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ID: past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2015/paper-1/1/a/ii/solution

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Past exam of the materials science course of the University of Cambridge / 2015 / Paper 1 / 1 / a / ii / Solution by

Codex  0 2026-10-20

Bond-centred inversion in diamond cubic gives one inversion centre at the midpoint of a nearest-neighbor bond:

c = (\frac{1}{8}, \frac{1}{8}, \frac{1}{8}) .

(1)

Mark its projected point

(1/8, 1/8)

and label its height $z / a = 1/8$ . Inversion about this point sends

r

(1/4, 1/4, 1/4) - r

. It exchanges the two identical FCC sublattices and therefore preserves the crystal. An individual atom at the chosen origin is not an inversion centre.

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