Re: U, V, W vs Fundamental Parameters

Armel Le Bail ( armel@fluo.univ-lemans.fr )
Wed, 27 May 1998 18:07:37 +0200

J"org Bergmann wrote :

>I took part on the "Size/Strain Round Robin", which was part of this
>conference. My software was BGMN, as I know the only Rietveld program
>with fundamental parameters research presented on this conference.

As far as I know, this Round Robin was not an open one... Participants
were selected by the organizer.

>And, as I know, BGMN was the only program which was able to detect
>the anisotropic strain in the virgilite specimen. All other participants
>have presented isotropic or anisotropic size parameters, but never
>anisotropic strain. My conclusion was: There was anisotropic strain, size
>was nearly isotropic.

Nobody seems to be able to give me the status of the book
"Microstructure Analysis by Diffraction" which is supposed to
contain the Round Robin results. Was it cancelled ?

About the previous Lachlan question if Size-Strain analysis is
mature ?-).

My answer is no. Moreover, you should not expect it.

Specialists do agree with a formula which is the Debye scattering
equation. They disagree on the various modifications of this
equation because they are applicable only to preconceived models
(for instance supposing that the size-strain affected compound
shows only a small departure from a perfect three-dimensional
order).

The problem is that the Debye equation allows you to calculate
the diffraction pattern from your model, no more. This equation
is hard to reduce to some physical parameters which could be
refined in the Rietveld method. I am afraid that the Size-Strain
science will never maturate, even not in the Bordeaux country :-).
Real defective materials are too complex for being described by
a few parameters on which scientists could agree. These materials
may combine well all sorts of defects (high dislocation density,
composition variation, stacking faults...). It is more easy to
describe instrumental effects (g) by fundamental parameters...
Now, yes, the true (h) profile could be obtained by convoluting
(g) by the sample profile (f). However this is true only if the
whole scattering due to the sample is really included
in those hkl reflections. I do believe that, for very defective
materials, this is not the case. The Warren equations for
size-strain analysis are limited to materials with little
(or no) defects. Maybe samples with size-effect only could
be more easily reduced to believable equations. Even in this
case, reducing the problem to a few parameters would
immediately lead to preconceived models and scientists
disagreement :-).

This problem of reducing complexity to something simple
could not have a solution, obviously.

Armel