Nucleation and polycrystalline solidification in binary phase field theory

We present a phase field theory for the nucleation and growth of one and two phase crystals solidifying with different crystallographic orientations in binary alloys. The accuracy of the model is tested for crystal nucleation in single component systems. It is shown that without adjustable parameters the height of the nucleation barrier is predicted with reasonable accuracy. The kinetics of primary solidification is investigated as a function of model parameters under equiaxial conditions. Finally, we study the formation of polycrystalline growth morphologies (disordered dendrites, spherulites and fractal-like aggregates).

[1]  H. D. Keith,et al.  Spherulitic Crystallization from the Melt. I. Fractionation and Impurity Segregation and Their Influence on Crystalline Morphology , 1964 .

[2]  J. Christian,et al.  The theory of transformations in metals and alloys , 2003 .

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

[4]  R. Meyer,et al.  The surface tension in a structural model for the solid-liquid interface , 1976 .

[5]  S. Hardy A grain boundary groove measurement of the surface tension between ice and water , 1977 .

[6]  George H. Gilmer,et al.  Molecular dynamics investigation of the crystal–fluid interface. I. Bulk properties , 1983 .

[7]  Taborek Nucleation in emulsified supercooled water. , 1985, Physical review. B, Condensed matter.

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

[9]  Kelton,et al.  Test of classical nucleation theory in a condensed system. , 1988, Physical review. B, Condensed matter.

[10]  R. Willnecker,et al.  Nucleation in bulk undercooled nickel-base alloys , 1988 .

[11]  G. Faivre,et al.  Bulk crystallization of liquid selenium Primary nucleation, growth kinetics and modes of crystallization , 1988 .

[12]  K. Kelton Crystal Nucleation in Liquids and Glasses , 1991 .

[13]  A. L. Greer,et al.  Nucleation in Lithium Disilicate Glass: A Test of Classical Theory by Quantitative Modeling , 1991 .

[14]  A. A. Wheeler,et al.  Thermodynamically-consistent phase-field models for solidification , 1992 .

[15]  B. Laird,et al.  The Crystal/Liquid Interface: Structure and Properties from Computer Simulation , 1992 .

[16]  R. Kobayashi Modeling and numerical simulations of dendritic crystal growth , 1993 .

[17]  Grant,et al.  Stochastic eutectic growth. , 1994, Physical review letters.

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

[19]  J. Warren,et al.  Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method , 1995 .

[20]  P. Clancy,et al.  The kinetics of crystal growth and dissolution from the melt in Lennard‐Jones systems , 1995 .

[21]  G. Caginalp,et al.  A Derivation and Analysis of Phase Field Models of Thermal Alloys , 1995 .

[22]  L. Bartell,et al.  Kinetics of Homogeneous Nucleation in the Freezing of Large Water Clusters , 1995 .

[23]  A. Karma,et al.  Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  M. Rappaz,et al.  The development of nucleation controlled microstructures during laser treatment of Al-Si alloys , 1996 .

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

[26]  D. Oxtoby,et al.  NUCLEATION OF LENNARD-JONES FLUIDS : A DENSITY FUNCTIONAL APPROACH , 1996 .

[27]  V. Fleury Branched fractal patterns in non-equilibrium electrochemical deposition from oscillatory nucleation and growth , 1997, Nature.

[28]  M. Conti Growth of a needle crystal from an undercooled alloy melt , 1997 .

[29]  W. Craig Carter,et al.  Modeling Grain Boundaries using a Phase Field Technique , 1998, cond-mat/9808319.

[30]  W. Carter,et al.  Vector-valued phase field model for crystallization and grain boundary formation , 1998 .

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

[32]  D. Crespo,et al.  Diffusion controlled grain growth in primary crystallization: Avrami exponents revisited , 1998 .

[33]  L. Gránásy Cahn–Hilliard-type density functional calculations for homogeneous ice nucleation in undercooled water , 1999 .

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

[35]  Jeff Simmons,et al.  Phase field modeling of simultaneous nucleation and growth by explicitly incorporating nucleation events , 2000 .

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

[37]  M. Grant,et al.  Phase-field modeling of eutectic growth. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[38]  Phase-field modeling of microstructural pattern formation during directional solidification of peritectic alloys without morphological instability. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  A. Karma Phase-field formulation for quantitative modeling of alloy solidification. , 2001, Physical review letters.

[40]  A. Karma,et al.  Method for computing the anisotropy of the solid-liquid interfacial free energy. , 2001, Physical review letters.

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

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

[43]  A. Haymet,et al.  The ice/water interface: Molecular dynamics simulations of the basal, prism, {202̄1}, and {21̄1̄0} interfaces of ice Ih , 2001 .

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

[45]  J. Warren,et al.  Growth pulsations in symmetric dendritic crystallization in thin polymer blend films. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[47]  J. Warren,et al.  Nonequilibrium pattern formation in the crystallization of polymer blend films. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  William L. George,et al.  A Parallel 3D Dendritic Growth Simulator Using the Phase-Field Method , 2002 .

[49]  T. Pusztai,et al.  Nucleation and bulk crystallization in binary phase field theory. , 2002, Physical review letters.

[50]  J. Warren,et al.  Phase Field Modeling of Alloy Polycrystals , 2003 .

[51]  M. Schreckenberg,et al.  Interface and Transport Dynamics : Computational Modelling , 2003 .

[52]  J. Warren,et al.  Growth of 'dizzy dendrites' in a random field of foreign particles , 2003, Nature materials.

[53]  Ruslan L. Davidchack,et al.  Direct calculation of the crystal–melt interfacial free energies for continuous potentials: Application to the Lennard-Jones system , 2003 .

[54]  T. Pusztai,et al.  Phase-field Theory of Nucleation and Growth in Binary Alloys , 2003 .

[55]  T. Pusztai,et al.  Phase field theory of crystal nucleation in hard sphere liquid , 2003, cond-mat/0306527.