(384h) Efficient Calculation of Solid-Fluid and Solid-Solid Coexistence, Including Consideration of Point Defects

Moustafa, S., University at Buffalo, The State University of New York
Kofke, D. A., University at Buffalo, The State University of New York
Schultz, A. J., University at Buffalo, The State University of New York

Thermodynamic stability of crystals is a topic of growing importance to a number of solid-state and nano-material applications of molecular modeling.  This includes molecular crystals, (especially pharmaceuticals), alloys, refractory materials, clathrate hydrates, colloids,  nanoparticles, and more. Some of these systems are amenable to the application of ab initio methods for calculating the molecular energy, and thus promise a first-principles approach to prediction of stable crystal structures. In other cases, the ``molecules" are models for nanoparticles, and the aim is to determine the structures that they will adopt via self-assembly. In any case, the crystal structure determines all other material properties, so knowledge of it for a given model is crucial to almost all materials applications.  In many cases there are a large number of candidate structures that can be adopted at equilibrium, and identification of the most stable crystal structure is performed via reference to the thermodynamic free energy.  Accordingly, it is important to have efficient methods to compute free energies for crystalline phases, and methods that work well for fluids often fail in this application. 

In previous work [1, 2],  we demonstrated that crystal free energies could be computed very efficiently using an interacting harmonic reference, following a path from low to high temperature, and using overlap sampling free-energy perturbation coupled with harmonically targeted perturbations in temperature. Such methods are inapplicable to hard potentials, which are of interest in modeling of nanoparticles and colloids. In the present work, we consider methods for such systems. We emphasize a quantitative comparison of the performance of the methods, using the hard sphere system as a prototype, and aiming to determine the most efficient scheme to evaluate the absolute free energy precisely in the shortest time. We find, for example, that the widely-used Frenkel-Ladd method is not the best approach to apply, and that other techniques can be as much as an order of magnitude more efficient in determining the free energy.
Another feature of phase equilibria of solids, and not seen in fluids, is the role of defects on behavior. Point defects are present in equilibrium solids, and can have an influence on properties disproportionate to their concentration.  While methods have been developed to evaluate defect concentrations, they are cumbersome to apply.  Here we present an approach that permits rapid evaluation of defect concentrations across a range of coexistence conditions. We demonstrate with the penetrable sphere model, which exhibits equilibrium between a fluid phase and a solid with vacancies, and between multiple-occupancy solids, and thus for which point defects are particularly important to the behavior.