A potential model for covalent crystals

A unified study of the static and dynamic properties of covalent crystals such as cohesive energy, equilibrium, elastic constants, variation of bulk modulus with pressure, the dispersion curve covalent bonding is presented. The well known two-body central Morse potential is taken to act between nearest neighbours. In addition, a three body interaction of Keating type is taken which depends on nearest neighbour distance and bond angles. For diamond the scheme works well; an agreement within 15% is achieved. However, for Si, Ge and α-Sn while the agreement for all the properties are good the characteristic flatness and low value of transverse accoustic (TA) frequencies near the zone boundary (z.b.) are not reproduced. Since z.b. Ta frequency depends on three body interaction parameter it is made wave vector dependent. A suitable wave vector dependence of the parameter reproduces the flatness. However, the agreement at certain wave vector are worsened e.g. at z.b. in (111) direction maximum error of the order of 30% occurs for LA mode. Since diamond is different from the other three, such a wave vector dependence is not introduced. (K.B.)