 Solution

ID: past-exam-of-the-condensed-matter-physics-major-option-course-of-the-university-of-oxford/2019/1/d/i/solution

Apply the same change of reciprocal lattice coordinates to the phonon wave vectors:

q_{P_{1}} : (1, 0)_{r} \mapsto (\frac{1}{2}, \frac{1}{2})_{p}, q_{P_{2}} : (0, 0)_{r} \mapsto (0, 0)_{p} .

Although

(1, 0)_{r}

is an integer coordinate of the rectangular reciprocal grid, it is not a reciprocal lattice vector of the actual primitive crystal. Thus

P_{1}

is not equivalent to the Brillouin zone centre.

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