Secondary boundary fluorescence correction in Probe for EPMA

[Probeman]

Perhaps some of you have noticed this (currently) disabled button the the Probe for EPMA Analyze! window:



This button (and the associated GUI and code) is intended to apply quantitative boundary fluorescence corrections for intensity data contained in Probe for EPMA database files, with a graphical user interface similar to (but somewhat different than) what we have already have in our CalcZAF application:

https://smf.probesoftware.com/index.php?topic=58.msg223#msg223

That is, one could simply subtract the calculated concentrations from secondary boundary fluorescence from one's quantitative results after the fact, e.g., in Excel, but it is more rigorous to subtract the actual boundary fluorescence intensities during the matrix correction, so that the new matrix is recalculated correctly (similar to the quantitative interference correction) since the matrix composition is changed by the correction. Yes, in many cases the correction is so small that it won't matter, but is some cases of boundary fluorescence the apparent (artifact) concentration of an element can be several percent or more, and therefore should be included in the matrix correction.

The reason for explaining all this is to say that I believe we are ready to start testing this new feature in Probe for EPMA, but we would like to have a suitable sample with a large boundary fluorescence correction for testing purposes. One such ideal sample would be a sample with a pure Fe and pure Ni vertical interface that has *not* been polished together, in order to avoid smearing of one element to another.

I have pure Fe and pure Ni materials (though other pure element pairs such as pure Cu and pure Co would be even better from a boundary fluorescence artifact perspective) and I would be happy to send those to someone who would be willing to produce a sample with suitable geometry for testing this new code.  If any one is willing to produce such a sample we would be happy to include them as a co-author.

Please let me know if you would be willing to help with this project.

[John Donovan]

We've been waiting for some test data for this new secondary fluorescence boundary correction, but this weekend I was going through some old samples and found a synthetic boundary sample consisting of a pure Fe metal next to a pure Ni metal which had been polished individually to yield a vertical boundary. Polishing the materials separately is necessary to avoid any "smearing" from one material to the other.

The idea being to measure trace Fe in a Ni material that is adjacent to a Fe material. The physics here is that any Ni Ka generated in the Ni material can easily travel a significant distance through the Ni and fluorescence the Fe K edge in the Fe material.  In addition any continuum created in the Ni material that is over the Fe K edge energy (7.1 keV) can also fluorescence Fe.

So the first step in this correction is to model the situation using the PENFLUOR/FANAL GUI in the Standard application as described in this topic:

https://smf.probesoftware.com/index.php?topic=58.0

Performing the steps described in the above topic yields the following plot:



Note that the beam incident material is pure Ni, the boundary material pure Fe and the standard material is pure Fe metal.  Your analytical situation will undoubtedly be different, but the steps are essentially the same for any emission line and materials.

When the plot is generated by Standard, it will create a folder containing the results using the naming convention: <takeoff>_<keV>_<beam incident>_<boundary>_<std>_<element atomic#>_<xray#> where <xray#> is the x-ray line number, ka=1, kb=2, la=3, lb=4, ma=5, mb=6.

Therefore, for the measurement of Fe Ka in Ni metal, adjacent to Fe metal, using an Fe standard at 15 keV measured at a takeoff angle at 40 degrees the necessary files for performing this correction are saved automatically in a sub folder in the C:\UserData\Penepma12\Fanal\Couple folder as seen here:



If secondary fluorescence from the boundary material is indicated, you will now be able to perform the correction in Probe for EPMA. After opening this folder you will see these files:



The k-ratios.dat file is the one you will be browsing for in a moment from Probe for EPMA.  The Fanal.txt file will also be utilized but is loaded automatically.

But before we go any further I just want to mention that this synthetic boundary sample is not ideal as there is a roughly 30 um gap between the Ni and Fe materials which means that the physics we just modeled above is not exactly correct, but I hope it will suffice as a demonstration example until you all can provide some real world examples of boundary fluorescence!

So we started the analysis points right at the edge of the Ni material and then went in 1 um steps inward. Now let's open our probe run database in Probe for EPMA and go to the Analyze! window as seen here and click the analyze button as usual and see our results :



Not that at the edge of the Ni material (and ~30 um) from the Fe material, we obtain almost 0.5 wt% of Fe in the pure Ni which is from these secondary boundary fluorescence effects.

[John Donovan]

Continuing from the post above...

Now let's correct for these SF effects.  Start by selecting the sample(s) in the Analyze! window sample list and then click the Boundary Corrections button in the Analyze! window. The Secondary Fluorescence Correction from Boundary Phase dialog will open as seen here:



Note that the above steps can be performed in any order but all need to be completed before the SF corrections can be performed. In the above example, we simply selected an image from our saved images, then we clicked the Define Boundary Method button to define the boundary to open the Secondary Fluorescence Boundary Correction Parameters dialog as seen here:



In the above example, we clicked the Specify Graphical Boundary option and then using the mouse, we drew a boundary on the image as shown (one can also specify the boundary geometry using stage positions if an image is not available). The boundary was drawn partially in the gap between the phases because the physics we modeled is not exactly correct because we assume no gap in PENFLUOR/FANAL physics calculations.  Note that normally you will not have a gap between your phases so this issue can be ignored for now, but there are ways of dealing with a gap between phases that can be discussed later.

Note also that we oriented this synthetic boundary in the instrument so that the boundary was pointing directly at the WDS spectrometer (Fe ka) making the trace measurement. For EDS spectrometers, this is not necessary, but until we implement a Bragg defocus geometry correction in Probe for EPMA (see https://academic.oup.com/mam/article-abstract/24/6/604/6901481 by Ben Buse et al. 2018) it is best to avoid Bragg defocus effects by orienting the sample relative to the spectrometer.  However, for boundary distances less than 10 or 15 um these Bragg defocus effects will be minimal.  If two trace elements need to be measured/corrected together, then spectrometers that are diametrically opposed to each other should be selected with the phase boundary pointing at both spectrometers.

Ok, let's proceed by now browsing for our modeled boundary fluorescence k-ratios.dat file as seen here:



If the correct file was selected, the k-ratios as a function of boundary distance will be loaded as shown previously above.  Note that on the right side we can see the Mat A, Mat B and Mat B std materials utilized in the PENFLUOR/FANAL calculations. Now we just click OK and click the Analyze button again:



Wasn't that easy!   

Ok, well it's better than doing it manually by hand...

To provide some additional details, these calculated k-ratios are subtracted from the measured k-ratios during the matrix correction procedures, so even if significant SF boundary corrections are performed, the calculation of the other elements in the modified matrix will be properly accounted for (in this regard this is similar to the quantitative spectral interference correction in PFE)

Though it should be mentioned that if the change in composition from the SF boundary correction is not large one can simply subtract the calculated concentrations in Excel or otherwise.  But the advantage of doing it in PFE is that the process is completely documented and fully quantitative.

Now one last note: the SF boundary calculation in PENFLUOR/FANAL assumes a vertical infinite boundary interface, which is not always the case of course with our samples.  We are also investigating the possibility of performing a geometrical correction to deal with hemispherical geometries for example, but in the meantime one can perform these boundary calculations the PENEPMA code using the Standard application as described here:

https://smf.probesoftware.com/index.php?topic=59.0

One would need to model each distance from the boundary so that will take a while, but one can use the Batch Mode button in the PENEPMA GUI to make it easy:

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

Then one would need to extract the k-ratios from each distance and create your own k-ratios.dat file similar to what is produced by PENFLUOR/FANAL (and the Fanal.txt file as well) and place it in an appropriately named folder.

Anyway, this is a new feature, so we'll be interested to hear from you all on using it for your own specific examples.

[John Donovan]

We've modified the secondary boundary fluorescence correction output in the latest Probe for EPMA to include the correction of the k-ratios and distances from the boundary to help troubleshoot any issues that arise:

SecondaryCorrection: SF k-ratios * 100, Line: 218, Dist: 14.25352
Element:   fe ka
Elm. Kr: .600537
Cal. Kr: .644139
Cor. Kr: -.04360

SecondaryCorrection: SF k-ratios * 100, Line: 218, Dist: 14.25352
Element:   fe ka
Elm. Kr: .600537
Cal. Kr: .644139
Cor. Kr: -.04360

SecondaryCorrection: SF k-ratios * 100, Line: 219, Dist: 15.25291
Element:   fe ka
Elm. Kr: .574921
Cal. Kr: .582388
Cor. Kr: -.00747

SecondaryCorrection: SF k-ratios * 100, Line: 219, Dist: 15.25291
Element:   fe ka
Elm. Kr: .574921
Cal. Kr: .582388
Cor. Kr: -.00747


Un    3 Fe in Ni SF boundary

Un    3 Fe in Ni SF boundary
TakeOff = 40.0  KiloVolt = 15.0  Beam Current = 30.0  Beam Size =    0
(Magnification (analytical) =  20000),        Beam Mode = Analog  Spot
(Magnification (default) =     1000, Magnification (imaging) =    633)
Image Shift (X,Y):                                         .00,    .00
Number of Data Lines: 101             Number of 'Good' Data Lines:   2
First/Last Date-Time: 09/10/2023 03:02:39 PM to 09/10/2023 06:30:15 PM

Average Total Oxygen:         .000     Average Total Weight%:   99.968
Average Calculated Oxygen:    .000     Average Atomic Number:   28.000
Average Excess Oxygen:        .000     Average Atomic Weight:   58.711
Average ZAF Iteration:        2.00     Average Quant Iterate:     2.00

No Sample Coating and/or No Sample Coating Correction

Un    3 Fe in Ni SF boundary, Results in Elemental Weight Percents

ELEM:       Fe      Ni
TYPE:     ANAL    ANAL
BGDS:      LIN     LIN
TIME:    60.00   60.00
BEAM:    29.87   29.87

ELEM:       Fe      Ni   SUM 
   218   -.031  99.997  99.966
   219   -.005  99.977  99.971

AVER:    -.018  99.987  99.968
SDEV:     .018    .014    .004
SERR:     .013    .010
%RSD:  -100.07     .01
STDS:      526     528

STKF:   1.0000  1.0000
STCT:   207.81  707.67

UNKF:   -.0003   .9999
UNCT:     1.25  726.33
UNBG:      .56    3.51

ZCOR:    .7202  1.0000
KRAW:    .0060  1.0264
PKBG:     3.24  208.14

The line numbers are duplicated because of the matrix correction iteration loop...

[John Donovan]

After responding to Alejandro's question here:

https://smf.probesoftware.com/index.php?topic=1620.msg12851#msg12851

I thought it might be worth expanding on the issue of Bragg defocus and the correction of secondary fluorescence from nearby grain boundaries for certain trace element situations...  because it is a bit related to the issue of *x-ray* interaction volumes (as opposed to electron interaction volumes).

For example, for EDS detectors, there is essentially no defocussing effect and therefore secondary fluorescence from grain boundaries (the x-ray interaction volume), will be present at levels as predicted by modeling softwares such as PENEPMA/PENFLUOR:

https://smf.probesoftware.com/index.php?topic=58.msg12652#msg12652

But because of Bragg defocus we need to consider the orientation effect of Bragg defocusing on the detection of emissions from grain boundaries when using WDS spectrometers.  That is, the magnitude of secondary fluorescence will depend on the relative orientation of the grain boundary to the Bragg crystal in a specific WDS spectrometer.

This orientation effect suggests two different approaches to dealing with boundary fluorescence. One approach is to perform analyses near grain boundaries (when secondary boundary fluorescence is present) where the grain boundary is *perpendicular* to the Bragg crystal orientation (the long axis of the crystal) in a specific spectrometer:

https://smf.probesoftware.com/index.php?topic=58.msg5710#msg5710

This boundary to Bragg crystal orientation ensures that the intensities from nearby grain boundaries are suppressed as much as possible by the WDS defocusing. In fact, using this *perpendicular* orientation, as long as one chooses spectrometers that are 180 degrees from each other (as mounted on the instrument) the secondary fluorescence intensities from the grain boundary will be defocussed similarly, and one can even measure the trace element on *two* WDS spectrometers using the aggregate feature in Probe for EPMA:

https://smf.probesoftware.com/index.php?topic=1316.0

Therefore if the boundary fluorescence effect is small and the Bragg defocus is large, one *might* be able to avoid applying the boundary fluorescence correction in Probe for EPMA.

However, note that boundary fluorescence correction in Probe for EPMA:

https://smf.probesoftware.com/index.php?topic=1545.msg12034#msg12034

does not have a WDS Bragg defocus correction for boundary secondary fluorescence (maybe this post will get us starting work on that!).  See Buse et al., 2018:

https://academic.oup.com/mam/article-abstract/24/6/604/6901481

Therefore if one attempts to correct for secondary fluorescence from nearby grain boundaries using this *perpendicular* orientation approach, one will tend to over correct the boundary fluorescence intensities using k-ratios generated by PENEPMA/PENFLUOR.  This could result in slightly negative concentrations being reported for trace elements after they are corrected for boundary fluorescence.

In the meantime it is worth considering another approach. An approach where we orient the sample (or choose a grain boundary) so that the grain boundary is *parallel* to the Bragg crystal (long axis) orientation in the spectrometer! A *parallel* orientation ensues that little to no Bragg defocusing occurs to the intensities generated from our (nearby) grain boundary.

Why should we do this? Because then we minimize the WDS Bragg defocus effects and therefore the secondary boundary fluorescence correction will be more accurate using k-ratios generated from our PENEPMA/PENFLUOR modeling. 

However, note that other geometric effects also need to be considered. For example the PENFLUOR/FANAL calculation assumes an infinite vertical grain boundary whereas our actual sample might not be.  Though it is worth noting that if one is willing to make the effort, one can model a specific grain boundary geometry in PENEPMA, along with a specific WDS spectrometer orientation (though I do not know of a way to specify a Bragg defocus effect in PENEPMA), to get a more accurate prediction of the boundary fluorescence effects.  But this will require significant modeling time as each beam position (distance from the grain boundary) will need to be modeled one at a time.

In summary, ensuring a grain boundary orientation *parallel* to the spectrometeer Bragg crystal in order to minimize WDS defocusing effects allows one to utilize PENFLUOR to generate the boundary fluorescence k-ratios.  And PENFLUOR is so much easier and faster to use!

[John Donovan]

I drew up this quick schematic to better illustrate the points made in the previous post of Bragg defocusing and secondary boundary fluorescence: