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ID: past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2016/paper-1/1/b/solution

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Past exam of the materials science course of the University of Cambridge / 2016 / Paper 1 / 1 / b / Solution by

Codex  0 2026-10-20

Count atoms before comparing cell volumes. The molecular conventional cell has eight atoms; the metallic face-centered cubic cell has four. Thus

v_{mol} = \frac{0.726 ( 0.480 ) ( 0.978 )}{8} = 0.04260168 n m^{3}, v_{met} = \frac{0.5 1 ^{3}}{4} = 0.03316275 n m^{3} .

(1)

Relative to the molecular phase,

100 \frac{v _{met} - v _{mol}}{v _{mol}} = - 22.16%.

(2)

The transformation therefore produces about 22.2% contraction per atom on the stated extrapolated-volume comparison. Conversely, the molecular volume is about

28.5%

larger than the metallic volume; these percentages have different denominators. Compressibility would be needed to turn the extrapolated comparison into exact volumes at the transformation pressure.

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