The covalent bond in diamond

Abstract

The generalized X -ray structure factor described in the preceding paper is used in an electron distribution study of the covalent bond in diamond. Numerical analysis is based on the X -ray powder measurements of G‪‪‪‪‪‪‪‪‪öttlicher & W‪‪‪‪‪‪‪‪‪ölfel and on Renninger’s measurement of the ‘forbidden’ reflexion 222. The T d symmetry of the atomic sites in diamond is used to express the charge distribution of the bonded atom as a simple sum of components consisting of radial functions combined with the appropriate Kubic Harmonics (KH) of Von der Lage & Bethe. The analysis is conducted in terms of the f (exp) values which typify the bonded-atom scattering power at room temperature. It is assumed that contributions to f (exp) made by the spherical component of the total bonded-atom charge distribution can be accurately described by combining ( a ) the theoretical f̄ values given by the Hartree—Fock approximation to the spherically averaged distribution of the isolated atom in its ground state with ( b ) the isotropic temperature factor exp (─0.20 sin 2 θ/λ 2 ). The non-spherical features of f (exp) reveal two other important components in the total distribution of the bonded atom. The major component, possessing antisymmetric character, combines the third order KH with the radial function F 3 ( r ) = 7.5 r 2 exp (─2.2 r 2 ): this component accounts quantitatively for the 222 reflexions and for the grosser nonspherical features of f (exp) for odd-index reflexions. The subsidiary component, of cubic (centro-) symmetry, combines the fourth order KH with the function G 4 ( r ) = -2.0 r 2 exp (─ 2⋅2 r 2 ): this accounts for finer nonspherical features of f (exp) for both odd- and even-index reflexions. These two nonspherical components are associated directly with the covalent bond in diamond. Their origin lies in an electron redistribution of the spherical unbonded atom involving only 0.087 electron per bond. It is shown that the covalent bond corresponds to a mid-bond peak of +0.64 e/Å 3 . Fourier representations of the bonding redistribution in (11̄0) of the structure are presented. It is shown that the f (exp) values for sin θ/λ < 0⋅7 Å -1 allow the electron density associated with covalent bonding to be resolved to a standard deviation of ca . 0.018 e/Å 3 .