Phase-field modeling of crystal nucleation in undercooled liquids – A review

Abstract

We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the conventional phase-field approaches that rely on spatially averaged (coarse grained) order parameters in capturing freezing, and by the recently developed phase-field crystal models that work on the molecular scale, while employing time averaged particle densities, and are regarded as simple dynamical density functional theories of classical particles. Besides simpler cases of homogeneous and heterogeneous nucleation, phenomena addressed by these techniques include precursor assisted nucleation, nucleation in eutectic and phase separating systems, phase selection via competing nucleation processes, growth front nucleation (a process, in which grains of new orientations form at the solidification front) yielding crystal sheaves and spherulites, and transition between the growth controlled cellular and the nucleation dominated equiaxial solidification morphologies. * granasy.laszlo@wigner.mta.hu arXiv:1907.05732v1 [cond-mat.mtrl-sci] 12 Jul 2019 D. Discussion: Nucleation in coarse grained PF models 32 IV. Molecular scale phase-field models of crystallization 34 A. The Phase-Field Crystal approach 34 1. The single-mode PFC model 34 2. The two-mode PFC model 35 3. The multi-mode PFC model 36 4. Other advanced PFC models 36 B. Application of the PFC models to crystal nucleation 37 1. Euler-Lagrange equation and other methods to find free energy extrema 37 2. PFC with diffusive dynamics (DPFC) 39 3. Hydrodynamic PFC model of freezing (HPFC) 46 4. Numerical methods 49 C.

Growth of different faces in a body centered cubic lattice: A case of the phase-field-crystal modeling

“…With this process the specific face decelerates and becomes wider. This defect structure was also previously observed, in two-dimensional case of solidification from an supercooled liquid [37,38]. This effect is explained as a consequence of the mismatch between the selected lattice parameter and the equilibrium lattice spacing.…”

Crystallization of Supercooled Liquids: Self-Consistency Correction of the Steady-State Nucleation Rate

“…In the analysis of thermodynamic aspects of phase formation, in general, and crystallization processes, in particular, different approaches have been employed (e.g., [ 29 , 30 , 31 , 32 , 33 , 34 , 35 ]) following and advancing the two alternative methods of theoretical description of thermodynamically heterogeneous systems developed by J. W. Gibbs [ 36 , 37 ] and J. D. van der Waals [ 38 , 39 ]. In application to nucleation, both methods deal with the appropriate description of the work of critical cluster formation, , i.e., the work to be performed in a reversible process to create a cluster of the new phase that is capable of further deterministic growth.…”

New Self‐Organization Route to Tunable Narrowband Optical Filters and Polarizers Demonstrated with ZnO–ZnWO4 Eutectic Composite

“…In this context, directional solidification of eutectic composites is a particularly promising approach for the fabrication of micro/nanostructured materials with special optical properties. Eutectic solidification enables fabrication of bulk highly crystalline materials in a one‐step process from a miscible liquid.…”