In my opinion, the short answer (regarding use of Caglioti parameters) is
that their use is historic and somewhat convenient, but their usual
application is based on no theory whatsoever, and they can be quite
troublesome to apply.
They came from a paper (Nuc. Instrum. & Methods, 1958) on the resolution
of a neutron powder diffractometer using mosaic crystals and S\"{o}ller
(that's an umlaut over the o; please, not solar) collimators, which gives
precise expressions for U, V, and W in terms the various geometric
parameters of the diffractometer. If (as was true of most samples on
neutron powder diffractometers at the time) the instrument dominated the
peak shape, they give a good representation of the observed linewidth.
Maybe you could tweak them up a bit to account for sample broadening.
Accordingly, they were ideally suited to Rietveld's method which was first
developed for CW neutron powder diffractometers. Historically, they seem
to have overstayed their welcome, I mean their theoretical justification.
This is especially so for high resolution x-ray powder diffractometers at
synchrotrons and elsewhere where the peak width is almost entirely from
the sample, not the instrument.
One problem with them is that for inappropriate choices of U, V, and W,
the linewidth can become an imaginary number over a certain range of
diffraction angles. This leads to some unpleasant instabilities in
refinement programs that use them.
The fundamental parameters approach would have you model the instrument
and the sample separately, and for any other kind of diffractometer, U, V,
and W are probably not a very good model of either. You can learn about
fundamental parameters e.g., from the Bruker Topas documentation, or from
Klug and Alexander, chapter 6.
If you are not going to try to separately model instrument and sample, you
can get a pretty good line through your data points and relative
intensities suitable for Rietveld analysis with U, V, and W (and some of
their extensions, such as Lorentzian X and Y in, e.g., GSAS) Toward that
end note that if you forget V, the (Gaussian) FWHM is $(U \tan^2 \theta +
W)^{1/2}$, which suggests that U is kind of like strain broadening and W
is kind of like size broadening, coming together in quadrature. I have
had generally OK luck leaving V set to zero and refining U and W. That
has the advantage of being more robust than refining the three (or more)
parameters. I guess once your refinement is pretty much under control,
you could let V vary to see if the fit improves. Just be careful not to
believe that the refined values of U, V, and W have any meaning in such a
refinement.
^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~
Peter W. Stephens
Professor, Department of Physics and Astronomy
Stony Brook University
Stony Brook, NY 11794-3800
fax 631-632-8176
