Cesium chloride , structure

It is necessary that the net charge in the unit cell be neutral. The cation in the middle is completely inside the unit cell and contributes a charge of +1. The eight anions on the comers have only 1/8 of their charge inside the unit cell, so they collectively contribute —1 to balance the cation charge. 

Compounds with this stmcture include CsBr, Csl, RbCl, AlCo, AgZn, BeCu, MgCe, RuAl, and SrTl. 

CsCl structure with coordination number 8. This is a simple cubic lattice, not a bcc lattice, with the counterion in the middle. 

Rock salt structure is fee with the counterions occupying all of the octahedral sites. The ionic bonds are shown as heavy lines. 

Again the charge of the cations (1 in the middle plus 12 on the edges, each contributing 1 /4 to the unit cell for a total of +4) is balanced by the charge of the anions (eight on the comers times 1/8 plus the six on the faces, each contributing 1/2 for a total of —4). 

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FIGURE 5.41 The cesium chloride structure (a) the unit cell and (b) the location of the centers of the ions. 

Estimate the density of each of the following solids from the atomic radii of the ions given in Fig. 1.48 (a) calcium oxide (rock-salt structure, Fig. 5.39) (b) cesium bromide (cesium chloride structure, Fig. 5.41). 

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 alkali halides with the cesium chloride structure also show satisfactory agreement, the observed values being about 2.5% larger than the sum of the theoretical radii. 

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. 

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°. 

The Transition to the Sphalerite Structure.—The oxide, sulfide and selenide of beryllium have neither the sodium chloride nor the cesium chloride structure, but instead the sphalerite or the wurzite structure. The Coulomb energy for the sphalerite arrangement is... 

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. 

Efforts to provide such a treatment for simple alternative structures, such as the sodium chloride and cesium chloride structures and the fluoride and rutile structures, have been made with the aid of the Bom potential expression and modifications of it. Assuming that all ions repel each... 

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.

As was discussed in Chapter 7, there are numerous solids that can exist in more than one form. It is frequently the case that high pressure is sufficient inducement for the structure to change. An example of this type of behavior is seen in KC1, which has the sodium chloride (rock salt) structure at ambient pressure, but is converted to the cesium chloride structure at high pressure. Other examples illustrating the effect of pressure will be seen throughout this book (see especially Chapter 20). It should be kept... 

Figure 3 shows the Mossbauer spectra for an alloy of 75% iron and 25% rhodium after two different heat treatments. Since absorption rather than transmission is plotted, these curves are right side up. The upper spectrum is taken from an alloy which was annealed in the low temperature field (cesium chloride structure), and there are two six-hne patterns... 

Metals generally have face-centred cubic (fee), body-centred cubic (bee) or hexagonal structures. The simplest is fee. In the bee structure, if the central atom is different, the lattice is known as a CsCl (cesium chloride) structure. A bee structure can be considered as two interpenetrating cubic lattices. These are shown schematically in figure 1.3. In catalysis, nanoscopic metallic particles supported on ceramic supports or carbon are employed in many catalytic applications as we show in chapter 5. Increasingly, a combination of two metals (bimetallic) or alloys of two or more metals with special properties are used for specific catalytic applications. 

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...

Among the alkali halides, the cesium chloride structure is found only in CsCl CsBr, and Csl at ordinary pressures, but all of the alkali halides except the salts of lithium can be forced into the CsCl structure at higher pressures. It is also adopted by the ammonium halides (except NH4F), TIC1, TlBr, T1CN, CsCN, CsSH, CsSeH, and CsNH2. 

Alternatively, we might examine the radius ratio of Oj BF and get a crude estimate of = 0.8. The accuracy of our values does not permit us to choose between coordination number 6 and 8, but since the value of the Madelung constant does not differ appreciably between the sodium chloride and cesium chloride structures, a value of 1.75 may be taken which will suffice for our present rough calculations. We may then use the Bom-Lande equation (Eq. 4.13), which provides an estimate of —616 kJ mor1 for the attractive energy, which will be decreased by about 10% (if... 

Fig. 5.44). The coordination number of each type of ion is 8, and overall the structure has (8,8)-coordination. The cesium-chloride structure is much less common than the rock-salt structure, but it is found for Csl as well as CsCl. 

The cesium chloride structure may be regarded as derived from the two equivalent atoms of the cubic bcp unit cell by changing one to Cs+ and the other to... 

Simple cubic. This is also called the cesium chloride structure. Examples are CsCl, CsBr and Csl. It is not as common as the other structures listed below. 

The calculation of Z for the cesium chloride structure is also quite direct and is discussed in Problem 14-2. However, the perturbation theory that we have used becomes inaccurate when we go to the rocksalt structure with Z = 2 or 3, or to the fluorite structure. The assumption of weak coupling restricts us to small percentages of. softening. For Z = 2 and = 5.3 from Table 14-2, Eq. (14-10) leads to a softening of 72 percent, and even larger values arc obtained for Z = 3 and for the fluorites. 

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