Modesty

[Armel Le Bail]

And he is modest as well :-)
I have to be modest. According to the CNRS, I am a
second-class researcher...
Armel

RE: Rietveld refinement and PDF refinement ?

[Radaelli, PG (Paolo)]

 do you really have the 
 resolution even on
 HRPD to see the diffuse scattering between Bragg peaks at 
 high Q ?

No we don't, but this is not the main point (by the way, we don't use HRPD
for PDF, it doesn't go to sufficiently short wavelengths).  The main reason
to go to high Q is to avoid truncation errors.  If you truncate S(Q), all
your G(r) peaks will be convoluted with the Fourier transform of a step
function, which is a sinx/x function.  The width of the central peak is
roughly 1/Qmax.  If you use a wavelength of 0.5 A, this corresponds to about
0.08 A, or an equivalent B of 0.5.  This in itself can be a problem when you
want to look at sharp correlation features.  Even worse, the ripples will
propagate to adjacent PDF peaks, generating unphysical features.  There are
ways to suppress the ripples by convoluting the data with an appropriate
smooth function rather than truncating them (these are extensively used in
disordered materials work), but they all tend to broaden the features.  You
can also fit a model including the ripples (as in PDFfit) but it is clearly
better not to have them if you are trying to exploit the model independence
of PDF.  Going to high Q does not solve all the problems. If the high-Q data
are noisy, your truncation function will have higher frequency but also
higher (and random) amplitude in the ripples, so there is always a
compromise Qmax, depending on statistics.  Finally, very high-Q data are
quite difficult to normalise, because of the epithermal background.   


 You may
 get better temperature factors with high-Q PDF refinement, 
 but you will
 also do that with high-Q Rietveld.

Generally, all crystallographic parameters come out worse from PDF
refinements than from Rietveld on the same data sets.  I think this is
because you are trying to fit an average structure to something that
contains correlations, so the fit is bound to be worse.  You could fit a
correlated model, but then you would not get temperature factors in the
usual sense. 

 I also doubt that just because PDF uses data between the 
 Bragg peaks, then
 it must be superior for seeing details not centered on atoms 
 in real space
 in a crystal, eg the split atom sites in (In/Ga)As). You 
 might do just as
 well with Bragg scattering if you use the result of Rietveld 
 refinement to
 construct a Fourier map of the structure. Happily, a sampling of
 reciprocal space (Bragg peaks) is sufficient to re-construct 
 the entire
 density of a periodic structure in real space, not just point 
 atoms, to a
 resolution limited only by Q.

You are right.  PDF is not always superior.  It is the interpretation of the
Fourier density in terms of correlated displacements that emerges uniquely
from PDF, although you can often guess it right from the Fourier map in the
first place.  The case of Jahn-Teller polarons in manganites (La,Ca)MnO3 is
quite illuminating.  Several groups noticed that the high-temperature phase
(above the CMR transition) has large DW factors for O.  We showed that this
affects primarily the longitudinal component along the Mn-O bonds, and
guessed that this was caused by an alternation of short and long Mn-O
distances.  Simon Billinge showed the same thing quite convincingly from PDF
data.  Only the latter can be considered direct evidence (with some
caveats).

 But you do agree that in a PDF experiment you integrate over 
 energy, so
 you only see an instantaneous snapshot of the structure...

Yes, I agree with this and the fact that inelasticity corrections are an
issue.  Sometimes they are exploited to obtain additional information, and
there is a claim that one can measure phonon dispersions with this method,
but the issue is quite controversial.

 
 So while I am convinced of the interest of PDF for non-crystalline
 materials, with short or intermediate range order, I am not 
 yet convinced
 that you gain much from PDF refinement of crystalline 
 materials, where you
 can also apply Rietveld refinement.

I agree completely.  The directional information gained from phasing and the
fact of locking in to specific Fourier components is a major asset of
Rietveld analysis.  PDF is useful when correlated disorder is important (and
large), even if superimposed on an ordered structure.

Paolo Radaelli

RE: Anisotropic line broadening in cubic material

[pstephens]

Jens,

Your effect might be more related to strain than size broadening.  You
would have to check widths at various diffraction orders in a given
direction (i.e., 111, 222, 333, etc., vs 200, 400, 600, etc. for an fcc
material).  If the widths increase roughly in proportion to diffraction
order, but with a different slope for the two directions, you have
anisotropic strain broadening.

This was noted by Stokes and Wilson (Proc. Phys. Soc. London 56, 174-181
(1944)) in cold-worked fcc metals, who had a model as a random distribution
of stresses.  N. Popa and I have independently considered the effect more
recently from a phenomenological viewpoint (J. Appl. Cryst. 31, 176 (1998)
and ibid 32, 281 (1999), respectively).  And there is a growing literature,
especially from the group of Tamas Ungar, on the effect of specific lattice
defects on strain-broadening in diffraction patterns.

Regarding your use of the anisotropic size broadening model in GSAS, as you
point out, broadening axis for a cubic material is a rather iffy concept.
If my understanding is correct, GSAS does not do the full symmetry
equivalents in that calculation, and so it's a matter of luck how the
calculation will be done.  That is, if you list a (111) broadening axis,
and the reflection list contains (111), you'll get one answer, but if you
list (-1 1 1) broadening axis, the (111) reflection will be calculated
differently.

-Peter

~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~
Peter W. Stephens, Professor
Department of Physics  Astronomy
State University of New York
Stony Brook, NY 11794-3800