Penepma/Penfluor/Fanal derived Alpha Factors For Matrix Corrections

[Probeman]

Now let's try the same thing using the Penfluor/Fanal fast Monte-Carlo method on this Bastin k-ratio dataset using polynomial alpha factor fitting:



Something has gone south on us and it's those very high overvoltage k-ratios as seen here:

Problematic k-ratio errors (< 0.8 or > 1.2)
  Line             ConcA   ConcB     TOA      eO      Uo   K-Exp   K-Cal   K-Err
14    Au ma in Cu .300000 .700000 40.0000 31.5000 14.2792 .177300 .216098 1.21883
15    Au ma in Cu .300000 .700000 40.0000 36.6000 16.5911 .171700 .207533 1.20869
16    Au ma in Cu .300000 .700000 40.0000 39.7000 17.9964 .168900 .202966 1.20169
227   Au ma in Cu .201200 .798800 52.5000 30.0000 13.5993 .122000 .146576 1.20144
228   Au ma in Cu .201200 .798800 52.5000 40.0000 18.1324 .110000 .134807 1.22552
345   Al ka in Mg .091000 .909000 75.0000 25.0000 16.0256 .025800 .033720 1.30698
346   Al ka in Mg .091000 .909000 75.0000 30.0000 19.2308 .019800 .027770 1.40252
347   Al ka in Mg .091000 .909000 75.0000 35.0000 22.4359 .015200 .023329 1.53478
348   Al ka in Mg .091000 .909000 75.0000 40.0000 25.6410 .012300 .019971 1.62368
351   Al ka in Mg .091000 .909000 52.5000 20.0000 12.8205 .030200 .037609 1.24535
352   Al ka in Mg .091000 .909000 52.5000 25.0000 16.0256 .022100 .029937 1.35460
353   Al ka in Mg .091000 .909000 52.5000 30.0000 19.2308 .016800 .024434 1.45442
355   Al ka in Mg .091000 .909000 20.0000 15.0000 9.61539 .025200 .030915 1.22677
356   Al ka in Mg .091000 .909000 20.0000 20.0000 12.8205 .016900 .022333 1.32147
357   Al ka in Mg .091000 .909000 20.0000 25.0000 16.0256 .012200 .017164 1.40685
358   Al ka in Mg .091000 .909000 20.0000 30.0000 19.2308 .009500 .013918 1.46507
359   Al ka in Mg .091000 .909000 20.0000 35.0000 22.4359 .007900 .011811 1.49501
360   Al ka in Mg .091000 .909000 20.0000 40.0000 25.6410 .006900 .010408 1.50844
367   Al ka in Fe .100000 .900000 75.0000 40.0000 25.6410 .021800 .027727 1.27190
371   Al ka in Fe .100000 .900000 52.5000 25.0000 16.0256 .033500 .040724 1.21563
372   Al ka in Fe .100000 .900000 52.5000 30.0000 19.2308 .026600 .033607 1.26343
375   Al ka in Fe .100000 .900000 20.0000 20.0000 12.8205 .024900 .030930 1.24219
376   Al ka in Fe .100000 .900000 20.0000 25.0000 16.0256 .018500 .024065 1.30079
377   Al ka in Fe .100000 .900000 20.0000 30.0000 19.2308 .014900 .019693 1.32171
378   Al ka in Fe .100000 .900000 20.0000 35.0000 22.4359 .012600 .016823 1.33512
379   Al ka in Fe .100000 .900000 20.0000 40.0000 25.6410 .011400 .014890 1.30614
436   Nb la in V  .080000 .920000 20.0000 40.0000 16.8705 .053000 .065254 1.23122
645   Al ka in Ni .125000 .875000 40.0000 31.9000 20.4487 .023300 .028246 1.21229
646   Al ka in Ni .125000 .875000 40.0000 37.2000 23.8462 .019500 .023487 1.20444
650   Al ka in Ni .049000 .951000 40.0000 21.2000 13.5897 .014300 .017270 1.20770
651   Al ka in Ni .049000 .951000 40.0000 26.6000 17.0513 .009800 .013345 1.36171
652   Al ka in Ni .049000 .951000 40.0000 31.9000 20.4487 .007500 .010757 1.43433
653   Al ka in Ni .049000 .951000 40.0000 37.2000 23.8462 .006800 .008957 1.31725

Yes, these are overvoltages of 10 or 20 and higher so it's not good, but not surprising when running Al Ka at 30 or 40 keV!

Let's examine one or two of these cases in more detail, for example Al Ka in Mg at 30 keV. Here is a plot of the alpha factors for all analytical expression matrix corrections but first at a more normal 15 keV:



There is a significant difference of opinion here, with about a 10% variation in the correction factor.  If we plot the same thing at 30 keV, there is even more disagreement in the analytical expressions:



The variation is now around 15% between the different models.  So where does our Penfluor/Fanal based Monte-Carlo method put us?



Pretty much "smack dab in the middle of the pack". The lesson here is that even a small difference in the matrix corrections can make a significant difference in accuracy, when their magnitude is this large.  I guess the other lesson is: don't run your analyses with an overvoltage of 20 or 30 if you want accuracy. For improving sensitivity? Maybe a larger analytical volume will help. But certainly not for accuracy.

Just for fun, let's run these Bastin k-ratios with the PAP correction (XPP):



Significantly better. Of course this makes sense as the PAP correction was optimized using a related dataset  from Pouchou which was selected for large absorption corrections.

My "bottom line"? If you are going to have excessively large absorption corrections, whether they be from very high overvoltages or from very low energy emission lines, I would stick with the analytical expressions.  But for large atomic number corrections or large fluorescence corrections I think the Penfluor/Fanal corrections will be your best bet.

As they say: your mileage (or kilometerage) may vary!   

[Probeman]

The latest distribution of CalcZAF (v. 11.5.1) contains an updated matrix.mdb k-ratio database with 3087 binaries (over 337K k-ratios) for the fast Monte-Carlo matrix correction option.

See here for the complete list:

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

[Probeman]

The latest CalcZAF.msi deployment contains a new matrix.mdb file for fast Monte-Carlo matrix corrections.

This database now contains 346K k-ratios for most element pairs in the periodic table (I'd be interested if anyone had the inclination to visualize these k-ratios in some way- it might make for interesting "science art").



This latest error distribution for the Pouchou binary database shows a slightly better average, and slightly worse variance than the previous database.  Still with a standard deviation of under 3%, this is better than any analytical based matrix correction I am aware of.

[Probeman]

I decided to try the new 4 coefficient non-linear alpha factor fit to the Pouchou binary k-ratio database and indeed the accuracy and variance are both improved slightly (compared to the previous post using polynomial alpha factors) as seen here:



I am now focusing on calculating k-ratios at higher precision to deal with low concentration and low overvoltage situations and will post these results soon...

[Probeman]

The latest CalcZAF.msi contains a new matrix.mdb k-ratio database with over 367K binary k-ratios from Monte-Carlo calculations that further improves accuracy for the fast Monte-Carlo based matrix corrections.  The previous error histogram from the Pouchou k-ratio database was here (the post just above the non-linear post):

http://probesoftware.com/smf/index.php?topic=47.msg4740#msg4740

The new matrix database is slightly improved in accuracy and with a smaller variance as seen here:



The main outliers are from extremely high overvoltage measurements for relatively low energy emission lines such as Al Ka in Ni at 48 keV... which is simply a limitation of the accuracy of the photon scattering factor tables utilized by the Penepma code.

[Probeman]

The latest matrix.mdb contains over 377K k-ratios for fast Monte Carlo calculations for matrix corrections.  Most of the new additions are mid z element pairs.
john

[Probeman]

The latest matrix.mdb k-ratio database now contains over 380K k-ratios for binary compositions from Penfluor-Fanal calculations.  The new additions are mostly high emitters absorbed by low matrices, e.g., Nb La in B or C. You can update by using the CalcZAF Help | Update CalcZAF menu or downloading the matrix.mdb directly here:

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

john

[John Donovan]

The latest version of CalcZAF/Probe for EPMA (v. 11.9.6) contains a new update to the matrix.mdb k-ratio database for fast Monte Carlo based matrix corrections.

This latest release adds about 100K more k-ratios for a total of ~394K k-ratios in the matrix.mdb database. Many of the new binaries are for REE and actinide binaries.

Please let me know if you have any questions.
john