Utilizing Empirical Mass Absorption Coefficients (MACs)

[John Donovan]

Recently a colleague contacted us about using empirical mass absorption coefficient (MACs) values in CalcZAF and Probe for EPMA. That is, instead of simply using the values for MACs that have been tabulated (Henke, Heinrich, FFAST, etc.), we carefully measure the emitter in question in the matrix in question at different accelerating voltages. Then we determine the specific emitter-absorber MAC based on methods by Pouchou (XMAC) or some other technique. This is a very common problem when quantifying low atomic number elements such as Li, Be, B, C, N, O (and others) when the low energy emission is strongly absorbed by the matrix, because the commonly tabulated MACs are simply not very accurate in many of these cases.

Now I had thought that we had a topic on the user forum discussing this already, but except for a few links that mention this issue briefly, e.g.,

https://probesoftware.com/smf/index.php?topic=1250.msg8722#msg8722

https://probesoftware.com/smf/index.php?topic=1194.msg8265#msg8265

https://probesoftware.com/smf/index.php?topic=1061.msg9282#msg9282

https://probesoftware.com/smf/index.php?topic=508.msg9221#msg9221

https://probesoftware.com/smf/index.php?topic=1185.msg8154#msg8154

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

and a link to a white paper here (see appendix A for some details),

https://pages.uoregon.edu/epmalab/reports/Withers%20hydrous%20glass.pdf

there hasn't been much discussion of the process itself. So this topic is an effort to address that omission.

Let's start by taking an example that minimizes the issue of area peak factors (APFs), which is another common problem when measuring low energy element emitters using the peak intensity, as opposed to measuring the integrated area under the peak. See here for details on the topic of area peak factors:

https://probesoftware.com/smf/index.php?topic=536.0

We'll use an example of Si Ka absorbed by Hf. This choice avoids the APF issue which can obscure evaluation of the MAC accuracy. But to reiterate: when looking at low energy emitters, be sure to always check first for peak shape issues by either searching the literature, or performing your own APF determinations using careful wavescans on your unknown and standard as described in the link above.

So what is the problem with Si Ka in a matrix with Hf? Well it so happens that Si ka is quite close to the Hf M (IV) edge and is subsequently quite absorbed by the presence of Hf in the matrix (matrix correction for Si Ka in Hf is around 80% so not insignificant). The default MAC here is Henke which shows Si Ka in Hf = 5449 (cm2/g) and produces these results using SiO2 as a standard relative to HfSiO4:



Definitely the total is too high and clearly it's the Si that is off by some 30% relative. We can examine other MAC table values in CalcZAF for Si Ka in Hf using the X-Ray | Display MAC Emitter Absorber Pair menu:



But even if we select the FFAST MAC value which is 4926 (cm2/g), we still get high totals:



In fact even trying all the different matrix corrections in CalcZAF/PFE we see consistently high totals, which tells us that something might be wrong with the MACs as seen here:



Now how do we go about empirically determining a more accurate MAC for Si Ka in Hf?  We will examine this in the next post...

[John Donovan]

Continuing from the previous post, to experimentally determine a mass absorption coefficient (MAC), we start with a material that contains the specified emitter and absorber pair with a known composition. Ideally this material is a binary composition, but often that is not available. Fortunately using an iterative technique such as the one Pouchou developed, a method to extract MACs for a specific emitter absorber pair can be performed, even in a complex matrix, when utilizing his XMAC program.

So now we make intensity measurements for the emitting x-ray in question, over a range of beam energies and load the intensities using the XMAC application input control or by loading an edited .XMC file (see example file attached below) as seen here, after clicking the Iexp button to display the intensities:



Next we click the m.a.c. button to perform the iterative MAC calculation as seen here:



Note the .XMC file format (a simple text file which can be edited using NotePad or another text editor):

3,1                                        <--- number of elements, number of datasets (usually 1)
"Si",.1038023                              <--- composition in weight fraction
"Hf",.6596766
"O",.2365212
40                                        <--- spectro angle
90                                        <--- azimuth angle
0                                          <--- tilt angle
40                                        <--- effective takeoff angle
"Si","Ka"                                 <--- emitting element and x-ray line (Ka, Kb, La, Lb, Ma, Mb)
2                                          <--- absorber index (Hf in this case)
8                                          <--- number of intensity measurements
4,13.3                                     <- keV beam energy, intensity in cps/nA
6,38.91
8,65.54
10,89.44
12,108.85
16,133.51
22,144.91
26,142.67

Once we have our experimentally determined MAC, we can add it to the empirical MAC text file that comes with CalcZAF and Probe for EPMA. In this case, the Si Ka in Hf MAC is already entered, as we can see in the EMPMAC.DAT text file, which is found in the C:\ProgramData\Probe Software\Probe for EPMA folder:

Code: [Select]

  "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)"
  "c"     "ka"    "b"       39000        "Pouchou (1992)"
  "c"     "ka"    "c"       2170         "Pouchou (1992)"
  "c"     "ka"    "si"       35000        "Pouchou (1992)"
  "c"     "ka"    "ti"       8097         "Pouchou (1992)"
  "c"     "ka"    "v "       8850         "Pouchou (1992)"
  "c"     "ka"    "cr"       10700        "Pouchou (1992)"
  "c"     "ka"    "fe"       13150        "Pouchou (1992)"
  "c"     "ka"    "zr"       25000        "Pouchou (1992)"
  "c"     "ka"    "nb"       24000        "Pouchou (1992)"
  "c"     "ka"    "mo"       20500        "Pouchou (1992)"
  "c"     "ka"    "hf"       18000        "Pouchou (1992)"
  "c"     "ka"    "ta"       17000        "Pouchou (1992)"
  "c"     "ka"    "w"       18000        "Pouchou (1992)"
  "n"     "ka"    "b"       15800        "Pouchou (1992)"
  "n"     "ka"    "n"       1640         "Pouchou (1992)"
  "n"     "ka"    "al"       13800        "Pouchou (1992)"
  "n"     "ka"    "si"       17000        "Pouchou (1992)"
  "n"     "ka"    "ti"       4270         "Pouchou (1992)"
  "n"     "ka"    "v "       4950         "Pouchou (1992)"
  "n"     "ka"    "cr"       5650         "Pouchou (1992)"
  "n"     "ka"    "fe"       7190         "Pouchou (1992)"
  "n"     "ka"    "zr"       24000        "Pouchou (1992)"
  "n"     "ka"    "nb"       25000        "Pouchou (1992)"
  "n"     "ka"    "mo"       25800        "Pouchou (1992)"
  "n"     "ka"    "hf"       14000        "Pouchou (1992)"
  "n"     "ka"    "ta"       15500        "Pouchou (1992)"
  "o"     "ka"    "li"       1600         "Bastin  (1992)"
  "o"     "ka"    "b"       8550         "Bastin  (1992)"
  "o"     "ka"    "o"       1200         "Bastin  (1992)"
  "o"     "ka"    "f"       1850         "Love et al. (1974)"
  "o"     "ka"    "ne"       2750         "Love et al. (1974)"
  "o"     "ka"    "na"       3630         "Love et al. (1974)"
  "o"     "ka"    "mg"       5170         "Bastin  (1992)"
  "o"     "ka"    "mg"       5918         "Donovan  (2011) MgO"
  "o"     "ka"    "al"       6720         "Bastin  (1992)"
  "o"     "ka"    "si"       8790         "Bastin  (1992)"
  "o"     "ka"    "p"       9820         "Love et al. (1974)"
  "o"     "ka"    "s"       12400        "Love et al. (1974)"
  "o"     "ka"    "cl"       14300        "Love et al. (1974)"
  "o"     "ka"    "ar"       16100        "Love et al. (1974)"
  "o"     "ka"    "k"       20500        "Love et al. (1974)"
  "o"     "ka"    "ca"       24600        "Love et al. (1974)"
  "o"     "ka"    "sc"       26800        "Love et al. (1974)"
  "o"     "ka"    "ti"       19900        "Bastin  (1992)"
  "o"     "ka"    "ti"       21046        "Donovan  (2011) TiO2"
  "o"     "ka"    "v"        35463        "Donovan  (2011) V2O3"
  "o"     "ka"    "v"        40509        "Donovan  (2011) V2O5"
  "o"     "ka"    "cr"       2900         "Bastin  (1992)"
  "o"     "ka"    "mn"       3470         "Bastin  (1992)"
  "o"     "ka"    "fe"       4000         "Bastin  (1992)"
  "o"     "ka"    "co"       4500         "Bastin  (1992)"
  "o"     "ka"    "ni"       5120         "Bastin  (1992)"
  "o"     "ka"    "cu"       5920         "Bastin  (1992)"
  "o"     "ka"    "zn"       6350         "Bastin  (1992)"
  "o"     "ka"    "ga"       7090         "Bastin  (1992)"
  "o"     "ka"    "y"       15100        "Bastin  (1992)"
  "o"     "ka"    "zr"       16200        "Bastin  (1992)"
  "o"     "ka"    "nb"       17100        "Bastin  (1992)"
  "o"     "ka"    "mo"       18000        "Bastin  (1992)"
  "o"     "ka"    "ru"       19700        "Bastin  (1992)"
  "o"     "ka"    "sn"       15050        "Bastin  (1992)"
  "o"     "ka"    "ba"       4560         "Bastin  (1992)"
  "o"     "ka"    "la"       3600         "Bastin  (1992)"
  "o"     "ka"    "ta"       10600        "Bastin  (1992)"
  "o"     "ka"    "w "       11300        "Bastin  (1992)"
  "o"     "ka"    "pb"       11000        "Bastin  (1992)"
  "o"     "ka"    "bi"       12100        "Bastin  (1992)"
  "o"     "ka"    "u"        8973         "Donovan (2011)"
  "f"     "ka"    "xe"       27300        "Henke et al. (1982)"
  "na"    "ka"    "zn"       10500        "Henke et al. (1982)"
  "na"    "ka"    "pm"       7920         "Henke et al. (1982)"
  "mg"    "ka"    "tb"       8240         "Henke et al. (1982)"
  "al"    "ka"    "tm"       4730         "Henke et al. (1982)"
  "si"    "ka"    "hf"       3477         "Donovan (2011)"
  "cr"    "la"    "te"       39500        "Henke et al. (1982)"
  "co"    "la"    "co"       1920         "Henke et al. (1982)"
  "ge"    "ka"    "ta"       265          "Henke et al. (1982)"
  "ge"    "la"    "gd"       8500         "Henke et al. (1982)"
  "mo"    "la"    "hg"       951          "Henke et al. (1982)"

For additional empirical MAC entries simply add another line to the file using the same format as the other lines (details are found in the PFE User Reference manual and the links in the previous post), again using a text editor such as NotePad. Once the EMPMAC.DAT file is properly edited for any new MAC entries, we can start CalcZAF or PFE applications and click the Analytical | Empirical MACs menu as seen here:



Now we load the specified empirical MAC(s):



and click OK:



It should be noted that when you have added a new empirical MAC to your run and clicked OK in the above dialog, the Use Empirical MACs flag will automatically be set, but it can be toggled on and off from the Analytical | Analysis Options dialog as seen here:



Once we have our empirical MAC(s) loaded, when can re-analyze the sample as seen here:



Much better totals now. And in fact if we select the Use All Matrix Corrections checkbox in the Analyze! window we see a very nice set of average compositions:



I hope this helps, but please let me know if anyone has any questions at all.

[Brian Joy]

Mass absorption coefficients aren't dimensionless!!!  Your answer should be 3447 cm²/g.  Aaaarrrrgggghhhhh!!!!!

[John Donovan]

Mass absorption coefficients aren't dimensionless!!!  Your answer should be 3447 cm²/g.  Aaaarrrrgggghhhhh!!!!!

Hi Brian,
Pouchou's XMAC program does say cm²/g until one clicks the m.a.c button...  and I added units for the last screenshot.

Happy New Year!     

[Probeman]

Here's an example using Pouchou's XMAC program to calculate an empirical MAC for B Ka in Mg.

This MAC value is very large due to the fact that B Ka is highly absorbed by Mg and so we utilized two boron compounds, MgB2 and MgB4 which we obtained from Ohio State University.  After performing intensity measurements at 5, 8, 10, 12, 14, 16 and 20 keV we see these data values after loading into XMAC for MgB2:



Clicking the m.a.c. button we obtain this MAC value:



Turning to the MgB4 compound we get these data values:



and this MAC determination:



The two values are remarkably close to each other so we averaged them and utilize 54500 cm2/g for B Ka in Mg, which is slightly different from the value that Pouchou determined from his measurements:



Since we don't have a FEG EPMA we cannot make measurements much below 5 keV, but maybe someone else has made these intensity measurements below 5 keV?

[AndrewLocock]

Thanks for the excellent discussion of how to measure and determine an empirical mass absorption coefficient using XMAC.

As XMAC is not easily available, but BadgerFilm is(!), would it be possible to ask you (or Aurélien Moy or John Fournelle) to post similar instructions that show explicitly how to use BadgerFilm to measure and determine an empirical MAC?

I have also just run into the "SnO2" problem for measuring oxygen, and the MAC value O-Sn from Bastin & Hijligers 1992 "(presumably approx 15,050 cm2/g)" does not appear to be entirely satisfactory.

Thanks in advance!
Andrew

[xllovet]

I have also just run into the "SnO2" problem for measuring oxygen, and the MAC value O-Sn from Bastin & Hijligers 1992 "(presumably approx 15,050 cm2/g)" does not appear to be entirely satisfactory.

What about if you use 14,225 cm2/g? It's the value measured by Ménesguen et al. 2018 (see figure 3b of the attached paper, still in press)
 
Xavier

[John Donovan]

As XMAC is not easily available, but BadgerFilm is(!), would it be possible to ask you (or Aurélien Moy or John Fournelle) to post similar instructions that show explicitly how to use BadgerFilm to measure and determine an empirical MAC?

Apparently BadgerFilm can now estimate mass absorption coefficients from multi-voltage intensity measurements a la XMAC.  It would be great if Aurelien could document how this is done in the BadgerFilm board:

https://probesoftware.com/smf/index.php?board=37.0