If you utilize Probe for EPMA for quantitative analysis you will have noticed that when one analyzes a standard sample, or an unknown sample that has been declared to be a standard:
https://smf.probesoftware.com/index.php?topic=71.msg10257#msg10257
the program will also display the "published" composition of that standard immediately after the composition is displayed, where the standard was calculated as though it were an unknown sample:
St 263 Set 1 Fe2SiO4 (synthetic fayalite), Results in Elemental Weight Percents
ELEM: Si Al Fe Mg Cr Ti Mn Ca O SUM
131 13.666 .005 55.082 -.006 -.010 -.029 -.010 -.020 31.407 100.084
132 13.742 -.006 55.007 -.004 .011 -.023 .052 .011 31.407 100.196
133 13.684 .002 55.244 -.006 .024 .002 -.042 .000 31.407 100.316
134 13.712 .002 55.079 .004 -.003 .041 -.038 .007 31.407 100.211
135 13.720 -.007 55.215 -.002 -.011 .029 -.002 .014 31.407 100.363
AVER: 13.705 -.001 55.125 -.003 .002 .004 -.008 .002 31.407 100.234
SDEV: .030 .005 .100 .004 .015 .031 .038 .014 .000 .109
SERR: .013 .002 .045 .002 .007 .014 .017 .006 .000
%RSD: .22 -523.26 .18 -151.47 650.93 769.82 -474.54 560.42 .00
PUBL: 13.785 n.a. 54.809 n.a. n.a. n.a. n.a. n.a. 31.407 100.001
%VAR: -.58 --- .58 --- --- --- --- --- .00
DIFF: -.080 --- .316 --- --- --- --- --- .000
STDS: 14 13 395 12 24 22 25 358 ---
Here, the secondary Fe2SiO4 standard was calculated using SiO2 (#14) as the primary standard for Si and magnetite (#395) as the primary standard for Fe.
In addition, the program will also display the calculated variance and algebraic difference of the "unknown" composition relative to the "published" composition, and also the identity of the primary standard.
This is all useful information, particularly when evaluating whether the given primary standard, yields an accurate result on a secondary standard. The same questions arise when evaluating the relative accuracy of various matrix corrections.
Some of you may also be aware that the "Use All Matrix Corrections" option in Probe for EPMA (and also CalcZAF) can provide useful information for a given composition for evaluating matrix correction accuracy:
(https://smf.probesoftware.com/gallery/395_30_11_21_12_15_49.png)
Previously, this feature provided the following output, in this case a analyzing SRM K-412 (#160) as a secondary standard using SRM K-411 (#162) as a primary standard for the major elements:
Summary of All Calculated (averaged) Matrix Corrections:
St 160 Set 2 NBS K-412 mineral glass
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Elemental Weight Percents:
ELEM: Na K Al Mg Fe Ca Mn Ti Si Cl O H TOTAL
1 .042 .004 4.911 11.679 7.838 10.931 .067 .004 21.007 -.001 43.597 .000 100.078 Armstrong/Brown/Scott-Love (prZ)
2 .042 .004 4.910 11.711 7.848 10.951 .068 .004 21.113 -.001 43.597 .000 100.246 Philibert/Duncumb-Reed
3 .042 .004 4.911 11.679 7.829 10.921 .066 .004 21.041 -.001 43.597 .000 100.093 Heinrich/Duncumb-Reed
4 .041 .004 4.911 11.690 7.838 10.934 .067 .004 21.045 -.001 43.597 .000 100.131 Love-Scott I
5 .042 .004 4.911 11.683 7.838 10.932 .067 .004 21.012 -.001 43.597 .000 100.088 Love-Scott II
6 .040 .004 4.911 11.755 7.840 10.960 .068 .004 21.073 -.001 43.597 .000 100.252 Packwood Phi(prZ) (EPQ-91)
7 .042 .004 4.910 11.692 7.849 10.960 .066 .004 21.104 -.001 43.597 .000 100.227 Bastin (original) (prZ)
8 .042 .004 4.909 11.676 7.845 10.945 .068 .004 21.110 -.001 43.597 .000 100.199 Bastin PROZA Phi (prZ) (EPQ-91)
9 .042 .004 4.910 11.692 7.845 10.944 .068 .004 21.095 -.001 43.597 .000 100.198 Pouchou and Pichoir-Full (PAP)
10 .041 .004 4.910 11.703 7.845 10.945 .068 .004 21.074 -.001 43.597 .000 100.190 Pouchou and Pichoir-Simplified (XPP)
11 .045 .007 4.911 11.679 7.837 10.931 .082 .007 21.013 .001 43.597 .000 100.111 PAP/Donovan and Moy BSC/BKS (prZ)
AVER: .042 .004 4.910 11.695 7.841 10.941 .069 .004 21.062 -.001 43.597 .000 100.165
SDEV: .001 .001 .001 .023 .006 .013 .005 .001 .041 .001 .000 .000 .066
SERR: .000 .000 .000 .007 .002 .004 .001 .000 .012 .000 .000 .000
MIN: .040 .004 4.909 11.676 7.829 10.921 .066 .004 21.007 -.001 43.597 .000 100.078
MAX: .045 .007 4.911 11.755 7.849 10.960 .082 .007 21.113 .001 43.597 .000 100.252
As we can see, all 11 matrix corrections give very similar results, but the question is which matrix correction gives the most accurate result?
It would be helpful if we could obtain a % relative accuracy variance compared to the published composition. Now, in the latest Probe for EPMA v. 14.2.8, we also obtain this output as seen here:
Percent Variances:
ELEM: Na K Al Mg Fe Ca Mn Ti Si Cl O H
PUBL: .043 n.a. 4.906 11.657 7.742 10.899 .077 n.a. 21.199 n.a. .000 .000
STDS: 336 374 160 162 162 162 25 22 162 285 --- ---
ELEM: Na K Al Mg Fe Ca Mn Ti Si Cl O H
1 -3.23 --- (.10) .19 1.24 .30 -12.99 --- -.91 --- .00 .00 Armstrong/Brown/Scott-Love (prZ)
2 -3.10 --- (.08) .46 1.36 .48 -11.95 --- -.41 --- .00 .00 Philibert/Duncumb-Reed
3 -2.15 --- (.09) .19 1.12 .20 -14.54 --- -.75 --- .00 .00 Heinrich/Duncumb-Reed
4 -3.62 --- (.10) .28 1.24 .32 -12.69 --- -.73 --- .00 .00 Love-Scott I
5 -3.26 --- (.10) .22 1.24 .30 -13.26 --- -.88 --- .00 .00 Love-Scott II
6 -5.89 --- (.11) .84 1.27 .56 -11.49 --- -.60 --- .00 .00 Packwood Phi(prZ) (EPQ-91)
7 -2.41 --- (.08) .30 1.38 .56 -14.71 --- -.45 --- .00 .00 Bastin (original) (prZ)
8 -3.01 --- (.06) .16 1.33 .42 -11.96 --- -.42 --- .00 .00 Bastin PROZA Phi (prZ) (EPQ-91)
9 -3.46 --- (.08) .30 1.32 .41 -11.86 --- -.49 --- .00 .00 Pouchou and Pichoir-Full (PAP)
10 -4.00 --- (.09) .39 1.33 .42 -12.25 --- -.59 --- .00 .00 Pouchou and Pichoir-Simplified (XPP)
11 5.39 --- (.11) .19 1.23 .29 7.04 --- -.88 --- .00 .00 PAP/Donovan and Moy BSC/BKS (prZ)
AVER: -2.61 .00 .09 .32 1.28 .39 -10.97 .00 -.64 .00 .00 .00
SDEV: 2.83 .00 .01 .20 .07 .12 6.07 .00 .19 .00 .00 .00
SERR: .85 .00 .00 .06 .02 .04 1.83 .00 .06 .00 .00 .00
MIN: -5.89 .00 .06 .16 1.12 .20 -14.71 .00 -.91 .00 .00 .00
MAX: 5.39 .00 .11 .84 1.38 .56 7.04 .00 -.41 .00 .00 .00
Values enclosed with parentheses indicates that the standard (or unknown) sample is the primary standard, so these values can be ignored.
From this output we can quickly see which matrix corrections yield the most accurate results. The sharp eyed among you will also notice that the last matrix correction (DAM BSE correction) gives a more accurate MAN correction for complicated reasons explained here:
https://smf.probesoftware.com/index.php?topic=1111.0
https://smf.probesoftware.com/index.php?topic=4.msg13411#msg13411
Now lets try a larger extrapolation, say from SiO2 (#14) as our primary standard, to ThSiO4 as a secondary standard:
Summary of All Calculated (averaged) Matrix Corrections:
St 16 Set 2 ThSiO4 (Thorite)
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Elemental Weight Percents:
ELEM: Si Pb Fe Th O TOTAL
1 9.056 .101 -.013 71.589 19.746 100.479 Armstrong/Brown/Scott-Love (prZ)
2 7.618 .100 -.013 71.589 19.746 99.040 Philibert/Duncumb-Reed
3 8.535 .100 -.014 71.589 19.746 99.957 Heinrich/Duncumb-Reed
4 8.240 .099 -.013 71.589 19.746 99.662 Love-Scott I
5 8.275 .099 -.013 71.589 19.746 99.697 Love-Scott II
6 7.170 .099 -.012 71.589 19.746 98.592 Packwood Phi(prZ) (EPQ-91)
7 9.109 .102 -.015 71.589 19.746 100.531 Bastin (original) (prZ)
8 8.462 .101 -.013 71.589 19.746 99.885 Bastin PROZA Phi (prZ) (EPQ-91)
9 8.270 .100 -.013 71.589 19.746 99.693 Pouchou and Pichoir-Full (PAP)
10 8.078 .100 -.013 71.589 19.746 99.499 Pouchou and Pichoir-Simplified (XPP)
11 8.609 .100 -.013 71.589 19.746 100.032 PAP/Donovan and Moy BSC/BKS (prZ)
AVER: 8.311 .100 -.013 71.589 19.746 99.733
SDEV: .566 .001 .001 .000 .000 .566
SERR: .171 .000 .000 .000 .000
MIN: 7.170 .099 -.015 71.589 19.746 98.592
MAX: 9.109 .102 -.012 71.589 19.746 100.531
Percent Variances:
ELEM: Si Pb Fe Th O
PUBL: 8.665 n.a. n.a. 71.589 19.746
STDS: 14 386 263 --- ---
ELEM: Si Pb Fe Th O
1 4.51 --- --- .00 .00 Armstrong/Brown/Scott-Love (prZ)
2 -12.09 --- --- .00 .00 Philibert/Duncumb-Reed
3 -1.50 --- --- .00 .00 Heinrich/Duncumb-Reed
4 -4.90 --- --- .00 .00 Love-Scott I
5 -4.50 --- --- .00 .00 Love-Scott II
6 -17.25 --- --- .00 .00 Packwood Phi(prZ) (EPQ-91)
7 5.12 --- --- .00 .00 Bastin (original) (prZ)
8 -2.35 --- --- .00 .00 Bastin PROZA Phi (prZ) (EPQ-91)
9 -4.56 --- --- .00 .00 Pouchou and Pichoir-Full (PAP)
10 -6.78 --- --- .00 .00 Pouchou and Pichoir-Simplified (XPP)
11 -.64 --- --- .00 .00 PAP/Donovan and Moy BSC/BKS (prZ)
AVER: -4.08 .00 .00 .00 .00
SDEV: 6.53 .00 .00 .00 .00
SERR: 1.97 .00 .00 .00 .00
MIN: -17.25 .00 .00 .00 .00
MAX: 5.12 .00 .00 .00 .00
First note how different the various matrix corrections behave with such an extrapolation. And as one can see, using the DAM BSE matrix correction we are sub percent level accuracy extrapolating from SiO2 to ThSiO4. A similar results is seen extrapolating again from SiO2 (#14) to PbSiO3:
Summary of All Calculated (averaged) Matrix Corrections:
St 386 Set 2 Alamosite (PbSiO3)
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Elemental Weight Percents:
ELEM: Si Pb Fe O TOTAL
1 10.483 73.325 -.008 16.939 100.738 Armstrong/Brown/Scott-Love (prZ)
2 8.955 72.716 -.008 16.939 98.602 Philibert/Duncumb-Reed
3 10.059 73.206 -.009 16.939 100.196 Heinrich/Duncumb-Reed
4 9.704 73.088 -.008 16.939 99.723 Love-Scott I
5 9.777 73.109 -.008 16.939 99.817 Love-Scott II
6 8.344 72.512 -.008 16.939 97.787 Packwood Phi(prZ) (EPQ-91)
7 10.476 73.301 -.010 16.939 100.706 Bastin (original) (prZ)
8 9.757 73.096 -.008 16.939 99.784 Bastin PROZA Phi (prZ) (EPQ-91)
9 9.632 73.056 -.008 16.939 99.619 Pouchou and Pichoir-Full (PAP)
10 9.497 73.008 -.008 16.939 99.436 Pouchou and Pichoir-Simplified (XPP)
11 9.999 73.189 -.008 16.939 100.118 PAP/Donovan and Moy BSC/BKS (prZ)
AVER: 9.698 73.055 -.009 16.939 99.684
SDEV: .623 .243 .000 .000 .864
SERR: .188 .073 .000 .000
MIN: 8.344 72.512 -.010 16.939 97.787
MAX: 10.483 73.325 -.008 16.939 100.738
Percent Variances:
ELEM: Si Pb Fe O
PUBL: 9.910 73.151 n.a. 16.939
STDS: 14 386 263 ---
ELEM: Si Pb Fe O
1 5.78 (.24) --- .00 Armstrong/Brown/Scott-Love (prZ)
2 -9.64 (-.59) --- .00 Philibert/Duncumb-Reed
3 1.51 (.08) --- .00 Heinrich/Duncumb-Reed
4 -2.08 (-.09) --- .00 Love-Scott I
5 -1.34 (-.06) --- .00 Love-Scott II
6 -15.80 (-.87) --- .00 Packwood Phi(prZ) (EPQ-91)
7 5.71 (.21) --- .00 Bastin (original) (prZ)
8 -1.55 (-.07) --- .00 Bastin PROZA Phi (prZ) (EPQ-91)
9 -2.80 (-.13) --- .00 Pouchou and Pichoir-Full (PAP)
10 -4.17 (-.20) --- .00 Pouchou and Pichoir-Simplified (XPP)
11 .89 (.05) --- .00 PAP/Donovan and Moy BSC/BKS (prZ)
AVER: -2.14 -.13 .00 .00
SDEV: 6.29 .33 .00 .00
SERR: 1.90 .10 .00 .00
MIN: -15.80 -.87 .00 .00
MAX: 5.78 .24 .00 .00
Update as usual from the Help menu or our Resources web page and see for yourself...