Regarding definition of S(q) equation

[GiHan Kwon]

Hi All

Some papers make me confusing because some papers user 1.S(q) equation (top) and another paper used second equation (which was not divided by number of atoms (N)). I don't know why each equation does not have a single definition. Even Liquid PDF community also use different S(q) equation ( Quantum Beam Sci. 2023, 7(2), 20). The current xPDFsuite has an scaling issue with liquid system. So Liquid community prefer to use pdfgetX2.

So, first I tested two types of S(q) equations published from references shown in the picture. The scale of S(q), F(q), and G(r) is quite different because one equation was not divided by number of atoms (N)

Please see the result, the far right column's data were from xPDFsute with the same parameter from my code which is on GitHub.
I understand why there are so many different equations because each experiment requires a specific case. But this way may lead to chaos for data interpretation in the future.

 It seems to be a silly question to you. To share code in my place, I need to make sure it is. I think an equation must have a single definition.
Is there any single definition of S(q)?

I will contact Chris, Takeshi, and so on to get their opinion.

thanks,

Gihan

[Simon Billinge]

Dear Gihan,

The 1/N should be there.   The most clear (imho) rederivation of these equations is in Farrow et al. Acta A 2009:

https://doi.org/10.1107/S0108767309009714

I think it is a good use of time to go through that.

Regarding the xPDFsuite/PDFgetX3 issue, the algorithm used there only gives a PDF up to an arbitrary unknown scale factor.  This is often a number close to 1, but in some circumstances can be wildly different.  However, it was shown in the PDFgetX3 paper (10.1107/S0021889813005190) that the G(r) was not affected by the scale-factor offset, so you should rescale it for comparison with G(r)/S(Q) obtained in other ways and you will find that after rescaling it will be of very high quality.

People who want to determine G(r) on an absolute scale, for example to extract a number of nearest neighbors in an amorphous or liquid material, have to do all the corrections correctly and can't use getX3, this is true.  However,  I think that there is some confusion in the community, that if you use PDFgetX2 or one of the other programs (gudrun/gudrunX) that make all the physics based corrections to the data explicitly, you will get a correct scale factor.  However, this is only true if you know all the different experimental factors in your setup exactly.   In general we often don't know the powder packing density and the amount of Compton and Fluorescence scattering, the beam intensity weighted illuminated sample volume and so on.  We are often only guessing at these parameters and so only getting an approximate scale factor even from these programs.  One has to go to a great deal of trouble to get all this right, and there are practitioners who are doing that but they are mostly not using the RAPDF setup with large area 2D detectors.   If you are not doing all those things carefully, you may as well just use PDFgetX3 and not worry about the scale factor.  Be careful about drawing scientific conclusions from scale factors!

S

--
You received this message because you are subscribed to the Google Groups "diffpy-users" group.
To unsubscribe from this group and stop receiving emails from it, send an email to diffpy-users...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/diffpy-users/2adfbb40-ea0d-42fb-9857-b4fac277d686n%40googlegroups.com.

--

Simon Billinge

Professor, 

Department of Applied Physics and Applied Mathematics

Columbia University

[GiHan Kwon]

Dear Simon,

I appreciate your explanation about the papers.
I concur that it is much harder to get all the precise data required for metal oxide and other systems than for the liquid case.
Thank you for sharing your opinion as well.

Sincerely,

Gihan

2023년 12월 3일 일요일 오후 8시 9분 22초 UTC-5에 Simon J. L. Billinge님이 작성: