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Determination of the Onset of Structural Transitions in Condensed Matter through Coarse Molecular Dynamics

Miguel A. Amat, University of Massachusetts, Amherst, 686 North Pleasant Street; 214 Goessmann Laboratory, Amherst, MA 01003, Yannis G. Kevrekidis, Princeton University, Department of Chemical Engineering, Princeton, NJ 08544, and Dimitrios Maroudas, University of Massachusetts, Department of Chemical Engineering, Amherst, MA 01003.

Accurate determination of the onset of structural transitions in complex physical systems is of crucial importance in condensed matter physics and materials science and engineering. As direct access to such physical responses is typically difficult to attain experimentally, computational techniques such as molecular dynamics (MD) have become powerful tools for probing the underlying atomic-scale dynamics and determining the transition onsets. One of the most attractive features offered by MD lies in its ability to ultimately relate atomistic dynamics to macroscopically observable physical behavior; however, computing the evolution of all of the atomic coordinates over coarse time scales poses a severe limitation to the method. In recent years, novel methods, such as hyperdynamics, transition path ensemble approaches, metadynamics, and coarse molecular dynamics (CMD), have been developed to address long-time dynamics issues directly through atomistic simulation. In CMD, coarse-grained information is estimated on the fly from many short and properly initialized independent replica MD simulations. This information can then be used to identify transition points in the physical behavior of the complex systems under consideration. The method is based on the description of the evolution of the probability density, P(Ψ,t), approximated by a Fokker-Planck equation where Ψ(t) is an appropriate coarse-grained observable that describes the state of the system.

In this presentation, we demonstrate the capabilities of CMD to determine the onset of structural transitions in condensed matter by analyzing the thermodynamic (heterogeneously nucleated) and mechanical (homogeneously nucleated) melting of crystalline silicon, as well as stress-induced structural transitions in crystals under hydrostatic loading. In the study of melting, we reconstruct the underlying effective free-energy landscape and calculate the effective free energy difference between the molten and solid states as a function of temperature; in conjunction with a phase coexistence criterion, this leads to an efficient and accurate determination of the melting temperature (as compared with predictions from long MD simulations). In the study of stress-induced structural transformations, we also obtain the effective free-energy landscape and determine its relation to the structural stability of the corresponding solid phases. We focus on bcchcp lattice transformations and aim at identifying the loading conditions that mark the onset of such transformations. We demonstrate that the CMD approach is quite general and may be helpful in determining other important types of structural-transition onsets in condensed matter, including order-to-disorder (e.g., solid-state amorphization) and disorder-to-order (e.g., crystallization) transitions. Selecting appropriate coarse-grained variables is crucial to the success of this approach; in this presentation, special emphasis is placed on the choice of such variables in the structural-transition problems analyzed.