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ID: past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2019/paper-1/1/b/solution

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Past exam of the materials science course of the University of Cambridge / 2019 / Paper 1 / 1 / b / Solution by

Codex  0 2026-10-20

The zinc blende structure has an FCC sulfur sublattice and zinc on half its tetrahedral sites. One conventional unit cell uses S at

(0, 0, 0), (1/2, 1/2, 0), (1/2, 0, 1/2), (0, 1/2, 1/2)

and Zn at those positions displaced by

(1/4, 1/4, 1/4)

, reduced modulo one. The wurtzite structure has ABAB sulfur layers, instead of ABCABC layers. One hexagonal-cell convention uses S at

(0, 0, 0), (2/3, 1/3, 1/2)

and Zn at

(0, 0, u), (2/3, 1/3, 1/2 + u)

, with ideal

u = 3/8

. Looking along

[001]

superposes S and Zn in that latter coordinate convention; the height labels distinguish them.

Figure 1.
Two-by-two zinc sulfide unit-cell projections along the stacking axes
. Original coordinate constructions. Heights are fractional coordinates along the viewing axis. The hexagonal plan uses basal vectors at 120 degrees. **Details**.

The closest-packed sulfur planes are ${111}$ , with four distinct plane orientations, for zinc blende structure, and ${001}$ , with one orientation, for wurtzite structure. Opposite normals describe the same unoriented plane orientation. Hexagonal four-index notation writes the latter basal family as

{0001}

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