Penepma/Penfluor/Fanal derived Alpha Factors For Matrix Corrections

[Probeman]

Although oxygen is not a major constituent of Julien's Ti-Pt alloy, I thought I would also compare O in Ti and O in Pt for fun. Here is O Ka in Ti using the default Armstrong/Love-Scott/Reed corrections for calculating alpha factors:



Now here is the same binary using Penepma Monte-Carlo derived k-ratios:



Considering the magnitude of the matrix correction (very large MAC), they are is rough agreement.  Now for O in Pt, again using the default Armstrong/Love-Scott/Reed corrections for calculating alpha factors:



and again using Penepma Monte-Carlo derived k-ratios:



All in all, in basic agreement...

[Probeman]

Although nitrogen is also not a significant component of Julien's Ti-Pt system, I decided to look at the N-Ti binary out of curiosity because as some of you may know, there is a nasty absorption edge there that produces a significant matrix correction (not to mention a nasty spectral interference). Unfortunately the matrix correction (and interference correction) is quite dependent on the chemical state if the Ti atom because it's a Ti L series interference and the M shell is involved in the chemical  bonding state.  But aside from all that this binary system display an interesting Monte-Carlo statistical issue that is worth mentioning.

Here is the N-Ti using the default Armatring/LogveScott/Reed analytical matrix corrections:



It looks pretty reasonable. Now here is the same binary calculated using fast Monte-Carlo k-ratios from Penfluor/Fanal (matrix.mdb):



Holy donut holes Batman! That does not look good. What is going on?  The problem is statistics. Because of the low energies involved, the default binary calculation time of 110 hours is insufficient to obtain decent statistics for N ka, so we could calculate longer, or... we could just remove the high N concentration binaries from our fit by selecting the Penepma Limits option at say 90%, in the ZAF/Phi-Rho-Z/Alpha factor and Calibration Curve Options menu dialog as seen here:



After we select this we get this:



Not perfect but good, and if we choose the non-linear fit we do even better:

[Probeman]

Finally we look at the Pt Ma in Ti binary. Again here is the default Armstrong/Love-Scott/Reed Phi-rho-z:



and note the significant difference with the Penepma Monte-Carlo:

[Probeman]

With the latest Penepma (Penfluor/fanal) binary k-ratio database update (see matrix.mdb), the following results are obtained with the Pouchou k-ratio database (without the B ka and Cu La measurements):



Compared to the previous result here:

http://smf.probesoftware.com/index.php?topic=47.msg3263#msg3263

this latest error distribution is slightly higher for the average and slightly improved for the standard deviation.

Progress...

[Probeman]

I'm about to release a new matrix.mdb k-ratio database from my ongoing Penepma Monte-Carlo calculations.

In particular, many of these latest binary compositions are for the REEs and actinide series elements.  And I would like to perform and post some comparisons between traditional analytical expressions and these new Penepma binary calculations for these elements, particularly the actinides...

Can those of you working in the EPMA nuclear characterization field please provide some examples of actinide binary pairs that you would find most helpful for your matrix corrections?  For example, Am La/Ma in Pu???

[Mike Matthews]

Al, Am, C, Fe, Ga, Ni, O and U would be the top requests in my list.

...and Pu

[Probeman]

Al, Am, C, Fe, Ga, Ni, O and U would be the top requests in my list.

Hi Mike,
Perfect.

The Penepma binaries that are already calculated for these elements are as follows:

Penepma K-Ratio Alpha Factors:
Xray  Matrix   Alpha1  Alpha2  Alpha3  Alpha4
Ni ka in U     .7367   .1837  -.1886   .0000    *from Penepma 2012 Calculations
Fe ka in U     .8127   .0905  -.0362   .0000    *from Penepma 2012 Calculations
Al ka in U    1.5105   .4800  -.1656   .0000    *from Penepma 2012 Calculations
O ka in U    3.5118 -5.5011  9.6713   .0000    *from Penepma 2012 Calculations
Ni ka in Ga     .7277   .3683  -.3001   .0000    *from Penepma 2012 Calculations
Fe ka in Ga     .8370   .2470  -.2436   .0000    *from Penepma 2012 Calculations
Al ka in Ga    2.6465  -.0290  -.0772   .0000    *from Penepma 2012 Calculations
O ka in Ga    3.0362 -7.2413 10.7289   .0000    *from Penepma 2012 Calculations
C ka in Ga    5.6139  1.7763 -1.9722   .0000    *from Penepma 2012 Calculations
U ma in Ni    1.3002   .1365  -.0661   .0000    *from Penepma 2012 Calculations
Ga ka in Ni    1.1508   .0200  -.0086   .0000    *from Penepma 2012 Calculations
Fe ka in Ni     .7620   .4592  -.3626   .0000    *from Penepma 2012 Calculations
Al ka in Ni    2.4398  -.1169  -.0413   .0000    *from Penepma 2012 Calculations
O ka in Ni    2.6317 -7.4839 10.9035   .0000    *from Penepma 2012 Calculations
C ka in Ni    4.4830   .5990  -.8225   .0000    *from Penepma 2012 Calculations
U ma in Fe    1.2105   .1559  -.0372   .0000    *from Penepma 2012 Calculations
Ga ka in Fe    1.1250   .0983  -.1315   .0000    *from Penepma 2012 Calculations
Ni ka in Fe    1.0798   .0256  -.0120   .0000    *from Penepma 2012 Calculations
Al ka in Fe    2.0251   .0243  -.0913   .0000    *from Penepma 2012 Calculations
O ka in Fe    2.2125 -7.4945 10.9570   .0000    *from Penepma 2012 Calculations
C ka in Fe    3.2583   .4177  -.4456   .0000    *from Penepma 2012 Calculations
U ma in Al    1.4492   .0996  -.0010   .0000    *from Penepma 2012 Calculations
Ga ka in Al    1.1008   .3902  -.3712   .0000    *from Penepma 2012 Calculations
Ni ka in Al    1.0528   .0758  -.0400   .0000    *from Penepma 2012 Calculations
Fe ka in Al    1.0780   .2010  -.2520   .0000    *from Penepma 2012 Calculations
O ka in Al    3.0586 -7.4658 10.7455   .0000    *from Penepma 2012 Calculations
C ka in Al    7.8972   .6031 -1.9221   .0000    *from Penepma 2012 Calculations
U ma in O    1.3779   .3482  -.1499   .0000    *from Penepma 2012 Calculations
Ga ka in O    1.1752   .6630  -.2488   .0000    *from Penepma 2012 Calculations
Ni ka in O    1.1135   .2717  -.0710   .0000    *from Penepma 2012 Calculations
Fe ka in O    1.1522   .4001  -.4122   .0000    *from Penepma 2012 Calculations
Al ka in O    1.6517  -.0568  -.1022   .0000    *from Penepma 2012 Calculations
C ka in O    1.8118  -.1394   .0949   .0000    *from Penepma 2012 Calculations
U ma in C    1.3601   .2630   .0155   .0000    *from Penepma 2012 Calculations
Ga ka in C    1.0964  2.1334 -2.3743   .0000    *from Penepma 2012 Calculations
Ni ka in C    1.0986   .5467  -.3687   .0000    *from Penepma 2012 Calculations
Fe ka in C    1.1466   .4063  -.2857   .0000    *from Penepma 2012 Calculations
Al ka in C    1.3034  -.2479   .3163   .0000    *from Penepma 2012 Calculations
O ka in C    6.9004 -8.8507 10.6434   .0000    *from Penepma 2012 Calculations


I will check for the others as soon as the calculations are ready.
john

[Probeman]

A good introduction to the use of alpha and beta factors can be found here:

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

Basically, the matrix elements are reduced to binaries for off-line Monte-Carlo calculations (alpha factors) in advance, but later combined again for matrix corrections (beta factors) in real time.

This allows us to perform the Monte-Carlo calculations in advance. Otherwise it would take the age of the universe.   

[wrigke]

I'd suggest the following pairs:
U ma  Pu mb
U ma Np ma
U ma Am mb
Pu mb Np ma
Pu mb Am mb
Np ma Am mb
U ma C ka
U ma O ka
U ma Zr la
Pu mb Zr la
U ma Mo la
U ma Nd la

Thanks for your efforts!

[Probeman]

Hi Karen,
No need to specify the x-ray lines, as all available lines are calculated automatically with the Penepma Monte-Carlo code.  By the way, some of these binary pairs are calculated and available already, and here's how one can find out if they are:

1.  Run CalcZAF and click the Enter Composition by Formula String button as seen here:



2. Enter the elements (all of them) that you are interested in as seen here:



For some of these actinide elements you may get some overvoltage warnings if your default operating voltage is under 20 keV. Just ignore these, or if you prefer, change the default keV to 20 in the Analytical | Operating Conditions menu and try again. 

Note also that you may get warnings regarding missing MAC values for some of these actinide elements (e.g., Am) if your x-ray databases do not have values for these elements.  These modified database files are available on request (and you already have them!) but, these missing MAC values are *not* necessary for the Penepma calculations as the k-ratio intensities are calculated from fundamental parameters!

3. From the Analytical | ZAF, Phi-Rho-Z, Alpha factor and Calibration Curve Selections menu, click the Polynomial Alpha Factors option and then check the Use Penepma K-ratios checkbox as seen here:



4. Finally click the Run | List Current Alpha Factors menu and see which binary pairs are available from Penepma Monte-Carlo calculations as seen here:

Penepma K-Ratio Alpha Factors:
Xray  Matrix   Alpha1  Alpha2  Alpha3  Alpha4
O ka in Pu    2.7028  -.6135  2.3234   .0000    *from Penepma 2012 Calculations
O ka in Np    3.6677   .2544  1.4957   .0000    *from Penepma 2012 Calculations
Mo la in U    1.1164  -.0435   .1787   .0000    *from Penepma 2012 Calculations
Zr la in U    1.2261   .0781   .0284   .0000    *from Penepma 2012 Calculations
O ka in U    4.1551   .6973  1.1366   .0000    *from Penepma 2012 Calculations
O ka in Nd    2.3311 -1.5983  2.8928   .0000    *from Penepma 2012 Calculations
C ka in Nd    2.1652   .9365  -.5294   .0000    *from Penepma 2012 Calculations
Zr la in Mo    1.0175  -.0331   .0910   .0000    *from Penepma 2012 Calculations
O ka in Mo    9.2251  1.2504 -1.1877   .0000    *from Penepma 2012 Calculations
C ka in Mo    9.6890  4.9851 -5.2894   .0000    *from Penepma 2012 Calculations
U ma in Zr    1.7090  -.0252  -.0740   .0000    *from Penepma 2012 Calculations
Mo la in Zr    1.8058  -.1545   .0953   .0000    *from Penepma 2012 Calculations
O ka in Zr    8.0640   .2963  -.0162   .0000    *from Penepma 2012 Calculations
C ka in Zr   10.9231  6.1915 -6.7884   .0000    *from Penepma 2012 Calculations
Pu la in O    3.4332-13.5762 20.2590   .0000    *from Penepma 2012 Calculations
Np la in O    3.7503-19.0111 29.3622   .0000    *from Penepma 2012 Calculations
U ma in O    1.1949   .4583  -.2719   .0000    *from Penepma 2012 Calculations
Nd la in O    1.2222   .1731  -.0761   .0000    *from Penepma 2012 Calculations
Mo la in O    1.1821   .0278   .0545   .0000    *from Penepma 2012 Calculations
Zr la in O    1.2404  -.0669   .1358   .0000    *from Penepma 2012 Calculations
C ka in O    2.0980  -.1984   .1442   .0000    *from Penepma 2012 Calculations
U ma in C    1.1587   .2905   .0099   .0000    *from Penepma 2012 Calculations
Nd la in C    1.2121   .0938   .1284   .0000    *from Penepma 2012 Calculations
Mo la in C    1.0433   .0165   .1176   .0000    *from Penepma 2012 Calculations
Zr la in C    1.0258   .1284  -.0654   .0000    *from Penepma 2012 Calculations
O ka in C    8.6296 -3.8210  2.4080   .0000    *from Penepma 2012 Calculations

Note that there is a fitting problem with C ka in U that I am fixing this weekend (not shown). Next week I should have a bunch more actinide pairs to release, so stay tuned!   

[Probeman]

Here is a comparison of the carbon-lead binary between the JTA correction and the fast Monte-Carlo method.

Some significant differences, but which one is "correct"? 

See attachments below.

[John Donovan]

The matrix.mdb Penepma (Penfluor/Fanal) binary k-ratio database now contains over 300,000 k-ratios (2805 binaries). That's almost 2/3 of the periodic table.

The complete list is here:

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

[Probeman]

I just released a new matrix.mdb k-ratio database with many new binaries, but because it doesn't get automatically updated unless you run the CalcZAF.msi file, I've provided a link below to allow one to download it manually.  It should be copied to the C:\ProgramData\Probe Software\Probe for EPMA folder (or under XP the C:\Documents and Settings\All Users\Probe Software\Probe for EPMA folder).

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

Here is the Pouchou database calculated using phi-rho-z (JTA/improved Reed):



And here with polynomial alpha factors fitted to k-ratios from Penepma (Penfluor/Fanal):



Cool.

[John Donovan]

The latest matrix.mdb (see above post for link) contains an additional 59 binaries, mostly REE and actinides.

That makes over 326K binary k-ratios!

[Probeman]

The error distributions for the Pouchou dataset comparing traditional analytical expressions (JTA/Modified Reed) and the new fast Monte-Carlo matrix correction methods have been previously compared here:

http://smf.probesoftware.com/index.php?topic=47.msg4159#msg4159

But I thought it would be interesting to try the same comparison for the Bastin k-ratio dataset which I obtained from Brian Joy earlier this year.  There is some overlap between the two datasets, but the Bastin dataset has some crazy large overvoltages that should really stress the corrections, so let's see how they do.  First the Bastin dataset using the traditional analytical expressions (JTA/Modified Reed):



The average is good, but the standard deviation is larger than what we get from the Pouchou dataset and the reason is the very high overvoltage outliers (plus one very low overvoltage k-ratio) seen circled in the image and listed here:

Problematic k-ratio errors (< 0.8 or > 1.2)
  Line             ConcA   ConcB     TOA      eO      Uo   K-Exp   K-Cal   K-Err
121   Ag la in Au .199600 .800400 52.5000 48.5000 14.4690 .079500 .063394 .797408
348   Al ka in Mg .091000 .909000 75.0000 40.0000 25.6410 .012300 .015082 1.22615
360   Al ka in Mg .091000 .909000 20.0000 40.0000 25.6410 .006900 .008550 1.23914
436   Nb la in V  .080000 .920000 20.0000 40.0000 16.8705 .053000 .064454 1.21612


These high overvoltage outliers also tend to be low concentrations, so accuracy errors in the "known" compositions could be an additional factor as seen here:



Note that I've included the complete k-ratio dataset including the B ka in carbon k-ratios, but these low energy emission lines do not seem to be problematic.