An Empirical Correlation of Electron Density with Optical Susceptibility and Ionicity in Partly Ionic Diatomic Crystals

Abstract

The bond-charge interpretation of the Penn model and Phillips-Van Vechten theory [l to 31 has been applied to different optical phenomena in crystals (see, e.g. references in [4, 51). According to this approach the long-wavelength optical susceptibility is given by where up is the plasma frequency, C and E, are the heteropolar and homopolar constituents of the effective energy gap, respectively, and A is a correction factor. In ANBsPN compounds C is expressed as) exp (e), -k R where rcr and rp are the distances from the AN and B8-N atom to the centre of gravity of the bond charge, respectively, Z , and Z , denote the numbers of valence electrons, R = r, + r p is the bond length, k, is the Thomas-Fermi screening wave number, and the factor b is introduced to account for the deficiency of the free electron model [3, 61. The homopolar term depends on R as E, = A,R-S, with s 2.48. In the theory the ionicity of crystals is described by the parameter fi = C'/(C' + E;).The aim of this note is to discuss the relationship between the position of the bond charge and the refractive data in partly covalent diatomic crystals. Previously, Wemple [7] noted that the values of C and E , obtained employing the expression for A given by Penn had to be revised. Therefore in our calculations we have also checked how the choice of A effects these parameters.In the Penn model the optical susceptibility of the crystal originates from transitions from the valence to the conduction band or to the exciton state. Thus individual ionic polarizabilities have no well-defined meaning. However, a factor D has been introduced in (1) to account for the excitations of core electrons [3]. According to this picture the optical susceptibility stems from the excitations which are both interionic and intraionic in nature.