Jon & others, Well, there is an attempt at this in GSAS - the "diffuse scattering" functions for fitting these contributions separate from the "background" functions. These things have three forms related to the Debye equations formulated for glasses. The possibly neat thing about them is that they separate the diffuse scattering component from the Bragg component unlike PDF analysis. As a test of them I can fit neutron TOF "diffraction" data from fused silica quite nicely. I'm sure others have tried them - we all might want to hear about their experience. Bob Von Dreele
________________________________ From: Jon Wright [mailto:[EMAIL PROTECTED] Sent: Sun 8/22/2004 6:13 AM To: [EMAIL PROTECTED] >Well, that is an old chestnut that Cooper and Rollet used to oppose to >Rietveld refinement. I think Rollet eventually agreed that Rietveld was >the better method. Has Bill really gone back on that ? > > The difference between the two approaches are just an interchange of the order of summations within a Rietveld program. Differences in esds should only arise through differences in accumulated rounding errors, assuming you don't apply any fudge factors. Since most people do apply fudge factors, the argument is really about which fudge factor you should apply. I will only comment that the conventional Rietveld approach (multiply the covariance matrix by chi^2) is often poor. As for the PDF "versus" Rietveld - you should get smaller esds on thermal factors if you were to write a program which treats the background as a part of the crystal structure and has no arbitrary degrees of freedom in modelling the background. This is just due to adding in more data points that are normally treated as "background" but which should help to determine the thermal parameters via the diffuse scattering. So, provided you were to remove the arbitrary background from the Rietveld program and compute the diffuse scattering the methods ought to be equivalent. Something like DIFFAX does this already for a subset of structures, but I think without refinement. The real difficulty arises with how to visualise the disordered component, decide what it is, and improve the fit - hence the use of the PDF. Although no one appears to have written such a program there does not seem to be any fundamental reason why it is not possible (compute the PDF to whatever Q limit you like, then transform the PDF and derivatives into reciprocal space). Biologists already manage to do this in order to use an FFT for refinement of large crystal structures! In practice a large percentage of the beamtime for these experiments at the synchrotron is used to measure data at very high Q which visually has relatively little information content - just so that a Fourier transform can be used to get the PDF. This is silly! The model can always be Fourier transformed up to an arbitrary Q limit and then compared whatever range of data you have. For things like InGaAs the diffuse scatter bumps should occur mainly on the length scale of the actual two bond distances. Wiggles on shorter length scales are going to be more and more dominated by the thermal motion of the atoms, and so don't really add as much to the picture (other than to allow an experimentalist to get some sleep!). In effect it is like the difference between measuring single crystal data to the high Q limit and then computing an origin removed Patterson function and doing a refinement against that Patterson as raw data. No one does the latter as you can trivially avoid the truncation effects by doing the refinement in reciprocal space. The question then is whether it is worth using up most of your beamtime to measure the way something tends toward a constant value very very precisely? Could the PDF still be reconstructed via maximum entropy techniques from a restricted range of data for help in designing the model? Currently the PDF approach beats crystallographic refinement by modelling the diffuse scattering. As soon as there is a Rietveld program which can model this too then one might expect the these experiments become more straightforward away from the ToF source. I'd be grateful if someone can correct me and show that most of the information is at the very high Q values. Visually these data contain very little compared to the oscillations at lower Q and seem to become progressively less interesting the further you go, as there is a larger and larger "random" component due to thermal motion. Measuring this just so you can do one transform of the data instead of transforms of the computed PDF and derivatives seems like a dubious use of resources? Since the ToF instruments get this data whether they like it or not, the one transform approach is entirely sensible there. For x-rays and CW neutrons, it seems there is a Rietveld program out there waiting to be modified. August is still with us, Happy Silly Season! Jon
