Traveling waves of the solidification and melting of cubic crystal lattices

Pattern Formation under Deep Supercooling by Classical Density Functional-Based Approach

Solidification patterns during nonequilibrium crystallization are among the most important microstructures in the natural and technical realms. In this work, we investigate the crystal growth in deeply supercooled liquid using the classical density functional-based approaches. Our result shows that the complex amplitude expanded phase-field crystal (APFC) model containing the vacancy nonequilibrium effects proposed by us could naturally reproduce the growth front nucleation (GFN) and various nonequilibrium patterns, including the faceted growth, spherulite, symmetric and nonsymmetric dendrites among others, at the atom level. Moreover, an extraordinary microscopic columnar-to-equiaxed transition is uncovered, which is found to depend on the seed spacing and distribution. Such a phenomenon could be attributed to the combined effects of the long-wave and short-wave elastic interactions. Particularly, the columnar growth could also be predicted by an APFC model containing inertia effects, but the lattice defect type in the growing crystal is different due to the different types of short-wave interactions. Two stages are identified during the crystal growth under different undercooling, corresponding to diffusion-controlled growth and GFN-dominated growth, respectively. However, compared with the second stage, the first stage becomes too short to be noticed under the high undercooling. The distinct feature of the second stage is the dramatic increments of lattice defects, which explains the amorphous nucleation precursor in the supercooled liquid. The transition time between the two stages at different undercooling is investigated. Crystal growth of BCC structure further confirms our conclusions.

Perspective: New directions in dynamical density functional theory

Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.

Kinetics of rapid growth and melting of Al50Ni50alloying crystals: phase field theoryversusatomistic simulations revisited. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022;34:494002. [PMID: 36228604 DOI: 10.1088/1361-648x/ac9a1c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

A revised study of the growth and melting of crystals in congruently melting Al₅₀Ni₅₀alloy is carried out by molecular dynamics (MDs) and phase field (PF) methods. An embedded atom method (EAM) potential of Purja Pun and Mishin (2009Phil. Mag.89 3245) is used to estimate the material's properties (density, enthalpy, and self-diffusion) of the B2 crystalline and liquid phases of the alloy. Using the same EAM potential, the melting temperature, density, and diffusion coefficient become well comparable with experimental data in contrast with previous works where other potentials were used. In the new revision of MD data, the kinetics of melting and solidification are quantitatively evaluated by the 'crystal-liquid interface velocity-undercooling' relationship exhibiting the well-known bell-shaped kinetic curve. The traveling wave solution of the kinetic PF model as well as the hodograph equation of the solid-liquid interface quantitatively describe the 'velocity-undercooling' relationship obtained in the MD simulation in the whole range of investigated temperatures for melting and growth of Al₅₀Ni₅₀crystals.

Structure diagram and dynamics of formation of hexagonal boron nitride in phase-field crystal model

The phase-field crystal (PFC-model) is a powerful tool for modelling of the crystallization in colloidal and metallic systems. In the present work, the modified hyperbolic phase-field crystal model for binary systems is presented. This model takes into account slow and fast dynamics of moving interfaces for both concentration and relative atomic number density (which were taken as order parameters). The model also includes specific mobilities for each dynamical field and correlated noise terms. The dynamics of chemical segregation with origination of mixed pseudo-hexagonal binary phase (the so-called 'triangle phase') is used as a benchmark in two spatial dimensions for the developing model. Using the free energy functional and specific lattice vectors for hexagonal crystal, the structure diagram of co-existence of liquid and three-dimensional hexagonal phase for the binary PFC-model was carried out. Parameters of the crystal lattice correspond to the hexagonal boron nitride (BN) crystal, the values of which have been taken from the literature. The paper shows the qualitative agreement between the developed structure diagram of the PFC model and the previously known equilibrium diagram for BN constructed using thermodynamic functions. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

The hodograph equation for slow and fast anisotropic interface propagation

Using the model of fast phase transitions and previously reported equation of the Gibbs-Thomson-type, we develop an equation for the anisotropic interface motion of the Herring-Gibbs-Thomson-type. The derived equation takes the form of a hodograph equation and in its particular case describes motion by mean interface curvature, the relationship 'velocity-Gibbs free energy', Klein-Gordon and Born-Infeld equations related to the anisotropic propagation of various interfaces. Comparison of the present model predictions with the molecular-dynamics simulation data on nickel crystal growth (obtained by Jeffrey J. Hoyt et al. and published in Acta Mater. 47 (1999) 3181) confirms the validity of the derived hodograph equation as applicable to the slow and fast modes of interface propagation. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.