 Solution

ID: past-exam-of-the-condensed-matter-physics-course-of-the-university-of-oxford/2018/1/a/solution

R = n_{1} a_{1} + n_{2} a_{2} + n_{3} a_{3}, n_{i} \in Z .

The two positions in the conventional cubic cell of alpha-tungsten give a body-centred cubic lattice, with one tungsten atom per primitive cell and two per conventional cell. One possible set of primitive lattice translation vectors is

a_{1} = \frac{a}{2} (- 1, 1, 1), a_{2} = \frac{a}{2} (1, - 1, 1), a_{3} = \frac{a}{2} (1, 1, - 1) .

Their primitive-cell volume is

a^{3} /2

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