I had started with LSQ but switched to peak fitting because I was worried about the Ce(IV) reference. I have data for bulk CeO2 and Ce(OH)4, but doesn't this have some Ce(III) impurity in it? I'm not quite sure how to account for this when I do LSQ. Another challenge I've had is in using the Ce(IV) refs for our nanoparticles, which are about 2-5 nm in diameter. Is there a good Ce(IV) ref for nanos that are in this size range? On Wed, Dec 7, 2016 at 2:37 PM, Matthew Marcus wrote:

Instead of doing a bunch of peak fitting, try LSQ. Use CeO2 (bulk or nanos) for one reference and some Ce(III) for the other. Consistency check: see that the Ce(III) fraction is consistent over some set of Ce(III) references. Ce(III) has an assymetric white line, so it doesn't really fit a single gaussian. CeO2, unlike other Ce(IV), has a shoulder on the first peak, and the first peak is shifted left a little with respect to other Ce(IV). mam

On 12/7/2016 10:33 AM, Stephanie Laga wrote:

...

Dear all,

I am trying to extract the % Ce(III) from some CeO2 nanoparticle XAS data. I have been using moved the peak fitting function in Athena to model the XANES with an arctan background function and a series of gaussians.

Looking through the literature I haven't seen too many specifics to using this approach (rationale for choosing the widths of peaks or how to define the background function). Similarly, doesn't seem to be much rationale for choosing a 4 vs 5 peak fit for the XANES.

My main question is then...1) Is there a rational for picking the background function, specifically the height and width (can I let the height vary or should I be keeping a constant arctan through all samples)?

Any advice is greatly appreciated!

Stephanie

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Thank you Matthew and Matt for your responses. Sorry if these are silly questions...so then does that mean arctan and gaussian shouldn't be used together? What was meant by "it does not inherently include any understanding of what that peak is"? That these functions aren't representative of the processes occuring because the single electronic assumption doesn't hold anymore...ie there are many electron effects once we get in the EXAFS region? And if I am primarily looking at XANES, I don't need to be worried about the initial EXAFS region right? On Thu, Dec 8, 2016 at 10:48 AM, Matthew Marcus wrote:

The usual justification for using gaussians for peaks, aside from "it works" is that there's inhomogeneous broadening over and above the lifetime. The usual justification for using an arctan for the step is exactly the opposite. Instrument broadening is often taken to be gaussian. Net result: A (pseudo)Voight for peaks often works. One issue is what to do about the post-white-line peaks, which sometimes are viewed as the first EXAFS wiggles. Manceau has a nice paper about S XANES (I don't have the ref handy right now) in which he goes through peak fitting and evaluates its uniqueness. mam

...

Hi Stephanie,

On Wed, Dec 7, 2016 at 12:33 PM, Stephanie Laga

wrote:

...

Dear all,

I am trying to extract the % Ce(III) from some CeO2 nanoparticle XAS

data.

...

I have been using moved the peak fitting function in Athena to model the XANES with an arctan background function and a series of gaussians.

Looking through the literature I haven't seen too many specifics to using this approach (rationale for choosing the widths of peaks or how to define the background function). Similarly, doesn't seem to be much rationale for choosing a 4 vs 5 peak fit for the XANES.

My main question is then...1) Is there a rational for picking the background function, specifically the height and width (can I let the height vary or should I be keeping a constant arctan through all samples)?

Any advice is greatly appreciated!

Stephanie

Matthew answered quickly, but sort of changed the subject, suggesting a different analysis (LSQ) and then discussing some of the pitfalls of that approach. Your original question is still worth discussing.

There is not a whole lot of justification in using one particular shape for the background. A step broadened as arctan, error function are common and seem to work well. Each has some theoretical explanation in that the integral of a series of Lorentzian gives an arc-tangent function while

...

integral of a series of Gaussians will give the error function. (If this is wrong, can someone please correct?). If you think as the above edge spectrum as a series of finely spaced individual transitions, then these functions have some justification. Whether it actually works well in detail on a particular spectrum is a separate question. FWIW, I've also seen people use (successfully) a single, very broad Lorentzian for the "main edge".

The use of Lorentzians, Gaussians, Voigts, and PseudoVoigts is somewhat more justified in that those are how you would expect a single electronic transition to appear, especially broadened in the way(s) you'd expect a monochromatic X-ray beam to be energy broadened. Using such functions is essentially asserting that there is a single electronic transition at

On Thu, Dec 8, 2016 at 5:40 AM, Matt Newville wrote: the that

...

energy, and you want to know it's size and shape. This is not wrong, but it does not inherently include any understanding of what that peak is. For pre-edge peaks, it's pretty well-justified, and works pretty well. For peaks on or after the main edge or "white line", it's less justified because we know that EXAFS-like effects can be important.

The biggest dangers in the peak-fitting approach are: 1) one always gets an answer, and that is rarely "no, this is not the right model to use". In fairness, most linear algebra methods used for XANES analysis or really most other spectroscopies have the same feature. 2) interpretation of the results can be challenging, or at least it is hard to know when they are misleading. Again, most linear algebra methods used for XANES analysis or really most other spectroscopies have the same feature. 3) it can sort of willfully ignore other parts of the spectra. In fairness, we all do this sort of thing all the time.

Hope that helps. Peak fitting is not exactly "theoretical XANES analysis", but it is not always done in an ad-hoc manner out of ignorance either.

Linear algebra techniques are completely justified too.

Hope that helps,

--Matt Newville

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Hi Stephanie, Typically, LCA fitting is done for the more widely applied speciation analysis while Gaussian fitting is done to obtain quantitative pre-edge information: a) metal-ligand covalency and b)ligand-field splitting and metal 3d-4p mixing. LCA In the context of S K-edge XANES, LCA is tricky- the very detailed structure you see in S XANES is almost always electronic in nature and can be correlated to molecular orbital in the molecule. The correlation of DFT derived MO energy level to metal and ligand pre-edges has exploded in the last decade and very good correlations can be obtained. In such cases the peaks actually do have meaning. I attach a paper on simple S compounds where the match with theory is rather good. This paper also talks a bit about why unknown LCA is BAD idea. Because small structural perturbations can lead to large changes in the S XANES the concept of "standards" is dangerous. Unless you know what you have in your mixture. If you are doing LCA for metal K-edges, you are mostly matching the "Structural" part of the XANES (post edge) and not the "electronic" part (restricted to pre-edges and to the low rising-edge). Therefore metal K-edge LCA still makes sense and gives reasonable results. Gaussian Fitting Gaussian fitting only makes sense for the pre-edge region. Anything post-edge or higher is pure speculation and you are doing so to obtain a good background function for the pre-edge region, where all the quantitative analysis rests. I attach on Fe K-pre-edge analysis, which basically fits a random function to the edge-region and treats it for background purposes. No quantitative/meaningful information can be (yet) obtained from such gaussian fitting. Take a look at the power of pre-edge analysis as shown in the Westre paper. Hope this helps, Best, -Riti Sarangi On Thu, Dec 8, 2016 at 9:06 AM, Stephanie Laga wrote:

Thank you Matthew and Matt for your responses. Sorry if these are silly questions...so then does that mean arctan and gaussian shouldn't be used together?

What was meant by "it does not inherently include any understanding of what that peak is"? That these functions aren't representative of the processes occuring because the single electronic assumption doesn't hold anymore...ie there are many electron effects once we get in the EXAFS region?

And if I am primarily looking at XANES, I don't need to be worried about the initial EXAFS region right?

On Thu, Dec 8, 2016 at 10:48 AM, Matthew Marcus wrote:

...

The usual justification for using gaussians for peaks, aside from "it works" is that there's inhomogeneous broadening over and above the lifetime. The usual justification for using an arctan for the step is exactly the opposite. Instrument broadening is often taken to be gaussian. Net result: A (pseudo)Voight for peaks often works. One issue is what to do about the post-white-line peaks, which sometimes are viewed as the first EXAFS wiggles. Manceau has a nice paper about S XANES (I don't have the ref handy right now) in which he goes through peak fitting and evaluates its uniqueness. mam

...

Hi Stephanie,

On Wed, Dec 7, 2016 at 12:33 PM, Stephanie Laga < stephanie.laga@yale.edu> wrote:

...

Dear all,

I am trying to extract the % Ce(III) from some CeO2 nanoparticle XAS

data.

...

I have been using moved the peak fitting function in Athena to model

...

...

XANES with an arctan background function and a series of gaussians.

Looking through the literature I haven't seen too many specifics to using this approach (rationale for choosing the widths of peaks or how to define the background function). Similarly, doesn't seem to be much rationale for choosing a 4 vs 5 peak fit for the XANES.

My main question is then...1) Is there a rational for picking the background function, specifically the height and width (can I let the height vary or should I be keeping a constant arctan through all samples)?

Any advice is greatly appreciated!

Stephanie

Matthew answered quickly, but sort of changed the subject, suggesting a different analysis (LSQ) and then discussing some of the pitfalls of

...

approach. Your original question is still worth discussing.

There is not a whole lot of justification in using one particular shape for the background. A step broadened as arctan, error function are common and seem to work well. Each has some theoretical explanation in that the integral of a series of Lorentzian gives an arc-tangent function while

...

integral of a series of Gaussians will give the error function. (If

...

wrong, can someone please correct?). If you think as the above edge spectrum as a series of finely spaced individual transitions, then these functions have some justification. Whether it actually works well in detail on a particular spectrum is a separate question. FWIW, I've also seen people use (successfully) a single, very broad Lorentzian for the "main edge".

The use of Lorentzians, Gaussians, Voigts, and PseudoVoigts is somewhat more justified in that those are how you would expect a single electronic transition to appear, especially broadened in the way(s) you'd expect a monochromatic X-ray beam to be energy broadened. Using such functions is essentially asserting that there is a single electronic transition at

...

energy, and you want to know it's size and shape. This is not wrong, but it does not inherently include any understanding of what that peak is. For pre-edge peaks, it's pretty well-justified, and works pretty well. For peaks on or after the main edge or "white line", it's less justified because we know that EXAFS-like effects can be important.

The biggest dangers in the peak-fitting approach are: 1) one always gets an answer, and that is rarely "no, this is not the right model to use". In fairness, most linear algebra methods used for XANES analysis or really most other spectroscopies have the same feature. 2) interpretation of the results can be challenging, or at least it is hard to know when they are misleading. Again, most linear algebra methods used for XANES analysis or really most other spectroscopies have the same feature. 3) it can sort of willfully ignore other parts of the spectra. In fairness, we all do this sort of thing all the time.

Hope that helps. Peak fitting is not exactly "theoretical XANES analysis", but it is not always done in an ad-hoc manner out of ignorance either.

Linear algebra techniques are completely justified too.

Hope that helps,

--Matt Newville

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On Thu, Dec 8, 2016 at 5:40 AM, Matt Newville wrote: the that the this is that options_ifeffit&d=CwICAg&c=-dg2m7zWuuDZ0MUcV7Sdqw&r=UZ6LahCC y9yRGAvO8QDSWFzQq7a3vkDZfWzr2SslhiE&m=1Dl796heiYduL4EDzxeWdc jHhaDpvCGzN-gt3GQjKtQ&s=FXCHDGbIdIGP3_1IjIkriL6-8jZe_v4iEjOfJUMnUl0&e=

...

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