First-principles pseudopotential calculations of the elastic properties of diamond, Si, and Ge

The reason why diamond has much different elastic properties, in particular a much smaller Poisson ratio, compared with Si and Ge is investigated using an ab initio pseudopotential method within the local-density-functional formalism. Besides the Poisson ratios, the equilibrium lattice constants, bulk moduli, elastic constants, and internal strain parameters are calculated. Good agreement with experiment is obtained. In order to eliminate the effects of the equilibrium-volume difference among these crystals, the reduced-second-volume derivatives are introduced into the individual energy terms. It is clearly shown that the kinetic energy and the ion-electron interaction energy play important roles in the response to homogeneous volume change and to distortions, respectively. The charge-density distributions display much different responses to strains between diamond and the others.