Diffuse interface analysis of crystal nucleation in hard-sphere liquid

We show that the increase of the interface free energy with deviation from equilibrium seen in recent Monte Carlo simulations [S. Auer and D. Frenkel, Nature (London) 413, 711 (2001)] can be recovered if the molecular scale diffuseness of the crystal–liquid interface is considered. We compare two models, Granasy’s phenomenological diffuse interface theory, and a density functional theory that relies on the type of Ginzburg–Landau expansion for fcc nucleation, that Shih et al. introduced for bcc crystal. It is shown that, in the range of Monte Carlo simulations, the nucleation rate of the stable fcc phase is by several orders of magnitude higher than for the metastable bcc phase, seen to nucleate first in other fcc systems. The nucleation barrier that the diffuse interface theories predict for small deviations from equilibrium is in far better agreement with the simulations than the classical droplet model. The behavior expected at high densities is model dependent. Granasy’s phenomenological diffuse inter...

[1]  Shen,et al.  bcc Symmetry in the Crystal-Melt Interface of Lennard-Jones Fluids Examined through Density Functional Theory. , 1996, Physical review letters.

[2]  D. Frenkel,et al.  Prediction of absolute crystal-nucleation rate in hard-sphere colloids , 2001, Nature.

[3]  Santos,et al.  Structure of hard-sphere metastable fluids. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  Pusey,et al.  Observation of a glass transition in suspensions of spherical colloidal particles. , 1987, Physical review letters.

[5]  Andrew Schofield,et al.  Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization , 2001, Science.

[6]  Direct calculation of the hard-sphere crystal /Melt interfacial free energy , 2000, Physical review letters.

[7]  Wang,et al.  Ginzburg-Landau theory for the solid-liquid interface of bcc elements. , 1987, Physical review. A, General physics.

[8]  Clark,et al.  Nucleation and growth of colloidal crystals. , 1986, Physical review letters.

[9]  D. Oxtoby.  Crystallization: Diversity suppresses growth , 2001, Nature.

[10]  A. Gast,et al.  On the solid–fluid interface of adhesive spheres , 1993 .

[11]  L. Gránásy.  Fundamentals of the Diffuse Interface Theory of Nucleation , 1996 .

[12]  Daan Frenkel,et al.  Suppression of crystal nucleation in polydisperse colloids due to increase of the surface free energy , 2001, Nature.

[13]  K. Hall.  Another Hard‐Sphere Equation of State , 1972 .

[14]  László Gránásy,et al.  DIFFUSE INTERFACE THEORY FOR HOMOGENEOUS VAPOR CONDENSATION , 1996 .

[15]  J. McTague,et al.  Should All Crystals Be bcc? Landau Theory of Solidification and Crystal Nucleation , 1978 .

[16]  László Gránásy,et al.  Comparison of experiments and modern theories of crystal nucleation , 1997 .

[17]  L. V. Woodcock.  Computation of the free energy for alternative crystal structures of hard spheres , 1997 .

[18]  B. Mulder,et al.  Why all crystals need not be bcc: symmetry breaking at the liquid-solid transition revisited. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  L. Bartell.  Structure and transformation: Large molecular clusters as models of condensed matter. , 1998, Annual review of physical chemistry (Print).

[20]  V. Talanquer,et al.  Density Functional Analysis of Phenomenological Theories of Gas-Liquid Nucleation , 1995 .

[21]  R. L. Davidchack,et al.  Simulation of the hard-sphere crystal–melt interface , 1998 .