Solid State Chemistry and its Applications. Anthony R. West

1.641 GaN 3.180 5.166 1.625 ZnTe 4.27 6.99 1.637 InN 3.533 5.693 1.611 BeO 2.698 4.380 0.378 1.623 TaN 3.05 4.94 1.620 CdS 4.1348 6.7490 1.632 NH₄F 4.39 7.02 0.365 1.600 CdSe 4.30 7.02 1.633 SiC 3.076 5.048 1.641 MnS 3.976 6.432 1.618 MnSe 4.12 6.72 1.631

      R. W. G. Wyckoff, Crystal Structures, Vols 1 to 6, Wiley (1971).

      The three anions at that form the base of this T_– site also form the base of a T₊ site shown in Fig. 1.35(e) centred at . The apex of this tetrahedron is the anion at the top corner with coordinates 0, 0, 1. Another T₊ site at is coordinated to three anions in the basal plane and an anion at (d). The triangular base of this site, at c = 0, is shared with a T_– site underneath (not shown) at . The equivalent T_– site that lies inside the unit cell is at (e).

      The octahedral site in Fig. 1.35(d) is coordinated to three anions at c = 0 and three anions at . The centre of gravity of the octahedron lies midway between these two groups of anions and has coordinates . The second octahedral site lies immediately above the octahedral site shown in (d) and has coordinates (e). The three anions at are therefore common to the two octahedra, which means that octahedral sites share opposite faces.

      The coordination environments of the cations in wurtzite and NiAs are emphasised in Fig. 1.35(f) and (g). Zinc is shown in T₊ sites and forms ZnS₄ tetrahedra (f), linked at their corners to form a 3D network, as in (j). A similar structure results on considering the tetrahedra formed by four Zn atoms around a S. The tetrahedral environment of S (1) is shown in (f). The SZn₄ tetrahedron which it forms points down, in contrast to the ZnS₄ tetrahedra, all of which point up; on turning the SZn₄ tetrahedra upside down, however, the same structure results.

      Comparing larger scale models of zinc blende [Fig. 1.33(b)] and wurtzite [Fig. 1.35(j)], they are clearly very similar and both can be regarded as networks of tetrahedra. In zinc blende, layers of tetrahedra form an ABC stacking sequence and the orientation of the tetrahedra within each layer is identical. In wurtzite, the layers form an AB sequence and alternate layers are rotated by 180° about c relative to each other.

      The NiAs₆ octahedra in NiAs are shown in Fig. 1.35(g). They share one pair of opposite faces (e.g. the face formed by arsenic ions 1, 2 and 3) to form chains of face‐sharing octahedra that run parallel to c. In the ab plane, however, the octahedra share only edges: As atoms 3 and 4 are shared between two octahedra such that chains of edge‐sharing octahedra form parallel to b. Similarly, chains of edge‐sharing octahedra form parallel to a (not shown). A more extended view of the octahedra and their linkages is shown in (k).

The NiAs structure is unusual in that the anions and cations have the same coordination number but different coordination environments. Since the cation:anion ratio is 1:1 and the Ni coordination is octahedral, As must also be six‐coordinate. However, the six Ni neighbours are arranged as in a trigonal prism and not octahedrally. This is shown for As at in Fig. 1.35(h), which is coordinated to three Ni at and three at . The two sets of Ni are superposed in projection down c and give trigonal prismatic coordination for As. [Note that in a similar projection for octahedral coordination, the two sets of three coordinating atoms are staggered relative to each other, as in (e).]

      The NiAs structure may also be regarded as built of AsNi₆ trigonal prisms, therefore, which link up by sharing edges to form a 3D array. In Fig. 1.35(i), each triangle represents a prism in projection down c. The prism edges that run parallel to c, i.e. those formed by Ni at and in (h), are shared between three prisms. Prism edges that lie in the ab plane are shared between only two prisms, however. In (i), the edge xy is shared between As at and c = 0. The structure therefore has layers of prisms arranged in an … ABABA … hexagonal stacking sequence, as shown further in (1).

      The NiAs structure can be described as hcp As with Ni in fully occupied octahedral interstitial sites. However, unlike the case of NaCl where Na and Cl positions are interchangeable, we cannot simply exchange Ni, As and arrive at the same structural description. If we consider the arrangement of Ni alone, it still forms cp layers but the stacking sequence along c is identical because Ni atoms are superposed in projection, Fig. 1.35(h). Since both As and Ni form cp layers, we