Matrix Corrections For Boron

[Probeman]

I'm starting a topic on boron matrix corrections in EPMA. 

This is a tough nut to crack (and worse for Be and Li quantification?), but there has been significant work already performed by Bastin and Pouchou for several light elements including boron. Matrix corrections and mass absorption coefficients are what counts with this situation and both these groups (and Henke), measured these low energy emission lines to determine empirical mass absorption coefficients (tough to do with gases, very difficult for solids). Bastin and Pouchou and Pichoir also developed analytical matrix corrections which are included in CalcZAF.

Because I'm just thinking out loud here, the following plots are just an initial pass at seeing where we are. I'm going to compare the JTA and PAP matrix corrections with both the Henke and FFAST MACs and also with empirical MACs from Bastin and Pouchou. The dataset is the Bastin boride k-ratio measurements which Brian Joy kindly sent me. I've attached it below if any one is interested in playing with it in CalcZAF.

Edit by John: there was a file format problem in the attached .dat file below.  This is now fixed.

[Probeman]

To start, here's an error distribution for these Bastin boride k-ratio measurements using the Armstrong prz and Henke MACs:



Not exactly great. Here using PAP and Henke:



Better, but still not great. Interestingly, the distributions for the FFAST MAC table are somewhat worse. Now let's try JTA and PAP using Bastin's empirical MACs. First JTA prz:



An improvement. And for PAP:



Not too shabby for boron ka emissions! Interestingly, the Pouchou empirical MACs produce somewhat worse results...

Empirical MACs are found in the CalcZAF Analytical menu as discussed here:

http://probesoftware.com/smf/index.php?topic=347.msg1811#msg1811

[Brian Joy]

I've collected the four T.U.E. reports of Bastin and Heijligers on analysis of borides, carbides, nitrides, and oxides here:

https://drive.google.com/folderview?id=0B6_F2_AzsMWOeS1RMXRWOGlHU00&usp=sharing

In each report, the k-ratio data are tabulated in an appendix.

You can also get the reports here:

borides:  alexandria.tue.nl/repository/books/304562.pdf
carbides:  alexandria.tue.nl/repository/books/304495.pdf
nitrides:  alexandria.tue.nl/repository/books/325592.pdf
oxides:  alexandria.tue.nl/repository/books/362529.pdf

[Brian Joy]

For purpose of comparison, here is a histogram for B Ka k_calc/k_meas constructed using the PROZA96 model of Bastin et al. (1998, X-ray Spectrometry 27:3-10) in conjunction with experimental data and MACs presented in Bastin and Heijligers (1997).  The mean is 1.0026, and the RMS deviation is 0.0329; these values are similar to those presented by Bastin et al. (1998).  The RMS deviation is slightly better than that obtained from PAP using the same empirical MACs or the Bastin MACs contained in the CalcZAF file empmac.dat and is considerably better than that obtained from PROZA.



I should note that I had to integrate numerically (Simpson’s rule) to obtain F(chi) due to precision issues in evaluation of exponential and error function terms in the analytical expression for emitted intensity (with generated intensity determined using PAP).  Imprecision becomes an important factor when the MAC is large relative to the values of the model alpha and beta parameters and can result in erroneous calculation of f(chi) = 0.  I’m not sure how Bastin et al. (1998) got around this problem.  Their “double-Gaussian” phi(rho*z) model is adapted from Merlet (1994, Mikrochimica Acta 114/115:363-376), and this is how it looks (from Bastin et al., 1998):





When I apply the FFAST MACs instead of those presented by Bastin and Heijligers (1997), I get horrible results.  The FFAST MACs are systematically low compared to the empirical MACs.  The resulting mean k_calc/k_meas is 1.1234, and the RMS deviation is 0.2821.



I’ve determined FFAST MACs for B Ka in a given pure element by polynomial interpolation of the tabulated calculated values available at the NIST website (NIST Standard Reference Database 66, updated August 2005).  The values that I get differ slightly from those used in CalcZAF, but generally the differences are small compared to the differences with the MACs of Bastin and Heijligers.

This leads to a question:  Regarding the chantler2005-xx.dat files, exactly how were the FFAST MACs for a given X-ray line in a given matrix determined?  In the plot below for a pure Zr matrix, the black dots are the tabulated values from NIST, the red dots are the values I get by means of polynomial interpolation, and the blue dot is the MAC for B Ka in Zr according to CalcZAF.



Edit 2016-02-24:  When I initially performed the numerical integration to obtain F(chi) for pure boron, I set the upper limit of integration a little too low.  I've corrected this and have replaced the histograms with new ones.  Using the MACs from Bastin & Heijligers (1997), the mean and RMS deviation are now improved slightly.

[Probeman]

I’ve determined FFAST MACs for B Ka in a given pure element by polynomial interpolation of the tabulated calculated values available at the NIST website (NIST Standard Reference Database 66, updated August 2005).  The values that I get differ slightly from those used in CalcZAF, but generally the differences are small compared to the differences with the MACs of Bastin and Heijligers.

This leads to a question:  Regarding the chantler2005-xx.dat files, exactly how were the FFAST MACs for a given X-ray line in a given matrix determined?  In the plot below, the black dots are the tabulated values from NIST, the red dots are the values I get by means of polynomial interpolation, and the blue dot is the MAC for B Ka in Zr according to CalcZAF.

Hi Brian,
The FFAST values I'm using were tabulated by Nicholas Ritchie at NIST.  I've sent him an email about your question above.

But I would only add that for such low energies I would not rely on any fitted model and instead utilize the empirically measured mass absorption coefficients from Pouchou or Bastin.

By the way, I had some magnesium borides I had to measure and ended up making my own empirical determinations using the method of Pouchou (XMAC).  Here is an excerpt from my EMPMAC.DAT file:
john

  "b"     "ka"    "b"       3400         "Bastin (1992)"
  "b"     "ka"    "b"       3500         "Pouchou (1998)"
  "b"     "ka"    "b"       3068         "Donovan (2011)"
  "b"     "ka"    "c"       6500         "Bastin (1992)"
  "b"     "ka"    "n"       11200        "Bastin (1992)"
  "b"     "ka"    "n"       11000        "Pouchou (1998)"
  "b"     "ka"    "n"       10421        "Donovan (2011)"
  "b"     "ka"    "mg"      59500        "Pouchou (1998)"
  "b"     "ka"    "mg"      54500        "Donovan (2011)"
  "b"     "ka"    "al"      64000        "Bastin (1992)"
  "b"     "ka"    "si"      84000        "Bastin (1992)"
  "b"     "ka"    "ti"      14700        "Bastin (1992)"
  "b"     "ka"    "v"       17700        "Bastin (1992)"
  "b"     "ka"    "cr"      20200        "Bastin (1992)"
  "b"     "ka"    "fe"      27300        "Bastin (1992)"
  "b"     "ka"    "co"      33400        "Bastin (1992)"
  "b"     "ka"    "ni"      42000        "Bastin (1992)"
  "b"     "ka"    "zr"      4000         "Bastin (1992)"
  "b"     "ka"    "nb"      4600        "Bastin (1992)"
  "b"     "ka"    "mo"      4550        "Bastin (1992)"
  "b"     "ka"    "la"      2500        "Bastin (1992)"
  "b"     "ka"    "ta"      22500        "Bastin (1992)"
  "b"     "ka"    "w"       21400        "Bastin (1992)"
  "b"     "ka"    "u"       8200        "Bastin (1992)"
  "b"     "ka"    "b"       3471         "Pouchou (1992)"
  "b"     "ka"    "c"       6750         "Pouchou (1992)"
  "b"     "ka"    "n"       11000        "Pouchou (1992)"
  "b"     "ka"    "o"       16500        "Pouchou (1992)"
  "b"     "ka"    "al"       64000        "Pouchou (1992)"
  "b"     "ka"    "si"       80000        "Pouchou (1992)"
  "b"     "ka"    "ti"       15000        "Pouchou (1992)"
  "b"     "ka"    "v"       18000        "Pouchou (1992)"
  "b"     "ka"    "cr"       20700        "Pouchou (1992)"
  "b"     "ka"    "fe"       27800        "Pouchou (1992)"
  "b"     "ka"    "co"       32000        "Pouchou (1992)"
  "b"     "ka"    "ni"       37000        "Pouchou (1992)"
  "b"     "ka"    "zr"       4400         "Pouchou (1992)"
  "b"     "ka"    "nb"       4500         "Pouchou (1992)"
  "b"     "ka"    "mo"       4600         "Pouchou (1992)"
  "b"     "ka"    "la"       2500         "Pouchou (1992)"
  "b"     "ka"    "ta"       23000        "Pouchou (1992)"
  "b"     "ka"    "w"       21000        "Pouchou (1992)"
  "b"     "ka"    "u"       7400         "Pouchou (1992)"

[Nicholas Ritchie]

FFAST is a NIST database of mass absorption coefficients.  There are described herehttp://www.nist.gov/pml/data/ffast/. They are the result of a purely theoretical calculation and include not only macs of the form Xs x-ray in Y element but macs for the full range of energies between 10 eV and 433 keV.  Chantler (the database's author) made some estimates of the uncertainties associated with the MACs.  As you might expect, the MACs are better at higher energies and away from absorption edges.  At the range of energies associated with the B K line, the uncertainties are huge. 

The dataset I gave to John is based on interpolation as implemented in DTSA-II.  I use the tablulations of each element's MACs as provided on the FFAST website and as I recall use a Log-Log interpolation to estimate the MACs at other energies.  I used the database of x-ray energies and edges also provided by FFAST to ensure consistency.

[Nicholas Ritchie]

I wonder if the empirical MACs might compensate for some other effect like chemical shifts?

[Probeman]

I wonder if the empirical MACs might compensate for some other effect like chemical shifts?

Hi Nicholas,
Absolutely they (empirically derived MACs), would help!   

See this post for some boron Ka examples:

http://probesoftware.com/smf/index.php?topic=667.msg4064#msg4064

I think Brian is just wanting to understand the fit method you utilized in DTSA-II, so I think you answered his question.
john

[Brian Joy]

The dataset I gave to John is based on interpolation as implemented in DTSA-II.  I use the tablulations of each element's MACs as provided on the FFAST website and as I recall use a Log-Log interpolation to estimate the MACs at other energies.  I used the database of x-ray energies and edges also provided by FFAST to ensure consistency.

I’m just trying to understand why the MAC for B Ka in Zr from the file chantler2005-ka.dat (the blue square on the plot above) plots above the calculated values tabulated in the NIST FFAST database.  I realize that the uncertainties could be huge.  In fact the value determined by Bastin and Heijligers (1997) -- 4330 cm^2/g -- suggests that B Ka is actually lower in energy than the Zr M5 edge.

[Brian Joy]

For a different perspective, I’ve added MACs from the CXRO model (Henke et al., 1993, Atomic Data and Nuclear Tables 54:181-342) to the plot above for comparison.  My interpolated values are in green.  Note that my interpolation algorithm fails between the Zr M4 and M5 edges (located slightly differently by Henke et al.) due to a lack of tabulated values near/between the edges.

[Probeman]

For a different perspective, I’ve added MACs from the CXRO model (Henke et al., 1993, Atomic Data and Nuclear Tables 54:181-342) to the plot above for comparison.  My interpolated values are in green.  Note that my interpolation algorithm fails between the Zr M4 and M5 edges (located slightly differently by Henke et al.) due to a lack of tabulated values near/between the edges.

Hi Brian,
It might be interesting to plot up these two empirical determinations for B ka in Zr in the above plot also:

  "b"     "ka"    "zr"      4000         "Bastin (1992)"
  "b"     "ka"    "zr"       4400         "Pouchou (1992)"

[Probeman]

For a different perspective, I’ve added MACs from the CXRO model (Henke et al., 1993, Atomic Data and Nuclear Tables 54:181-342) to the plot above for comparison.  My interpolated values are in green.  Note that my interpolation algorithm fails between the Zr M4 and M5 edges (located slightly differently by Henke et al.) due to a lack of tabulated values near/between the edges.

It's interesting that the old Johnson & White table has B Ka at 183 eV (as is yours), but the latest NIST x-ray database has it at 185 eV.

So if you did plot the CalcZAF FFAST MAC at 185 eV, it would fall right on the FFAST table values trend.

Are there other more recent determinations of the boron Ka emission line energy (in zirconium boride at least)?

[Brian Joy]

It's interesting that the old Johnson & White table has B Ka at 183 eV (as is yours), but the latest NIST x-ray database has it at 185 eV.

So if you did plot the CalcZAF FFAST MAC at 185 eV, it would fall right on the FFAST table values trend.

Are there other more recent determinations of the boron Ka emission line energy (in zirconium boride at least)?

I guess that would explain it.  But which database are you referring to?  The one presented by NIST here by Deslattes et al. (2003) only includes transition energies for elements Z > 9 (and also does not include M lines).

[John Donovan]

It's interesting that the old Johnson & White table has B Ka at 183 eV (as is yours), but the latest NIST x-ray database has it at 185 eV.

So if you did plot the CalcZAF FFAST MAC at 185 eV, it would fall right on the FFAST table values trend.

Are there other more recent determinations of the boron Ka emission line energy (in zirconium boride at least)?

I guess that would explain it.  But which database are you referring to?  The one presented by NIST here by Deslattes et al. (2003) only includes transition energies for elements Z > 9 (and also does not include M lines).

It's the one displayed from the X-Ray menu in CalcZAF. It was generated by Nicholas Ritchie for the first order lines as seen here:

[Brian Joy]

It's interesting that the old Johnson & White table has B Ka at 183 eV (as is yours), but the latest NIST x-ray database has it at 185 eV.

So if you did plot the CalcZAF FFAST MAC at 185 eV, it would fall right on the FFAST table values trend.

Are there other more recent determinations of the boron Ka emission line energy (in zirconium boride at least)?

I guess that would explain it.  But which database are you referring to?  The one presented by NIST here by Deslattes et al. (2003) only includes transition energies for elements Z > 9 (and also does not include M lines).

It's the one displayed from the X-Ray menu in CalcZAF. It was generated by Nicholas Ritchie for the first order lines

What publications do the references "JD" and "ES" refer to?  When I press F1 with the X-ray database window open, I only see a list of the older publications.