Octahedral radii

Octahedral Radii.—In pyrite (Fig. 7-8) each iron atom is surrounded by six sulfur atoms, which are at the corners of a nearly regular octahedron, corresponding to the formation by iron of 3d 24 4p bonds. The iron-sulfur distance is 2.27 A. from which, by subtraction of the tetrahedral radius of sulfur, 1.04 A, the value 1.23 A for the cPsp9 octahedral covalent radius of bivalent iron is obtained (Table 7-15). 

From similar data for other crystals with the pyrite structure or a closely related structure (of the marcasite or arsenopyrite types), given 

For all of these atoms the number of electrons is such that all of the stable orbitals are occupied by unshared pairs or are used in bond formation. In CoS2, Co e2, NiAsR. and AuSb2 the atoms Co(II), Ni(IIl), and Au(IV) contain one more electron than can be fitted into the three 3d orbitals (5d for Au) that are left after the Psp orbitals are usurped 

Tabus 7-16.—-Intbhatomic Distances in Pykite-Ttpe Ckystals 

Substance Distance M- -X Radius of M Substance 1 distance M—X Radius of M 

---

Octahedral Radii from Pyrite-type Cry stales. 

Standard Octahedral Radii (from Pyrite-type Crystals). 

Additional Octahedral Radii. From the d obs values in Table XIB the following approximate octahedral radii are deduced. 

The octahedral radii of the table are applicable to complex ions such as [PtCle]—. The radius sum Pt(IV)—Cl is 2.30 A, and the several reported experimental values for salts of chloroplatinic acid range from 2.26 A to 2.35 A. The radii can also be applied to the sulfides, selen-ides, and tellurides of quadrivalent palladium and platinum (PdS2, etc.), which crystallize with the cadmium iodide structure, consisting of layers of MX octahedra so packed together that each X is common to three octahedral complexes. The average deviation between radius sums and reported distances for these substances is about 0.02 A. 

From the observed values of interatomic distances in complex ions such as [SnCh]—, [PbBr0], and [SeBr ]— and from crystals such as TiS2 with the cadmium iodide structure the octahedral radii given in Table 7-17 have been obtained. These correspond not to cPsp bonds, involving d orbitals of the shell within the valence shell, but to sp d2 orbitals, use being made of the unstable d orbitals of the valence shell itself. 

Fig. 11-9.—Metallic radii for the elements oi the first long period and the second long period. Values of octahedral radii and tetrahedral radii are also represented.

That this interpretation is reasonable is indicated by a comparison with the octahedral radii of iron, cobalt, and nickel, indicated in Figure 11-9 by squares, with the oxidation numbers also shown. The smaller octahedral radii correspond to d2sp8 orbitals, with 33 percent d character, and the radii that are about 0.10 greater correspond to dsp orbitals, with 20 percent d character. It is evident that there is a rapid decrease in single-bond radius with increase in the amount of d character... 

Figure 7.6 Activation energies of ionic diffusion in p-alumina crystals [63] versus octahedral radii ofthe mobile ions [64].

We consider first the effect of -orbital splittings on the variation of ionic radii with atomic number in a series of ions of the same charge. We shall use as an example the octahedral radii of the divalent ions of the first transition series. Fig. 20-27 shows a plot of the experimental values. The points for Cr2H and Cu2+ are indicated with open circles because the Jahn-Teller effect, to be discussed below, makes it impossible to obtain these ions in truly... 

The three widely used types of covalent radii are the normal (rnor), the tetrahedral (rte), and the octahedral (roc) ones rnor is defined as half the single-bond distance in a homo-atomic molecule with = v, and rte as half the bond distance in a diamondlike structure, hence r or = rte for tetravalent elements. The systems of tetrahedral and octahedral radii have been first introduced by Huggins and Pauling [128-131, 139-142], who observed that rte < r nor for nonmetals while rte > rnor for metals. The difference can be qualitatively explained by the fact that metals have fewer than 4 outer electrons, hence an increase of from 1 to 4 is bound to reduce the number of electrons per bond, while nonmetals have enough outer electrons to provide for all these bonds. 

---