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Title: Crystal-liquid interfacial free energy via thermodynamic integration

Abstract

A novel thermodynamic integration (TI) scheme is presented to compute the crystal-liquid interfacial free energy (γ{sub cl}) from molecular dynamics simulation. The scheme is applied to a Lennard-Jones system. By using extremely short-ranged and impenetrable Gaussian flat walls to confine the liquid and crystal phases, we overcome hysteresis problems of previous TI schemes that stem from the translational movement of the crystal-liquid interface. Our technique is applied to compute γ{sub cl} for the (100), (110), and (111) orientation of the crystalline phase at three temperatures under coexistence conditions. For one case, namely, the (100) interface at the temperature T = 1.0 (in reduced units), we demonstrate that finite-size scaling in the framework of capillary wave theory can be used to estimate γ{sub cl} in the thermodynamic limit. Thereby, we show that our TI scheme is not associated with the suppression of capillary wave fluctuations.

Authors:
;  [1]
  1. Institut für Theoretische Physik II: Soft Matter, Heinrich Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf (Germany)
Publication Date:
OSTI Identifier:
22419961
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CAPILLARIES; CRYSTALS; FLUCTUATIONS; FREE ENERGY; INTERFACES; LIQUIDS; MOLECULAR DYNAMICS METHOD; SIMULATION

Citation Formats

Benjamin, Ronald, and Horbach, Jürgen, E-mail: horbach@thphy.uni-duesseldorf.de. Crystal-liquid interfacial free energy via thermodynamic integration. United States: N. p., 2014. Web. doi:10.1063/1.4891220.
Benjamin, Ronald, & Horbach, Jürgen, E-mail: horbach@thphy.uni-duesseldorf.de. Crystal-liquid interfacial free energy via thermodynamic integration. United States. doi:10.1063/1.4891220.
Benjamin, Ronald, and Horbach, Jürgen, E-mail: horbach@thphy.uni-duesseldorf.de. Mon . "Crystal-liquid interfacial free energy via thermodynamic integration". United States. doi:10.1063/1.4891220.
@article{osti_22419961,
title = {Crystal-liquid interfacial free energy via thermodynamic integration},
author = {Benjamin, Ronald and Horbach, Jürgen, E-mail: horbach@thphy.uni-duesseldorf.de},
abstractNote = {A novel thermodynamic integration (TI) scheme is presented to compute the crystal-liquid interfacial free energy (γ{sub cl}) from molecular dynamics simulation. The scheme is applied to a Lennard-Jones system. By using extremely short-ranged and impenetrable Gaussian flat walls to confine the liquid and crystal phases, we overcome hysteresis problems of previous TI schemes that stem from the translational movement of the crystal-liquid interface. Our technique is applied to compute γ{sub cl} for the (100), (110), and (111) orientation of the crystalline phase at three temperatures under coexistence conditions. For one case, namely, the (100) interface at the temperature T = 1.0 (in reduced units), we demonstrate that finite-size scaling in the framework of capillary wave theory can be used to estimate γ{sub cl} in the thermodynamic limit. Thereby, we show that our TI scheme is not associated with the suppression of capillary wave fluctuations.},
doi = {10.1063/1.4891220},
journal = {Journal of Chemical Physics},
number = 4,
volume = 141,
place = {United States},
year = {Mon Jul 28 00:00:00 EDT 2014},
month = {Mon Jul 28 00:00:00 EDT 2014}
}
  • Cited by 3
  • The interfacial free energy between a crystal and a fluid, γ{sub cf}, is a highly relevant parameter in phenomena such as wetting or crystal nucleation and growth. Due to the difficulty of measuring γ{sub cf} experimentally, computer simulations are often used to study the crystal-fluid interface. Here, we present a novel simulation methodology for the calculation of γ{sub cf}. The methodology consists in using a mold composed of potential energy wells to induce the formation of a crystal slab in the fluid at coexistence conditions. This induction is done along a reversible pathway along which the free energy difference betweenmore » the initial and the final states is obtained by means of thermodynamic integration. The structure of the mold is given by that of the crystal lattice planes, which allows to easily obtain the free energy for different crystal orientations. The method is validated by calculating γ{sub cf} for previously studied systems, namely, the hard spheres and the Lennard-Jones systems. Our results for the latter show that the method is accurate enough to deal with the anisotropy of γ{sub cf} with respect to the crystal orientation. We also calculate γ{sub cf} for a recently proposed continuous version of the hard sphere potential and obtain the same γ{sub cf} as for the pure hard sphere system. The method can be implemented both in Monte Carlo and Molecular Dynamics. In fact, we show that it can be easily used in combination with the popular Molecular Dynamics package GROMACS.« less
  • The crystal–liquid interfacial free energy γ has been calculated as a function of the crystal orientation in a molecular dynamics experiment in a system of Lennard-Jones (LJ) particles with a cutoff radius of the potential r{sub c}{sup *}=r{sub c}/σ=6.78 at a triple-point temperature T{sub t}{sup *}=k{sub B}T{sub t}/ε=0.692 and temperatures above (in the region of the stable coexistence of liquid and solid phases) and below (metastable continuation of the coexistence curve of liquid and solid phases) the temperature T{sub t}{sup *}. At T{sup *}=T{sub t}{sup *}, for determining γ use was made of the method of cleaving potential. The temperaturemore » dependence of γ on the crystal–liquid coexistence curve has been determined by the Gibbs-Cahn thermodynamic integration method. In the region of stable phase coexistence (T{sup *}>T{sub t}{sup *}) good agreement with the data of Davidchack and Laird [J. Chem. Phys. 118, 7651 (2003)] has been obtained with respect to the character of the temperature dependence of γ and the orientation anisotropy. In the region of metastable phase coexistence (T{sup *}« less
  • Abstract not provided.