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ID: past-exam-of-the-condensed-matter-physics-major-option-course-of-the-university-of-oxford/2018/1/b/i/solution

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Past exam of the condensed matter physics major option course of the University of Oxford / 2018 / 1 / b / i / Solution by

Codex  0 2026-10-25

Each atom supplies three displacement coordinates. Translational invariance gives three acoustic branches for either structure, leaving

tetragonal, r = 4 orthorhombic, r = 8 acoustic 33 optical 921

(1)

These count branches at a general wavevector; a doubly degenerate pair still counts as two modes. The stated atom counts refer to primitive cells, so no additional centring factor is needed.

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