Cubic lattices sodium chloride structure

Figure 5.18.1 The NaCl crystal structure consisting of two interpenetrating face-centered cubic lattices. The face-centered cubic arrangement of sodium cations (the smaller spheres) is readily apparent with the larger spheres (representing chloride anions) filling what are known as the octahedral holes of the lattice. Calcium oxide also crystallizes in the sodium chloride structure.

The formation energy of Schottky defects in NiO has been estimated at 198 kJ mol-1. The lattice parameter of the sodium chloride structure unit cell is 0.417 nm. (a) Calculate the number of Schottky defects per cubic meter in NiO at 1000°C. (b) How many vacancies are there at this temperature (c) Estimate the density of NiO and hence the number of Schottky defects per gram of NiO. 

The sodium chloride structure. Sodium chloride crystallizes in a face-centered cubic structure (Fig. 4.1a). To visualize the face-centered arrangement, consider only the sodium ions or the chloride ions (this will require extensions of the sketch of the lattice). Eight sodium ions form the comers of a cube and six more are centered on the faces of the cube. The chloride ions are similarly arranged, so that the sodium chloride lattice consists of two interpenetrating face-centered cubic lattices. The coordination number (C.N.) of both ions in the sodium chloride lattice is 6. that is, there are six chloride ions about each sodium ion and six sodium ions about each chloride ion. 

The nitrides and carbides of titanium and zirconium and the carbide of hafnium are extremely hard substances, resembling metals both in appearance and in electrical conductivity. Their formulae approach AxBh but some departure from stoichiometry is possible. Each of these refractory substances has the sodium chloride structure, described alternately (p. 190) as cubic close-packed arrays of metal atoms with the small nonmetal atoms in the octahedral holes. Note, however, that the parent metals themselves do not have cubic close-packed structures. Thus, the older view of such nitrides and carbides as lattices of the parent metals that are expanded to accommodate nitrogen or carbon atoms in the holes (interstices) is not admissible. The nature of the bonding in such refractory nitrides and carbides appears to be linked to the nature of bonding in metals in general, an important and interesting topic, but best pursued in more advanced works. 

A few moments thought about the nature of the surface of an oxide leads to the conclusion that the surface oxide ion should have quite different properties than the bulk lattice ions. For example, consider a simple cubic oxide such as MO with a sodium chloride structure where each ion is sixfold coordinated if this is cleaved along a <100) plane, then the coordination of the ions in this plane is reduced from six- to fivefold. This new surface will not be ideal, and ions of still lower coordination will also be present where higher index planes are exposed at the surface. However, for MgO prepared by thermal decomposition of the hydroxide or carbonate, evidence from electron microscopy (130) indicates that these have high index planes that... 

The sodium chloride (NaCl) and zinc blende (ZnS) structures are based on a face-centered cubic lattice. In both structures the anions sit on the lattice points that lie on the corners and faces of the unit cell, but the two-atom motif is slightly different for the two structures. In NaCl the Na ions are displaced from the Cl ions along the edge of the unit cell, whereas in ZnS the Zn ions are displaced from the ions along the... 

The relative sizes of the cation and anion determine the type of lattice an ionic compound adopts. For example, although caesium and sodium are both in the same group of the periodic table, the chlorides crystallize with different types of lattice. Sodium chloride adopts the simple cubic structure (Chapter 4), whereas caesium chloride adopts the lattice shown in Figure 15.10. In caesium chloride, the caesium ions cannot get as close to the chloride ions as the smaller sodium ions. Eight caesium ions can pack around a chloride ion if they are positioned at the corners of a cube. The structure of ionic lattices is determined by X-ray crystallography (see Chapter 21, and Chapter 22 on the accompanying website). 

The structure-dependent coefficients have been calculated for the three primitive cubic lattices.4 For the sodium chloride lattice we have A — 2a3, where a denotes the anion-cation lattice spacing, and if we define a parameter bi by the equation... 

Where the lithium ions fit best will be determined by their size relative to the iodide ions. Note from above that there are two types of interstices in a closest packed structure. These represent tetrahedral (f) and octahedral (o) holes because the coordination of a small ion fitted into them is either tetrahedral or octahedral (see Fig. 4.12). The octahedral holes are considerably larger than the tetrahedral holes and can accommodate larger cations without severe distortion of the structure. In lithium iodide the lithium ions fit into the octahedral holes in a cubic closest packed lattice of iodide ions. The resulting structure is the same as found in sodium chloride and is face-centered (note that face-centered cubic and cubic closest packed describe the same lattice). 

William B. Pearson (1921-2005) developed a shorthand system for denoting alloy and intermetallic structure types (Pearson, 1967). It is now widely used for ionic and covalent solids, as well. The Pearson symbol consists of a small letter that denotes the crystal system, followed by a capital letter to identify the space lattice. To these a number is added that is equal to the number of atoms in the unit cell. Thus, the Pearson symbol for wurtzite (hexagonal, space group PS mc), which has four atoms in the unit ceU, is hPA. Similarly, the symbol for sodium chloride (cubic, space group Fm3m), with eight atoms in the unit cell, is cF8. 

Sodium chloride occurs as a white crystalline powder or colorless crystals it has a saline taste. The crystal lattice is a face-centered cubic structure. Solid sodium chloride contains no water of crystallization although, below 0°C, salt may crystallize as a dihydrate. 

Most salts crystallize as ionic solids with ions occupying the unit cell. Sodium chloride (Figure 13-28) is an example. Many other salts crystallize in the sodium chloride (face-centered cubic) arrangement. Examples are the halides of Li+, K+, and Rb+, and M2+X2 oxides and sulfides such as MgO, CaO, CaS, and MnO. Two other common ionic structures are those of cesium chloride, CsCl (simple cubic lattice), and zincblende, ZnS (face-centered cubic lattice), shown in Figure 13-29. Salts that are isomorphous with the CsCl structure include CsBr, Csl, NH4CI, TlCl, TlBr, and TIL The sulfides of Be2+, Cd2+, and Hg2+, together with CuBr, Cul, Agl, and ZnO, are isomorphous with the zincblende structure (Figure 13-29c). 

Evaporation of the water from salt solutions results in solid salt crystals the ions involved form an ion lattice corresponding to the salt structure. If one allows the water to slowly evaporate from the saturated solution, this often results in large and beautiful crystals. Particularly the alum salt, when growing crystals from saturated solutions (E4.1), results in beautifully formed octahedron (see Fig. 4.4). In the process, K+(aq) ions, Al3+(aq) ions and S042- ions join together to form an ion lattice of cubic symmetry. If one adds approximately 10% of urea to a saturated sodium chloride solution the salt crystals do not crystallize in the expected cubic form, but in an octahedron form with identical symmetry elements as the cube. 

Crystal Structure Periclase has a cubic face-centered crystal lattice iso-morphous with that of sodium chloride and calcium oxide see Figure 8.1. 

The second structure common to a number of T1-B1 systems is that of sodium thallide, sometimes called the Zintlphase. This structure (fig. 13.12) is closely related to that of caesium chloride in that the pattern of sites occupied forms a cubic body-centred lattice. The distribution of the atoms, however, is such that each atom has four neighbours of each kind, and the true cell is therefore the larger unit shown, containing sixteen instead of only two atoms. Some phases in which the sodium thallide structure occurs are LiZn, LiCd, LiAl, LiGa, Liln, Naln and NaTl. It is a characteristic feature of all of these phases that in them the alkali metal atom appears to have a radius considerably smaller than in the structure of the element (even when allowance is made for the change in co-ordination number), suggesting that this atom is present in a partially ionized condition and that forces other than purely metallic bonds are operative in the structure. 

A crystal represents a coherent rigid lattice of molecules, or arrangements of atoms or ions the juxtaposition of which are characteristic of the substance. For example crystals of sodium chloride form a simple cubic structure involving the ions Na and Cl- (see Fig. 8.1). 

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