Radii, metals

The crystal stmeture and stoichiometry of these materials is determined from two contributions, geometric and electronic. The geometric factor is an empirical one (8) simple interstitial carbides, nitrides, borides, and hydrides are formed for small ratios of nonmetal to metal radii, eg, < 0.59. 

Figure 3. The lattice parameter for the family of rock-salt structure actinide-antimonide compounds is shown where the line is for the corresponding lanthanide compounds. The metallic radii for the light actinide elements are plotted. The smooth line simply connects Ac to the heavy actinides. In both cases the smooth line represents the ideal tri-valent behavior.

Because the metallic radii of the d-block elements are all similar, they can form an extensive range of alloys with one another with little distortion of the original crystal structure. An example is the copper-zinc alloy used for some copper coins. Because zinc atoms are nearly the same size as copper atoms and have simi-... 

In the discussion of metallic radii we may make a choice between two immediate alternative procedures. The first, which I shall adopt, is to consider the dependence of the radius on the type of the bond, defined as the number (which may be fractional) of shared electron pairs involved (corresponding to the single, double, and triple bonds in ordinary covalent molecules and crystals), and then to consider separately the effect of resonance in stabilizing the crystal and decreasing the interatomic distance. This procedure is similar to that which we have used in the discussion of interatomic distances in resonating molecules.7 The alternative procedure would be to assign to each bond a number, the bond order, to represent the strength of the bond with inclusion of the resonance effect as well as of the bond type.8... 

Values of Single-bond Radii and Metallic Radii for Coordination Number 12... 

In applying the metallic radii in the discussion of the structure of a metal or intermetallic compound either the observed distances may be used with the single-bond radii to calculate the bond numbers, the sums of which may then be compared with the expected valences, or the distances may be compared with the sums of radii for suitable coordination numbers, such as CN12. The correction to be added to i (CN12) to give the radius for another coordination number, the va-... 

In Figs. 2, 3 and 4 the single-bond metallic radii are plotted against atomic number, together... 

The curve of single-bond metallic radii for the elements of the first long period has a characteristic appearance (Fig. 3) which must be attributed in the main to variation in the type of bond orbital. The rapid decrease from potassium to chromium results from increase in bond strength due to increasing s-p and d-s—p hybridization. The linear section of the curve from chromium to nickel substantiates the assumption that the same bonding orbitals (hybrids of 2.56 3d orbitals, one 4s orbital, and 2.22 4p orbitals) are effective throughout this series. The increase in radius from nickel to copper is attributed not... 

The radii for the elements of the two short periods are shown in Fig. 2. The metallic radii for the elements sodium to silicon lie on a common smooth curve with the normal covalent radii silicon to chlorine. Also the curve of the metallic... 

After rising at copper and zinc, the curve of metallic radii approaches those of the normal covalent radii and tetrahedral covalent radii (which themselves differ for arsenic, selenium, and bromine because of the difference in character of the bond orbitals, which approximate p orbitals for normal covalent bonds and sp3 orbitals for tetrahedral bonds). The bond orbitals for gallium are expected to be composed of 0.22 d orbital, one s orbital, and 2.22 p orbitals, and hence to be only slightly stronger than tetrahedral bonds, as is indicated by the fact that R(l) is smaller than the tetrahedral radius. 

The octahedral d2sp3 covalent radii for Fe11, Co111, and NiIV are seen to lie on a straight line parallel to and just 0.06 A. above the line of the metallic radii. This is reasonable in consideration of the decreased contribution of d orbitals to the bonding. A roughly linear relation is found to hold between the radius (corrected to atomic... 

The resonating-valence-bond theory of metals discussed in this paper differs from the older theory in making use of all nine stable outer orbitals of the transition metals, for occupancy by unshared electrons and for use in bond formation the number of valency electrons is consequently considered to be much larger for these metals than has been hitherto accepted. The metallic orbital, an extra orbital necessary for unsynchronized resonance of valence bonds, is considered to be the characteristic structural feature of a metal. It has been found possible to develop a system of metallic radii that permits a detailed discussion to be given of the observed interatomic distances of a metal in terms of its electronic structure. Some peculiar metallic structures can be understood by use of the postulate that the most simple fractional bond orders correspond to the most stable modes of resonance of bonds. The existence of Brillouin zones is compatible with the resonating-valence-bond theory, and the new metallic valencies for metals and alloys with filled-zone properties can be correlated with the electron numbers for important Brillouin polyhedra. 

Table 6. Metallic radii oe elements of the ascending branches...

Goldschmidt (1926) grouped metals and covalent crystals together, and Bernal (1929) pointed out that many properties of metals indicate that metallic bonds are closely similar to covalent bonds. I developed this idea further (Pauling, 1938), and formulated a set of metallic radii in 1947, with use of the empirical equa-... 

The set of metallic radii and the equation permit the reasonably satisfactory discussion of observed interatomic distances in many intermetallic compounds. In some crystals, however, the simple application of the radii and the equation leads to disagreement with observation. 

This correction of i i for ligancy, together with the bond-number equation and a set of values of the new single-bond metallic radii, provides an improved system of correlating interatomic distances not only in metals and alloys but also in other crystals and molecules. 

It is possible to discuss the interatomic distances in relation to the valences of lead and thallium. From the system of metallic radii (Pauling, 1949) and the relation =DX-0-600 log n... 

The approximate correctness of the relative values of fav given in the table is supported by the observed values of the metallic radii. Values of R for ligancy 12 are shown in Figure 1, with a straight line with slope that represents the change in radius with atomic number for constant valence and type of orbital, as given in Figure 3 of an earlier paper.17 The points lie above the line by amounts that indicate a monotonic decrease in valence to both sides of molybdenum. 

Strong boron-transition metal interaction interatomic distances are shorter by 5-10%, as compared to the sum of the metal radii. 

Most of the known borides are compounds of the rare-earth metals. In these metals magnetic criteria are used to decide how many electrons from each rare-earth atom contribute to the bonding (usually three), and this metallic valence is also reflected in the value of the metallic radius, r, (metallic radii for 12 coordination). Similar behavior appears in the borides of the rare-earth metals and r, becomes a useful indicator for the properties and the relative stabilities of these compounds (Fig. 1). The use of r, as a correlation parameter in discussing the higher borides of other metals is consistent with the observed distribution of these compounds among the five structural types pointed out above the borides of the actinides metals, U, Pu and Am lead to complications that require special comment. 

Table 1. Correlation of Metallic Radii with the Existence of the Various Type Structures of the Higher Borides...

Figure 1. Metallic radii of rare-earth metals and cubic lattice parameters of the rare-earth hexaborides.

The actinide borides must be considered a special case. The metallic radii exhibited in the borides are correlated with the abilities of the metals to form various... 

Although Zr and Sc have close metallic radii, the former has the UB,2-type structure and the latter exhibits a tetragonal symmetry, but its structure is not Imown. This indicates that in the series of the metals able to form borides with UB,2-type structure the metallic radius of Zr corresponds to the lowest limit (t = 1.60 X 10 pm). 

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