Crystal structure cesium chloride

Figure 9.3 Cluster of unit cells of the cesium chloride crystal structure. This figure shows that ions of the same sign in this structure line up along the 100 directions. Thus the three rows are orthogonal to one another. Translation of a (100) plane of ions over its nearest (100) neighboring plane keeps ions of opposite sign adjacent to one another. This is also the case on the (110) planes, but the translation vector is V2 larger than for the the (100) planes.

Which of the cations in Table 12.3 would you O predict to form fluorides having the cesium chloride crystal structure Justify your choices. 

The cesium thlontle structure. Cesium chloride crystallizes in the cubic arrangement shown in Fig. 4.1b. The cesium or chloride ions occupy the eight comers of the cube and the counterion occupies the center of the cube.1 Again,... 

Cesium chloride crystallizes with a structure derived from the simple cubic primitive cell. Ch ions occupy the 8 comer sites with Cs+ in the center of the cell note that this is not a body-centered cubic unit cell since the ion at the center is not the same as those at the comers. Thus there is one CsCl unit per unit cell and the coordination numbers of Cs+ and Ch are both 8. Crystals of CsBr and Csl adopt the CsCl structure, but all other alkali halides crystallize in the NaCl structure. 

To sec how this occurs, let us consider the simplest interesting case, that of cesium chloride. The structure of CsCl is shown in Fig. 2-1,a. The chlorine atoms, represented by open circles, appear on the corners of a cube, and this cubic array is repeated throughout the entire crystal. At the center of each cube is a cesium atom (at the body-center position in the cube). Cesium chloride is very polar, so the occupied orbitals lie almost entirely upon the chlorine atoms. As a first approximation we can say that the cesium atom has given up a valence electron to... 

In fact, only CsCi, CsBr, and Csl, under normal conditions, possess the bcc structure. Cesium chloride crystallizes with the rock-salt structure (cfc) at temperatures above 445°C. This indicates that the bcc and cfc structures have similar energies. One should note in Table 14 the too-weak values obtained for LiC , LiBr, and Lil, which would crystallize in the zinc-blende or wurtzite structures. Finally, let us note that the distances between nearest neighbors in the arrangements bcc and cfc, observed in halides possessing both structures, are practically the same AgF, in spite of the value p 0.9, crystallizes in the cfc structure. 

Cesium chloride CsCl structure (Fig. 2.9) has the symmetry of symmorphic space group N221 and two equivalent descriptions Cs(la)Cl(lb) and Cs(lb)Cl(la). This structure was found for crystals CsBr, Csl, RbCl, AlCo, AgZn, BeCu, MgCe, RuAl, SrTl. 

Huggins, who has particularly emphasized the fact that different atomic radii are required for different crystals, has recently [Phys. Rev., 28, 1086 (1926)] suggested a set of atomic radii based upon his ideas of the location of electrons in crystals. These radii are essentially for use with crystals in which the atoms are bonded by the sharing of electron pairs, such as diamond, sphalerite, etc. but he also attempts to include the undoubtedly ionic fluorite and cesium chloride structures in this category. 

The Sodium Chloride and Cesium Chloride Structures.—The agreement found between the observed inter-atomic distances and our calculated ionic radii makes it probable that the crystals considered are built of only slightly deformed ions it should, then, be possible, with the aid of this conception, to explain the stability of one structure, that of sodium chloride, in the case of most compounds, and of the other, that of cesium chloride, in a few cases, namely, the cesium and thallous halides. 

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. 

Figure 9.2 is schematic diagram of the crystal structure of most of the alkali halides, letting the black circles represent the positive metal ions (Li, Na, K, Rb, and Cs), and the gray circles represent the negative halide ions (F, Cl, Br, and I).The ions lie on two interpenetrating face-centered-cubic lattices. Of the 20 alkali halides, 17 have the NaCl crystal structure of Figure 9.1. The other three (CsCl, CsBr, and Csl) have the cesium chloride structure where the ions lie on two interpenetrating body-centered-cubic lattices (Figure 9.3). The plastic deformation on the primary glide planes for the two structures is quite different.

In most ionic crystals, the anion is larger than the cation and, therefore, the packing of the anions determines the arrangement of ions in the crystal lattice. There are several possible arrangements for ionic crystals in which the anions are larger than cations, and cations and anions are present in equal molar amounts. For example. Figure 4.22 shows two different arrangements found in the structures of sodium chloride, NaCl, and cesium chloride, CsCl. 

The observed interionic distances for the cesium and rubidium halogenides (the latter bemg at high pressure) with the cesium chloride structure are compared with the crystal radius sums in Table 13-8. 

Table 13-8.—Interionic Distances fob Crystals with the Cesium Chloride Structure...

Fig. 4.1 Crystal structures of two 1 1 ionic compounds (a) unit cell of sodium chloride, cubic, space group Fm3m (b) unit cell of cesium chloride, cubic, space group Fm3m. [From Ladd, M.F C Structure and Bonding in Solid State Chemistry, Wiley New York, 1979. Reproduced with permission.]...

Fig. 4. Computer-generated crystal structure models nop row. left to right) Cuprite, zinc-blende, rutile, perovskite. iridymite (second row) Cristobalite. potassium dihydrogen phosphate, diamond, pyrites, arsenic (third rowt Cesium chloride, sodium chloride, wurtzite. copper, niccolite (fourth row) Spinel, graphite, beryllium, carbon dioxide, alpha i uanz. [AT T Bel Laboratories ...

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