[Ifeffit] LCF on Larch - EXAFS Region

[Martin McBriarty]

Matt,

Glad to read your impressions of EXAFS LCF. I've had reasonable success
with LCF using EXAFS spectra generated by ab initio molecular dynamics
(AIMD) to figure out the local structure of dopants whose preferred
coordination is symmetrically dissimilar from the crystals they inhabit,
i.e. for which there are no good experimental standards. This can be pretty
tough to do accurately with shell-by-shell fitting.

As you point out, disorder is a huge hurdle (in both LCF and shell-by-shell
EXAFS analysis). We assume that a good AIMD model will simulate thermal
disorder pretty well, but there are likely differences in configurational
disorder between a periodic infinite structure and the real material due to
defects. Fortunately, defects can be explicitly accounted for in a
simulation, assuming you have the computational capability to screen a set
of defect configurations.

Background subtraction should ideally be done using the same procedure for
all data. Theoretical data could be used to refine a background subtraction
procedure; spline fit parameters such as Rbkg or clamping may be tweaked to
improve agreement between a simulated chi(k) and a measured standard over a
reasonable k-range.

Simulating spectra with a range of binding energy offsets can explicitly
address the problem of E0 choice, but it can also be used as a fudge factor
for strain. In my LCFs, dE0 is the only parameter besides the fractions of
the chosen phases.

To address the above problems, benchmarking is key. Quantitative agreement
should be sought between simulated spectra and experimental standards to
ensure the theory is sound and the chi(k) extraction is reasonable.
However, there are probably still systematic sources of error which are
larger than the uncertainties Athena's LCF tool will report; I agree with
Mike's practical estimate of 10% or so.

I discuss these issues in somewhat greater detail in my recent (open
access!) article that demonstrates how LCF using AIMD-simulated spectra
yields answers that shell-by-shell fitting struggles with due to multiple
overlapping components: https://pubs.acs.org/doi/10.1021/acs.est.8b00297

Martin


On Sun, Aug 12, 2018 at 10:19 PM, Matt Newville <newville at cars.uchicago.edu>
wrote:

> Hi Mike,
>
> On Thu, Aug 9, 2018 at 10:04 PM Mike Massey <mmassey at gmail.com> wrote:
>
>> This is interesting. Could you say more about your skepticism of the
>> robustness of EXAFS LCF, Matt?
>>
>> To be fair, it suffers from many of the same drawbacks of XANES LCF, plus
>> others. But I'm curious about your thoughts on it since yours seems to be
>> what amounts to a "strong opinion" on the subject.
>>
>
>
> I would not say that no one should ever do linear combination fitting for
> EXAFS.  For sure, linear analysis of XANES is quite robust and verified
> many times to give good results, at least at level of a few percent.
> Linear analysis of EXAFS suffers more data processing challenges and
> conceptual problems that limit its robustness.  For sure, there are cases
> for which it can work well.
>
> Longer answer:
> Any linear analysis (LCF, PCA, MCR-ALS, etc) of XANES works reasonably
> well (typically to a few percent) because:
>    a) the processing needed is minimal.  Data need to have a common energy
> calibration better than the intrinsic energy resolution -- typically energy
> calibration of 0.25 eV or better will be OK.  Data need to have a
> consistent normalization of mu(E), typically to a few percent.   Variations
> in these processing steps will have a direct and negative effect on the
> results.
>
>    b) conceptually, the assumption is that there exists a nearly 1 to 1
> correspondence between "local chemical configuration" and "measured XANES",
> and that the "local chemical configurations" that are being investigated
> are discrete and well-defined (ie "iron carbonate") and not continuous.
>  That is, if you determine that your Fe XANES spectra is "50% iron
> carbonate and 50% iron sulfate" then implicit conclusion is that 50% of the
> iron atoms are iron carbonate and 50 percent are iron sulfate, not that all
> irons are 50% carbonate and 50% sulfate.
>
> To be clear, linear analysis of XANES does not work well to ppm levels,
> partly due to the poor experimental contrast (that is, mu(E) tend to all
> look alike and features are intrinsically broadened to the ~eV level), but
> also conceptually, because at the ppm level, local chemical configurations
> are not always limited to 3 to 10 discrete states.
>
> Linear Combination EXAFS is more challenging from both the processing and
> conceptual point of view.
>
> For Processing, EXAFS requires more data processing than XANES.  The
> selection of E0 and the background mu0(E) will have an effect on linear
> analysis of EXAFS if not done consistently.  It is not really obvious how
> E0 or mu0(E) can be selected consistently for very different spectra.
>
> Conceptually, EXAFS is much more sensitive to disorder and subtle
> variations in the bond lengths (thermal or static disorder) and can have
> significant variation in its sensitivity to second and further neighbors.
>  In that sense, EXAFS is much less discrete and much more continuous in its
> variability across different kinds of local structures.
>
> Again, this is not to say that linear analysis of EXAFS cannot ever work,
> just that is probably more limited in applicability and absolute accuracy
> than linear analysis of XANES.  Of course, for EXAFS you can also do an
> actual fit of structural parameters.  The information content is somewhat
> limited so that refining multiple overlapping components may not always be
> possible, and linear combinations of end-member spectra may look
> attractive....
>
> Hopefully, anyone who has other insights or experiences will be able to
> correct any of my misunderstandings.
>
> --Matt
>
>
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