Alan
I think you are misunderstanding what the PDF method is used for. The
idea is to fourier transform directly the whole range of scattering
including peaks and background (after removing artifacts in the
background due to the diffractometer, air scattering etc). In a highly
ordered crystal structure most of the diffracted intensity resides in
the peaks, and there is little background. In such a case normal
structure factor refinement to get the crystal structure is the way to
go. However in a disordered structure there is a contribution to the
background and then the PDF method is useful to obtain local information
about atoms (it is a bit like the results of NMR or EXAFS). Thus for
instance if we have a structure in say a hexagonal symmetry with an atom
displaced along [001], we can find this using the usual structure
factor methods which gives the AVERAGE crystal structure. However in the
example I am thinking of we also find a very large aniotropic
displacement parameter for this atom suggesting that the atom is not
actually displaced along [001] but at the unit cell level is slightly
displaced off this direction. PDF methods then show that the distance
between this atom and its nearest neighbours is consistent with the
off-axis displacement rather than for the atom being actually along
[001].
Sp the point is that the PDF method is useful for looking at local order
whereas the structure factor method is for average structures. Note byt
the way that there is no phase problem for the PDF method.
The main problems with the PDF are
1. Being able to account properly for extraneous background so that the
remaining background which we need truly represents the crystal
2. The need for very high Q in order to obtain suficient resolution. The
use of copper radiation for example does not give sufficientky high Q
and so one needs generally to use vedry short wavelengths from a
synchrotron or use time of flight neutrons.
Mike Glazer
