Simulation of homogeneous crystal nucleation close to coexistence

We discuss a numerical scheme to study homogeneous crystal nucleation. Using this approach, it is possible to compute the height of the free energy barrier that separates the solid from the liquid phase and the rate at which this barrier is crossed. We point out that there is a fundamental difference between the use of a global- and a local-order parameter to measure the degree of crystallinity. Using a global-order parameter, precritical nuclei may break up spontaneously for entropic reasons. Near the top of the barrier the nuclei combine to form a relatively large cluster. The transition from many small clusters to one large cluster is discussed in some detail. Finally we present a new method that allows us to avoid this entropic cluster break up.

[1]  D. Kofke,et al.  Thermodynamic and structural properties of model systems at solid-fluid coexistence: I. Fcc and bcc soft spheres , 1995 .

[2]  G. Torrie,et al.  Monte Carlo free energy estimates using non-Boltzmann sampling: Application to the sub-critical Lennard-Jones fluid , 1974 .

[3]  Aneesur Rahman,et al.  Crystal nucleation in a three‐dimensional Lennard‐Jones system. II. Nucleation kinetics for 256 and 500 particles , 1977 .

[4]  J. McTague,et al.  Crystal nucleation in a three‐dimensional Lennard‐Jones system: A molecular dynamics study , 1976 .

[5]  George H. Gilmer,et al.  Molecular dynamics investigation of the crystal–fluid interface. VI. Excess surface free energies of crystal–liquid systems , 1986 .

[6]  Andersen,et al.  10(6)-particle molecular-dynamics study of homogeneous nucleation of crystals in a supercooled atomic liquid. , 1990, Physical review. B, Condensed matter.

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

[8]  W. W. Wood,et al.  Equation of State of Classical Hard Spheres at High Density , 1962 .

[9]  David Turnbull,et al.  Rate of Nucleation in Condensed Systems , 1949 .

[10]  Carey K. Bagdassarian,et al.  Crystal nucleation and growth from the undercooled liquid: A nonclassical piecewise parabolic free‐energy model , 1994 .

[11]  J. Q. Broughton,et al.  Crystallization of fcc (111) and (100) crystal‐melt interfaces: A comparison by molecular dynamics for the Lennard‐Jones system , 1988 .

[12]  David Chandler,et al.  Statistical mechanics of isomerization dynamics in liquids and the transition state approximation , 1978 .

[13]  G. Ciccotti,et al.  Constrained reaction coordinate dynamics for the simulation of rare events , 1989 .

[14]  Aneesur Rahman,et al.  Interaction potentials and their effect on crystal nucleation and symmetry , 1979 .

[15]  Klein,et al.  Crystalline nucleation in deeply quenched liquids. , 1986, Physical review letters.

[16]  D. Oxtoby,et al.  A molecular theory of crystal nucleation from the melt , 1984 .

[17]  J. Q. Broughton,et al.  Crystallization Rates of a Lennard-Jones Liquid , 1982 .

[18]  T. Kelly,et al.  Solidification structures in submicron spheres of iron-nickel: Analytical evaluation☆ , 1988 .

[19]  P. Steinhardt,et al.  Bond-orientational order in liquids and glasses , 1983 .

[20]  M. J. Ruiz-Montero,et al.  Numerical evidence for bcc ordering at the surface of a critical fcc nucleus. , 1995, Physical review letters.

[21]  H. C. Andersen,et al.  Small system size artifacts in the molecular dynamics simulation of homogeneous crystal nucleation in supercooled atomic liquids , 1986 .

[22]  Daan Frenkel,et al.  COMPUTER-SIMULATION STUDY OF FREE-ENERGY BARRIERS IN CRYSTAL NUCLEATION , 1992 .