Anthony R. West - Solid State Chemistry and its Applications

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 1and 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 0.375 c . 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	NH 4F	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).