Defocus Beam Effects in X-ray Mapping

[Probeman]

You could say I'm somewhat surprised this isn't as large an effect as I thought it might be, but still it is an effect we should try to avoid. What am I talking about?

Well, some have argued that one should defocus the beam so that the beam diameter matches the pixel size, but it occurs to others that defocusing the beam will produce a greater probability of acquiring intensities from more than one phase.

So I ran a small (32 x 32 pixel) acquisition of a Cu-Al eutectic allow that consists of a Cu-Al alloy and a relatively pure Al phase, first with a fully focused beam and a second acquisition with an 8 um defocused beam where the acquisition size for both was 256 um x 256 microns (256um/32 = 8um).

The results are attached below, but it is clear that there are somewhat more "edge" pixels in the defocused beam acquisitions. Specifically, the 0 um beam size acquisition shows 44% "edge" pixels, while the 8 um defocused beam acquisition shows 51% "edge" pixels. I suspect the relatively small difference between the two acquisitions is because the beam scan is smoothly scanning across the sample surface so in the sense you are stuck with an acquisition area equal to the pixel size- at least in the scan direction!

Now you might say, ok, we're not surprised. But as I said in the beginning, some people have argued that we should be defocusing our beam for x-ray mapping and I think the data shows we should not unless there is a specific reason for doing so, but I can't think of why unless it is for symmetry...

[Kent Ross]

I compared bulk compositions of 3 Al-rich chondrules from an ordinary chondrite, using defocused beam analysis, EDS mapping, quantified using thermofisher software (NSS), and WDS mapping, quantified using calcimage.  I've attached our abstract from the M&M 2019 meeting in Portland OR, and I'm attaching the ppt of my talk. The results for the 3 methods were similar for most elements, but I concluded that the PFE-Calcimage results were best, because it calculates compositions pixel by pixel, unlike the other two methods, which violate the fundamental assumption of matrix corrections, where we are quantifying mixed x-ray counts from more than one phase.

[Kent Ross]

Here's the abstract attachment, from comparison of three methods for determiningg bulk composition.

[Probeman]

There's been some discussion in the Athens EPMA Workshop on the problems with using "defocused beam analysis" or DBA.

Yes, it might seem that one could obtain a quick "average" analysis of a heterogeneous sample, but it is not quantitative for the basic reason that x-ray absorption is a non-linear process, so averaging x-ray intensities is not quantitative. Another way to put it is as stated years ago by Chuck Fiori (NIST), "if the interaction volume is not homogeneous, all bets are off"!

Instead one must acquire x-ray maps as usual, making sure that the beam size is smaller than the features of interest and then one needs to quantify the pixels, correcting for background and matrix effects and then (and only then), one can average the concentrations of the pixels.  Here are some references regarding the problems with "defocus beam analysis":

     Sorbier, L., Rosenberg, E., Merlet, C. & Llovet, X. EPMA of Porous Media: A Monte Carlo Approach. Mikrochim. Acta 132, 189–199 (2000).
    A von der Handt et al., Microscopy and Microanalysis, Volume 29, Issue Supplement 1, 1 August 2023, Pages 844–845, https://doi.org/10.1093/micmic/ozad067.419
    JJ Donovan et al., American Mineralogist: Journal of Earth and Planetary Materials 106 (11) (2021), p. 1717
    J Barkman et al., Microscopy and Microanalysis 19 (S2) (2013), p. 848 . doi:10.1017/S1431927613006235
    P Carpenter et al, 40th Lunar and Planetary Science Conference (2009), p. 2531
    J Berlin et al., Microscopy and Microanalysis, Volume 14, Issue S2, 1 August 2008, Pages 110–111, https://doi.org/10.1017/S1431927608084845
    J Berlin et al., 37th Lunar and Planetary Science Conference (2006), p. 2370.
    DJ Lindstrom (1999) LPS XXX, No. 1917.
    PH Warren, 28th Lunar and Planetary Science Conference (1997) #1406
    MA Nazarov et al. (1982) LPS XIII, 582-583.
    AL Albee et al., Lunar and Planetary Science Conference (1977) 7-9
    AL Albee et al., 8th International Congress on X-ray Optics and Microanalysis (1977), p. 526-537.
    J Bower et al, 8th International Congress on X-ray Optics and Microanalysis (1977), p. 182-184.

Also see this topic:

https://smf.probesoftware.com/index.php?topic=198.0

Note that such averaging only provides an average composition based on the area of each phase.  For some applications we need the mass fraction of each phase, and for that we need to normalize the %area with the phase densities.  See here:

https://smf.probesoftware.com/index.php?topic=1071.msg7095#msg7095

[Probeman]

I wanted to re-start this discussion of defocused beam analysis (DBA), because some of our colleagues still aren't sure why this is a bad idea for quantitative analysis.

The problem with electron beam methods for fine grained materials is that when the grain size is somewhat smaller than the beam interaction volume, then as Chuck Fiori used to say: "all bets are off". This is because the x-rays from the emission volume will not have interacted completely or even at all with the other phase compositions.  Note that I used the term to emission volume rather than interaction volume, because what really matters is the volume from which the x-rays are emitted.  We really don't care what happens below the emission depth (except for cases of substrate fluorescence, like trying to measure phosphorus in a film on a Si substrate!). 

But also note that high energy x-rays tend to come from deeper in the sample, while lower energy x-rays tend to come from closer to the surface. So we have a sampling issue as well, if we don't ask where our x-rays coming from.  Of course the overvoltage matters too because at low overvoltages, even high energy x-rays will tend to come from only the surface as well (hence the rationale for Cameca's "Shallow Probe" instrument).  So it's a mix of beam energy, emission energy and overvoltage that needs to be considered.

Think of it like this: in a homogeneous interaction volume we have "bulk" matrix physics and we can apply normal matrix corrections to our measured x-ray intensities.  At the other extreme, if our grain sizes are very small compared to our interaction/emission volume (say approaching atomic scale), then every x-ray tends to interact with every phase composition, and we again approach the situation of bulk matrix physics.  And in between, well, it's in between physics!    The worst case of course is an interaction volume with two phases.

This is why we utilize particle or thin film geometry corrections when analyzing particles or thin films.  Applying bulk matrix corrections to heterogeneous volumes will produce significant errors. Basically we will get a different answer depending on the beam energies involved.

Because of these geometry effects, if one does want an average composition of different phases, then one needs to quant at the finest scale possible (making sure that the emission volues are smaller than the gran size, then quant each pixel/point, and only *then*, average the results to get an average composition:

http://smf.probesoftware.com/index.php?topic=198.msg896#msg896

Let's consider the situation of an interaction/emission volume at a phase boundary (thought experiment):



Here we have a boundary between pure Cu and pure Al with the electron beam sitting at the boundary. Note that depending on the detector orientation relative to the sample we could have the emitted Cu Ka x-rays absorbed only by Cu, but in other orientations we will have Cu Ka x-rays absorbed by both Cu and Al.  Conversely for Al ka, in some detector orientations we will have Al Ka x-rays absorbed by only Al, but in other detector orientations we will have Al Ka x-rays absorbed by both Al and Cu.  And everything in between for in between orientations!

It gets worse.  What does our detector see in any detector orientation?  We see lots of Cu Ka x-rays, and also lots of Al ka x-rays.  So our detector thinks it's seeing Cu-Al *alloy*!  But again, some emitted/detected x-rays are only absorbed by one of the phases.  And remember, the matrix correction for pure Cu Ka in Cu is 1.0 (relative to a pure Cu standard), and for Al Ka in pure Al it's also 1.0 (again relative to a pure Al standard).

And while the matrix correction for Cu Ka in a Cu-Al alloy is close to 1.0 (it's about a 10% correction in a 50:50 composition), the matrix correction for Al Ka in a Cu-Al alloy is around 50% (actually 60% in a 50:50 Cu-Al alloy).  So our bulk matrix correction happily churns out a composition that totals 150% or so.  Of course if one isn't using standards (shudder), then one sees a 100% total and it all looks just fine!

This by the way is often the reason we often see high totals in EPMA as our point traverses cross phases boundaries.  Because in a heterogeneous volume at a phase boundary, the application of bulk physics often over estimates our matrix corrections. Of course it could go either way depending on the physics details, but because absorption usually dominates and each phase by itself might be "simpler" physics than a "mix" of the two phases, it's often a high total that we see.

Here's a question to consider: in what detector orientation (relative to a phase boundary) will the emitted Cu and Al x-rays be absorbed *only* in their own respective phases?