Compound or Specified Area Peak Factors (APFs)

[aducharme]

Before seeing the final result, recall the APF is defined as the ratio of the normalized integrated intensities of the unknown to the standard. Equivalently,

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where I^I_U is the integrated unknown peak intensity, I^P_U is the maximum intensity of the unknown peak, I^P_S is the integrated standard peak intensity, and I^P_S is the maximum intensity of the standard peak. Because I need to integrate a spectrum containing several overlapping peaks, there is not an immediately well-defined location to set my lower and upper bounds. My thought was to just try all the symmetric bounds about the maxima (if the peaks were not approximately symmetric, the integration region would need to be asymmetric) and see what happens. My result:

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This plot shows calculations of the area peak factors for four different versions of my data with varying integral interval sizes (window sizes). These versions are: 1. raw, 2. background-corrected (bgd), 3. background-corrected and Al-interference corrected, and 4. background-corrected, Al-interference corrected, and MgAl2O4 O peak maximum-corrected data.

Big takeaway #1: Choice of integration region seriously impacts the APF result. APFs are reported with two to five decimals places of significant digits! Changing my window is altering the third, and even second, decimal place.

Big takeaway #2: Measuring the maxima right matters. APFs are directly proportional to the standard's peak maximum, so if that measurement is 5% too high or too low, your APF is going to increased 5% or decreased by 5%.

The second point is just good to know. I'm going to focus on the first point. The most intuitive locations to set your bounds are probably where the modeled background intersects the spectrum. The first problem is that you have two different spectra with two different background models, so two different locations for each endpoint to balance (imo you must have identical integral bounds to properly calculate the APF, so just using each spectrum's intercepts with the background will not work). Probably some averaging of the two intercepts would produce some compromise that barely affects the final calculation. The second, more serious problem is that there isn't a guarantee the background will cross at locations such that only the elemental peak of interest is included. Here's the background and my MgAl2O4 spectrum around the oxygen peak:

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You can see a small broad peak centered at 35000 spectrometer units. This peak is responsible for the decrease in APF of about 0.05 between window sizes 115 to 150 in the second image in this post. Maybe those extra counts are from oxygen, but I'm suspicious. Regardless, it demonstrates my point that defaulting to where the modeled background crosses the spectrum may include counts generated by not-of-interest elements.

Right now (big caveat, having looked at one (1) dataset), it looks to me like experimentalists need to carefully manually select and justify their integration region. My plot, for purposes of demonstration, went from 1 to 200, but the integration window must include every point where the standard and unknown peaks obviously exist. The total size of the integration window will depend on the peak sizes, which depend on chemical and instrument effects, but in any case, 10 data points in an integration window is too few.

If you twist my arm, I would say the APF for MgAl₂O₄/MgO/PC1 is 1.021. The below plot shows the spectra with increasing window sizes. The best balance of including the peaks' tails and not including non-oxygen counts from that broader peak on the far left looks to me like window sizes between 75 and 115. 1.021 corresponds to the APFs calculated for the background- and Al-interference-corrected (but not peak-maximium-corrected) data for the window sizes I liked.

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I'm definitely curious if people know a good algorithm for, or have thoughts on, determining the integration region. I'd also love to get my hands on more data used to generate APF corrections to better judge how serious this window size effect is. Please send any such data you have my way!

[aducharme]

Area/peak factors (or area peak factors, APFs) are both a more fundamental measurement of quantitative elemental concentration and a time-saving procedure. Lately I've performed a lit review to find sources of APFs, from which I've generated an Excel database and a new .dat file of APFs for binary compounds that can be used in PFE today. Edit: Both files are attached below. The .dat file has been updated to include John's suggested changes.

One of Castaing's key insights was that the elemental concentration of the sample is almost always proportional to the height of the element's characteristic x-ray emission peak (Edit: after accounting for ZAF or phi-rho-z corrections). APFs are a method to perform quantitative EPMA when this assumption fails. Strictly speaking, elemental concentration corresponds to the area of the characteristic x-ray emission peak. This distinction tends to matter in the case of "chemical effects," when looking at an x-ray line for electrons which are bonding to other atoms in the sample, e.g. the Ka line for B, C, N, and O or the La and LB line for Fe and other transition metals. By measuring peak areas in these case, you are making a more fundamentally accurate measurement of elemental concentration.

An area peak factor is additionally a timesaver because recording a whole peak area in WDS takes a lot longer than simply measuring the peak intensity and two background points. APFs do not change with accelerating voltage, so by measuring the ratio of the integrated peak intensity to the maximum peak intensity once, a microanalyst can apply their APF to any future standard intensity measurements on the same sample using the same spectrometer crystal.

Probe for EPMA already has multiple built-in methods to use APFs, including an existing database that can be seen from the menu Analytical > Empirical APFs. Usage has been already explained on the forum  here. The file ducharme_binary_apfs.dat attached in this post is a personally updated version of the PfE APF database where every APF measurement has been confirmed in the literature. The sources can be found in the aforementioned Excel spreadsheet. Differences from the default PfE database include:

• many more nitride APFs, especially those measured with W/Si LDEs
• fewer boride APFs, as many borides demonstrate variable APFs depending on the relative angle of the atomic lattice and the spectrometer
• fewer oxide APFs, because I could not find citations for many of the originals (I have not found the following work, which may contain the missing oxide APFs. If you have a pdf, please reach out! L. Pouchou, F. Pichoir, La Recherche Aerospatiale (English edition), 1984,3, 13.)
• a net increase of 29 binary APFs

The Excel spreadsheet contains 168 total APFs for various compounds. The .dat file contains the subset of 119 APFs for binary compounds. This new .dat file can used in PfE today by removing the file "empapf.dat" in the PfE Program Data folder (alternatively, use your file manager's search function to find it), uploading "ducharme_binary_apfs.dat" in the same location, then renaming the ducharme .dat file to "empapf.dat".

[John Donovan]

The file ducharme_binary_apfs.dat attached in this post is a personally updated version of the PfE APF database where every APF measurement has been confirmed in the literature. The sources can be found in the aforementioned Excel spreadsheet. Differences from the default PfE database include:

• many more nitride APFs, especially those measured with W/Si LDEs
• fewer boride APFs, as many borides demonstrate variable APFs depending on the relative angle of the atomic lattice and the spectrometer
• fewer oxide APFs, because I could not find citations for many of the originals (I have not found the following work, which may contain the missing oxide APFs. If you have a pdf, please reach out! L. Pouchou, F. Pichoir, La Recherche Aerospatiale (English edition), 1984,3, 13.)
• a net increase of 29 binary APFs

The Excel spreadsheet contains 168 total APFs for various compounds. The .dat file contains the subset of 119 APFs for binary compounds. This new .dat file can used in PfE today by removing the file "empapf.dat" in the PfE Program Data folder (alternatively, use your file manager's search function to find it), uploading "ducharme_binary_apfs.dat" in the same location, then renaming the ducharme .dat file to "empapf.dat".

I think it would be worth including the citations in your Ducharme DAT file along with the quoted primary/secondary materials and Bragg crystal string.  For example this line:

"o"    "ka"    "si"    1.044    "SiO2/Fe2O3/WSi/59.8"

should be:

"o"    "ka"    "si"    1.044    "SiO2/Fe2O3/WSi/59.8, Bastin <year>"

and this line:

"o"    "ka"    "si"    1.07    "SiO2/MgO/WSi/59.8"

should be :

"o"    "ka"    "si"    1.07    "SiO2/MgO/WSi/59.8, Donovan <unpublished>"

Also it would be good to group the binaries by absorber together as I did here for the EMPMAC.DAT file:

https://smf.probesoftware.com/index.php?topic=40.msg13930#msg13930

and is also the case for the current EMPAPF.DAT file:

https://smf.probesoftware.com/index.php?topic=536.msg2993#msg2993

As long as this citation info is included inside the double quotes, the file format can still be read by Probe for EPMA.

[aducharme]

Now grouped by absorber (second element in binary) and with citations. See attached.