Simulation of Crystal-Melt Interfaces for a System of Binary Hard Spheres
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Simulation of Crystal-Melt Interfaces for a System of Binary Hard Spheres Rachel Sibug-Aga and Brian B. Laird Department of Chemistry, University of Kansas Lawrence, KS 66045, USA ABSTRACT Crystal-melt interfaces of binary hard spheres are investigated using molecular-dynamics simulation. For a diameter ratio α=0.414, two crystal phases coexisting with the fluid are possible, depending on the pressure. At low pressures, the liquid coexists with a pure fcc crystal of the larger particle, while at high pressures a 1:1 binary crystal of “NaCl” type is the coexisting phase. For both of these systems, we study the structural and dynamical changes as the interface is traversed from bulk crystal to bulk fluid through the calculation of density and diffusion coefficient profiles. It is observed that the total width of the interfacial region is narrower in the “NaCl”/binary fluid interface than in the corresponding lower pressure fcc/binary fluid system.
INTRODUCTION A detailed microscopic picture of the structure, dynamics and thermodynamics of interface between a crystal and its melt is essential in understanding nucleation, growth kinetics, and morphology of crystals grown from the melt. Computer simulations have become an important tool in the investigation of such crystal/melt interfaces, especially given the extreme difficulty (and lack) of direct experimental studies [1]. The hard sphere potential, despite its simplicity, is an important reference model for the study of simple liquids [2] and liquid mixtures [3]. This is especially true for the phenomena associated with freezing transition. For example, it has been recently shown that the interfacial free energy of close-packed metals can be described with quantitative accuracy using a hard sphere model [4]. Recent phase boundary calculations have shown that binary hard spheres form a wide range of crystal structures depending on the diameter ratio, α , of the small particles to the large particles. A substitutionally disordered fcc crystal is the stable phase for 1.0 > α > 0.85 [5] while only ordered crystal structures are seen to be stable for α < 0.85 [6-10]. A detailed study of the disordered fcc crystal/melt interface for α = 0.9 has been recently performed [11]. Here, we extend this work to binary hard spheres with considerably larger size asymmetry, given by α = 0.414 . The phase diagram for this system has been determined using MC and MD simulations [6]. (This size ratio is significant in that the small particles are the largest ones that can be accommodated in the interstitials of a densest packed fcc crystal of the larger ones). A pure fcc crystal of the large particles is stable at low pressures while the “NaCl” structure is stable at higher pressures. Earlier cell theory calculations also predicted the stability of the “NaCl” at this diameter ratio [7]. In this paper, we present a summary of the results of molecular dynamics simulations on the interface between each of these ordered cystal phases and their coexisting binary fluid. A more detailed discussi
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