L. Keller wrote :
>I am not sure if it is a good idea to derive average coherent domain lengths
>from Rietveld analysis programs. I am not aware of any package currently
>available which is set up to follow the strict analytical procedures
>necessary (= profile deconvolution, Fourier analysis of line profile etc).
>Exact size cannot be determined reliably from simple profile width.
The Rietveld method essentially compares calculated and observed
whole patterns, extracting structure parameters, and sometimes
"approaching" microstructure effects. The analytical procedures you
mention have to be reversed. No deconvolution is necessary. The
calculated pattern is constructed by convolution f*g where g comes
from a measurement on a sample unaffected by microstructures, and
f is built from a model of the microstructure (size, microstrain...)
affecting your sample.
That is a good idea.
But current models are unsufficients and this is all the problem.
Theory on which is based the Fourier analysis is too much
idealized and oversimplified, so that it applies mainly to materials
with very small departure from strict three-dimensionnal order.
Real models should take account of considerable deviations from
strict order, including all these awful disorders that may affect real
materials (concentration variation, all kinds of dislocations and
stacking faults). These effects can no longer be resumed
in a few oversimplified parameters. Size effect takes a clear sense
only when there is no distortion effect (size effect only). Most of us
think that a pure distortion effect is only possible in our current
simple equations, but is in reality impossible because distortion
generates a size effect. Our equations are not representing well
the reality, they are too simple.
We are there now : after years of description of complexity
by approximated formulae, we have really to face complexity...
Waiting for that, we dispose of some Rietveld programs, imperfect,
but trying to describe the whole powder patterns of real materials,
using the too simple models of this century end.
Certainly not a bad idea : a step in advancing knowledge. Let us
see if the coming microstructure round robin will dare to propose
the analysis of samples showing thousand of more or less large
diffraction peaks, or if only cubic samples with few if no overlapping
will be retained.
Anyway, the intrinsic limitation of the Rietveld method is that it
needs a hkl-based description of the diffraction phenomenon.
Many real materials show diffraction patterns that do not enter
exclusively in that too simple scheme.
More details at :
http://sdpd.univ-lemans.fr/egypte/conf2/
Best,
Armel Le Bail
