A crystal has an -glide plane perpendicular to its -axis

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Solid State Physics, Ch Symmetry and the classification of crystals

Problem

A crystal has an aa-glide plane perpendicular to its cc-axis, with glide translation a/2a/2: the operation sends a general point (x,y,z)(x,y,z) to (x+12,y,−z)(x+\tfrac12,y,-z). For reflections of the class (hk0)(hk0) (that is, l=0l=0), state which of (100)(100), (200)(200), (210)(210), (300)(300) and (410)(410) are systematically absent because of this glide alone, and which are allowed by it.

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