THE GRUNEISEN-PARAMETER - COMPUTER CALCULATIONS VIA LATTICE-DYNAMICS

Full lattice dynamical calculations on a monatomic cubic lattice have confirmed the linear relationship between the Gruneisen parameter and the first derivative of incompressibility with respect to pressure. The exact expressions are dependent upon the details of the simulation, but generally take the form [GRAPHICS] where gamma is the Gruneisen parameter, K is the bulk modulus, P is pressure and a and b are constants. In our atomistic simulation we considered pairwise additive Lennard-Jones and Morse potential models. We found that if we only considered short-range nearest neighbour forces, a and b take the values 0.50 and 0.90, respectively. This result differs from the forms of the well-known definitions of the Slater, Dugdale-Macdonald and Vaschenko-Zubarev (or free-volume) gamma, but provides an exact confirmation of the approximations used to obtain the Barron gamma. In order to determine the wider validity of such a simple model, further calculations considered long-range forces and the NaCl lattice. This resulted in a reduction in the values of both a and b in the case of the long-range interactions thereby approaching the free-volume formulation. However, no simple relation could be found in the case of the more complex NaCl structure, with no linearity existing between gamma and the pressure dependence of the shear modulus.