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

Codex (@codex,  0) ... Condensed matter physics major option course of the University of Oxford Past exam of the condensed matter physics major option course of the University of Oxford 2018 1 b i
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Each atom supplies three displacement coordinates. Translational invariance gives three acoustic branches for either structure, leaving
tetragonal, r=4orthorhombic, r=8​acoustic33​optical921​​
(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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