Determination of the Charge Distribution in Nonmetallic Crystals II. Compounds with d‐orbitals. Corundum

Abstract

Abstract. A S.C.F. method using localized molecular orbitals, previously proposed to determine net charges in zincblende-and wurtzite-type crystals, has been adapted to the corundum case (AI 203-a )~. The presence of d -orbitals in hybrid atomic orbitals and the difference between coordination numbers give rise to some problems. Then, the choice of Slater-type orbital exponents, the introduction of corrective factors in the calculation of charges, the molecular orbitals orthogonalization and the introduction of Madelung-type constants are discussed. The net charge found for Al atoms (Q~0.57) is, given the hypotheses used in the calculation, in good agreement with the one (0.33) determined from an empirical relation connecting hardness and ionicity of a crystal.Although corundum is not as precious a stone as diamond, it is a much appreciated gem, because of its colours when metallic ion impurities are inserted: Fe." or Ti 4 + (blue sapphire), Cr" (ruby), Mn " (oriental amethyst), ... on the one hand, and for its high hardness (9 in Mohs' scale), on the other. In a recent paper, one of us' established a connection between hardness of a crystal and bond ionicity of the corresponding lattice, a high hardness corresponding to a strongly covalent framework. In order to define the degree of ionicity of a crystal, we generalized thewhere p,.,. and p.. respectively are the Mulliken electron population carried by the atomic orbitals X,. and X. used to build the bond molecular orbital. In a crystal with a stoichiometric composition MfJ.,N~", where M is the metal atom the coordination number of which in the lattice is II,., we define the ionicity as (2) where 0,. is the actual net point charge of the atom M and O~O) is the net point charge it would have if the lattice was perfectly ionic.On the other hand, we improved by smoothing the hardness Mohs' scale by a comparison with results obtained by various physical methods. Starting from some experimental and theoretical data we proposed an empirical relation between the improved hardness Hand ionicity as defined by relation (2):where p and q are the principal quantum numbers of the valence orbitals of the atoms M and N. In the corundum case (Ah03-a)~, H = 8.9 and by relation (3) we obtain OAI = 0.33, 00 = -0.22. These values look a priori small. But in quartz, for example, the hardness of which is 7.0. the charge on Silicon also obtained by relation (3) and by various theoretical calculations':' is about 3.0. For corundum we do not have any experimental data about charges. Therefore a theoretical determination of these charges presents a double interest: to obtain a correct estimation of these quantities on the one hand and to test relation (3) in the case of a mineral of strong hardness on the other. Indeed, we can find, in many high school books and even in University lectures, ions A1 3 + and 0 2 -to describe the structure of corundum. Therefore, even qualitatively, it is interesting to know whether we are closer to the ionic structure or to the covalent one. Moreover, now ...

Synchrotron X-ray study of the electron density in α-Al2O3

“…the band-structure calculation of Ciraci & Batra (1983) the A1 charge was + 1. The study of Julg, Pellegatti & Marinelli (1980) by a self-consistent field method gives an A1 charge of + 0.57, and + 0.33 was obtained from an empirical relation connecting hardness and ionicity of a crystal. On the other hand, the cluster MSX,~ approach (Nagel, 1985) gave +2.57 and an ab initio calculation (Salasco, Dovesi, Orlando, Causa' & Saunders, 1991) gave + 1.78.…”