Atomic mean-square displacement of a solid: A Green’s-function approach

We have presented a Green’s-function method of calculating the atomic mean-square displacement (MSD) of a solid. The method effectively sums a class of all anharmonic contributions to the MSD. From the point of view of perturbation theory (PT) our expression for MSD includes the lowest-order (${\lambda }^2$) PT contributions (cubic and quartic) with correct numerical coefficients. The numerical results obtained by this method in the high-temperature limit for a fcc nearest-neighbor Lennard-Jones-solid model are in excellent agreement with the Monte Carlo (MC) method for the same model over the entire temperature range of the solid. Highly accurate results for the order-${\lambda }^2$ PT contributions to MSD are obtained by eliminating the uncertainty in the convergence of the cubic contributions in the earlier work of Heiser, Shukla, and Cowly and they are now in much better agreement with the MC results but still inferior to the Green’s-function method at the highest temperature.