Tetrahedral bond radii

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. 

With this structure the nickel atom lias achieved the krypton electron configuration its outer shell contains five unshared pairs (in the five M orbitals) and five shared pairs (occupying the 4s4p3 tetrahedral bond orbitals). The Ni—C bond length expected for this structure is about 2.16 A, as found by use of the tetrahedral radius 1.39 A obtained by extrapolation from the adjacent values in Table 7-13 (Cu, 1.35 A Zn, 1.31 A). 

The Be—C bridge bonds are considerably longer than the single Be—C bonds in monomeric dimethylberyllium or di-fert-butylberyllium = 1.70 A (see below), and 0.10 A longer than the sum of the tetrahedral covalent radii of Be and C = 1.83 A. The Be—Be distance on the other hand is slightly shorter than twice the tetrahedral covalent radius of Be =... 

In this compound, too, the intemuclear distances indicate that bonding between the metal atoms is important The Al-Al distance is only 0.10 A more than the value calculated for a single bond by doubling the tetrahedral covalent radius, and 0.24 A less than the Al—Al distance in the metal The Al—Cb bonds on the other hand are 0.18 A longer than the Al—Cj bonds. The latter are equal to the Al—C single-bond value 1.96 A, calculated from the tetrahedral covalent radii of carbon and aluminum and the revised Schomaker-Stevenson mle. 

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. 

It is interesting that a straight line drawn through the tetrahedral radii passes through the metallic radius for calcium this suggests that the metallic bonding orbitals for calcium are sp orbitals, and that those for scandium begin to involve d-orbital hybridization. 

There are two forms of zinc sulfide that have structures known as wurtzite and zinc blende. These structures are shown in Figures 7.7a and 7.7b. Using the ionic radii shown in Table 7.4, we determine the radius ratio for ZnS to be 0.39, and as expected there are four sulfide ions surrounding each zinc ion in a tetrahedral arrangement. Zinc has a valence of 2 in zinc sulfide, so each bond must be 1/2 in character because four such bonds must satisfy the valence of 2. Because the sulfide ion also has a valence of 2, there must be four bonds to each sulfide ion. Therefore, both of the stmctures known for zinc sulfide have a tetrahedral arrangement of cations around each anion and a tetrahedral arrangement of anions around each cation. The difference between the structures is in the way in which the ions are arranged in layers that have different structures. 

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