 Solution

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

The primitive translations connect the two centred-rectangular sublattices. In the orientations marked in the source,

a_{p}

points right and down, whereas

b_{p}

points right and up. Thus

a_{p} = \frac{1}{2} (a_{r} - b_{r}), b_{p} = \frac{1}{2} (a_{r} + b_{r}) .

Their parallelogram has half the area of the rectangular cell, confirming that the latter contains two primitive unit cells.

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