Atomistic simulations of crystal-melt interfaces in a model binary alloy: Interfacial free energies, adsorption coefficients, and excess entropy
CA Becker and DL Olmsted and M Asta and JJ Hoyt and SM Foiles, PHYSICAL REVIEW B, 79, 054109 (2009).
Monte Carlo and molecular-dynamics simulations are employed in a study of the equilibrium structural and thermodynamic properties of crystal- melt interfaces in a model binary alloy system described by Lennard- Jones interatomic interactions with zero size mismatch, a ratio of interaction strengths equal to 0.75, and interspecies interactions given by Lorentz-Berthelot mixing rules. This alloy system features a simple lens-type solid-liquid phase diagram at zero pressure, with nearly ideal solution thermodynamics in the solid and liquid solution phases. Equilibrium density profiles are computed for (100)-oriented crystal- melt interfaces and are used to derive the magnitudes of the relative adsorption coefficients (Gamma((j))(i)) at six temperatures along the solidus/liquidus boundary. The values for Gamma((2))(1), the relative adsorption of the lower melting-point species (1) with respect to the higher melting point species (2), are found to vary monotonically with temperature, with values that are positive and in the range of a few atomic percent per interface site. By contrast, values of Gamma((1))(2) display a much more complex temperature dependence with a large peak in the magnitude of the relative adsorption more than ten times larger than those found for Gamma((2))(1). The capillary fluctuation method is used to compute the temperature dependence of the magnitudes and anisotropies of the crystal-melt interfacial free energy (gamma). At all temperatures we obtain the ordering gamma(100)>gamma(110)>gamma(111) for the high- symmetry (100), (110), and (111) interface orientations. The values of gamma monotonically decrease with decreasing temperature (i.e., increasing concentration of the lower melting-point species). Using the calculated temperature-dependent values of gamma and Gamma((2))(1) in the Gibbs adsorption theorem, we estimate that roughly 25% of the temperature dependence of gamma for the alloys can be attributed to interface adsorption, while the remaining contribution arises from the relative excess entropy S-xs((2)).
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