ATOMISTIC SIMULATIONS INCORPORATING NONLINEAR ELASTICITY - SLOW-STRESS RELAXATION AND SYMMETRY-BREAKING

Complementary molecular-dynamics and Metropolis Monte Carlo algorithms for the atomistic simulation of crystals with imposed laboratory cond itions of temperature and tensorial pressure are presented. Inclusion of the nonlinear expression for the elastic energy of a crystal yields simulations that conserve the Gibbs potential of the crystal despite finite deformations. The molecular-dynamics equations of motion contai n an explicit expression of the virial theorem for nonlinear elastic m edia; the dynamical balance of the ''internal'' and ''external'' press ures includes the elastic response of the system to the applied stress . Thus the ''internal'' and ''external'' pressures remain in dynamical equilibrium even when the microscopic dynamics generate a phase trans formation and the initial isotropy of the macroscopic stress field is broken. Deterministic molecular-dynamics trajectories for a simple pai r-potential model of a pressure-induced martensitic transformation are presented; manifestly nonlinear behavior is observed while satisfying the tensorial virial theorem for nonlinear elastic media. Stochastic Monte Carlo trajectories yield comparable results, and independently v erify the nonlinear extension of the virial theorem. This is despite t he fact that the Monte Carlo algorithm contains no explicit driving te rms that insure the theorem be satisfied.