The sodium chloride structure

In this structure (Fig. 6.1(a)) the A and X atoms alternate in a simple cubic sphere packing, each atom being surrounded by 6 others at the vertices of a regular octahedron. An alternative description, that the A (X) atoms occupy octahedral holes in a cubic closest packing of X (A) atoms is realistic only for compounds such as LiCl in which each Cl is actually in contact with 12 Cl atoms. This structure was derived by Barlow (1898) as a possible structure for crystals composed of 

The sodium chloride and related structures (a) NaCl, (b) yellow Til, (c) tetragonal GeP, 

Compounds with the sodium chloride structure range from the essentially ionic halides and hydrides of the alkali metals and the monoxides and monosulphides of Mg and the alkaline-earths, through ionic-covalent compounds such as transition-metal monoxides to the semi-metallic compounds of B subgroup metals such as PbTe, InSb, and SnAs, and the interstitial carbides and nitrides (Table 6.1). Unique and different distorted forms of the structure are adopted by the Group IIIB 

When subjected to high pressure certain phosphides and arsenides of metals of Groups IIIB and IVB adopt either the cubic NaCl structure (InP, InAs) or a tetragonal variant of this structure (GeP, GeAs) shown in Fig. 6.1(c) in which there are bonds of three different lengths and effectively 5-coordination. The compounds of Ge and Sn, with a total of nine valence electrons, are metallic conductors. This property is not a characteristic only of the distorted NaCl structure, for SnP forms both the cubic and tetragonal structures, and both polymorphs exhibit metallic conduction. (IC 1970 9 335 JSSC 1970 1 143.) 

The full cubic symmetry of the NaCl structure is retained in (a) high temperature defect structures with random distribution of vacancies, (b) solid solutions in which there is random arrangement of ions of two or more kinds in the anion and/or cation positions, and (c) crystals containing complex ions either if the complex ions have full cubic symmetry, as in [Co(NH3)6] [Tide], or if there is rotation or random orientation of less symmetrical groups, as in the high-temperature forms of alkaline-earth carbides, KSH, and KCN. In the latter cases the low-temperature forms have lower symmetry. 

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Taking the ionic radii for Cs+, Cl , Br , and I from Table 42, calculate in cubic centimeters per mole the volumes which the cesium halides would have if they crystallized in the sodium chloride structure, nnd compare with the values plotted in Fig. 57. 

The Alkali Halides.—In Table V are given the experimental interatomic distances for the alkali halides with the sodium chloride structure, together with the sum of the radii of Table II. 

Alkali Halides with the Sodium Chloride Structure... 

The experimental values for the lithium halides are high. This is due to two different phenomena. In the case of the chloride, bromide and iodide the anions are in mutual contact, that is, the repulsive forces operative are those between the anions, and the anion radius alone determines the inter-atomic distances. The geometry of the sodium chloride structure requires that, for less than 0.414, the anions come into contact... 

Other Binary Compounds.—Scandium nitride and zirconium and titanium carbide do not conform with the theoretical radii. It is possible that these crystals do not consist essentially of Sc+3, N 3, Ti+4, Zr+4 and C-4 ions, especially since zirconium and titanium nitride, ZrN and TiN, also form crystals with the sodium chloride structure but possibly also the discrepancy can be attributed to deformation of the anions, which have very high mole refraction values. 

These considerations also explain the occurrence of cases of dimorphism involving the sodium chloride and cesium chloride structures. It would be expected that increase in thermal agitation of the ions would smooth out the repulsive forces, that is, would decrease the value of the exponent n. Hence the cesium chloride structure would be expected to be stable in the low temperature region, and the sodium chloride structure in the high-temperature region. This result may be tested by comparison with the data for the ammonium halides, if we assume the ammonium ion to approximate closely to spherical symmetry. The low-temperature form of all three salts, ammonium chloride, bromide and iodide, has the cesium chloride structure, and the high-temperature form the sodium chloride structure. Cesium chloride and bromide are also dimorphous, changing into another form (presumably with the sociium chloride structure) at temperatures of about 500°. 

In Table XVIII are given values of the radius ratio for the salts of beryllium, magnesium and calcium (those of barium and strontium, with the sodium chloride structure, also obviously satisfy the radius ratio criterion). It is seen that all of the sodium chloride type crystals containing eight-shell cations have radius ratios greater than the limit 0.33, and the beryl-... 

The effect of double repulsion for the sodium chloride structure may raise this limit a few per cent. 

The prediction may be made that the still unstudied crystal magnesium telluride, with the radius ratio 0.29, has the sphalerite or wurzite structure rather than the sodium chloride structure. 

The radius ratios for sphalerite and wurzite type crystals with eighteen-shell cations do not conform to our criterion, so that some other influence must be operative. Without doubt this is deformation. Here again it is seen that the tetrahedral structure is particularly favorable to deformation, for the observed Zn++—O distance (1.93 A.) is 0.21 A. shorter than the theoretical one, while in cadmium oxide, with the sodium chloride structure, the difference is only 0.01 A. 

It is also shown that theoretically a binary compound should have the sphalerite or wurzite structure instead of the sodium chloride structure if the radius ratio is less than 0.33. The oxide, sulfide, selenide and telluride of beryllium conform to this requirement, and are to be considered as ionic crystals. It is found, however, that such tetrahedral crystals are particularly apt to show deformation, and it is suggested that this is a tendency of the anion to share an electron pair with each cation. 

The elucidation of the factors determining the relative stability of alternative crystalline structures of a substance would be of the greatest significance in the development of the theory of the solid state. Why, for example, do some of the alkali halides crystallize with the sodium chloride structure and some with the cesium chloride structure Why does titanium dioxide under different conditions assume the different structures of rutile, brookite and anatase Why does aluminum fluosilicate, AljSiCV F2, crystallize with the structure of topaz and not with some other structure These questions are answered formally by the statement that in each case the structure with the minimum free energy is stable. This answer, however, is not satisfying what is desired in our atomistic and quantum theoretical era is the explanation of this minimum free energy in terms of atoms or ions and their properties. 

Fig. 2.—The arrangement of ions in cube-face layers of alkali halide crystals with the sodium chloride structure.

Galena, PbS, has the sodium chloride structure, with ligancy 6 for each atom. The Pb-S distance is 2.968 A. A possible structure is that based on the normal sulfur atom... 

Fig. 5-l Ball-and-stick model of the sodium chloride structure... 

The lines are not covalent bonds (Sec. 5.5), but only indications of the positions of the ions. Sodium fluoride is only one compound having the 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.

Based on the ionic radii, nine of the alkali halides should not have the sodium chloride structure. However, only three, CsCl, CsBr, and Csl, do not have the sodium chloride structure. This means that the hard sphere approach to ionic arrangement is inadequate. It should be mentioned that it does predict the correct arrangement of ions in the majority of cases. It is a guide, not an infallible rule. One of the factors that is not included is related to the fact that the electron clouds of ions have some ability to be deformed. This electronic polarizability leads to additional forces of the types that were discussed in the previous chapter. Distorting the electron cloud of an anion leads to part of its electron density being drawn toward the cations surrounding it. In essence, there is some sharing of electron density as a result. Thus the bond has become partially covalent. 

Although the structure of CsCl is quite different from that of NaCl, even CsCl can be transformed into the sodium chloride structure when heated to temperatures above 445 °C. Some of the other alkali halides that do not have the sodium chloride structure under ambient conditions are converted to that structure when subjected to high pressure. Many solid materials exhibit this type of polymorphism, which depends on the external conditions. Conversion of a material from one structure to another is known as a phase transition. 

By means of the radius ratio, we have already described the type of local environment around the ions in several types of simple crystals. For example, in the sodium chloride structure (not restricted to NaCl itself), there are six anions surrounding each cation. The sodium chloride crystal structure is shown in Figure 7.4. 

Each of the compounds shown in Eq. (9.101) has the same crystal structure, the sodium chloride structure, so the Madelung constant is the same for all of them. The term containing 1/n is considered to be a constant for the two pairs of compounds (reactants and products). Actually, an average value of n... 

The sulfides of the group IIA metals generally have the sodium chloride structure, but those of the group IA metals have the antifluorite structure because the ratio of anions to cations is 2. Solutions of the sulfides are basic as a result of the hydrolysis reaction... 

Assume that the iron atoms in the crystal are in a perfect array, identical to the metal atoms in the sodium chloride structure, and that the 0.058 excess of oxygen is due to interstitial oxygen atoms being present, over and above those on the normal anion positions. The unit cell of the structure now contains 4 Fe and (4 x 1.058) O. The density is calculated to be 6076 kg m-3. 

Assume that the oxygen array is perfect and identical to the nonmetal atom array in the sodium chloride structure and that the unit cell contains some vacancies on the iron positions. In this case, one unit cell will contain 4 atoms of oxygen and (4/1.058) atoms of iron, that is, 4Feo.94sO. The density is calculated to 5741 kg m-3. 

Nickel oxide, NiO, which adopts the sodium chloride structure (Fig. 1.14), can readily be made slightly oxygen rich, and, because the solid then contains more oxygen than nickel, the crystal must also contain a population of point defects. This situation can formally be considered as a reaction of oxygen gas with stoichiometric NiO, and the simplest assumption is to suppose that the extra oxygen extends the crystal by adding extra oxygen sites. Atoms are added as neutral atoms, and... 

Cadmium oxide, CdO, like nickel oxide, also adopts the sodium chloride structure (Fig. 1.14). However, unlike nickel oxide, this compound can be made to contain more metal than oxygen. The defects that cause this metal excess are usually considered to be interstitial Cd atoms or ions. In this case the reaction is one in which the solid formally loses oxygen. Because of the rules of equation writing, this must involve the removal of neutral oxygen atoms. Each oxygen lost results in the loss of a nonmetal site. In order to keep the site ratio correct, a metal site must also be lost, forcing the metal into interstitial sites ... 

Nickel oxide, NiO, is doped with lithium oxide, Li20, to form Li Ni, xO with the sodium chloride structure, (a) Derive the form of the Heikes equation for the variation of Seebeck coefficient, a, with the degree of doping, x. The following table gives values of a versus log[(l-x)/x] for this material, (b) Are the current carriers holes or electrons (c) Estimate the value of the constant term k/e. 

Some values for the enthalpy of formation of Schottky defects in alkali halides of formula MX that adopt the sodium chloride structure are given in Table 2.1. The experimental determination of these values (obtained mostly from diffusion or ionic conductivity data (Chapters 5 and 6) is not easy, and there is a large scatter of values in the literature. The most reliable data are for the easily purified alkali halides. Currently, values for defect formation energies are more often obtained from calculations (Section 2.10). 

Figure 2.2 Variation of Schottky formation energy of the sodium chloride structure halides MX M = Li, Na, K X = F, Cl, Br, I.

In order for the battery to function, the lithium iodide must be able to transfer ions. Lil adopts the sodium chloride structure, and there are no open channels for ions to use. In fact, the cell operation is sustained by the Schottky defect population in the... 

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