William Stratton Ph.D. Thesis - MINDS@UW Home

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Figure 2.4: The unit sphere representation of Ahkl for an Al crystal for: a 1.0 nm (a) 3.0 nm (b) at
a {111} reflection and a 1.0 nm (c) and 3.0 nm (d) at a {220} reflection. The great circle ribbons
(shown in white) correspond to intersections with the respective planes, and their width is Δθ. As
seen, smaller crystals will have thicker great circle ribbons and therefore larger Ahkl values.
Figure from 87 .
Equation (2.24) in Figure 2.5 for different families of reflections of a cubic crystal. The
discrepancy only becomes significant for Δθ > 0.15 radians, which occurs only for the smallest
crystals we consider (d ~ 1 nm).
Though the shape function, Ahkl is a function of one of our sample parameters d. To
highlight this dependence, we introduce the Bragg active fraction constant, Chkl. Since, for small
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