Relationship Between Lattice Energy and the Physicochemical Properties of Single Crystals of the Cesium Chloride, Wurtzite, Zinc Blende, and Rutile Types

E. K. ZAVADOVSKAYA

For single crystals of alkali-halide salts having a crystal lattice of the rock-salt type, the regular variation of many properties with the energy of the crystal lattice has been described [1].

It was of interest to investigate to what extent the principal regularities observed for alkali-halide compounds are also found for other diatomic chemical compounds and other types of crystal lattices.

From the expression for the energy of the crystal lattice, given by A. F. Kapustinskii [2] for any ionic crystals, it follows that the dependence of the lattice energy on the valence and radii of the ions entering into the compound remains the same for all types of ionic lattices.

This circumstance makes it possible to expect a relationship with lattice energy for the properties of ionic crystals of various lattice types, and not only crystals of the rock-salt type.

From this point of view it was of interest to consider the oxides of metals of the second group of the Mendeleev table, since it had been shown earlier [3] that some of the oxides of these metals should form dielectrics with high electrical properties.

For alkali-halide compounds it was established that cations and anions are deformed differently in different compounds. As a result of the different interaction of cations and anions in the compounds, their volume and polarizability prove to be different.

We shall use the data on the variation in the volume of the oxygen ion in various compounds with metals of the second group of the Mendeleev table and its polarizability from the work of Tessman, Kahn, and Shockley [4], and compare them with the magnitude of the lattice energy for these oxides.

Figure 1 presents the variation in the volume of the oxygen ion and the associated variation in polarizability for oxides of metals of the second group and the energy of the crystal lattice.

Figure 2 presents the variation in the lattice energy of oxides of metals of the second group of the Mendeleev table with the volume of the cations and the polarizability of the cations. All the compounds considered crystallize in a lattice of the NaCl type.

The lattice energy of the oxides considered increases with a decrease in the volume of the cations and anions.

The observed change in the volume of certain anions in chemical compounds is associated with the chemical interaction of ions. The regular change in the polarizability of an ion in compounds may be associated with the chemical nature of molecular forces. The observed change in the volume of ions should cause a change in the concentration of ions per unit volume of the crystal.

Figure 3 presents the change in lattice energy with the change in the number of ions in \(1\ \mathrm{cm}^3\) for alkali-halide compounds and for oxides of certain metals crystallizing in a lattice of the NaCl type.

Fig. 1. Change in the volume and polarizability of anions \((\mathrm{O}^{--})\) with lattice energy for oxides of metals of the second group of the Mendeleev table, crystallizing in a lattice of the NaCl type, according to the data of Tessman, Kahn, and Shokai.

The observed dependence of lattice energy on the volume of molecules, polarizability, and concentration of ions for lattices of the NaCl type can also be extended to other types of lattices.

Fig. 2. Change in the volume and polarizability of cations with lattice energy for oxides of metals of the second group of the Mendeleev table, crystallizing in a lattice of the NaCl type, according to the data of Tessman, Kahn, and Shokai.

Figure 4 presents the change in lattice energy with change in molecular volume for compounds crystallizing in lattices of the fluorite, cesium chloride, wurtzite, and zinc blende types.

Fig. 3. Change in ion concentration with lattice energy for oxides, some metals crystallizing in lattices of the NaCl type, and for alkali-halide compounds.

Let us note two interesting results: with decreasing molecular volume and polarizability of compounds crystallizing in lattices of the rock-salt, cesium chloride, zinc blende, fluorite, and wurtzite types, the—

Dependence of molecular volume on lattice energy for compounds crystallizing in lattices of the following types:
○○○ — rock salt,
△△△ — fluorite,
●●● — cesium chloride,
××× — wurtzite,
✳✳✳ — zinc blende.

Fig. 4.

... is determined by the lattice energy. Among the compounds we have considered, the greatest lattice-energy values are possessed by compounds crystallizing in a wurtzite-type lattice, and the smallest by crystals with a cesium chloride-type lattice. The lattice energy increases as the crystal lattice becomes more complex.

Fig. 5. Dependence of the melting temperature on the lattice energy for compounds crystallizing in a CsCl-type lattice.

In addition, having examined the nature of the change in lattice energy as a function of other properties of crystals, it is interesting to note that the same dependence between the lattice energy and the refractive index is preserved for fluorite-type crystals as for alkali-halide crystals of the rock-salt type. As the lattice energy increases, the refractive index decreases. With an unchanged cation, the refractive index and polarizability of fluorides prove to be smaller than those of chlorides.

Dependence of the heat of formation on the lattice energy for compounds crystallizing in lattices of the following types:

○○○ — NaCl,
◇◇◇ — wurtzite,
●●● — zinc blende,
××× — fluorite,
◉◉◉ — nickel,

Fig. 6.

With a change in lattice energy, the thermal stability of crystals also changes; it increases with increasing crystal-lattice energy.

Figure 5 presents the dependence of the melting temperature on the lattice energy for alkali-halide compounds crystallizing in a cesium-chloride-type lattice. With increasing lattice energy, the melting temperature increases. Also, with increasing lattice energy, the specific heat of compounds crystallizing in fluorite- and cesium-chloride-type lattices increases, as is observed for alkali-halide salts crystallizing in an NaCl-type lattice.

From Fig. 6 it can be seen that, with increasing heat of formation of compounds forming crystal lattices of various types, the lattice energy of the crystals increases.

The results of the investigations show that the regular changes noted earlier in the physicochemical, thermal, and also the related electrical properties [5] with change in lattice energy for rock-salt-type crystals can be extended more broadly to ionic crystals of other lattice types as well. This circumstance may make it possible, from the magnitude of the lattice energy, to judge important qualities of insulating materials and to choose the direction for designing dielectrics with predetermined properties.

REFERENCES

1. Vorob’ev A. A. and Zavadovskaya E. K. DAN, 81, 3, 1951.
2. Kapustinskii A. F. Advances in Physical Chemistry, 5, 59, 1934.
3. Zavadovskaya E. K. DAN, XXIII, 5, 709, 1952.
4. I. R. Tessman, A. H. Kahn and W. Schockly. Phys. Rev. 92, 4, 890, 1953.
5. Vorob’ev A. A. and Zavadovskaya E. K. ZhFKh, XXVIII, 7, 1210, 1954.