibration Curve Selection menu:
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/otnhp2.jpg)
If we plot these alpha factors derived from the k-ratios from the Armstrong/Reed/CITZMU calculations (see the Analytical | Calculate and Plot Binary Alpha factors menu) we obtain this plot for Ir La at 20 keV:
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/2zzoykj.jpg)
and this plot for Si ka at 20 keV where we can see that even with a 2nd order polynomial, the fit is not perfect due to the non-linear nature of the absorption correction:
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/21294ky.jpg)
Now we get roughly similar results to the "straight" phi-rho-z calculation fitting the Armstrong/Reed/CITZMU k-ratios to polynomial alpha factors as seen here:
ELEMENT ir la si ka Total
UNK KRAT .7909 .1173
UNK WT% 84.990 14.951 99.941
UNK AT% 45.375 54.625 100.000
UNK BETA 1.0746 1.2746
ALPITER 6.0000
The point being that the polynomial alpha factor fitting allows one to pre-calculate the physics for each binary system, and subsequently combine them using the beta factor expression for arbitrary compositions as described here:
http://smf.probesoftware.com/index.php?topic=139.msg637#msg637
Now we enable the Penepma 2012 k-ratios as seen here, again from the Analytical | ZAF, Phi-Rho-Z, Alpha Factor, Calibration Curve Selection menu:
(https://smf.probesoftware.com/oldpics/i58.tinypic.com/16lwggz.jpg)
and obtain these intermediate results using the Penepma 2012 Penfluor/Fanal derived k-ratios for Si and Ir:
Initializing alpha-factors...
Number of alpha-factor binaries to be calculated = 1
Calculating alpha-factor binary ir la in si
AFactorPenepmaReadMatrix: Ir la in Si at 40 degrees and 20 keV
Conc Kratios Alpha
99.0000 98.006218 2.01400
95.0000 92.924858 1.44663
90.0000 86.025154 1.46206
80.0000 73.216965 1.46322
60.0000 50.819466 1.45163
50.0000 40.913555 1.44418
40.0000 31.832989 1.42760
20.0000 15.031998 1.41312
10.0000 7.298365 1.41130
5.00000 3.682503 1.37660
1.00000 .738135 1.35835
AFactorPenepmaReadMatrix: Si ka in Ir at 40 degrees and 20 keV
Conc Kratios Alpha
99.0000 98.885162 1.11614
95.0000 93.915077 1.23104
90.0000 88.040230 1.22260
80.0000 76.524353 1.22709
60.0000 55.550423 1.20025
50.0000 45.765198 1.18507
40.0000 36.368473 1.16642
20.0000 18.166149 1.12619
10.0000 9.182739 1.09889
5.00000 4.624117 1.08557
1.00000 .924762 1.08218
NON-LINEAR Alpha Factors, Takeoff= 40, KeV= 20
P=1, Pt#1, C=.9900, K=.9801, Alpha=2.0140
P=2, Pt#2, C=.9500, K=.9292, Alpha=1.4466
P=3, Pt#3, C=.9000, K=.8603, Alpha=1.4621
P=4, Pt#4, C=.8000, K=.7322, Alpha=1.4632
P=5, Pt#5, C=.6000, K=.5082, Alpha=1.4516
P=6, Pt#6, C=.5000, K=.4091, Alpha=1.4442
P=7, Pt#7, C=.4000, K=.3183, Alpha=1.4276
P=8, Pt#8, C=.2000, K=.1503, Alpha=1.4131
P=9, Pt#9, C=.1000, K=.0730, Alpha=1.4113
P=10, Pt#10, C=.0500, K=.0368, Alpha=1.3766
P=11, Pt#11, C=.0100, K=.0074, Alpha=1.3583
Xray Matrix Alpha1 Alpha2 Alpha3 %MaxDev
ir la in si 1.4124 -.3141 .5920 16.50
P=1, Pt#1, C=.9900, K=.9889, Alpha=1.1161
P=2, Pt#2, C=.9500, K=.9392, Alpha=1.2310
P=3, Pt#3, C=.9000, K=.8804, Alpha=1.2226
P=4, Pt#4, C=.8000, K=.7652, Alpha=1.2271
P=5, Pt#5, C=.6000, K=.5555, Alpha=1.2003
P=6, Pt#6, C=.5000, K=.4577, Alpha=1.1851
P=7, Pt#7, C=.4000, K=.3637, Alpha=1.1664
P=8, Pt#8, C=.2000, K=.1817, Alpha=1.1262
P=9, Pt#9, C=.1000, K=.0918, Alpha=1.0989
P=10, Pt#10, C=.0500, K=.0462, Alpha=1.0856
P=11, Pt#11, C=.0100, K=.0092, Alpha=1.0822
Xray Matrix Alpha1 Alpha2 Alpha3 %MaxDev
si ka in ir 1.0654 .3966 -.2790 6.13
Penepma K-Ratio Alpha Factors:
Xray Matrix Alpha1 Alpha2 Alpha3
Si ka in Ir 1.0654 .3966 -.2790 *From Penepma 2012 Calculations
Ir la in Si 1.4124 -.3141 .5920 *From Penepma 2012 Calculations
All Alpha Factors:
ir si
ir la 1.0000 1.4124
ir la .0000 -.3141
ir la .0000 .5920
si ka 1.0654 1.0000
si ka .3966 .0000
si ka -.2790 .0000
Plotted up these Penepma derived alpha-factors look like this for Ir La:
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/fn8i0w.jpg)
and this for Si Ka:
(https://smf.probesoftware.com/oldpics/i60.tinypic.com/2d9e8og.jpg)
Obviously there are some fit problems as we approach the pure end-member. This is primarily a precision problem that occurs from subtracting two large numbers from each other, but they don't have a very significant effect on the results because the alpha factor for an element in itself is 1.0.
The calculation utilizing these Penepma derived alpha factors is here (primary intensity from Penfluor Monte-Carlo, fluorescence from Fanal analytical model:
ELEMENT ir la si ka Total
UNK KRAT .7909 .1173
UNK WT% 83.343 13.746 97.089
UNK AT% 46.977 53.023 100.000
UNK BETA 1.0538 1.1719
ALPITER 5.0000
Somewhat ambiguous one might say. Now we limit the polynomial fit to avoid low precision calculations as the pure element concentrations are approached by selecting this option:
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/29byj29.jpg)
Initializing alpha-factors...
Number of alpha-factor binaries to be calculated = 1
Calculating alpha-factor binary ir la in si
AFactorPenepmaReadMatrix: Ir la in Si at 40 degrees and 20 keV
Conc Kratios Alpha
99.0000 98.006218 2.01400
95.0000 92.924858 1.44663
90.0000 86.025154 1.46206
80.0000 73.216965 1.46322
60.0000 50.819466 1.45163
50.0000 40.913555 1.44418
40.0000 31.832989 1.42760
20.0000 15.031998 1.41312
10.0000 7.298365 1.41130
5.00000 3.682503 1.37660
1.00000 .738135 1.35835
AFactorPenepmaReadMatrix: Si ka in Ir at 40 degrees and 20 keV
Conc Kratios Alpha
99.0000 98.885162 1.11614
95.0000 93.915077 1.23104
90.0000 88.040230 1.22260
80.0000 76.524353 1.22709
60.0000 55.550423 1.20025
50.0000 45.765198 1.18507
40.0000 36.368473 1.16642
20.0000 18.166149 1.12619
10.0000 9.182739 1.09889
5.00000 4.624117 1.08557
1.00000 .924762 1.08218
NON-LINEAR Alpha Factors, Takeoff= 40, KeV= 20
P=3, Pt#1, C=.9000, K=.8603, Alpha=1.4621
P=4, Pt#2, C=.8000, K=.7322, Alpha=1.4632
P=5, Pt#3, C=.6000, K=.5082, Alpha=1.4516
P=6, Pt#4, C=.5000, K=.4091, Alpha=1.4442
P=7, Pt#5, C=.4000, K=.3183, Alpha=1.4276
P=8, Pt#6, C=.2000, K=.1503, Alpha=1.4131
P=9, Pt#7, C=.1000, K=.0730, Alpha=1.4113
P=10, Pt#8, C=.0500, K=.0368, Alpha=1.3766
P=11, Pt#9, C=.0100, K=.0074, Alpha=1.3583
Xray Matrix Alpha1 Alpha2 Alpha3 %MaxDev
ir la in si 1.3700 .2149 -.1261 1.50
P=3, Pt#1, C=.9000, K=.8804, Alpha=1.2226
P=4, Pt#2, C=.8000, K=.7652, Alpha=1.2271
P=5, Pt#3, C=.6000, K=.5555, Alpha=1.2003
P=6, Pt#4, C=.5000, K=.4577, Alpha=1.1851
P=7, Pt#5, C=.4000, K=.3637, Alpha=1.1664
P=8, Pt#6, C=.2000, K=.1817, Alpha=1.1262
P=9, Pt#7, C=.1000, K=.0918, Alpha=1.0989
P=10, Pt#8, C=.0500, K=.0462, Alpha=1.0856
P=11, Pt#9, C=.0100, K=.0092, Alpha=1.0822
Xray Matrix Alpha1 Alpha2 Alpha3 %MaxDev
si ka in ir 1.0743 .2858 -.1283 .52
Penepma K-Ratio Alpha Factors:
Xray Matrix Alpha1 Alpha2 Alpha3
Si ka in Ir 1.0743 .2858 -.1283 *From Penepma 2012 Calculations
Ir la in Si 1.3700 .2149 -.1261 *From Penepma 2012 Calculations
All Alpha Factors:
ir si
ir la 1.0000 1.3700
ir la .0000 .2149
ir la .0000 -.1261
si ka 1.0743 1.0000
si ka .2858 .0000
si ka -.1283 .0000
Plotting up these 90% limited alpha factors we obtain more precise fits as seen here for Ir la:
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/fz162s.jpg)
and here for Si Ka:
(https://smf.probesoftware.com/oldpics/i59.tinypic.com/rh9a42.jpg)
And we now obtain these results, which are somewhat better, though still not as unequivocal as one would hope.
ELEMENT ir la si ka Total
UNK KRAT .7909 .1173
UNK WT% 83.604 13.990 97.595
UNK AT% 46.617 53.383 100.000
UNK BETA 1.0571 1.1927
ALPITER 5.0000
Though it is closer to Si55Ir45 as expected. But this is the "state of the art" for this particular Monte-Carlo physics!
Just for "funsies" I ran the last calculation using an 80% limit for the best possible Penepma 2012 alpha factor extrapolation which you set here:
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/qovgbt.jpg)
and, which looks like this for Ir la:
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/2lc3902.jpg)
and this for Si Ka:
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/2h6zj11.jpg)
and the result is further improvement to the "truth"... though perhaps it would be worthwhile at this point to use a larger dataset...
ELEMENT ir la si ka Total
UNK KRAT .7909 .1173
UNK WT% 83.630 14.074 97.703
UNK AT% 46.477 53.523 100.000
UNK BETA 1.0574 1.1998
ALPITER 5.0000
For further investigation let's examine the Pb-Si system which is a good proxy for the Si-Ir system due to the large difference in A/Z between the two elements (remember, we need to eliminate all normalizations to mass in this physics!), and instead utilize a single crystal of PbSiO3 for which the stoichiometry is perfect as only Nature can accomplish (you know, most recently the Tsumeb locality). :-*
http://www.minersoc.org/pages/Archive-MM/Volume_29/29-218-933.pdf
By the way:
Element A/Z
Ir 2.49
Pb 2.52
Si 2.00
Next week we'll do some measurements on this material!
But before we do that I just wanted to make sure everyone saw the interesting comparison between the analytical expressions and the Monte-carlo as seen here for Ir La which are actually fairly similar in magnitude though somewhat different in slope:
(https://smf.probesoftware.com/oldpics/i59.tinypic.com/t50i2e.jpg)
But this isn't too surprising since Ir La is a very energetic x-ray around 10 keV.
The bigger surprise is for Si Ka which though a fairly simple atom is experiencing some very different physics depending on who's doing the calculation as seen here:
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/2pyuwsh.jpg)
Related to the Si-Ir problem is the ability to measure Si ka in various matrices. Here are results from some silicate measurements I recently did. SiO2 was the primary standard (20 keV, 30 nA, 10 um beam). These are:
SiO2 yes, I know it's technically *not* a silicate
Mg2SiO4 synthetic (Japan, Takei)
Fe2SiO4 synthetic (Oak Ridge, Boatner)
Mn2SiO4 synthetic (Purdue)
Co2SiO4 synthetic (Purdue)
ZrSiO4 synthetic (Hanchar)
PbSiO3 natural (Tsumeb)
HfSiO4 synthetic (Hanchar)
ThSiO4 synthetic (Hanchar)
CaMgSi2O6 natural (Chesterman)
I will also post some Penepma 2012 calculations for these silicates for comparison. To start here are all the standard plotted using our Evaluate application which allows one to easily compare standard accuracy. I thank Paul Carpenter and John Fournelle for helping me with this app.
(https://smf.probesoftware.com/oldpics/i62.tinypic.com/neic12.jpg)
Here we can see that there are a few "outliers" particularly HfSiO4, which is a mass absorption coefficient problem for Si Ka by Hf which is close to an absorption edge. CalcZAF reports the following MACs from this binary from various sources:
MAC value for Si ka in Hf = 5449.15 (LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV)
MAC value for Si ka in Hf = 5151.30 (CITZMU Heinrich (1966) and Henke and Ebisu (1974))
MAC value for Si ka in Hf = 5635.09 (MCMASTER McMaster (LLL, 1969) (modified by Rivers))
MAC value for Si ka in Hf = 5037.41 (MAC30 Heinrich (Fit to Goldstein tables, 1987))
MAC value for Si ka in Hf = 5152.54 (MACJTA Armstrong (FRAME equations, 1992))
MAC value for Si ka in Hf = 4926.87 (FFAST Chantler (NIST v 2.1, 2005))
MAC value for Si ka in Hf = 4926.87 (USERMAC User Defined MAC Table)
We can see that the more modern FFAST value is smaller, which should help the correction, so we specify the FFAST MAC table from the Analytical | ZAF, Phi-Rho-Z, Alpha factor and Calibration Curve Selections menu dialog (MACs button) and get this somewhat better result, though some of the other standards are now slightly worse:
(https://smf.probesoftware.com/oldpics/i59.tinypic.com/2pocxhd.jpg)
So let's try some other corrections, for example the PAP correction, which shows considerable improvement (at least the HfSiO4 now agrees with the other secondary standards!), even though all these secondary standards are a little low compared with the SiO2 priamry standard:
(https://smf.probesoftware.com/oldpics/i62.tinypic.com/2md4y8.jpg)
So, now let's try the XPP (PAP) correction which gives similar results:
(https://smf.probesoftware.com/oldpics/i58.tinypic.com/ea333r.jpg)
Bastin's Proza correction is however, yields quite different results:
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/x2npc8.jpg)