Will termination effects affect the integrated intensity in PDF peak?

[sun...@yahoo.com.tw]

Dear all,

Recently, I use PDFfit to calculate G(r) of a structural model
determined from XRD, and then I convert G(r) to R(r) through equation
of R(r)=r*[G(r)+4*pi*r*(number density)]. However when I do an
integration on the first peak of R(r), I found the coordination number
is much smaller than what I predicted. I am pretty much sure the peak
does not overlap with other peaks and the input structure model is
correct. Number density is also correct. I double checked several time
and still can not figure out why I did not get the correct
coordination number. Therefore, I am wondering whether the termination
effects will affect the integrated intensity in PDF peak. I also
change the value of Qmax but I still can not obtain the correct
coordination number. Does anyone have ideas?

P.S, When I switch to simple structure, such as Ni, I do obtain the
correct correction number.

Many thanks,

Wen

[chris farrow]

Dear Wen,

Thanks for posting!

To answer your question, termination effects transfer intensity from a PDF peak into the termination ripples. Thus, to get the proper peak integration, you need to be sure your integration includes the termination ripples. However, this does not sound like a termination ripple issue. It sounds like your structural model has multiple elements. In this case, you must consider the scattering factors that scale each peak of the experimental PDF and RDF. 

Each peak of the experimental RDF has a scale factor equal to
f_i f_j / < f >^2,
where f_i (f_j) is the forward-scattering power for atom i (atom j) that contributes to the peak, and < f >^2 is the squared sample-average of the scattering powers. (For neutron scattering, f_i is the neutron scattering length of atom i.)  In the nickel case, f_i f_j = < f >^2, so you get the answer you expect. In your case, since there is no overlap between peaks, you need to normalize your calculated coordination number by the scattering weight of the peak to get the actual coordination number.

I hope this works for you. If you don't mind, I've forwarded this to totalsc...@googlegroups.com, which is a good place to ask general questions about the PDF techniques.

Good luck! Please let us know if you have any more questions or issues.

Sincerely,

Chris Farrow

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[sun...@yahoo.com.tw]

Dear Chris Farrow,

After I normalize calculated coordination number, I still was not able
to obtain the correct coordination number. Therefore, I calculate
several other simple structures such as, halite and quartz. The first
RDF (converted from G(r)) peak should have integrated peak area of 6.
I obtain 5.65 without normalizing (which is very close to 6). However,
the first RDF peak in quartz only has integrated peak area of 2.96
without normalizing (which is away from 4). The value of f_i f_j / < f
>^2 in halite is 0.95 and in quartz is 1.12. So far I am not quite
sure how to normalized calculated coordination number. Do I just
simply divide the calculated coordination number by the scattering
weight? Another question is if RDF is converted directly from
calculated G(r), why we need to correct the the scattering weight.

Sincerely,

Wen






On Apr 12, 6:52 pm, chris farrow <farro...@gmail.com> wrote:

> email: clf2...@columbia.edu
> web:http://www.columbia.edu/~clf2121

[chris farrow]

Dear Wen,

I've gone through the halite example and get a peak integration of 5.72448, which is similar to your value. The proper way to normalize this is to divide by the peak weight, which is 0.95, to get 6. In the case of quartz, the first peak might overlap with the second depending on their widths. In order to get the coordination number from these, you need to somehow separate the peaks. It is helpful to fit Gaussians to the two peaks, and get the coordination number from the peak amplitudes. (This won't work if the peaks are perfectly overlapping.)

The RDF is calculated from G(r), but both of these values are "scattering" correlation functions, which is different from the probabilistic definition of these quantities. The distinction comes from the scattering probe. Peaks in the PDF are biased according to how strongly the x-rays scatter from the atoms that contribute to the peaks. This is the origin of the scattering weight. PDFfit2 simulates the PDF that would be measured from a scattering experiment, therefore you must normalize by scattering weight to get the proper coordination numbers.

Cheers,

Chris

[Golddawn]

Hi all,

Regarding to what mentioned by Chris, that is:

"Each peak of the experimental RDF has a scale factor equal to
f_i f_j / < f >^2"

I just wonder that whether f_i for X-ray RDF is dependent on peak position or not. I know scattering power is depending on Q value but from halite example, it is obvious that f_i value is considered independent of peak position. So for all peaks in X-ray RDF, f_i = f(0) that is scattering powder at Q =0, and the same peak weight is applied (11*17/{(11+17)/2}^2 = 0.95) . Is it true? If not, how to related f_i to X-ray RDF peak position.

Thanks, 

Sau Nguyen

[Simon Billinge]

yup, you got it.  The f_i's in those equations are f_i(Q=0), i.e., the value of the form factor at Q=0.

S

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[Wanuk Choi]

Hello. I am a PDFgetX3 user and am experiencing issues with measuring the first coordination number of a silicon reference sample.

I measured crystalline silicon powder (NIST Silicon Powder, SRM 640 series) contained in a 1 mm capillary using Mo X-ray with a 2D detector. 

After removing the container scattering, I obtained the G(r) of silicon. The resultant pattern matched well with the simulated PDF pattern generated using PDFgui.

However, when I calculated the coordination number of the first peak, the integrated RDF value was approximately 3.6–3.7, rather than the expected 4.0.

I used the following equation and assumed a number density of ~0.0499 atoms/ų:

RDF(r)=r⋅[G(r)+4πr⋅(number density)]

If I arbitrarily use ~0.7 as the number density, the coordination number becomes ~4.0.

This implies that during the measurement and data processing, the G(r) value might have been underestimated.

How can I improve the measurement or processing to obtain an accurate G(r) value?
Alternatively, can I add an empirical constant somewhere in the equation to correct it?

r⋅[G(r)+4πr⋅(number density)]

Sincerely,

-Wanuk

2013년 5월 5일 일요일 오전 6시 23분 11초 UTC+9에 Simon J. L. Billinge님이 작성:

[Simon Billinge]

Thanks for posting Wanuk!

In general, PDFgetX3 does not return a reliable overall scale factor, and it is not designed to do so.   The rationale is that (a) if you are modeling using PDFgui or diffpy-cmi this is easy to refine as a global parameter and (b) this is extremely difficult to know precisely in most experiments.   Even data reduction programs that make all the corrections explicitly tend to have parameters that are not well controlled, such as packing fraction, effective absorption correction, and incident intensity. 

What this means is that you cannot simply use PDFgetX3 to get a PDF and then integrate the first peak to get a coordination number.    If you want to get reliable coordination numbers from the nearest neighbor PDF peak you have to work very hard at controlling all the experimental variables that affect this, and then make all the corrections explicitly.

S

On Mon, Jan 27, 2025 at 11:14 PM Wanuk Choi <wanu...@gmail.com> wrote:

Hello. I am a PDFgetX3 user and am experiencing issues with measuring the first coordination number of a silicon reference sample. I measured crystalline silicon powder (NIST Silicon Powder, SRM 640 series) contained in a 1 mm capillary using

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[Wanuk Choi]

Thank you very much for your kind explanation.

I now understand that PDFgetX3 does not return an overall scale factor (which varies depending on the r range), making the integrated RDF unreliable.
Regarding your answer (a), if I use PDFgui, would it be possible to obtain parameters related to the overall scale factor (e.g., scale factor or Qdamp) and apply them to RDF calculations?
Additionally, if the scale factor is unreliable, even if I manage to fit the background (B(r) = −4πρ/r), would it still be impossible to extract peak intensities from G(r) via peak fitting? (I noticed that HighScore, by Malvern Panalytical, offers a peak fitting function for this purpose.) Or would it be impossible to obtain reliable background too?

I now realize that understanding PDF analysis is incredibly challenging, both theoretically and experimentally. I recently purchased your book, and it is right here next to me. I hope it contains some helpful hints for these corrections.
(Previously, I thought I had a little understanding of crystallography, but I now see that I was merely familiar with how to use software without making errors.)

Best regards,
Wanuk

2025년 1월 28일 화요일 오후 11시 44분 18초 UTC+9에 Simon J. L. Billinge님이 작성: