Structures, lattice wurtzite

Consider a closest packed lattice of sulfide ions. Zinc ions tend to occupy tetrahedral holes in such a framework since they are quite small (74 pm) compared with the larger sulfide ions (170 pm) ff the sulfide ions form a ccp array, the resulting structure is zinc blende if they form an hep array, the resulting structure is wurtzite. See Fig. 4.15. 

Fig. 3.1. (a) Primitive cell (heavy lines) of the wurtzite-structure lattice placed within a hexagonal prism, a and c are the lattice constants, (b) Schematic drawing of surfaces cut from a hexagonal single crystal with different crystallographic orientations (surface planes)... 

AIN, GaN and InN crystallise in the wurtzite structure which is characterised by lattice parameters a and c, as well as by u-value (u = b/c, where b is a bond-length in the c-direction). For the ideal wurtzite structure, c/a = 1.633 and u = 0.375. In contrast to the cubic sphalerite structure, the wurtzite structure offers two possibilities to deviate from the ideal arrangement, by changing the c/a ratio and by changing the u value. Such deviations are often observed in wurtzite-type structures [1] but there exists a strong correlation between the c/a ratio and the u parameter if c/a decreases, then u increases in such a way that the four tetrahedral distances remain nearly constant and the tetrahedral angles are distorted [2]. The bond lengths would be equal if ... 

The crystal structure for this complex lattice (wurtzite structure) is shown in Figure 2.15. This is best described as an hep lattice of sulfide ions, with zinc ions occupying one-half of the available tetrahedral interstitial sites. For this lattice, there are two units of ZnS per unit cell ... 

A majority of the important oxide ceramics fall into a few particular structure types. One omission from this review is the structure of silicates, which can be found in many ceramics [1, 26] or mineralogy [19, 20] texts. Silicate structures are composed of silicon-oxygen tetrahedral that form a variety of chain and network type structures depending on whether the tetrahedra share comers, edges, or faces. For most nonsilicate ceramics, the crystal structures are variations of either the face-centered cubic (FCC) lattice or a hexagonal close-packed (HCP) lattice with different cation and anion occupancies of the available sites [25]. Common structure names, examples of compounds with those structures, site occupancies, and coordination numbers are summarized in Tables 9 and 10 for FCC and HCP-based structures [13,25], The FCC-based structures are rock salt, fluorite, anti-fluorite, perovskite, and spinel. The HCP-based structures are wurtzite, rutile, and corundum. 

Table 7.4. Lattice constants (A) and bandgaps (eV) for the set of 40 simple and binary semiconductors ( [419]), a-sphalerite structure, c-wurtzite structure...

Betyllium, because of its small size, almost invariably has a coordination number of 4. This is important in analytical chemistry since it ensures that edta, which coordinates strongly to Mg, Ca (and Al), does not chelate Be appreciably. BeO has the wurtzite (ZnS, p. 1209) structure whilst the other Be chalcogenides adopt the zinc blende modification. BeF2 has the cristobalite (SiOi, p. 342) structure and has only a vety low electrical conductivity when fused. Be2C and Be2B have extended lattices of the antifluorite type with 4-coordinate Be and 8-coordinate C or B. Be2Si04 has the phenacite structure (p. 347) in which both Be and Si... 

The predominantly ionic alkali metal sulfides M2S (Li, Na, K, Rb, Cs) adopt the antifluorite structure (p. 118) in which each S atom is surrounded by a cube of 8 M and each M by a tetrahedron of S. The alkaline earth sulfides MS (Mg, Ca, Sr, Ba) adopt the NaCl-type 6 6 structure (p. 242) as do many other monosulfides of rather less basic metals (M = Pb, Mn, La, Ce, Pr, Nd, Sm, Eu, Tb, Ho, Th, U, Pu). However, many metals in the later transition element groups show substantial trends to increasing covalency leading either to lower coordination numbers or to layer-lattice structures. Thus MS (Be, Zn, Cd, Hg) adopt the 4 4 zinc blende structure (p. 1210) and ZnS, CdS and MnS also crystallize in the 4 4 wurtzite modification (p. 1210). In both of these structures both M and S are tetrahedrally coordinated, whereas PtS, which also has 4 4... 

Figure 29.1 Crystal structures of ZnS. (a) Zinc blende, consisting of two, interpenetrating, cep lattices of Zn and S atoms displaced with respect to each other so that the atoms of each achieve 4-coordination (Zn-S = 235 pm) by occupying tetrahedral sites of the other lattice. The face-centred cube, characteristic of the cep lattice, can be seen — in this case composed of S atoms, but an extended diagram would reveal the same arrangement of Zn atoms. Note that if all the atoms of this structure were C, the structure would be that of diamond (p. 275). (b) Wurtzite. As with zinc blende, tetrahedral coordination of both Zn and S is achieved (Zn-S = 236 pm) but this time the interpenetrating lattices are hexagonal, rather than cubic, close-packed.

The XRD pattern of the as-prepared ZnSe nanoparticles (Figure 3) exhibited predominantly wurtzite crystal structure with distinct diffraction peaks corresponding to the crystalline planes of hexagonal ZnSe and lattice constant of 0.397 nm, which was... 

Every ionic crystal can formally be regarded as a mutually interconnected composite of two distinct structures cationic sublattice and anionic sublattice, which may or may not have identical symmetry. Silver iodide exhibits two structures thermodynamically stable below 146°C sphalerite (below 137°C) and wurtzite (137-146°C), with a plane-centred I- sublattice. This changes into a body-centred one at 146°C, and it persists up to the melting point of Agl (555°C). On the other hand, the Ag+ sub-lattice is much less stable it collapses at the phase transition temperature (146°C) into a highly disordered, liquid-like system, in which the Ag+ ions are easily mobile over all the 42 theoretically available interstitial sites in the I-sub-lattice. This system shows an Ag+ conductivity of 1.31 S/cm at 146°C (the regular wurtzite modification of Agl has an ionic conductivity of about 10-3 S/cm at this temperature). 

In the first case, along the direction of the diagonal of the cubic cell, there is a sequence ABC of identical unit slabs ( minimal sandwiches ), each composed of two superimposed triangular nets of Zn and S atoms, respectively. The thickness of the slabs, which include the Zn and S atom nets, is 0.25 of the lattice period along the superimposition direction (that is along the cubic cell diagonal aj3). It is (0.25,3 X 541) pm = 234 pm. In the wurtzite structure there is a sequence BC of similar slabs formed by sandwiches of the same triangular nets of Zn and S atoms. Their thickness is —0.37 X c = 0.37 X 626.1pm = 232 pm). 

Below 146°C, two phases of Agl exist y-Agl, which has the zinc blende structure, and (3-Agl with the wurtzite structure. Both are based on a close-packed array of iodide ions with half of the tetrahedral holes filled. However, above 146°C a new phase, a-AgI, is observed where the iodide ions now have a body-centred cubic lattice. If you look back to Figure 5.7, you can see that a dramatic increase in conductivity is observed for this phase the conductivity of a-Agl is very high, 131 S m , a factor of 10 higher than that of (3- or y-AgI, comparable with the conductivity of the best conducting liquid electrolytes. How can we explain this startling phenomenon ... 

The parameter is obtained by relating the static dielectric constant to Eg and taking in such crystals to be proportional to a - where a is the lattice constant. Phillips parameters for a few crystals are listed in Table 1.4. Phillips has shown that all crystals with a/ below the critical value of0.785 possess the tetrahedral diamond (or wurtzite) structure when f > 0.785, six-fold coordination (rocksalt structure) is favoured. Pauling s ionicity scale also makes such structural predictions, but Phillips scale is more universal. Accordingly, MgS (f = 0.786) shows a borderline behaviour. Cohesive energies of tetrahedrally coordinated semiconductors have been calculated making use... 

Structure tP4 (CuAu) is ordered with respect to an underlying face-centred cubic lattice, so that it takes the Jensen symbol 12/12. The CuAu lattice does show, however, a small tetragonal distortion since the ordering of the copper and gold atoms on alternate (100) layers breaks the cubic symmetry. Zinc blende (cF8(ZnS)) and wurtzite (hP4(ZnS)) are ordered structures with respect to underlying cubic and hexagonal diamond lattices respectively. Since both lattices are four-fold tetrahedrally coordinated, differing only in... 

Figure 27. Crystal lattice of cadmium pigments (wurtzite structure) a) Sulfur (selenium) b) Cadmium (zinc, mercury)...

The luminescent properties can be influenced by the nature of the activators and coactivators, their concentrations, the composition of the flux, and the firing conditions. In addition, specific substitution of zinc or sulfur in the host lattice by cadmium or selenium is possible, which also influences the luminescent properties. Zinc sulfide is dimorphic and crystallizes below 1020 °C in the cubic zinc-blende structure and above that temperature in the hexagonal wurtzite lattice. When the zinc is replaced by cadmium, the transition temperature is lowered so that the hexagonal modification predominates. Substitution of sulfur by selenium, on the other hand, stabilizes the zinc-blende lattice. 

The zinc blende and wurtzite structures. Zinc sulfide crystallizes in two distinct lattices hexagonal wurtzite (Fig. 4.2a) and cubic zinc blende (Fig. 4.2b). We shall not elaborate upon them now (see page 121), but simply note that in both the coordination number is 4 fbr both cations and anions. The space groups are Ptync and F43m. Can you tell which is which ... 

The use of radius ratios to rationalize structures and to predict coordination numbers may be illustrated as follows.27 Consider beryllium sulfide, in which rn,a /r5i- = 59 pm/170 pm = 0.35. We should thus expect a coordination number of 4 as the Be2+ ion fits most readily into the tetrahedral holes of the closest packed lattice, and indeed this is found experimentally BcS adopts a wurtzite structure. 

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