The Role of Chaos in Molecular Dynamics. B.J. Reardon and J. Kieffer, Department of Materials Science and Engineering, University of Illinois, Urbana, IL 61801

A key element in understanding the mechanisms of thermally activated processes in condensed matter, is the ability to establish the relationship between the elementary degrees of freedom for motion and the structure within which these processes take place. For example, in the framework of classical statistical thermodynamics, the probability for an irreversible atomic displacement is expressed as a function of the free energy difference between the ground state and an activated state, where each of these states is derived from the structural description of the substance. While this approach sets a precedent for a static configuration to provide clues as to the mobility of its structural entities, the challenge remains to expand such formalisms to include situations which involve highly disordered structures, such as the diffusive mass transport in liquids, ionic conduction in amorphous electrolytes, and phase transformations.

The concepts and formalisms of chaos theory facilitate a novel approach to the subject. In this context, irreversible atomic displacements are regarded as a departure from an attractor in the phase space representation of the Hamiltonian system. Such an event is characterized by intermittend chaotic behavior, and hence, the chance for it to occur can be estimated by using the Lyapunov exponents and Kolmogorov entropy for the dynamical system.

Phase space trajectories of atomic configurations have been generated using classical molecular dynamic simulations. As a model system we chose alkali halides, because of the high accuracy with which their physical properties can be reproduced, using central interaction potential functions. The usefulness of this analysis will be illustrated using two case studies:

(i) Accurate qualitative and quantitative predictions with regard to the stability ranges of crystalline alkali halide polymorphs can be made. These stability ranges are delimited by the pressure induced phase transformation between rock salt and CsCl polymorphs on one side, and melting or sublimation on the other side.

(ii) The diffusive motion in sodium chloride melts can be described by means of a direct relationship with the dominant escape rate from the attractors corresponding to the average configuration at a given temperature.