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]


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