Tight-binding calculation of the elastic constants of fcc and hcp transition metals

The elastic constants of face-centered-cubic and hexagonal-close-packed structures are calculated within an empirical tight-binding d-band model. The variation with band filling of the shear elastic constants is in contrast with the roughly parabolic behavior of the bulk modulus, cohesive energy, and atomic volume. The general trends are in very good agreement with available experimental and ab initio data. In particular, the model accounts for the anomalous stiffening of C and C44 observed experimentally in Rh and Ir, as well as the negative value of C for elements of groups 5 and 6 in the hypothetical fcc structure as predicted by ab initio calculations. Using the recursion method we show that these trends are reproduced within the fifth-moment approximation of the density of states. Pronounced minima are the other main features in the elastic-constant curves. They occur when the Fermi level passes through sharp peaks in the density of states and are due to strain-splitting effects.