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These structures have in common an hcp arrangement of anions and differ only in the positions of the cations, as follows:

 wurtzite: T+ (or T–) sites occupied; T– (or T+), O empty

 nickel arsenide: O sites occupied; T+, T– empty.

These structures are the hcp analogues of the ccp sphalerite and rock salt structures, respectively. Note that there is no hexagonal equivalent of the fluorite and antifluorite structures.

Both wurtzite and nickel arsenide have hexagonal symmetry and unit cells. A unit cell containing hcp anions is shown in Fig. 1.35(a). It is less easy to visualise and draw on paper than a cubic cell because of the γ angle of 120°. The unit cell contains two anions, one at the origin and one inside the cell:

In Fig. 1.35(b) is shown a projection down c of the same structure. Close packed layers occur in the basal plane, i.e. at c = 0 (blue circles), at c = 1 (not shown) and at (pink circles). The layer stacking arrangement is repeated every other layer … ABABA. … The contents of one unit cell are shown in (c). Dashed circles represent atoms at the top four corners of the unit cell, i.e. at c = 1.

Figure 1.35 The wurtzite and nickel arsenide structures: (a–c) the hexagonal unit cell of an hcp anion array; (d, e) interstitial sites in an hcp array; (f, g) structures of wurtzite and NiAs; (h, i) trigonal prismatic coordination of arsenic in NiAs; (j–l) models of the ZnS and NiAs structures showing the arrangement and linkages of the polyhedra.

In metals which have hcp structures, adjacent metal atoms are in contact, e.g. along a ₁ and a ₂ (≡b) edges of the unit cell (b, c). In eutactic cp ionic structures, however, the anions may be pushed apart by the cations in the interstitial sites. Assuming for the moment that the anions are in contact, then the hexagonal unit cell has a definite shape given by the ratio c/a = 1.633. This is because a is equal to the shortest distance X–X, i.e. the diameter of an anion, and c is equal to twice the vertical height of a tetrahedron comprising four anions. The ratio c/a may then be calculated by geometry (see Appendix C).

The interstitial sites available for cations in an hcp anion array are shown in Fig. 1.35(d) for the bottom half of the unit cell between c = 0 and and in (e) for the top half of the unit cell. Since the cell contains two anions, there must be two each of T₊, T_– and O.

A detailed description of the sites that are occupied in wurtzite and NiAs is now given for completeness; such a degree of detail may, however, not be necessary to gain an overview of these two structures and is not compulsory reading! In Fig. 1.35(d), a T_– site occurs along the c edge of the cell at height above the anion at the origin. This T_– site is coordinated to three anions at and one anion at the corner, c = 0. The tetrahedron so formed, therefore, points downwards. The position of the T_– site inside this tetrahedron is at the centre of gravity, i.e. at one‐quarter of the vertical distance from base to apex (see Appendix C). Since the apex and base are at c = 0 and , this T_– site is at . In practice, the occupant of this T_– site in the wurtzite structure may not be at exactly 0.375c. For those structures which have been studied accurately, Table 1.12, values range from 0.345 to 0.385; the letter u represents the fractional c value.

Table 1.12 Some compounds with the wurtzite structure

Compound			u	c/a	Compound			u	c/a
ZnO	3.2495	5.2069	0.345	1.602	AgI	4.580	7.494		1.636
ZnS	3.811	6.234		1.636	AlN	3.111	4.978	0.385	1.600
ZnSe	3.98	6.53		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 may describe the combined layer stacking sequence parallel to c as ACBCACBC… where Ni atoms in C positions (red) separate the A and B layers of As (black).

A selection of compounds with wurtzite and NiAs structures is given in Table 1.12 and Table 1.13 with values of their hexagonal cell parameters a and c. The wurtzite structure is formed mainly by chalcogenides of divalent metals and is a fairly ionic structure. The NiAs structure is more metallic and is adopted by a variety of intermetallic compounds and some transition metal chalcogenides (S, Se, and Te). The value of the ratio c/a is approximately constant in the wurtzite structures but varies considerably in compounds with the NiAs structure. This is associated with the presence of metallic bonding which arises from metal–metal interactions in the c direction, as follows. First consider the environment of Ni and As:

 Each As is surrounded by (Table 1.11):6 Ni in a trigonal prism at distance 0.707a12 As, hcp arrangement, at distance a.Table 1.13 Some compounds with the NiAs structureCompounda/Åc/Åc/aCompounda/Åc/Åc/aNiS3.43925.34841.555CoS3.3675.1601.533NiAs3.6025.0091.391CoSe3.62945.30061.460NiSb3.945.141.305CoTe3.8865.3601.379NiSe3.66135.35621.463CoSb3.8665.1881.342NiSn4.0485.1231.266CrSe3.6846.0191.634NiTe3.9575.3541.353CrTe3.9816.2111.560FeS3.4385.8801.710CrSb4.1085.4401.324FeSe3.6375.9581.638MnTe4.14296.70311.618FeTe3.8005.6511.487MnAs3.7105.6911.534FeSb4.065.131.264MnSb4.1205.7841.404δ′‐NbN^a2.9685.5491.870MnBi4.306.121.423PtB^a3.3584.0581.208PtSb4.1305.4721.325PtSn4.1035.4281.323PtBi4.3155.4901.272^a Anti‐NiAs structure.R. W. G. Wyckoff, Crystal Structures, Vols 1 to 6, Wiley (1971).Figure 1.36 The primitive cubic unit cell of CsCl.

  Each Ni is surrounded by:6 As, octahedrally, at distance 0.707a2 Ni, linearly, parallel to c, at distance 0.816a (i.e. c/2)6 Ni, hexagonally, in ab plane at distance a.

The main effect of changing the value of the c/a ratio is to alter the Ni–Ni distance parallel to c. Thus, in FeTe, c/a = 1.49, and the Fe–Fe distance is reduced to 0.745a [i.e.], thereby bringing these Fe atoms into close contact and increasing the metallic bonding in the c direction. Simple quantitative calculations of the effect of changing the c/a ratio are difficult to make since it is not readily possible to distinguish between, for example, an increase in a and a decrease in c, either of which could cause the same effect on the c/a ratio.