Soluble models of rate processes in periodic systems with many degrees of freedom.

Abstract

We show that the parameters of classical many-body rate theory can be evaluated exactly for activated processes in large, chainlike systems. The methods are applied to four simple systems which simulate, in some degree, activated atomic motions in crystals. Each is a linear chain of atoms interacting with near-neighbor forces. One represents evaporation of an adatom from a surface, one an interstitialcy migration, one a vacancy migration, and one the motion of the interface between two phases. Exact analytical calculation of the parameters of many-body rate theory, namely the activation energy and the effective, or attack, frequency are given for each model. The results illustrate the role of cooperative effects in atomic jumps. The commonly made assumption that the attack frequency for such jumps is the characteristic lattice-vibration frequency is shown to be valid in some conditions, but to be a very poor approximation in others. For the evaporating adatom the relative mass of the adatom is allowed to be arbitrary. It is found that the transition rate is proportional to the square root of the relative mass for very light atoms, but otherwise the relative mass enters in a more complicated way, and, in particular, the transition rate remainsmore » finite for an adatom of infinite mass.« less