Nucleation and Post-Nucleation Growth in Diffusion-Controlled and Hydrodynamic Theory of Solidification

Abstract

Two-step nucleation and subsequent growth processes were investigated in the framework of the single mode phase-field crystal model combined with diffusive dynamics (corresponding to colloid suspensions) and hydrodynamical density relaxation (simple liquids). It is found that independently of dynamics, nucleation starts with the formation of solid precursor clusters that consist of domains with noncrystalline ordering (ringlike projections are seen from certain angles), and regions that have amorphous structure. Using the average bond order parameter q¯6, we distinguished amorphous, medium range crystallike order (MRCO), and crystalline local orders. We show that crystallization to the stable body-centered cubic phase is preceded by the formation of a mixture of amorphous and MRCO structures. We have determined the time dependence of the phase composition of the forming solid state. We also investigated the time/size dependence of the growth rate for solidification. The bond order analysis indicates similar structural transitions during solidification in the case of diffusive and hydrodynamic density relaxation.

Thermodynamics, formation dynamics, and structural correlations in the bulk amorphous phase of the phase-field crystal model

“…without the addition of any further noise) transition into the crystalline phase, (ii) direct amorphous nucleation leading to the bulk amorphous phase, (iii) direct crystal nucleation with a bulk crystalline final state, and (iv) competing nucleation of the crystalline and the amorphous phase, leading to a mixture of coexisting amorphous and crystalline grains. This variety of solidification pathways is in a good agreement with previous theoretical predictions 38,39,[45][46][47][48][49][50] and experimental observations [51][52][53][54] of the so-called amorphous precursor mediated multi-step crystallisation process and the formation of a glassy phase (called the q-glass 55 ) in a first order phase transition 55,56 . We believe that our results contribute to the better theoretical understanding of the thermodynamic and structural properties of amorphous solids as well as their role in complex solidification processes.…”

Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks

“…The derived equations of motion are similar to the model proposed in Ref. [22]. However, we provide a different physical interpretation of the source of free energy dissipation, which is related to the small-scale variations (microscopic structures) of the density field.…”

“…Being a simplified hydrodynamic framework, similar to that of Ref. [22], we use the acronym sHPFC in this paper. In Ref.…”

“…This term was reintroduced into the model for computational efficiency in Ref. [22] as a phenomenological damping coefficient. Damping coefficients, however, typically imply the interaction with a colloid or surrounding media and are hard to justify when considering a single component system.…”

Perspective: New directions in dynamical density functional theory

“…Recent studies of PFC models have focused on active matter with [212][213][214] and without [215][216][217][218][219][220][221] inertia, amorphous solids [222], bifurcation diagrams [219,220,[223][224][225], colored noise [226], cubic terms [227], crystals [228], dislocation lines [229], electromigration [230], grain boundaries [231,232], mixtures [200,220,[233][234][235], nucleation [236], solidification [237,238], and stress tensors [239].…”