strain derivation

[陈天奔]

Dear all，


I find a literature which mentions that PDF can provide information about local/ averagr strain of the sample. I am wondering does anyone know how to derive strain from the XPDF by using PDFgui ?

Kind regards



Connie

[Simon Billinge]

There are many ways to delve into this question and which is the most relevant depends on exactly what scientific problem you are studying.  Connie, would you be willing to share some more contextual information about what you want to learn about your system and we can answer more effectively?

S

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Simon Billinge

Professor, Columbia University

Physicist, Brookhaven National Laboratory

[ali dordaee]

 Hi everybody, Is there a module which could yield the strain of nanoparticles? If so, could you please give some guidance? I am looking for something like: 

From Diffpy.... import .....

FitRecipe().addVar(....,....)

.etc.

If there's no such module, what can we do?

I would appreciate your guidance.

[Simon Billinge]

Thanks for the question Ali.

We may need you to make your question a bit more precise to help.  Homogenous strain is captured in a change in the average position of a PDF peak, e.g., in the change in position of near neighbor peaks vs NP size in NPs, for example (discussed here for example: Xiaohao Yang, Ahmad S. Masadeh, James R. McBride, Emil S. Bo zin, Sandra J. Rosenthal, and
Billinge, Simon J. L. \Conrmation of disordered structure of ultrasmall CdSe nanoparticles from x-ray atomic pair distribution function analysis". In: Phys. Chem. Chem. Phys. 15.22 (2013),
pp. 8480{8486. doi: 10.1039/C3CP00111C. url: http://pubs.rsc.org/en/content/articlelanding/2013/cp/c3cp00111c). 

Inhomogenous strain (more correctly "heterogeneous strain". i.e., strain that varies from place to place on the nanoparticle) affects the PDF peak width.  It is also described in the paper cited above.

Strain only makes sense with respect to a reference "unstrained" state, which might be a PDF from the material without a stress applied, or for residual stresses/strains, some "ideal" state that you, as the scientist have to define.

Crystallographically, we often discuss strain in terms of changes in planar d-spacings, which can vary by direction in the crystal, and it is determined by measuring the positions of individual Bragg peaks and, for example, their position can vary more in some directions than others in the crystal in response to a particular stress state, because the crystal is softer in some directions than others.  This implies measuring the position of individual Bragg peaks, or having a model that captures this behavior.  You are probably aware of complete communities of people studying this in crystals (i.e., "size-strain").  The real-space PDF equivalent is studying PDF peaks that correspond to interatomic vectors that point in different directions in the crystal.  There is not a large community of people studying this yet, but in principle building models with diffpy-CMI that parameterize and capture that behavior will be possible.....but the first step is coming up with the (mathematical) model, or models, as a hypothesis that you want to test.  Only then can it be discussed how to code it in CMI....

S

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[ali dordaee]

 Thanks Dear Simon for the very useful info. As comprehendo, No strain for now! Cause I am really interested in diffpy cmi... maybe with my own point of view I can discuss what I mean by strain and if you approve, I can write the code then. What you mentioned at the last paragraph is what I mean as well. I just need to really think about it before I tell what I exactly mean. Also thanks for the article link. Is there any books in which they have scrutinized and digested the subject of "Strain" or "Strain in nanoparticles"? I'd be more than grateful.

[Simon Billinge]

Hi Ali,

All the rules about strain in crystals apply in the PDF too.  In general, crystals have elastic constants that are different in different directions.   Crystallographically, this means that it is easier to separate certain sets of crystallographic planes than others.  But this depends on the bonding topologically which is encoded in interatomic distances and PDF peaks in the PDF.  So, understanding one helps to understand the other.  A good start is to understand strain and elastic constants in crystals.   I have not kept up with the field of strain in nanoparticles.  Maybe others more expert can chime in on the best resources (books, review articles) for understanding strain in nanoparticles beyond what we did way back when....

Thanks for the discussion Ali

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[Jonas Beyer]

Dear Connie, Ali, and Simon

Microcrystalline (heterogeneous) strain effects will give rise to broadening of Bragg peaks with a tanθ dependency. The broadening can be Gaussian and/or Lorentzian. In PXRD analysis, the microstrain is modelled by fitting the peak shape of a pseudo-Voigt peak profile function. Typically, the Thompson-Cox-Hastings formalism is used, where the strain parameters are U and X of the peak profile function.

We have derived the corresponding effects on the PDF peaks in a recent publication (https://doi.org/10.1107/S2053273321011840).

It turns out that Gaussian and/or Lorentzian strain broadening will results in Gaussian and/or Lorentzian broadening of the PDF peaks, respectively.

We have implemented a fitting routine in TOPAS Academic v6, which takes care of the strain broadening (See Supporting Information in the paper above).

The effect becomes most pronounced at high r-values, so if you have very small nanoparticles with only short correlation lengths, it may not be relevant to include in the model.

Best regards,

Jonas Beyer from Aarhus University