Fast and Easy Modeling of Matrix Corrections in Standard.exe (Penfluor/Fanal)

[Probeman]

If you are not familiar with the theory and application of so called "alpha factors", a good introduction is here:

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

Also please see the abstract attached below (remember to login to see attachments).

One can easily and quickly calculate matrix corrections for arbitrary compositions by using pre-calculated k-ratios from the matrix.mdb file. These k-ratios are fit to polynomial alpha factors and utilized to create beta (matrix) factors as described here:

http://probesoftware.com/smf/index.php?topic=47.msg578#msg578

If your composition contains a binary system that has not been calculated please post it to the same topic and I will add it to the "list":

http://probesoftware.com/smf/index.php?topic=47.0

In the meantime, the procedure is easy. Simply run Standard.exe, click the Analytical | Penepma (Secondary Fluorescence Profile) Calculations menu to open the Penfluor/Fanal window:



Here we are calculating the matrix effects for Si ka in PbSiO3 (Alamosite) at 15 keV. Note that the beam incident *and* the boundary materials are the same for bulk matrix calculations. Click the big yellow Run Fanal button and we will obtain the following output to the window:



Note that difference between CalcZAF and Fanal (Calc. Wt.% (Ideal). Make sure the "Send To Excel" box is checked and we also obtain this output to Excel:



Note that the Fanal and CalcZAF matrix corrections are significantly different- this is a nasty matrix with a big atomic number correction.

Please post other questions you may have.

[UofO EPMA Lab]

The latest version of Penfluor/Fanal input file (takeoff angle fix) now outputs the following improved matrix correction for Si Ka in PbSiO3 (Alamosite):





Still a nasty atomic number correction...

[Probeman]

Note that very rarely one may attempt a k-ratio calculation using the Penfluor/Fanal GUI as discussed above, and obtain an error similar to this:



Apparently this can occur when the overvoltage of a secondary emission line in Fanal is too close to the critical edge energy for that emission line. In the above example, the primary emission line (Nb La) edge is easily excited with a 19 keV electron beam, but not so for the secondary emission line of Nb Ka whose edge energy is 18.98 keV.

The actual Fanal FORTRAN error, which can be seen using the Fanal prompt button in the GUI, is seen here:



It seems that the Fanal code isn't handling this situation due to a precision issue, because if we run the 64 bit version of Fanal (which is not normally distributed due to 32 bit OSs out there), it works fine.

Therefore, if you see this issue, please download the attached 64 bit version of Fanal attached below (remember you must be logged in as a member to see or download attachments!).

[John Donovan]

A new Matrix.mdb database has been released for CalcZAF and Probe for EPMA (v. 10.6.9) which includes many light element binaries and some newly recalculated k-ratios with double precision pure element standards for improved calculations.

To see what binaries are currently available please see the following link:

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

There are now 1859 binaries calculated which is around 1/3 of the entire periodic table...  so, slowly, we're getting' there!
john

[Probeman]

The latest matrix.mdb Penepma (Penfluor/Fanal) k-ratio database file can be downloaded here:

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

Currently the database contains k-ratios for 11 compositions for about 1/3 of the binary systems in the periodic table from 1 to 50 keV and 6 x-ray emission lines (ka, kb, la, lb, ma, mb) mostly at 40 degrees takeoff, though some systems also at 52.5 degrees.  Or roughly over 200K k-ratios intensities...

This database can be utilized for non-commercial academic use free of charge.  However, I would ask that you post your results from utilizing this database to this forum in addition to any other print media or web locations.
john

[Probeman]

Here is a model running one of Phil Gopon and John Fournelle's iron silicide compositions:



Note that the CalcZAF calculation is only different from the Penfluor/Fanal Monte-Carlo calculation by less than 2% (4.92 wt. % vs. 5.0 wt. %).

I would like to perform some Fe Ln or Ll calculations as well, but I will need to re-calculate my Si-Fe Monte-Carlo binaries to down below 1 keV... working...

But for Ln/Ll lines above 1 keV, such as Ge Ln, it already works:



Note the the difference between the Monte-carlo and CalcZAF calculations is only around 0.2%.  Remember, you have to select the FFAST MAC table for quantification of these additional x-rays lines!

Thank-you to Gareth Seward for the snazzy, new plot graphics!

[Probeman]

Ok, I calculated the Fe-Si Ln and Ll x-ray k-ratios at 5 keV (5% Si in Fe) as one can see below.  First the Fe Ln x-ray emission line:



and now the Fe Ll emission line:



The calculated wt% from CalcZAF for the Ll and Ln lines seem to be close to the Penfluor/Fanal calculations, but clearly show some disagreement. For these very low energy emission lines (~600 eV) I would probably stick with Penfluor calculations, but perhaps Phil Gopon can do some comparisons with his measurements for us. Please note that the Ln and Ll emission lines are not yet included in the fast Monte-Carlo matrix.mdb database (I'm working on that!).

And just for comparison here is the Fe La emission line:



If you'd like to play with this binary for these different L emission lines, I've zipped up these 500 eV Penfluor PAR files so you can try them yourselves in Standard.exe. See attached ZIP file below.

By the way, just as a "sanity check" I exported the data to Excel and although it is hard to see in the graphs, these calculated numbers from Penepma/Fanal really are different. Here are the calculated k-ratio (%) intensities for each emission line :

Fe La:   93.9848
Fe Ln:   93.9868
Fe Ll:   93.6206

Interestingly, the Fe La and Fe Ln lines have similar matrix corrections.  Too bad the La line is so affected by chemical states!

[Probeman]

Just for fun I also ran the same Fe Ln, Ll and La calculations on 5% Si 95% Fe at 5 keV. But this time using the PAP (full) correction matrix correction. Here is Fe Ln:



Quite a bit worse than JTA phi-rho-z. Here is Fe Ll:



A bit better than JTA p/r/z. And here is Fe La:



Quite good.

Of course this is without any chemical state effects in the calculations...

[Probeman]

Hi Phil,
I finished calculating Penepma/Penfluor PAR files for the Si-Fe-Ni binaries and pure elements down to 500 eV for modeling the Fe (and Ni) Ln, Ll, Lg, etc. emission lines.

See attached ZIP (remember to log in to see attachments).
john

[Probeman]

I am often asked: how can I know if a particular elemental binary has been calculated using Penepma (Penfluor/Fanal) and is available for matrix corrections?

First note that to be sure that your matrix.mdb database is the most recent version, you should run the CalcZAF.msi installer. Next enter some elements in the CalcZAF | Calculate ZAF Corrections window and then from the Analytical | ZAF, Phi-rho-Z, Alpha factor and calibration Curve Corrections menu, select one of the alpha factor options and check the Use Penpma Alpha factors checkbox as seen here:



Next click the Calculate button from the Calculate ZAF Corrections window and observe the output. If a binary is available you will see the following text, here highlighted in red (in DebugMode):

POLYNOMIAL Alpha Factors, Takeoff= 40, KeV= 15

P=1, C=.9900, K=.9882, Alpha=1.1865
P=2, C=.9500, K=.9413, Alpha=1.1855
P=3, C=.9000, K=.8839, Alpha=1.1820
P=4, C=.8000, K=.7702, Alpha=1.1938
P=5, C=.6000, K=.5576, Alpha=1.1903
P=6, C=.5000, K=.4567, Alpha=1.1898
P=7, C=.4000, K=.3584, Alpha=1.1936
P=8, C=.2000, K=.1739, Alpha=1.1873
P=9, C=.1000, K=.0858, Alpha=1.1845
P=10, C=.0500, K=.0426, Alpha=1.1827
P=11, C=.0100, K=.0084, Alpha=1.1917
Xray  Matrix   Alpha1  Alpha2  Alpha3  Alpha4 %AvgDev   *from Penepma 2012 Calculations
U  ma in Ce    1.1854   .0229  -.0234   .0000 .297077

P=1, C=.9900, K=.9887, Alpha=1.1292
P=2, C=.9500, K=.9466, Alpha=1.0719
P=3, C=.9000, K=.8939, Alpha=1.0688
P=4, C=.8000, K=.7892, Alpha=1.0687
P=5, C=.6000, K=.5862, Alpha=1.0589
P=6, C=.5000, K=.4870, Alpha=1.0532
P=7, C=.4000, K=.3886, Alpha=1.0488
P=8, C=.2000, K=.1932, Alpha=1.0439
P=9, C=.1000, K=.0964, Alpha=1.0411
P=10, C=.0500, K=.0480, Alpha=1.0449
P=11, C=.0100, K=.0097, Alpha=1.0344
Xray  Matrix   Alpha1  Alpha2  Alpha3  Alpha4 %AvgDev   *from Penepma 2012 Calculations
Ce la in U     1.0425  -.0256   .0812   .0000 1.28308

Also, from both CalcZAF and Probe for EPMA once can simply click the List Current Alpha Factors menu and you will get the following output:

Penepma K-Ratio Alpha Factors:
Xray  Matrix   Alpha1  Alpha2  Alpha3  Alpha4
Th ma in U     .9844   .1689  -.2185   .0000    *from Penepma 2012 Calculations
Pb ma in U    1.0714   .0256  -.0355   .0000    *from Penepma 2012 Calculations
Ce la in U    1.0425  -.0256   .0812   .0000    *from Penepma 2012 Calculations
U ma in Th     .9969   .0265  -.0398   .0000    *from Penepma 2012 Calculations
Pb ma in Th    1.0299   .2789  -.3529   .0000    *from Penepma 2012 Calculations
Ce la in Th    1.0517   .0229   .0083   .0000    *from Penepma 2012 Calculations
U ma in Pb    1.4536  -.0541   .0451   .0000    *from Penepma 2012 Calculations
Th ma in Pb    1.4183  -.0651   .0477   .0000    *from Penepma 2012 Calculations
Ce la in Pb    1.0240   .0423  -.0365   .0000    *from Penepma 2012 Calculations
U ma in Ce    1.1854   .0229  -.0234   .0000    *from Penepma 2012 Calculations
Th ma in Ce    1.1997   .0530  -.0678   .0000    *from Penepma 2012 Calculations
Pb ma in Ce    1.3818   .1603  -.2692   .0000    *from Penepma 2012 Calculations

[Probeman]

The "fast Monte Carlo" method discussed in this topic has finally been written up by myself, Philippe Pinard and Hendrix Demers. See the pdf attached below for the full paper which will be coming out in Microscopy & Microanalysis relatively soon:

In the meantime we thought we would mention that during the writing of the paper we discovered that we (Donovan!) had not properly handled the modeling of alpha factors for the gaseous elements in the periodic table, specifically N, O, Cl, F, Ar, Kr, and Xe and Rn.  Basically we had utilized the room temperature elemental densities for all the elements, but because the default "bulk" sample geometry file in Penepma (Penfluor/Fanal) utilizes a thickness of 0.1 cm, at moderate to high electron energies a 1mm thickness can not be considered "infinity" thick for the purposes of a bulk calculation.  That is to say, some of the electrons will not come to rest if the density is insufficiently low. This wasn't a problem when the binary composition was mostly a non gaseous element, but it could become a problem for pairs of gaseous elements or when the gaseous element comprised the major element of the binary composition.

Hence we started recalculating all the alpha factor for these gaseous elements about six months ago, but this time using a minimum density of 1.0 if the binary compositional density was less than that.  Again for binaries containing the gaseous elements already mentioned above. These calculations take a long time to complete but just so everyone knows, the current matrix.mdb file contains completed calculations for Xe and Rn binaries, and about half the periodic table for the other gaseous elements (both as emitters and absorbers).

Of course the point of these "fast Monte Carlo" alpha factors is to have a way to test our assumptions for the current analytically derived expressions (ZAF, phi-rho-z) which are generally "tuned" to some experimental k-ratios. The point being that these Penepma derived k-ratios are based on quantum mechanical models and therefore not tuned to any specific material datasets.

We suspect that the most interesting application of these Penepma based alpha factors will be for exotic materials where experimental k-ratios do not exist, and therefore have not been utilized in "tuning" our current analytical expressions for quantification.

Just to demonstrate that we are now correctly handling quantification of light elements using these "fast Monte Carlo" alpha factors here is a calculation using the Armstrong phi-rho-z analytical expression for a glass material (of course containing oxygen):

Un   30 MAM IW2 C4-ext-4, Results in Oxide Weight Percents

ELEM:     Na2O    SiO2     K2O   Al2O3     MgO     CaO    TiO2     MnO     FeO    P2O5   Cr2O3       O     H2O   SUM 
   241    .571  56.566    .502   8.301   7.801   8.146   1.547    .442  15.643    .416    .080    .000    .000 100.016
   242    .467  56.499    .473   8.160   7.843   8.064   1.459    .452  15.984    .398    .092    .000    .000  99.892
   243    .560  55.914    .526   8.032   4.472   8.648   1.696    .457  19.873    .400    .066    .000    .000 100.643
   244    .421  56.258    .480   8.020   6.266   8.415   1.501    .493  17.406    .408    .056    .000    .000  99.722
   245    .551  56.193    .500   8.070   5.606   8.627   1.482    .439  18.083    .407    .084    .000    .000 100.042
   246    .413  56.655    .471   8.268   7.487   8.015   1.474    .459  16.260    .407    .064    .000    .000  99.972

AVER:     .497  56.347    .492   8.142   6.579   8.319   1.526    .457  17.208    .406    .074    .000    .000 100.048
SDEV:     .072    .278    .021    .121   1.371    .283    .089    .019   1.597    .006    .014    .000    .000    .314
SERR:     .029    .113    .009    .050    .560    .115    .036    .008    .652    .003    .006    .000    .000
%RSD:    14.53     .49    4.33    1.49   20.84    3.40    5.80    4.19    9.28    1.59   18.89 -558.57     .00
STDS:      336     160     374     336     162     162      22      25     162     285     396     ---     ---

Now here is the same sample, but this time quantified using the Penepma based "fast Monte Carlo" alpha factor method:

Un   30 MAM IW2 C4-ext-4, Results in Oxide Weight Percents

ELEM:     Na2O    SiO2     K2O   Al2O3     MgO     CaO    TiO2     MnO     FeO    P2O5   Cr2O3       O     H2O   SUM 
   241    .569  56.703    .503   8.298   7.787   8.130   1.549    .442  15.616    .415    .080    .000    .000 100.092
   242    .465  56.643    .474   8.156   7.828   8.049   1.462    .451  15.957    .397    .092    .000    .000  99.974
   243    .557  56.111    .526   8.013   4.461   8.638   1.701    .457  19.838    .398    .066    .000    .000 100.767
   244    .420  56.424    .480   8.009   6.252   8.402   1.503    .492  17.375    .407    .056    .000    .000  99.820
   245    .549  56.367    .501   8.056   5.593   8.614   1.485    .439  18.052    .406    .085    .000    .000 100.146
   246    .411  56.806    .471   8.263   7.472   8.001   1.476    .459  16.232    .406    .064    .000    .000 100.060

AVER:     .495  56.509    .493   8.133   6.565   8.306   1.529    .457  17.178    .405    .074    .000    .000 100.143
SDEV:     .072    .257    .021    .127   1.370    .284    .089    .019   1.594    .006    .014    .000    .000    .326
SERR:     .029    .105    .009    .052    .559    .116    .036    .008    .651    .003    .006    .000    .000
%RSD:    14.50     .45    4.34    1.56   20.86    3.42    5.84    4.19    9.28    1.58   18.82  -36.51     .00
STDS:      336     160     374     336     162     162      22      25     162     285     396     ---     ---

Again, we have no reason to suspect that such a (low Z) material would benefit from such an "untuned" quantification model, but if anyone does run across a composition that does show significant differences between our current "tuned" phi-rho-z models and this "untuned" Penepma based model, we would be very interested in hearing about it.

[Probeman]

The "fast Monte Carlo" method discussed in this topic has finally been written up by myself, Philippe Pinard and Hendrix Demers.

Here is the link to the formatted pdf:

https://www.cambridge.org/core/journals/microscopy-and-microanalysis/article/high-speed-matrix-corrections-for-quantitative-xray-microanalysis-based-on-monte-carlo-simulated-kratio-intensities/48A116A81D6CB946549ABA79D61CA647

[Probeman]

We recently added a bunch of new Penepma (Penfluor/fanal) Monte Carlo calculated binary k-ratios to the matrix.mdb database.  The latest matrix.mdb can be downloaded here:

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

Currently the matrix k-ratio database contains k-ratios for 11 compositions for about 1/2 of the binary systems in the periodic table from 5 to 50 keV and 6 x-ray emission lines (ka, kb, la, lb, ma, mb) mostly at 40 degrees takeoff, though some systems also at 52.5 and 75 degrees.  Or roughly over 435K k-ratios intensities, so far... 

These Monte Carlo derived k-ratios can be utilized in CalcZAF (and Probe for EPMA) for "untuned" matrix corrections:

https://probesoftware.com/smf/index.php?topic=152.msg4242#msg4242

[John Donovan]

We recently added more Penepma (Penfluor/fanal) Monte Carlo calculated binary k-ratios to the matrix.mdb database.  The latest matrix.mdb can be downloaded here:

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

Or by updating your CalcZAF application from the Help menu. The database now contains over 517K k-ratios for binary compositions.

[Probeman]

The latest release of CalcZAF includes the most recent matrix.mdb k-ratio database, which now contains over half a million (565K) k-ratio intensities. This database can be found in the C:\ProgramData\Probe Software\Probe for EPMA folder.

The matrix.mdb is a Microsoft Access (2000) relational database which contains k-ratio intensities calculated from binary compounds and pure elements from Penepma (Penfluor/Fanal). These binary compositions range from 1% to 99% with 11 compositions per binary for electron beam energies between 5 and 50 keV for elements carbon to californium. More details are found in this topic above. For calculations using the full Penepma code see here:

https://probesoftware.com/smf/index.php?topic=151.0

There are a number of benefits to these intensity calculations, the primary one being that the Penepma code is not "tuned" to a particular dataset, as is the case for the analytical expressions that we normally utilize in our matrix corrections.  These intensity calculations are purely based on the best quantum mechanical models (and fundamental parameters) available at the time.

So one possible use of this intensity database could be in comparing these "untuned" calculated intensities with calculations from our analytical expressions, and note where we see significant discrepancies, which we could possibly resolve through empirical measurements.

In addition this matrix.mdb database is also utilized for matrix corrections in Probe for EPMA (and CalcZAF) by fitting the intensities to hyperbolic expressions via so called "alpha factors". This is described in more detail here in the forum:

https://probesoftware.com/smf/index.php?topic=47.0

And also in a paper published by Donovan, Pinard and Demers which describes this method in detail here:

https://epmalab.uoregon.edu/publ/high_speed_matrix_corrections_for_quantitative_xray_microanalysis_based_on_monte_carlo_simulated_kratio_intensities.pdf

The main takeaway from the above work is that the alpha factor method works quite well, except in cases of extreme fluorescence, so in some instances where the analytical expressions fail, this method might be somewhat useful.

On a more adventurous note, it might also be interesting to attempt to utilize this database of k-ratio intensities to train a neural net. However, the database is still incomplete with some areas of the periodic table still being calculated. But if someone is interested in pursuing this line of inquiry, I'd be pleased to participate.