Radii, covalent metallic

Fig. 12.2 The ratio of radii, k (=ionic radius/covalent radius), for alkali metal eations (M ) and halide anions (X ) in aqueous solutions (Eqs. 12.6a, b). In the right angled triangle, ABC, E and D are the mid points of AB and AC...

It is valuable to be able to predict the internuclear distance of atoms within and between molecules, and so there has been much work done in attempting to set up tables of "atomic radii" such that the sum of two will reproduce the internuclear distances. Unfortunately there has been a proliferation of these tables and a bewildering array of terms including bonded, nonbonded, ionic, covalent, metallic, and van der Wauls radii, as well as the vague term atomic radii. This plethora of radii is a reflection of the necessity of specifying what is being measured by an atomic radius. Nevertheless, it is possible to simplify the treatment of atomic radii without causing unwarranted errors. 

The van der Waals radius, covalent radius and ionic radius are important parameters for metallic elements and features such as the lanthanide contraction have important chemical consequences. 

The crystal structure of a solid is determined by forces acting between its various components. These forces may be of the ionic, covalent, metallic or Van der Waals type. The relative strength of each contribution depends upon the position of the elements within the Periodic Table, i.e. upon their valence electron configuration and size. The higher the principal quantum number of the valence electrons, the less important is the specific character of the valence electrons and the structures then are mainly determined by the size and the radius ratio of the elements. 

Since the atomic sizes are different in the substances with different kinds of chemical bond. It is necessary to assign the atoms of elements three kinds of system of atomic radius. In ionic systems, we call the size of ions as ionic radius. In covalent compounds, system of covalent radius is used. And the atomic radius in metallic systems is called metallic radius of elements. In his classical work, Pauling has assigned the values of these three kinds of radius. Pauling s values of atomic or ionic radii have been widely used till now. But there are still other systems proposed by other authors in later years. 

Atomic radius refers to metallic radius for metals and covalent radius for nonmetals. Ionization energies refer to first ionization energy. Metallic character relates generally to the ability to lose electrons, and nonmetallic character to the ability to gain electrons. 

Shannon and Prewitt base their effective ionic radii on the assumption that the ionic radius of (CN 6) is 140 pm and that of (CN 6) is 133 pm. Also taken into consideration is the coordination number (CN) and electronic spin state (HS and LS, high spin and low spin) of first-row transition metal ions. These radii are empirical and include effects of covalence in specific metal-oxygen or metal-fiuorine bonds. Older crystal ionic radii were based on the radius of (CN 6) equal to 119 pm these radii are 14-18 percent larger than the effective ionic radii. 

Ionic bond, 287, 288 dipole of, 288 in alkali metal halides, 95 vs. covalent, 287 Ionic character, 287 Ionic crystal, 81, 311 Ionic radius, 355 Ionic solids, 79, 81, 311 electrical conductivity, 80 properties of, 312 solubility in water, 79 stability of, 311... 

In other crystals an octahedral metal atom is attached to six non-metal atoms, each of which forms one, two, or three, rather than four, bonds with other atoms. The interatomic distance in such a crystal should be equal to the sum of the octahedral radius of the metal atom and the normal-valence radius (Table VI) of the non-metal atom. This is found to be true for many crystals with the potassium chlorostannate (H 61) and cadmium iodide (C 6) structures (Table XIB). Data are included in Table XIC for crystals in which a tetrahedral atom is bonded to a non-metal atom with two or three covalent bonds. The values of dcalc are obtained by adding the tetrahedral radius for the former to the normal-valence radius for the latter atom. 

Other Covalent Radii. In Cu20 and Ag20 each metal atom is equidistant from two nearest oxygen atoms, the interatomic distances corresponding to the radius values 1.18 and 1.39 A for Cu1 and Agl with coordination number two. In KAg(GN)2, in which each silver atom is similarly attached to two cyanide groups1), the effective radius of Agl is 1.36 A. It has been pointed out to us by Dr. Hoard that the work of Braekken2) indicates the presence of strings —Ag—G=N—Ag—G... 

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... 

The values of f (l) given in the table for electronegative atoms are their normal covalent single-bond radii28 (except for boron, discussed below). The possibility that the radius 0.74 A. of Schomaker and Stevenson29 should be used for nitrogen in the metallic nitrides should be borne in mind. 

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... 

An equation has been formulated to express the change in covalent radius (metallic radius) of an atom with change in bond number (or in coordination number, if the valence remains constant), the stabilizing (bond-shortening) effect of the resonance of shared-electron-pair bonds among alternative positions being also taken into consideration. This equation has been applied to the empirical interatomic-distance data for the elementary metals to obtain a nearly complete set of single-bond radii. These radii have been compared with the normal covalent... 

Values of the reciprocal of the covalent radius for ligancy 12 are shown in Fig. 3. It is seen that the points for each sequence can be represented by three curves. The first curve for each sequence represents the effect of the increase in valence from 2 to 6 and the corresponding increase in binding energy for C to Cr, Sr to Mo, and Ba to W. Each of these curves is extrapolated to a maximum at v — 8.3, corresponding to nine spd orbitals with 0.7 metallic electron. It is seen that for all three sequences the values deviate from the extrapolated curves. From Cr to Ni they are represented by a straight line, interpreted as corresponding to the constant value 6 for the metallic valence. 

The amount of resonance energy for a metal or intermetal-lic compound is determined by" the number of resonance structures. The resonance energy affects the covalent radius, the stability (as evidenced by the resistance of the noble metals to chemical attack), and other properties, in ways that we hope to discuss later. 

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