the characteristics of atoms that permit the approximate evaluation of interatomic distances in substances. According to quantum mechanics an atom does not have definite boundaries, but the probability of finding an electron at a given distance from the atomic nucleus, starting from a certain distance, decreases very rapidly. Consequently it is possible to assign some approximate dimension to an atom. For all atoms this dimension is on the order of 10-8 cm—that is, 1 Å or 0.1 nanometer. Experimental data show that by adding the values of the quantities called the atomic radii for atoms A and B, it is possible in many cases to obtain the value of the interatomic distance AB in chemical compounds and crystals which is close to the true value. This property of interatomic distances, known as additivity, justifies the use of atomic radii. The latter are subdivided into metallic and covalent radii.
The metallic radius is taken to be half the shortest interatomic distance in the crystalline structure of a metallic element. It is a function of the number of neighbors closest to the atom in the structure (the coordination number K). If the atomic radius K = 12 (this is a value frequently encountered in metals) is taken to be 100 percent, then for K = 8, 6, and 4 the atomic radii will be 98, 96, and 88 percent respectively. The atomic radii of metals are used to predict the possibilities of formation and analysis of the structures of alloys and intermetallic compounds. Thus, the close agreement of atomic radii is a necessary but insufficient condition for the mutual solubility of metals according to the kind of substitution: magnesium (atomic radius 1.60 Å) forms solid solutions over a wide range with lithium (1.55 Å) and practically none with sodium and potassium (1.89 Å and 2.36 Å). The additivity of atomic radii makes it possible to predict roughly the lattice parameters of intermetallic compounds (for example, on the tetragonal structure β-AlCr2, calculation gives a = 3.06 Å and c = 8.60 Å; the corresponding experimental values are 3.00 Å and 8.63 Å).
Covalent radii are half the length of the single bonds X—X where X is a nonmetallic element. Thus, for instance, in the case of the halogens the atomic radii are half the interatomic distances in the molecules X2, for sulfur and selenium in the molecules of Xg, and for carbon they are half the length of the bond in the crystal structure of diamond or in molecules of saturated hydrocarbons. An increase in the multiplicity of the bonds (such as in the molecules of benzene, ethylene, and acetylene) results in a reduction of their lengths which is sometimes taken into account by introducing a suitable correction. The approximate realization of additivity for covalent radii makes it possible to calculate their values for metals (from the lengths of Me—X covalent bonds, where Me is a metal). In some studies, by comparing the experimentally determined Me—X distances with the sums of the covalent radii and the ionic radii, the degree of ionicity of bonds can be judged. However, the interatomic distances X—X and Me—X are materially dependent on the valence state of the atoms. The latter diminishes the universality of covalent radii and limits the possibility of their use.
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Zhdanov, G. S. Fizika tverdogo tela. Moscow, 1962.
Kitaigorodskii, A. I. Organicheskaia kristallokhimiia. Moscow, 1955.
Bastiansen, O., and M. Traetteberg. “The Nature of Bonds Between Carbon Atoms.” Tetrahedron, 1962, vol. 17, no. 3.
P. M. ZORKII