Bridging the phase-field and phase-field crystal approaches for anisotropic material systems

In this paper the amplitude representation of the anisotropic phase-field crystal (APFC) model recently proposed as a generalized model for isotropic as well as anisotropic crystal lattice systems is developed. The relationship between the amplitude equations and the standard phase-field model for solidification of pure substances with elasticity effects is derived which provide an explicit connection between the phase-field and APFC models. On the one hand we present a computationally more efficient model and highlight its potential as a bridge between the PFC and phase-field models with anisotropic interface energies and kinetics on the other hand.

[1]  N. Provatas,et al.  Phase-field crystals with elastic interactions. , 2006, Physical review letters.

[2]  M. Grant,et al.  Diffusive atomistic dynamics of edge dislocations in two dimensions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Yunzhi Wang,et al.  Large-scale three-dimensional phase field simulation of γ ′-rafting and creep deformation , 2010 .

[4]  M. Grant,et al.  Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  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.

[6]  Badrinarayan P. Athreya,et al.  Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[8]  H. Emmerich,et al.  Phase-field modeling of the γ′-coarsening behavior in Ni-based superalloys , 2012 .

[9]  H. Emmerich,et al.  Phase-field crystal modeling of anisotropic material systems of arbitrary Poisson's ratio , 2012 .

[10]  A. Karma,et al.  Phase field modeling of crack propagation , 2010, 1001.4350.

[11]  Wheeler,et al.  Phase-field model for isothermal phase transitions in binary alloys. , 1992, Physical review. A, Atomic, molecular, and optical physics.

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

[13]  Robert Spatschek,et al.  Amplitude equations for polycrystalline materials with interaction between composition and stress , 2010, 1002.1580.

[14]  Martin Grant,et al.  Modeling elasticity in crystal growth. , 2001, Physical review letters.

[15]  R. Prieler,et al.  An anisotropic phase-field crystal model for heterogeneous nucleation of ellipsoidal colloids , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[16]  Paul C. Fife,et al.  Thermodynamically consistent models of phase-field type for the kinetics of phase transitions , 1990 .

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

[18]  G. Caginalp,et al.  Phase-field and sharp-interface alloy models. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[20]  Daming Li,et al.  DDFT calibration and investigation of an anisotropic phase-field crystal model. , 2011, Journal of physics. Condensed matter : an Institute of Physics journal.

[21]  M. Grant,et al.  Phase-field crystal modeling and classical density functional theory of freezing , 2007 .

[22]  Zhi-Feng Huang,et al.  Density-amplitude formulation of the phase-field crystal model for two-phase coexistence in two and three dimensions , 2010 .

[23]  N. Provatas,et al.  Amplitude expansion of the binary phase-field-crystal model. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Badrinarayan P. Athreya,et al.  Renormalization Group Approach to Multiscale Modelling in Materials Science , 2005, cond-mat/0508671.

[25]  Badrinarayan P. Athreya,et al.  Renormalization-group theory for the phase-field crystal equation. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.