# Atomic Radii

## Atomic Radii

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.

### REFERENCES

Bokii, G. B. Kristallokhimiia, 2nd ed. Moscow, 1960.
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

References in periodicals archive ?
This fact could be attributed to the phenomenon of activation energy "atomic diffusion that takes place during the sintering process." In agreement with the Hume-Rothery rule, the substitutional solution occurs when the relative difference between the atomic radii of the two species is less than 15%.
The difference of atomic radii between added elements and the silicon might be the dominant factor for the modification.
The alteration in lattice parameter was due to dominance of higher atomic radii [Mn.sup.2+] ions over [Co.sup.2+] ions whose atomic radii was small during comparision.
Although electroaffinity difference between theses metals (2.13 eV for Pt and 0.43 eV for Ga) and the difference between the structures (FCC for Pt and orthorhombic for Ga) can lead to formation of a new phase, the difference of 8% between the atomic radii (Pt, 139 pm, and Ga, 122 pm) and the same valence state of these metals does not rule out the formation of substitutional solid solution.
In other atoms the similar phenomenon is expected, because their atomic radii are greater than the Bohr one and therefore still greater than the finite elliptic ones:
May also be assumed that doubling of the microhardness of the Cu--1.7% Fe condensates, in comparison with the copper condensates, is too large and is not characteristics of the solid solution hardening of the metals by interstitial elements, especially if it is taken into account that the atomic radii of copper and iron are almost the same, i.e., the strength properties of the investigated Cu--Fe condensates are determined not only by the condition of the solid solution of iron in FCC copper but mostly by the characteristics of their microstructure.
Forming these alloys has been limited to elements close in atomic radii and electronegativity up until now," said Professor Rajeev Ahuja of UU.
The 89th edition continues the format of the past, with new tables added for atomic radii, composition and properties of common oils and fats, global warming potential of greenhouse gases, weather-related scales, energy content of fuels, properties of gas clathrate hydrates, melting curve of mercury, enthalpy of hydration of gases, and electrical resistivity of graphite materials.
In analogy with the finding of three dimensional periodic structures by fitting balls with atomic radii together, plausible quasiperiodic structures have been constructed by fitting atomic surfaces into six dimensional unit cells (28).
"Because of the differences in the atomic radii of silicon and magnesium, when the sheets fall one atop the other they grow into a hollow tube," Petrakis says.
The size of the atomic radii are 1.81, 1.71 and 1.53 A[degrees] for Pb, Cd and Zn, respectively, compared to the 0.79 A[degrees] for H.

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