I've been working on improving the Reed fluorescence correction to include fluorescence by beta lines (and also fluorescence of beta lines, if one really insists on using them as one's analytical line!), but there is not much data to use as a "test bed".
The Pouchou data set is limited by the fact that the binary compositions selected were chosen to exclude as much as possible large fluorescence correction situations! The idea being to test the Z and A parts of the analytical expressions.
I've run some Penfluor/Fanal simulations and created a subset of large fluorescence corrections based on that output and that helps. I will be making more rigorous simulations based on the full Penepma but that will take some additional time.
In the meantime there is improvement evident for some 1500 binary compositional situations with large fluorescence corrections. First the original Reed fluorescence analytical correction:
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/2nth43k.jpg)
and here is the same data calculated with the Reed fluorescence correction modified to include beta lines :
(https://smf.probesoftware.com/oldpics/i58.tinypic.com/t5fxfo.jpg)
Significant improvement though it could be better and I will continue to improve the relative line weight calculations. And don't forget, this is for worst case fluorescence situations, not normal samples.
Well I have to admit this hurts a little.
After all that work on improving the Reed fluorescence to include fluorescence *by* beta lines, it sure doesn't have much of an effect for monazite compositions- which I guess is just as well.
Correction Method and Mass Absorption Coefficient File:
ZAF or Phi-Rho-Z Calculations
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Current ZAF or Phi-Rho-Z Selection:
Armstrong/Love Scott (default)
Correction Selections:
Phi(pz) Absorption of Armstrong/Packwood-Brown 1981 MAS
Stopping Power of Love-Scott
Backscatter Coefficient of Love-Scott
Backscatter of Love-Scott
Mean Ionization of Berger-Seltzer
Phi(pz) Equation of Love-Scott
Reed/JTA w/ M-Line Correction and JTA Intensity Mod.
Fluorescence by Beta Lines Included
Un 13 Montel Madagascar 6-1
TakeOff = 40.0 KiloVolt = 20.0 Beam Current = 150. Beam Size = 5
(Magnification (analytical) = 20000), Beam Mode = Analog Spot
(Magnification (default) = 0, Magnification (imaging) = 100)
Image Shift (X,Y): .00, .00
Number of Data Lines: 3 Number of 'Good' Data Lines: 3
First/Last Date-Time: 09/10/2003 10:26:45 AM to 09/10/2003 11:00:49 AM
Average Total Oxygen: 26.248 Average Total Weight%: 99.895
Average Calculated Oxygen: 26.248 Average Atomic Number: 43.366
Average Excess Oxygen: .000 Average Atomic Weight: 40.599
Average ZAF Iteration: 4.00 Average Quant Iterate: 4.00
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Un 13 Montel Madagascar 6-1, Results in Elemental Weight Percents
ELEM: Ca Si Al Y Pr Nd Sm Gd Ce La P U Pb Th Dy Er O
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL CALC
BGDS: LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN
TIME: 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 20.00 20.00 20.00 240.00 240.00 240.00 80.00 80.00 ---
BEAM: 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 ---
ELEM: Ca Si Al Y Pr Nd Sm Gd Ce La P U Pb Th Dy Er O SUM
188 .528 1.211 .014 .053 2.440 8.014 .795 .323 24.076 11.885 11.466 .088 .260 12.347 .027 -.007 26.265 99.786
189 .521 1.198 .007 .057 2.477 8.005 .828 .338 24.126 11.916 11.465 .095 .254 12.375 .054 -.012 26.274 99.976
190 .518 1.214 .012 .051 2.450 8.000 .780 .285 24.248 12.029 11.384 .094 .265 12.372 .036 -.019 26.205 99.923
AVER: .523 1.208 .011 .054 2.456 8.006 .801 .316 24.150 11.943 11.438 .092 .260 12.364 .039 -.012 26.248 99.895
SDEV: .005 .009 .004 .003 .019 .007 .025 .027 .088 .076 .047 .004 .006 .015 .014 .006 .038 .098
SERR: .003 .005 .002 .002 .011 .004 .014 .016 .051 .044 .027 .002 .003 .009 .008 .003 .022
%RSD: .98 .71 34.90 5.63 .79 .09 3.07 8.54 .37 .63 .41 4.06 2.15 .12 35.32 -48.43 .14
STDS: 305 305 305 1016 1010 1009 1011 1005 1001 1007 1001 15 17 16 1002 1003 ---
STKF: .0862 .1608 .1136 .4598 .5438 .5479 .5533 .5555 .5348 .5383 .0783 .8994 .7907 .7095 .5625 .5656 ---
STCT: 122.89 443.60 303.18 42.38 58.63 69.20 90.67 109.30 47.53 40.77 30.38 214.22 199.42 136.30 125.91 139.67 ---
UNKF: .0049 .0062 .0000 .0003 .0222 .0721 .0071 .0026 .2155 .1056 .0695 .0008 .0020 .1108 .0003 -.0001 ---
UNCT: 6.99 17.11 .11 .03 2.39 9.10 1.16 .51 19.16 8.00 26.95 .20 .50 21.28 .07 -.02 ---
UNBG: 2.10 2.95 1.68 .24 .55 .69 .86 .98 .49 .40 .28 1.39 .67 1.07 1.20 1.49 ---
ZCOR: 1.0648 1.9470 2.5906 1.5934 1.1067 1.1109 1.1349 1.2078 1.1205 1.1305 1.6459 1.0838 1.3131 1.1161 1.2371 1.2401 ---
KRAW: .0569 .0386 .0004 .0007 .0408 .1315 .0128 .0047 .4030 .1962 .8870 .0009 .0025 .1562 .0006 -.0002 ---
PKBG: 4.33 6.80 1.07 1.13 5.32 14.15 2.34 1.52 40.31 21.06 95.97 1.15 1.75 20.84 1.06 .98 ---
INT%: .00 -3.89 -.03 ---- -24.57 -.90 -18.26 -85.44 ---- -.16 ---- -60.41 -.35 ---- -59.11 62.88 ---
Correction Method and Mass Absorption Coefficient File:
ZAF or Phi-Rho-Z Calculations
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Current ZAF or Phi-Rho-Z Selection:
Armstrong/Love Scott (default)
Correction Selections:
Phi(pz) Absorption of Armstrong/Packwood-Brown 1981 MAS
Stopping Power of Love-Scott
Backscatter Coefficient of Love-Scott
Backscatter of Love-Scott
Mean Ionization of Berger-Seltzer
Phi(pz) Equation of Love-Scott
Reed/JTA w/ M-Line Correction and JTA Intensity Mod.
Fluorescence by Beta Lines NOT Included
Un 13 Montel Madagascar 6-1
TakeOff = 40.0 KiloVolt = 20.0 Beam Current = 150. Beam Size = 5
(Magnification (analytical) = 20000), Beam Mode = Analog Spot
(Magnification (default) = 0, Magnification (imaging) = 100)
Image Shift (X,Y): .00, .00
Number of Data Lines: 3 Number of 'Good' Data Lines: 3
First/Last Date-Time: 09/10/2003 10:26:45 AM to 09/10/2003 11:00:49 AM
Average Total Oxygen: 26.249 Average Total Weight%: 99.901
Average Calculated Oxygen: 26.249 Average Atomic Number: 43.367
Average Excess Oxygen: .000 Average Atomic Weight: 40.600
Average ZAF Iteration: 4.00 Average Quant Iterate: 4.00
Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Un 13 Montel Madagascar 6-1, Results in Elemental Weight Percents
ELEM: Ca Si Al Y Pr Nd Sm Gd Ce La P U Pb Th Dy Er O
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL CALC
BGDS: LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN
TIME: 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 20.00 20.00 20.00 240.00 240.00 240.00 80.00 80.00 ---
BEAM: 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 149.54 ---
ELEM: Ca Si Al Y Pr Nd Sm Gd Ce La P U Pb Th Dy Er O SUM
188 .528 1.212 .014 .053 2.440 8.014 .795 .323 24.076 11.886 11.466 .088 .260 12.350 .027 -.007 26.266 99.792
189 .521 1.198 .007 .057 2.477 8.005 .828 .338 24.127 11.917 11.465 .095 .254 12.378 .054 -.012 26.275 99.982
190 .518 1.214 .012 .051 2.450 8.000 .780 .285 24.248 12.030 11.384 .094 .265 12.375 .036 -.019 26.206 99.929
AVER: .523 1.208 .011 .054 2.456 8.007 .801 .315 24.150 11.944 11.438 .092 .260 12.368 .039 -.012 26.249 99.901
SDEV: .005 .009 .004 .003 .019 .007 .025 .027 .088 .076 .047 .004 .006 .015 .014 .006 .038 .098
SERR: .003 .005 .002 .002 .011 .004 .014 .016 .051 .044 .027 .002 .003 .009 .008 .003 .022
%RSD: .98 .71 34.90 5.63 .79 .09 3.07 8.54 .37 .63 .41 4.06 2.15 .12 35.33 -48.42 .14
STDS: 305 305 305 1016 1010 1009 1011 1005 1001 1007 1001 15 17 16 1002 1003 ---
STKF: .0862 .1608 .1135 .4592 .5438 .5479 .5533 .5555 .5348 .5383 .0783 .8994 .7907 .7095 .5625 .5656 ---
STCT: 122.89 443.60 303.18 42.38 58.63 69.20 90.67 109.30 47.53 40.77 30.38 214.22 199.42 136.30 125.91 139.67 ---
UNKF: .0049 .0062 .0000 .0003 .0222 .0721 .0071 .0026 .2155 .1056 .0695 .0008 .0020 .1108 .0003 -.0001 ---
UNCT: 6.99 17.11 .11 .03 2.39 9.10 1.16 .51 19.16 8.00 26.95 .20 .50 21.28 .07 -.02 ---
UNBG: 2.10 2.95 1.68 .24 .55 .69 .86 .98 .49 .40 .28 1.39 .67 1.07 1.20 1.49 ---
ZCOR: 1.0652 1.9481 2.5913 1.5946 1.1068 1.1109 1.1349 1.2078 1.1205 1.1306 1.6460 1.0842 1.3133 1.1164 1.2371 1.2401 ---
KRAW: .0569 .0386 .0004 .0007 .0408 .1315 .0128 .0047 .4030 .1962 .8870 .0009 .0025 .1562 .0006 -.0002 ---
PKBG: 4.33 6.80 1.07 1.13 5.32 14.15 2.34 1.52 40.31 21.06 95.97 1.15 1.75 20.84 1.06 .98 ---
INT%: .00 -3.89 -.03 ---- -24.57 -.90 -18.26 -85.44 ---- -.16 ---- -60.41 -.35 ---- -59.12 62.88 ---
But consideration of fluorescence by Kb lines IS important for accurate quantification in certain cases, such as analysis of Mn in fayalitic olivine, Fe in cobaltite, or Co in pentlandite or heazlewoodite.
If you're using monazite as a test case, then I assume that you are also separating fluorescence effects of La and Lb1 lines in your improved correction?
Quote from: Brian Joy on May 23, 2015, 04:55:36 PM
But consideration of fluorescence by Kb lines IS important for accurate quantification in certain cases, such as analysis of Mn in fayalitic olivine, Fe in cobaltite, or Co in pentlandite or heazlewoodite.
Hi Brian,
Yes of course. Fe ka by Ni comes to mind! And that is exactly why I've made this request:
http://smf.probesoftware.com/index.php?topic=47.msg2768#msg2768
Quote from: Brian Joy on May 23, 2015, 04:55:36 PM
If you're using monazite as a test case, then I assume that you are also separating fluorescence effects of La and Lb1 lines in your improved correction?
The monazite analysis is a just a handy composition I use for testing a large number of corrections in my software for internal accuracy.
As for L line fluorescence effects I separate all these like this:
' Variable fluor_type2%() is code for type of fluorescence: 0 = none
' 1=Ka by Ka 2=Ka by Kb 3=Ka by La 4=Ka by Lb 5=Ka by Ma 6=Ka by Mb
' 7=Kb by Ka 8=Kb by Kb 9=Kb by La 10=Kb by Lb 11=Kb by Ma 12=Kb by Mb
'13=La by Ka 14=La by Kb 15=La by La 16=La by Lb 17=La by Ma 18=La by Mb
'19=Lb by Ka 20=Lb by Kb 21=Lb by La 22=Lb by Lb 23=Lb by Ma 24=Lb by Mb
'25=Ma by Ka 26=Ma by Kb 27=Ma by La 28=Ma by Lb 29=Ma by Ma 30=Ma by Mb
'31=Mb by Ka 32=Mb by Kb 33=Mb by La 34=Mb by Lb 35=Mb by Ma 36=Mb by Mb
It's not completely rigorous, but it's a significant improvement over previous analytical efforts. Note I define these transition as this:
"K L3" (Ka)
"K M3" (Kb)
"L3 M5" (La)
"L2 M4" (Lb)
"M5 N7" (Ma)
"M4 N6" (Mb)
Of course, if one prefers full rigor, then a quantum mechanical Monte Carlo method such as Penepma is the way to go. I'm about 1/3 of the way through the entire periodic table calculating k-ratios for binary systems which are then combined in seconds for on-line analyses. My most recent efforts in this area are described in more detail here:
http://smf.probesoftware.com/index.php?topic=47.msg2680#msg2680
And that was before I implemented the non-linear alpha fit as seen here:
http://smf.probesoftware.com/index.php?topic=239.msg2763#msg2763
which is very important for situation with extreme fluorescence (and absorption) effects. The problem for modeling fluorescence corrections is as you know, the lack of decent measurements of highly fluoresced systems to check the models. Hence my measurement request above...
But as the Penepma alpha factor topic link above shows, a 2.8% error distribution standard deviation at 0.9928 accuracy (Pouchou dataset) is pretty darn good. And this Penepma Monte Carlo parameterization performs on-line calculations in seconds.
So in another year or so I'll have the complete periodic table. After that... well we always need more precision!
For all, attached below is a chart I find helpful.
The point of the above post being more that even in a relatively complex composition as monazite with significant high Z element emissions going every which way, we still see only a small contribution from beta fluorescence.
As for a system more along the lines (pun intended!), which Brian mentioned here is an example of a high alloy steel, first with fluorescence *with* beta lines:
Correction Method and Mass Absorption Coefficient File:
ZAF or Phi-Rho-Z Calculations
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Current ZAF or Phi-Rho-Z Selection:
Armstrong/Love Scott (default)
Correction Selections:
Phi(pz) Absorption of Armstrong/Packwood-Brown 1981 MAS
Stopping Power of Love-Scott
Backscatter Coefficient of Love-Scott
Backscatter of Love-Scott
Mean Ionization of Berger-Seltzer
Phi(pz) Equation of Love-Scott
Reed/JTA w/ M-Line Correction and JTA Intensity Mod.
Fluorescence by Beta Lines Included
St 651 Set 2 NIST SRM C2402 (Hastelloy C)
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 30.0 Beam Size = 0
(Magnification (analytical) = 20000), Beam Mode = Analog Spot
(Magnification (default) = 1000, Magnification (imaging) = 100)
Image Shift (X,Y): .00, .00
High temperature alloy
Number of Data Lines: 5 Number of 'Good' Data Lines: 5
First/Last Date-Time: 03/14/2015 08:09:05 PM to 03/14/2015 08:20:58 PM
WARNING- Using Exponential Off-Peak correction for cr ka
Average Total Oxygen: .000 Average Total Weight%: 98.011
Average Calculated Oxygen: .000 Average Atomic Number: 31.181
Average Excess Oxygen: .000 Average Atomic Weight: 62.245
Average ZAF Iteration: 3.00 Average Quant Iterate: 2.00
St 651 Set 2 NIST SRM C2402 (Hastelloy C), Results in Elemental Weight Percents
SPEC: Co Si Mn V Cu
TYPE: SPEC SPEC SPEC SPEC SPEC
AVER: 1.500 .850 .640 .220 .190
SDEV: .000 .000 .000 .000 .000
ELEM: Fe Ni Cr Mo W
BGDS: LIN LIN EXP LIN LIN
TIME: 100.00 100.00 100.00 100.00 100.00
BEAM: 29.84 29.84 29.84 29.84 29.84
ELEM: Fe Ni Cr Mo W SUM
207 7.607 52.452 16.336 14.459 3.857 98.111
208 7.377 51.317 16.431 15.585 3.698 97.808
209 7.501 52.075 16.397 14.743 3.799 97.915
210 6.505 46.098 16.133 21.935 4.225 98.296
211 7.317 51.365 16.461 15.703 3.679 97.925
AVER: 7.261 50.662 16.352 16.485 3.852 98.011
SDEV: .437 2.596 .131 3.093 .221 .193
SERR: .196 1.161 .058 1.383 .099
%RSD: 6.02 5.12 .80 18.76 5.75
PUBL: 7.300 51.500 16.150 17.100 4.290 99.740
%VAR: -.53 -1.63 1.25 -3.60 -10.22
DIFF: -.039 -.838 .202 -.615 -.438
STDS: 526 528 524 542 574
STKF: 1.0000 1.0000 .9988 .9910 .9979
STCT: 6346.7 20768.3 15241.3 8726.4 2235.2
UNKF: .0797 .5171 .1722 .1346 .0269
UNCT: 505.7 10739.8 2627.0 1185.5 60.4
UNBG: 19.5 118.8 71.3 14.9 4.7
ZCOR: .9115 .9795 .9498 1.2257 1.4303
KRAW: .0797 .5171 .1724 .1359 .0270
PKBG: 26.98 91.45 37.85 80.39 13.83
And next *without* fluorescence by beta lines:
Correction Method and Mass Absorption Coefficient File:
ZAF or Phi-Rho-Z Calculations
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Current ZAF or Phi-Rho-Z Selection:
Armstrong/Love Scott (default)
Correction Selections:
Phi(pz) Absorption of Armstrong/Packwood-Brown 1981 MAS
Stopping Power of Love-Scott
Backscatter Coefficient of Love-Scott
Backscatter of Love-Scott
Mean Ionization of Berger-Seltzer
Phi(pz) Equation of Love-Scott
Reed/JTA w/ M-Line Correction and JTA Intensity Mod.
Fluorescence by Beta Lines NOT Included
St 651 Set 2 NIST SRM C2402 (Hastelloy C)
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 30.0 Beam Size = 0
(Magnification (analytical) = 20000), Beam Mode = Analog Spot
(Magnification (default) = 1000, Magnification (imaging) = 100)
Image Shift (X,Y): .00, .00
High temperature alloy
Number of Data Lines: 5 Number of 'Good' Data Lines: 5
First/Last Date-Time: 03/14/2015 08:09:05 PM to 03/14/2015 08:20:58 PM
WARNING- Using Exponential Off-Peak correction for cr ka
Average Total Oxygen: .000 Average Total Weight%: 98.158
Average Calculated Oxygen: .000 Average Atomic Number: 31.171
Average Excess Oxygen: .000 Average Atomic Weight: 62.230
Average ZAF Iteration: 3.00 Average Quant Iterate: 2.00
St 651 Set 2 NIST SRM C2402 (Hastelloy C), Results in Elemental Weight Percents
SPEC: Co Si Mn V Cu
TYPE: SPEC SPEC SPEC SPEC SPEC
AVER: 1.500 .850 .640 .220 .190
SDEV: .000 .000 .000 .000 .000
ELEM: Fe Ni Cr Mo W
BGDS: LIN LIN EXP LIN LIN
TIME: 100.00 100.00 100.00 100.00 100.00
BEAM: 29.84 29.84 29.84 29.84 29.84
ELEM: Fe Ni Cr Mo W SUM
207 7.673 52.461 16.419 14.459 3.856 98.267
208 7.439 51.326 16.511 15.586 3.697 97.959
209 7.566 52.084 16.479 14.743 3.798 98.070
210 6.553 46.106 16.200 21.936 4.225 98.419
211 7.379 51.374 16.541 15.703 3.678 98.075
AVER: 7.322 50.670 16.430 16.485 3.851 98.158
SDEV: .445 2.596 .136 3.093 .221 .183
SERR: .199 1.161 .061 1.383 .099
%RSD: 6.07 5.12 .83 18.76 5.75
PUBL: 7.300 51.500 16.150 17.100 4.290 99.740
%VAR: .30 -1.61 1.73 -3.59 -10.24
DIFF: .022 -.830 .280 -.615 -.439
STDS: 526 528 524 542 574
STKF: 1.0000 1.0000 .9988 .9910 .9976
STCT: 6346.7 20768.3 15241.3 8726.4 2235.2
UNKF: .0797 .5171 .1722 .1346 .0269
UNCT: 505.7 10739.8 2627.0 1185.5 60.4
UNBG: 19.5 118.8 71.3 14.9 4.7
ZCOR: .9191 .9797 .9544 1.2257 1.4304
KRAW: .0797 .5171 .1724 .1359 .0270
PKBG: 26.98 91.45 37.85 80.39 13.83
The largest effects as expected for Fe ka and Cr Ka, both highly fluoresced by beta lines.
Quote from: Brian Joy on May 23, 2015, 04:55:36 PM
But consideration of fluorescence by Kb lines IS important for accurate quantification in certain cases, such as analysis of Mn in fayalitic olivine, Fe in cobaltite, or Co in pentlandite or heazlewoodite.
Just to clarify, I was trying to point out some cases in which the measured X-ray (respectively Mn Ka, Fe Ka, or Co Ka) is fluoresced by a Kb line of a matrix element, but NOT by the Ka line. For instance, for the last case, the energy of the Co K edge falls between that of Ni Ka and Ni Kb. The problem is exacerbated by the fact that the measured element is present in relatively low concentration relative to the fluorescing element. For instance, heazlewoodite (nominally Ni3S2) might contain ~71 wt% Ni and ~2 wt% Co. When analyzed using a 20 kV potential, the intensity of Co Ka produced by secondary fluorescence (due entirely to Ni Kb) is about 3.4% of the primary Co Ka intensity.
Also, when considering measurement of transition metal K lines (or virtually any X-ray that can be diffracted by LiF), the continuum fluorescence correction can also be significant. Do you have any plans to add this correction to CalcZAF?
Quote from: Brian Joy on May 24, 2015, 09:29:41 AM
Quote from: Brian Joy on May 23, 2015, 04:55:36 PM
But consideration of fluorescence by Kb lines IS important for accurate quantification in certain cases, such as analysis of Mn in fayalitic olivine, Fe in cobaltite, or Co in pentlandite or heazlewoodite.
Just to clarify, I was trying to point out some cases in which the measured X-ray (respectively Mn Ka, Fe Ka, or Co Ka) is fluoresced by a Kb line of a matrix element, but NOT by the Ka line. For instance, for the last case, the energy of the Co K edge falls between that of Ni Ka and Ni Kb. The problem is exacerbated by the fact that the measured element is present in relatively low concentration relative to the fluorescing element. For instance, heazlewoodite (nominally Ni3S2) might contain ~71 wt% Ni and ~2 wt% Co. When analyzed using a 20 kV potential, the intensity of Co Ka produced by secondary fluorescence (due entirely to Ni Kb) is about 3.4% of the primary Co Ka intensity.
Also, when considering measurement of transition metal K lines (or virtually any X-ray that can be diffracted by LiF), the continuum fluorescence correction can also be significant. Do you have any plans to add this correction to CalcZAF?
Hi Brian,
Yup, those are cases of significant fluorescence by beta lines.
The continuum fluorescence correction is fully implemented in the Penepma alpha factor matrix correction. The continuum fluorescence cannot be included in the normal Phi-rho-z calculations because historically it was "inadvertently incorporated" into the absorption analytical models! So adding it in now just makes things worse!
A good test is to run such a suspected case of large continuum fluorescence using both analytical and Penepma Monte Carlo alpha factor models and note the differences in the matrix corrections.
Easy to do in CalcZAF!
Quote from: Probeman on May 24, 2015, 11:47:46 AM
The continuum fluorescence cannot be included in the normal Phi-rho-z calculations because historically it was "inadvertently incorporated" into the absorption analytical models! So adding it in now just makes things worse!
Can you elaborate on this?
Quote from: Brian Joy on May 24, 2015, 03:24:48 PM
Quote from: Probeman on May 24, 2015, 11:47:46 AM
The continuum fluorescence cannot be included in the normal Phi-rho-z calculations because historically it was "inadvertently incorporated" into the absorption analytical models! So adding it in now just makes things worse!
Can you elaborate on this?
Just that I've been told this by John Armstrong a while back. Apparently because earlier work on analytical expressions didn't treat the continuum fluorescence separately, it got (very poorly) accounted for in the absorption corrections which were tuned to various data sets.
john
After a couple of minor tweaks to the Ka by Ma/Mb relative line weights in the (improved) Reed fluorescence correction, the Pouchou database error distribution now looks like this:
(https://smf.probesoftware.com/oldpics/i60.tinypic.com/ke83y8.jpg)
This can be compared to the error distribution using the previous code as seen in the first screen snap in this post:
http://smf.probesoftware.com/index.php?topic=47.msg3060#msg3060
So a small improvement in the average and variance. If I run the large flu correction "database" from Penepma12 calculations we now get this:
(https://smf.probesoftware.com/oldpics/i58.tinypic.com/30adts0.jpg)
This should be compared to the previous calculation (2nd screen snap) in this post:
http://smf.probesoftware.com/index.php?topic=490.msg2710#msg2710
and again we see a small but significant improvement in the "further improved" Reed fluorescence correction.
Ok, after further "tuning" of the Reed relative line weights to Penepma k-ratios I now get this for the Pouchou database:
(https://smf.probesoftware.com/oldpics/i60.tinypic.com/122gd1x.jpg)
This is a slightly better (smaller) variance than the previous attempt (see first plot in this post):
http://smf.probesoftware.com/index.php?topic=490.msg3085#msg3085
Now all this is a little silly as the Pouchou database was selected to *minimize* fluorescence effects, so what if we use a better MAC table such as FFAST? Here you go:
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/28wij2t.jpg)
Now that's a bit better! Actually slightly better (smaller) variance than the Penepma alpha method shown here:
http://smf.probesoftware.com/index.php?topic=47.msg3105#msg3105
but with a worse average error than the Penepma alpha method. So this is looking promising if one is using the best MACs.
I'll also speculate about the high average error (greater than 1.000) compared to Penepma, and have to wonder that if because they were using a fairly primitive fluorescence correction when they were "tuning" the phi-rho-z analytical models, they didn't inadvertently compensate for some fluorescence problems with the ZA correction?
Sorry to resurrect an old topic, but I figured this was the most appropriate one. I have implemented the "Reed" fluorescence correction by characteristic radiation to my specturm modeling code a long time ago, and was thinking I should add bremsstrahlung fluorescence as well in the free days at the end of the year. I am taking the formulas from Reed's "Electron Microprobe Analysis", 2nd edition, but I have a hard time wrapping my head around equation 16.10 which reads "If/IA = 9.7 * 10-8 * Z4" as an approximation for the continuum fluorescence as a fraction of primary X-ray production (for K lines).
This fourth power seems hard to believe. This would mean that for any element with Z > 56, the bremsstrahlung fluorescence would be larger than the primary radiation. Now I understand that for normal EPMA/SEM use cases, these K lines are not "in view" anyway, but how about in TEM? Or is this formula limited in applicability to lower-Z elements?
Quote from: Sander on December 20, 2024, 09:49:35 AMSorry to resurrect an old topic, but I figured this was the most appropriate one. I have implemented the "Reed" fluorescence correction by characteristic radiation to my specturm modeling code a long time ago, and was thinking I should add bremsstrahlung fluorescence as well in the free days at the end of the year. I am taking the formulas from Reed's "Electron Microprobe Analysis", 2nd edition, but I have a hard time wrapping my head around equation 16.10 which reads "If/IA = 9.7 * 10-8 * Z4" as an approximation for the continuum fluorescence as a fraction of primary X-ray production (for K lines).
This fourth power seems hard to believe. This would mean that for any element with Z > 56, the bremsstrahlung fluorescence would be larger than the primary radiation. Now I understand that for normal EPMA/SEM use cases, these K lines are not "in view" anyway, but how about in TEM? Or is this formula limited in applicability to lower-Z elements?
I can't speak to the Reed model but one can obtain fluorescence intensities (separately) for both characteristic and continuum productions using PENEPMA:
https://smf.probesoftware.com/index.php?topic=202.0
Here is one such output (column labeled "B") found in the pe-intens-01.dat file:
# Results from PENEPMA. Output from photon detector # 1
#
# Angular intervals : theta_1 = 4.500000E+01, theta_2 = 5.500000E+01
# phi_1 = 0.000000E+00, phi_2 = 3.600000E+02
#
# Intensities of characteristic lines. All in 1/(sr*electron).
# P = primary photons (from electron interactions);
# C = flourescence from characteristic x rays;
# B = flourescence from bremsstrahlung quanta;
# TF = C+B, total fluorescence;
# unc = statistical uncertainty (3 sigma).
#
# IZ S0 S1 E (eV) P unc C unc B unc TF unc T unc
26 L3 M1 6.1530E+02 1.046338E-04 4.59E-05 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 1.046338E-04 4.59E-05
26 L2 M1 6.2780E+02 3.720313E-05 2.77E-05 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 3.720313E-05 2.77E-05
26 L3 M4 7.0480E+02 2.325196E-06 6.97E-06 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 2.325196E-06 6.97E-06
26 L3 M5 7.0480E+02 2.325196E-05 2.20E-05 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 2.325196E-05 2.20E-05
26 L3 N1 7.1316E+02 4.650392E-06 9.86E-06 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 4.650392E-06 9.86E-06
26 L2 M4 7.1832E+02 1.395117E-05 1.70E-05 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 1.395117E-05 1.70E-05
26 L1 M2 7.9220E+02 2.325196E-06 6.97E-06 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 2.325196E-06 6.97E-06
14 K L2 1.7394E+03 9.300783E-06 1.39E-05 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 9.300783E-06 1.39E-05
14 K L3 1.7400E+03 1.395117E-05 1.70E-05 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 1.395117E-05 1.70E-05
26 K L2 6.3910E+03 1.860157E-05 1.97E-05 0.000000E+00 0.00E+00 5.226922E-07 1.11E-06 5.226922E-07 1.11E-06 1.912426E-05 1.97E-05
26 K L3 6.4040E+03 3.720313E-05 2.94E-05 0.000000E+00 0.00E+00 2.613461E-07 7.84E-07 2.613461E-07 7.84E-07 3.746448E-05 2.94E-05
26 K M2 7.0582E+03 2.325196E-06 6.97E-06 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 0.000000E+00 0.00E+00 2.325196E-06 6.97E-06Download the CalcZAF/Standard installer here:
https://www.probesoftware.com/resources/
and you can perform PENEPMA runs using the GUI in the Standard app.