Based on our recent paper:
https://academic.oup.com/mam/article-abstract/29/4/1436/7224307
Aurelien 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:
(https://smf.probesoftware.com/gallery/1_19_09_23_9_31_44.png)
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:
(https://smf.probesoftware.com/gallery/1_19_09_23_9_32_33.png)
And with the new DAM backscatter correction we obtain this error distribution:
(https://smf.probesoftware.com/gallery/1_19_09_23_9_32_52.png)
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.
Re-processing all 826 binary k-ratios in the Pouchou2.Dat file, we obtain this error distribution using the Armstrong/Love-Scott matrix correction:
(https://smf.probesoftware.com/gallery/1_21_09_23_2_32_46.png)
Not too bad, but now using the Armstrong/Donovan and Moy (BSC) correction we obtain this error distribution:
(https://smf.probesoftware.com/gallery/1_21_09_23_2_33_01.png)
A significant improvement (take a look at the y axes)!
We've also now added the ability to specify a variable exponent for the Donovan and Moy (DAM) backscatter calculation as shown here:
(https://smf.probesoftware.com/gallery/1_23_09_23_8_24_26.png)
The calculated "optimized" exponent is based on the electron beam energy from PENEPMA Monte Carlo modeling of pure elements and compounds at various electron beam energies.
If all your elements are run at the same beam energy you could just specify the exponent explicitly. The optimized exponent is calculated as shown here by Aurelien Moy:
(https://smf.probesoftware.com/gallery/1_23_09_23_8_29_55.png)