Penepma/Penfluor/Fanal derived Alpha Factors For Matrix Corrections

[Probeman]

Pretty impressive!

Thanks, Mike!

Here are some additional thoughts on this new "fast Monte-Carlo" method:

I should mention at the outset that matrix k-ratios utilized for this method, can be derived from *any* Monte-Carlo program. One only needs to calculate k-ratios for a range of composition for each binary (for each takeoff-angle, each beam energy and each emitting x-ray).  I have chosen to utilize these compositions for each emitting binary (that is what is in the matrix.mdb file):

1 : 99, 5 : 95, 10 : 90, 20 : 80, 40 : 60, 50 : 50, 60 : 40, 80 : 20, 90 : 10, 95 : 5, 99 : 1

For the k-ratio extractions I've mostly performed 40 degree takeoff angle calculations (and some 52.5 and 75 degree geometries for comparison to the empirical Pouchou k-ratio database) and beam energies from 1 to 50 keV in 1 keV steps. Note Penfluor only calculates down to 5 keV by default so I should probably not scan in k-ratios for beam energies below 5 keV into the matrix.mdb database (note to self). Though of course we can utilize k-ratios calculated for any instrument/beam condition of interest.

This means that *any* MC program can be utilized for these k-ratio calculations though currently I use Penepma (Penfluor) and Fanal for my k-ratios because it is MC based for the primary and continuum intensities, though the fluorescence calculation is analytical. One aspect to these MC calculations is that because one does not know the actual composition in advance (after all this is for matrix correction of arbitrary measured unknowns), the k-ratio calculation must be run to an arbitrary precision. This is mostly an issue for very weak emission lines and/or low over voltage situations.

Currently I am Running Penepma (Penfluor) for 3600 sec for each of the 10 beam energies for each binary composition. That is then 10 hours times 11 compositions or 110 hours per binary. The nice thing about using Penfluor is that once one has the Penfluor .PAR file for a specific composition, one can then "extract" k-ratios for *any* takeoff angle, for *any* beam energy (up to 50 keV), for any emitting line. In addition, because 11 compositions are being regressed to the alpha vs. concentration fit for each binary, statistical noise is actually reduced compared to single composition calculations as seen here:

http://probesoftware.com/smf/index.php?topic=47.msg3019#msg3019

In any event, because the MC k-ratio calculations occur off-line on one's MC servers, the speed of the MC program performing the k-ratio calculations isn't as important as the *accuracy*.  That is because once the k-ratios are pre-calculated to some arbitrary precision, they can be utilized in the matrix iteration by use of the alpha and beta expressions described here:

http://epmalab.uoregon.edu/bence.htm

for arbitrary compositions!

The situation today reminds me of the early days of microanalysis when everyone was trying to implement analytical expressions for electron-solid physics on computers that were simply too slow to handle a full blown treatment of all the parameters. That is why approximations were introduced into these early analytical expressions (with the possible exception of COR from NIST). More recently some investigators have modified these traditional codes to make them more rigorous (John Armstrong comes to mind).

However, now that computers today are so much faster, we can perform even more rigorous treatments of the physics in analytical expressions and some investigators  (Hendrix Demers and Nicholas Ritchie are two that come to mind) have done just that.

But... computers today are *still too slow* for on-line Monte Carlo calculation of matrix corrections. And that is why I am proposing that we perform these time consuming binary k-ratio calculations for the periodic table off-line (to arbitrary precision) and save the k-ratios for a range of composition for each binary and then utilize these k-ratios on-line in alpha expressions for high accuracy MC matrix corrections of arbitrary compositions.

In other words, there is no more need to "optimize" MC calculations for speed since we now have a way to utilize them for *fast* on-line matrix corrections.  Instead we should be solely concentrating on creating the most *accurate* MC programs for electron-solid physics...

Let's not compromise the physics for speed as was done 20 years ago because of computer technology limitations.

[Probeman]

And it just keeps getting better and better...

This is a error distribution from the Pouchou database (without B ka and Cu la) now with the 52.5 degree k-ratios included.



As you can see it is even better than before (smaller variance).  I should also point out that a significant portion of the above variance is due to two low over voltage binaries as seen here:

Problematic k-ratio errors (< 0.8 or > 1.2)
  Line             ConcA   ConcB     TOA      eO      Uo   K-Exp   K-Cal   K-Err
715   Cu ka in Ni .565000 .435000 40.0000 10.1000 1.12485 .558000 .719701 1.28979
722   Cu kb in Ni .565000 .435000 40.0000 10.2000 1.13598 .549400 .719902 1.31034

But this can be improved from increasing the modeling time from 3600 to 7200 sec per keV.  See the last error plot in this post calculated at 7200 sec:

http://probesoftware.com/smf/index.php?topic=47.msg2680#msg2680

By the way, the entire Pouchou database was calculated in about the same time as using Phi-rho-z, so yes, it is fast.

This version of the matrix.mdb database will be distributed in v. 10.9.6 of CalcZAF (and Probe for EPMA).

[hdemers]

Hi John,

Very interesting results.

However, I don't completely agree with your statement "there is no more need to "optimize" MC calculations for speed". I think we need both: accurate MC and sometime we need very fast MC. Outside the microanalysis world, we use MC to simulate imaging conditions and detector and still the MC are too slow (especially for SE micrograph). Event for x-ray microanalysis, most our sample now have feature size less than 50-10 nm and we need to be able to simulate different geometry "quickly".

But I agree we need the most accurate MC programs for electron-solid physics as we need to able to validate with a good reference other MC programs or analytical models.

Regards,
Hendrix

[Probeman]

However, I don't completely agree with your statement "there is no more need to "optimize" MC calculations for speed". I think we need both: accurate MC and sometime we need very fast MC. Outside the microanalysis world, we use MC to simulate imaging conditions and detector and still the MC are too slow (especially for SE micrograph). Event for x-ray microanalysis, most our sample now have feature size less than 50-10 nm and we need to be able to simulate different geometry "quickly".

Hi Hendrix,
Ok, I'll rephrase the statement to this: "there is no more need to optimize MC calculations for speed in order to perform quantitative matrix corrections on arbitrary compositions". Does that work for you?

I agree with you that we also need to perform full arbitrary geometry calculations and that will require a fast MC (and/or much faster computers). 

My point was mainly that I don't want us to sacrifice MC accuracy for speed as was done 20 and 30 years ago with the analytical expression modeling approximations.

On a related note, Xavier once said to me: why don't you implement a fully rigorous fundamental parameters matrix correction in your software. And I replied: give me the equations and I'll do it!  I even have a place holder for it in the software already:



As soon as you guys send me the code I'll implement it with full attribution!
john

[hdemers]

Hi John

Ok, I'll rephrase the statement to this: "there is no more need to optimize MC calculations for speed in order to perform quantitative matrix corrections on arbitrary compositions". Does that work for you?

OK for me

On a related note, Xavier once said to me: why don't you implement a fully rigorous fundamental parameters matrix correction in your software. And I replied: give me the equations and I'll do it!  I even have a place holder for it in the software already:
As soon as you guys send me the code I'll implement it with full attribution!

Interesting idea, you just need to solve the electron transport equation in the sample and calculate the x-ray generation from the electron distribution (energy and position) to get the phirhoz curve. The work of Rex and Dapor should be a good starting point.

Regards,
Hendrix

[Probeman]

On a related note, Xavier once said to me: why don't you implement a fully rigorous fundamental parameters matrix correction in your software. And I replied: give me the equations and I'll do it!  I even have a place holder for it in the software already:
As soon as you guys send me the code I'll implement it with full attribution!

Interesting idea, you just need to solve the electron transport equation in the sample and calculate the x-ray generation from the electron distribution (energy and position) to get the phirhoz curve. The work of Rex and Dapor should be a good starting point.

That sounds simple... not!   

In any event here is the Pouchou database re-calculated with some 75 degree k-ratios extracted and added to the matrix.mdb file:



Basically the same results, just very slightly worse in the 4th or 5th decimal place. Again the main problem here are the low over voltage Cu Kb in Ni measurements as noted in the image above. I will be adding higher precision MC calculations to the matrix.mdb file shortly which will take care of this for many elements.

[John Donovan]

I am pleased to report that after re-calculating the Ni-Cu binary at 7200 sec per beam energy (20 hours per binary for 11 binary compositions or 220 hours), the Pouchou database calculated errors from using the Penfluor/Fanal derived k-ratio for alpha factor fits looks even better (error variance down to 2.9 % compared to 3.2 % from the previous post above), as seen here:



This new matrix k-ratio database will be folded into the main CalcZAF/PFE release this weekend.

Edit by John: well it came together faster than I thought.  The current release of CalcZAF or Probe for EPMA now has the matrix.mdb file used to produce the Pouchou database error distribution in the above post.

In case anyone is wondering (because I have an assortment of different kratios with different precisions), I always contruct the release matrix.mdb in the following fashion:

1. Copy the default precision files, then the high precision files, then the very high precision files (which are only CuAuAg binaries at the moment), so the higher precision calculations overwrite the lower precision calculations.

2. I then do the same for the files where the minimum energy was limited to 1 keV.  These files are best for calculating matrix corrections for emitters absorbed by low Z elements where a low minimum energy calculation would provide insufficient precision for high energy emission line matrix corrections.

[Probeman]

The latest matrix.mdb penepma k-ratio database is available here:

http://probesoftware.com/download/Matrix.mdb

Over 266K binary k-ratios.
john

[Probeman]

I'm uploading the latest matrix.mdb now (which comes with the last version of PFE v. 11.05, though you'll need to re-run the latest CalcZAF.msi installer to get it).

This version contains a number of new binaries, particularly for actinide elements, e.g., oxygen in U, Np and Pu.

[Philipp Poeml]

Sounds cool. Let me know what I can do to provide some experimental data.

[Probeman]

Sounds cool. Let me know what I can do to provide some experimental data.

Can you post some beam conditions (keV) and k-ratios here?

And of course also post what the actual concentrations are... based on, what?

[John Donovan]

The latest "fast" Monte-Carlo matrix.mdb file now contains many of the actinide binaries as seen here:

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[Probeman]

I've recently updated the matrix.mdb file for fast Monte-Carlo matrix corrections.  The new binaries include additional light elements, actinides and rare-earth binaries, particularly Ce, La, P, U, Th and Pb.

See the link here for a list:

http://probesoftware.com/download/Calculated%20Matrix%20Binaries.txt

Again here is a comparison of a monazite composition with traditional phi-rho-z:

Code: [Select]

Un   11 Montel Madagascar 4-1, 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:   149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50     ---

ELEM:       Ca      Si      Al       Y      Pr      Nd      Sm      Gd      Ce      La       P       U      Pb      Th      Dy      Er       O   SUM 
   183    .550   1.078    .010    .071   2.525   8.165    .811    .381  24.575  12.188  11.662    .097    .252  11.320    .039    .004  26.428 100.157
   184    .550   1.105    .010    .068   2.535   8.119    .806    .374  24.392  12.079  11.445    .108    .238  11.385    .050    .008  26.131  99.404
   185    .537   1.131    .010    .091   2.440   8.067    .820    .386  24.441  11.911  11.544    .114    .249  11.713    .052    .003  26.294  99.802

AVER:     .546   1.105    .010    .077   2.500   8.117    .812    .381  24.470  12.059  11.550    .106    .246  11.473    .047    .005  26.284  99.788
SDEV:     .007    .027    .000    .012    .052    .049    .007    .006    .095    .140    .109    .008    .008    .210    .007    .003    .149    .377
SERR:     .004    .015    .000    .007    .030    .028    .004    .003    .055    .081    .063    .005    .004    .122    .004    .002    .086
%RSD:     1.33    2.42    1.17   15.97    2.10     .60     .83    1.55     .39    1.16     .94    7.98    3.06    1.83   15.54   52.36     .57
STDS:      305     305     305    1016    1010    1009    1011    1005    1001    1007    1001      15      17      16    1002    1003     ---

STKF:    .0862   .1608   .1137   .4593   .5438   .5479   .5534   .5556   .5348   .5384   .0783   .8994   .7907   .7095   .5626   .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:    .0051   .0057   .0000   .0005   .0226   .0732   .0072   .0032   .2188   .1072   .0701   .0010   .0019   .1026   .0004   .0000     ---
UNCT:     7.29   15.61     .10     .04    2.44    9.24    1.17     .62   19.45    8.12   27.19     .23     .47   19.71     .08     .01     ---
UNBG:     2.10    2.91    1.68     .23     .54     .69     .87     .96     .49     .39     .27    1.36     .68    1.06    1.20    1.47     ---

ZCOR:   1.0668  1.9521  2.5987  1.5967  1.1047  1.1093  1.1340  1.2080  1.1182  1.1251  1.6481  1.0858  1.3164  1.1182  1.2381  1.2413     ---
KRAW:    .0593   .0352   .0003   .0010   .0416   .1336   .0129   .0057   .4092   .1991   .8950   .0011   .0024   .1446   .0007   .0001     ---
PKBG:     4.47    6.36    1.06    1.19    5.52   14.34    2.35    1.65   40.45   22.03  101.47    1.17    1.70   19.66    1.07    1.01     ---
INT%:      .00   -4.29    -.03    ----  -24.42    -.90  -18.24  -83.12    ----    -.16    ----  -55.80    -.53    ----  -52.11  -44.11     ---

and the same composition with the latest matrix.mdb fast Monte-Carlo binaries:

Code: [Select]

Un   11 Montel Madagascar 4-1, 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:   149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50  149.50     ---

ELEM:       Ca      Si      Al       Y      Pr      Nd      Sm      Gd      Ce      La       P       U      Pb      Th      Dy      Er       O   SUM 
   183    .547    .996    .009    .068   2.540   8.176    .814    .399  24.405  12.055  11.415    .105    .264  11.526    .038    .004  25.997  99.357
   184    .546   1.021    .009    .065   2.550   8.130    .809    .392  24.221  11.946  11.200    .117    .249  11.590    .049    .008  25.700  98.601
   185    .534   1.045    .009    .087   2.455   8.079    .822    .404  24.265  11.776  11.295    .123    .260  11.924    .051    .003  25.856  98.987

AVER:     .542   1.020    .009    .073   2.515   8.128    .815    .398  24.297  11.926  11.303    .115    .258  11.680    .046    .005  25.851  98.982
SDEV:     .007    .025    .000    .012    .052    .049    .007    .006    .096    .141    .108    .009    .008    .214    .007    .003    .149    .378
SERR:     .004    .014    .000    .007    .030    .028    .004    .003    .056    .081    .062    .005    .005    .124    .004    .002    .086
%RSD:     1.35    2.40    1.18   15.95    2.08     .60     .84    1.52     .40    1.18     .95    7.97    3.07    1.83   15.86   52.38     .57
STDS:      305     305     305    1016    1010    1009    1011    1005    1001    1007    1001      15      17      16    1002    1003     ---

STBE:   1.1015  1.6109  1.5555  1.0815  1.1033  1.1045  1.1121  1.1192  1.1052  1.1074  1.7178  1.0285  1.0041  1.0602  1.1277  1.1331     ---
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     ---

UNBE:   1.0523  1.9534  2.5985  1.5694  1.1233  1.1249  1.1499  1.2111  1.1264  1.1310  1.6553  1.2332  1.4100  1.1961  1.2438  1.2452     ---
UNCT:     7.29   15.59     .10     .04    2.45    9.24    1.18     .65   19.45    8.12   27.19     .23     .47   19.71     .08     .01     ---
UNBG:     2.10    2.91    1.68     .23     .54     .69     .87     .96     .49     .39     .27    1.36     .68    1.06    1.20    1.47     ---
KRAW:    .0593   .0351   .0003   .0010   .0418   .1336   .0130   .0059   .4092   .1991   .8950   .0011   .0024   .1446   .0007   .0001     ---
PKBG:     4.47    6.35    1.06    1.19    5.54   14.34    2.36    1.68   40.45   22.03  101.47    1.17    1.70   19.66    1.07    1.01     ---
INT%:      .00   -4.43    -.03    ----  -24.06    -.89  -18.07  -82.33    ----    -.17    ----  -55.73    -.53    ----  -53.13  -44.13     ---

Scroll to the bottom of each "code" window to compare. It would be interesting for someone to calculate the differences in the U-Th-Pb "chemical dating" results between the two matrix corrections...

[Probeman]

I've recently updated the matrix.mdb file for fast Monte-Carlo matrix corrections.  The new binaries include additional light elements, actinides and rare-earth binaries, particularly Ce, La, P, U, Th and Pb.

I should add that I have one or two Monte-Carlo servers that could be pressed into service for some additional particular binaries or compositions that haven't yet been calculated...

Suggestions?

[Probeman]

Julien Allaz asked me to calculate the Ti-Pt binary using Penepma (Penfluor/Fanal) and I've finished part of the calculation (Ti Ka in Pt)... here are the results:

Ti Ka in Pt calculated using the default Phi-rho-z from Armstrong/Love Scott/Reed with non-linear alpha factors:



and here is the same binary, but using Penepma derived k-ratios:



Interesting that both both methods give about the same absolute correction, a small fluorescence correction, but with opposite slopes!   However, it should be pointed out that the different analytical methods don't agree very much either, and they are shown here all using the same fluorescence correction!



Most surprising to me is that the old Heinrich method appears to yield the best agreement with the Penepma Monte-Carlo method!  Luck or skill?