Based on our recent paper:
https://academic.oup.com/mam/article-abstract/29/4/1436/7224307Aurelien Moy and I have a developed a new backscatter correction (which we call the DAM backscatter correction, get it?), which utilizes Z fraction averaging as opposed to traditional mass fraction averaging. This new backscatter correction is especially important for situations with large atomic number effects, particularly when compounds contain elements with different A/Z ratios as discussed in the above paper.
Here is the new ZAF/Phi-rho-z dialog:
We're basically using the Armstrong/Brown absorption correction and replaced the mass based Love/Scott backscatter correction with our new Z fraction based correction. Here's a good example of what this new BSE correction can do, where we've analyzed PbS using FeS2 as a sulfur standard, first using the default Armstrong/Brown/Love-Scott correction:
St 731 Set 4 Galena U.C. #7400, Results in Elemental Weight Percents
ELEM: Fe S Pb
TYPE: ANAL ANAL ANAL
BGDS: LIN LIN EXP
TIME: 60.00 60.00 60.00
BEAM: 29.88 29.88 29.88
ELEM: Fe S Pb SUM
440 -.001 14.229 87.048 101.276
441 .003 14.258 86.510 100.771
442 .010 14.303 86.553 100.867
443 .020 14.216 86.300 100.535
444 .005 14.307 86.617 100.930
AVER: .007 14.263 86.606 100.876
SDEV: .008 .042 .275 .269
SERR: .004 .019 .123
%RSD: 107.77 .29 .32
PUBL: n.a. 13.400 86.600 100.000
%VAR: --- 6.44 (.01)
DIFF: --- .863 (.01)
STDS: 730 730 731
STKF: .4276 .5015 .8698
STCT: 319.56 459.23 72.26
UNKF: .0001 .1520 .8697
UNCT: .07 139.21 72.25
UNBG: 4.07 1.28 .90
ZCOR: .8501 .9383 .9958
KRAW: .0002 .3031 .9999
PKBG: 1.02 109.75 81.62
Note the 6.4% relative error in the sulfur value when extrapolating from FeS2. Now the same material, using the DAM backscatter correction:
St 731 Set 4 Galena U.C. #7400, Results in Elemental Weight Percents
ELEM: Fe S Pb
TYPE: ANAL ANAL ANAL
BGDS: LIN LIN EXP
TIME: 60.00 60.00 60.00
BEAM: 29.88 29.88 29.88
ELEM: Fe S Pb SUM
440 -.001 13.138 86.989 100.126
441 .003 13.167 86.467 99.636
442 .010 13.209 86.515 99.734
443 .019 13.128 86.257 99.404
444 .005 13.213 86.577 99.795
AVER: .007 13.171 86.561 99.739
SDEV: .008 .039 .268 .263
SERR: .003 .018 .120
%RSD: 107.77 .30 .31
PUBL: n.a. 13.400 86.600 100.000
%VAR: --- -1.71 (-.05)
DIFF: --- -.229 (-.04)
STDS: 730 730 731
STKF: .4266 .5045 .8526
STCT: 319.56 459.23 72.26
UNKF: .0001 .1529 .8525
UNCT: .07 139.21 72.25
UNBG: 4.07 1.28 .90
ZCOR: .8246 .8612 1.0154
KRAW: .0002 .3031 .9999
PKBG: 1.02 109.75 81.62
Note that the relative error is now only ~1.7% using this new Z fraction based backscatter correction method. Now let's look at the Pouchou k-ratio dataset for compounds with larger than 10% atomic number corrections. The traditional Armstrong/Brown/Love-Scott method shows this error distribution for the Armstrong/Brown/Love-Scott correction:
And with the new DAM backscatter correction we obtain this error distribution:
A considerable improvement for large atomic number corrections.
We believe this correction can be further improved by calculating the optimized average Z BSE exponent based on the electron beam energy and we are modeling this now and will implement it soon.