Prediction of Holz Pattern Shifts in Convergent Beam Diffraction

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In general, diffraction patterns from the higher-order Laue zones are shifted with respect to the zero-order pattern. Expressions for the shift (t) have been derived in terms of the indices [u, v, w] of a zone, the interplanar spacing (H), and a reciprocal lattice vector [gL (hkl)] in a holz. The resulting vector possesses the direction of t in terms of a zolz reciprocal lattice vector and has a magnitude which is a fraction of that of the zolz vector. Hence, the calculation of t allows quantitative determination of the location of specific planes in a holz with respect to the zolz, thus simplifying the determination of plane indices consistent with those used in the zolz. The expressions for determining t for cubic, hexagonal close-packed (hep), tetragonal, orthorhombic, and monoclinic crystal types are presented in a table and, when applied, allow calculation of t expressed as a fraction of a zolz vector. An example for graphite is presented to illustrate the use of the equation, and tvectors for several zones for the simple cubic system are tabulated.