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!