[sdpd] estimating U, V, W

[pstephens...@notes.cc.sunysb.edu]

In response to the question posted by Xia  Changtai:

There's nothing fundamental about U, V, and W, except for the case of a
steady-state neutron source, with mosaic monochromator and Soller slits.
But they are widely used.  My usual experience with synchrotron data (high
resolution) is that you can start with W and V both equal to zero, and
adjust only U.  For a sample with sharp peaks, give it a starting value of
0.02.  Usually I leave V turned off completely - it generally serves only
to make the fit unstable.

The square of FWHM < 0 problem comes because FWHM is defined as (U tan^2
theta + V tan theta + W)^1/2, and with the wrong choice of U, V, W, the
argument is negative.  This will happen in a refinement, even if you've
chosen positive values, because the refinement jumps over the correct value
to one that gives a negative argument.  If you're having trouble, it's best
to sneak up on the correct values from below.  It's also helpful to look at
a plot of FWHM vs. theta from individual peak fits (essentially a
Williamson-Hall plot) to see the slope and intercept by eye, and then
choose initial estimates of U and W from that.

Good luck,
Peter Stephens