Donovan and Moy (DAM) backscatter correction

[John Donovan]

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:



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.

[John Donovan]

Re-processing all 826 binary k-ratios in the Pouchou2.Dat file, we obtain this error distribution using the Armstrong/Love-Scott matrix correction:



Not too bad, but now using the Armstrong/Donovan and Moy (BSC) correction we obtain this error distribution:



A significant improvement (take a look at the y axes)!

[John Donovan]

We've also now added the ability to specify a variable exponent for the Donovan and Moy (DAM) backscatter calculation as shown here:



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: