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4.1.3 Indexing HOLZ Lines
There area a number of ways to index HOLZ lines
(Steeds, 1979; Ecob et al., 1981). The approach taken in
this study is somewhat different from the approach
described in the above references in that the actual HOLZ
diffracting conditions are calculated. This method gives
a more intuitive feel for HOLZ detail and permits a more
rapid indexing of the patterns. The subsequent use of the
HOLZ lines for lattice parameter measurements is similar
to that developed by Jones et al. (1977).
To calculate the HOLZ line positions, one need only
determine the intersections of the Ewald sphere with the
reciprocal lattice beyond the zero order zone of the
reciprocal lattice. The equations necessary to do this
for a cubic crystal are presented below.
Let h, k, 1 be the Miller indices of
planes in the diffracting crystal.
These will also define the g vector for
the diffraction pattern.
Let a be the lattice parameter of the
material.
Let U, V, W be the idices of the beam
direction, B, in the crystal. These
indices are, by convention, given in
crystal coordinates. They are also
taken as antiparallel to the actual beam
direction in the instrument.
In reciprocal space, the center of the Ewald sphere for
the cubic crystal will be at
UR/|B|, VR/|B|, and WR/|B|, where R = 1/ .