Equilibrium Properties Of Solids Research Articles

To slip or not to slip?

Molecular dynamics (MD) simulations, in which materials are modelled on super-computers at the level of their interacting molecules, have become an invaluable tool for studying complex systems on microscopic scales. Many problems in condensed matter physics and chemistry, which have otherwise eluded experimental and theoretical analysis, have been resolved with MD techniques. For three decades, most applications of MD focused on equilibrium properties of solids, liquids, and other condensed systems. Recently, the availability of supercomputers has led to a proliferation of exciting studies involving inhomogeneous, non-equilibrium systems. New applications include studies of fluid dynamics, atomic force microscopy, micro-indentation and ‘stick–slip’ phenomena.

Correlated Einstein model for the equilibrium properties of solids

The correlated Einstein model (CEM) is a new approach to the problem of determining the equilibrium properties of anharmonic solids. It is based on the use of the zeroth-order term in an expansion for the average of a product of one- and two-particle functions, where the average is a classical canonical average for a system of independent Einstein oscillators. The parameters that characterize the oscillators are chosen so that the first- and second-order terms in the expansion vanish. A diagrammatic representation of the expansion is given. Explicit formulas for determining the Helmholtz free energy of a monatomic cubic crystal are given and are evaluated both for a Lennard-Jones and a $\frac{1}{{r}^{12}}$ potential. The results obtained are compared with available Monte Carlo values. The CEM is found to be at least as accurate as the uncorrelated-pairs approximation, the cell-cluster method, the simple cell model, and improved self-consistent phonon theory.