Phase-Field Simulations at the Atomic Scale in Comparison to Molecular Dynamics

Early solidification is investigated using two different simulation techniques: the molecular dynamics (MD) and the phase-field (PF) methods. While the first describes the evolution of a system on the basis of motion equations of particles, the second grounds on the evolution of continuous local order parameter field. The aim of this study is to probe the ability of the mesoscopic phase-field method to make predictions of growth velocity at the nanoscopic length scale. For this purpose the isothermal growth of a spherical crystalline cluster embedded in a melt is considered. The system in study is Ni modeled with the embedded atom method (EAM). The bulk and interfacial properties required in the PF method are obtained from MD simulations. Also the initial configuration obtained from MD data is used in the PF as input. Results for the evolution of the cluster volume at high and moderate undercooling are presented.

[1]  Karma,et al.  Phase-field model of eutectic growth. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[3]  J. Horbach,et al.  Nucleation barriers for the liquid-to-crystal transition in Ni: experiment and simulation. , 2011, Physical review letters.

[4]  Britta Nestler,et al.  Phase-field model for solidification of a monotectic alloy with convection , 2000 .

[5]  B. Stinner,et al.  Multicomponent alloy solidification: phase-field modeling and simulations. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  J. Warren,et al.  Modelling polycrystalline solidification using phase field theory , 2004 .

[7]  K. Binder,et al.  Molecular-dynamics computer simulation of crystal growth and melting in Al50Ni50 , 2008, 0802.2529.

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

[9]  A. Karma,et al.  Phase-Field Simulation of Solidification , 2002 .

[10]  R. Trivedi,et al.  Crystal–Melt Interfaces and Solidification Morphologies in Metals and Alloys , 2004 .

[11]  M. Zhu,et al.  A Modified Cellular Automaton Model for the Simulation of Dendritic Growth in Solidification of Alloys , 2001 .

[12]  A. Karma,et al.  Quantitative phase-field modeling of dendritic growth in two and three dimensions , 1996 .

[13]  R. Smith,et al.  Dynamic simulation of crystal growth by Monte Carlo method—I. Model description and kinetics , 1992 .

[14]  H. Wadell,et al.  Volume, Shape, and Roundness of Quartz Particles , 1935, The Journal of Geology.

[15]  A. Karma,et al.  Quantitative phase-field model of alloy solidification. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Long-Qing Chen Phase-Field Models for Microstructure Evolution , 2002 .

[17]  B. Nestler,et al.  Phase-field simulations of nuclei and early stage solidification microstructures , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[18]  Augusto Visintin,et al.  Nucleation and Growth , 1996 .

[19]  A. Karma,et al.  Atomistic and continuum modeling of dendritic solidification , 2003 .

[20]  R. Trivedi,et al.  Phase-field study of three-dimensional steady-state growth shapes in directional solidification. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Alain Karma,et al.  Multiscale finite-difference-diffusion-Monte-Carlo method for simulating dendritic solidification , 2000 .

[22]  Britta Nestler,et al.  A multi-phase-field model of eutectic and peritectic alloys: numerical simulation of growth structures , 2000 .

[23]  Foiles,et al.  Application of the embedded-atom method to liquid transition metals. , 1985, Physical review. B, Condensed matter.

[24]  Harald Garcke,et al.  A Diffuse Interface Model for Alloys with Multiple Components and Phases , 2004, SIAM J. Appl. Math..

[25]  László Gránásy,et al.  Multiscale approach to CO2 hydrate formation in aqueous solution: phase field theory and molecular dynamics. Nucleation and growth. , 2006, The Journal of chemical physics.

[26]  R. Rozas,et al.  Capillary wave analysis of rough solid-liquid interfaces in nickel , 2011 .

[27]  Mark Asta,et al.  Kinetic coefficient of Ni solid-liquid interfaces from molecular-dynamics simulations . , 2004 .

[28]  Jean Bragard,et al.  Linking Phase-Field and Atomistic Simulations to Model Dendritic Solidification in Highly Undercooled Melts , 2001 .