Hi, > It is all powder diffraction, we are all family! :-) Nice to get hundreds of fathers and brothers.
OS Thursday, July 31, 2008, 4:53:04 AM, you wrote: > Hi all, > I was encouraged by Alan to respond to these PDF questions on-list, > rather than redirecting the discussion to a PDF-only list, so my > previous comments that such PDF discussions are not appropriate for > the Rietveld list may have been overstated. It is all powder > diffraction, we are all family! :-) >> Stimulated by the topics on pair distribution functions, can I ask some >> questions here about PDF analysis? What is the proper way of scaling in PDF >> calculation, so that one may obtain the actual structure factor and >> coordination numbers? I used both PDFGetN and PDFGetX to get PDF, and also >> tried to do that by hand. What I found is that however I adjust the >> parameters in both softwares, there is always a scale factor (not equal to >> 1) when one try to refine the obtained G(r) in PDFFit. It seems the scale >> factor is determined by some parameters such as the size of sample and >> vanadium bar, and packing ratios etc, which may not be so accurate when one >> inputs them in PDFGetN. In order to obtain the right coordination numbers, >> the reduced PDF (G(r)=4pi*rho*r[g(r)-1], according to Egami and Billinge's >> definition) must be properly scaled. The scale factor may be found by >> fitting with known model, but may not be so clear for amorphous or unknown >> materials. Is this scale factor arbitrary, or are there some criteria, >> theoretically or empirically? In other words, how can one normalize the >> scattering intensity to get actual structure factor? >> > Ideal normalization is something that people studying glasses care a > great deal about and spend much effort in the pursuit thereof. Whilst > you can do very well using Neutrons and normalizing by a totally > incoherent scatterer such as V/Nb alloy, or even pure vanadium, my > personal view is that the resulting errors are somewhat large and > somewhat uncontrolled. Without model fitting (this is a Rietveld list > afterall, go modelling!) I would hesitate to say that I can determine > a coordination number from a PDF with better than 10% accuracy, and > 20% is more likely to be correct. The difficulty is the uncontrolled > errors. If you are unlucky, the occupancy can be off by much more. > By model fitting you can refine an overall scale factor which takes > care of this problem. The relative intensities between different PDF > peaks is determined very accurately, so once the overall scale is > determined, other structural parameters can be refined with high > accuracy, comparable to Rietveld. > In principle we normalize the S(Q) by measuring it to high-Q where the > coherent scattering disappears (because of the Debye-Waller factor, > and additionally the x-ray form factor in the case of x-rays). At > this point, all the scattering from the sample is incoherent and so > the intensity, normalized to the number of atoms which is the normal > convention, is given by the the number of atoms times the average > scattering cross-section of the atoms, or <f>^2. We can simply > multiply our measured intensity by whatever number it takes such that > this incoherent part of the scattering lies on the theoretical <f>^2 > line for our sample. When we Fourier transform the resulting > intensity we can get perfect coordination numbers by using the correct > (Faber-Ziman) expressions. However, things are not as simple as they > seem and here is where the problem originates. Before we get to the > "normalization" point we have to make some corrections to the data. > We should subtract parasitic scattering (from containers etc.), > Compton Scattering, multiple scattering, correct for absorption and > extinction, polarization, detector deadtime, angular dependence of > detector efficiencies, etc. etc. etc.. This we do with great care, > but what you immediately realise is that some of the corrections are > additive/subtractive and some are multiplicative. If we make any > errors in these corrections (and many of them are quite approximate) > we run the risk of compensating an additive correction with a > multiplicative one when we do the normalization, resulting in an > incorrect absolute scale on the data. In many cases, the signal is > much larger than any relevant backgrounds and corrections and we get > rather good normalizations, in other cases this is no longer true, > especially for weakly scattering samples. > My glass-studying colleagues will get mad at me for saying it, but in > general, treat coordination numbers determined directly from PDF peak > fitting with some degree of doubt. However, when you fit with models, > we have shown [1] that data that are even far from ideally normalized > (i.e., the normalization lim Q->infty S(Q)=1 is good, but additive > offsets were corrected with with a multiplicative correction) give > quantitatively identical refined parameters so, as they say in > Brooklyn, donworryaboudit. > [1] P. F. Peterson, E. S. Bozin, Th. Proffen and S. J. L. Billinge, > Improved measures of quality for atomic pair distribution functions, > J. Appl. Crystallogr. 36, 53 (2003). > Simon > PS, are you using PDFgetX or PDFgetX2 for your x-ray data...the latter > is the version of the code that we are supporting and, if that was not > a typo, I encourage you to switch. -- Best regards, Olga mailto:[EMAIL PROTECTED]
