Dear all,

 

>>R is a scalar, not a vector: it has no direction, it is only length.
>>There are no directional component to <R>, sigma^2, or other
>>moments/cumulants of g(R).

 

Yes, I totally agree on that.

>>There is no such thing as "parallel to R" or "perpendicular to R". 
>>I would point out that they use "u^2_perp" and
>>"u^2_parallel", and that the diffraction <u^2> values DO have
>>directionality, while sigma^2 does not.

 

Matt, on this point I feel there is a lot of confusion and misunderstanding,
mainly due to different notation. The "parallel" and "perpendicular"
things arise as *projections* on the distance between average atomic positions
defined by crystallography and measured by diffraction.

I attach a three-pages pdf which could make Fornasini's geometry and
notation about local dynamics clearer.

Just to be sure: Fornasini calls it C1*, John calls it sigma^1 and most
of you call it simply R. They are the same thing: EXAFS distance!
Furthermore, Fornasini's C2* is exactly your sigma^2.

>>This can be important if you want relate distances measured by XAFS to those
>>measured by diffraction in systems with high thermal disorder (say, hot
>>metals).

 

Actually most of Fornasini's work refers to systems at very low temperatures,
down to 10K. The effect is particularly interesting in systems where
XRD lattice parameter shows a negative expansion, while EXAFS distance increases... 

>>As a result, analysis of most real data suffers from various
>>systematic sources of error such that the uncertainty on the fitted
>>sigma^2 in the EXAFS equation is quite large.

 

Bruce, I agree that most of us are not concerned by all those subtle details.
Most of experimental data are short, noisy, difficult to interpret, etc.
However, Fornasini's work refers to very accurate temperature-dependent
EXAFS measurements, at low temperatures, with excellent samples, in simple
systems, etc... in order to detect very tiny variations.

>>It is because XRD does not measure bond length but only the interplanar spacing

 

Just to say that this was already well known 50 years ago in crystallography.
See for example W. R. Busing and H. A. Levy, Acta Crystallographica 17, 145 (1964)
(ref 30 of the pdf attached).