Solidification fronts in supercooled liquids: how rapid fronts can lead to disordered glassy solids

Abstract

We determine the speed of a crystallisation (or more generally, a solidification) front as it advances into the uniform liquid phase after the system has been quenched into the crystalline region of the phase diagram. We calculate the front speed by assuming a dynamical density functional theory model for the system and applying a marginal stability criterion. Our results also apply to phase field crystal (PFC) models of solidification. As the solidification front advances into the unstable liquid phase, the density profile behind the advancing front develops density modulations and the wavelength of these modulations is a dynamically chosen quantity. For shallow quenches, the selected wavelength is precisely that of the crystalline phase and so well-ordered crystalline states are formed. However, when the system is deeply quenched, we find that this wavelength can be quite different from that of the crystal, so that the solidification front naturally generates disorder in the system. Significant rearrangement and ageing must subsequently occur for the system to form the regular well-ordered crystal that corresponds to the free energy minimum. Additional disorder is introduced whenever a front develops from random initial conditions. We illustrate these findings with results obtained from the PFC.

14 pages, 7 figures

References in corpus (13)

• Front propagation into unstable states
• Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals
• Dynamic Density Functional Theory of Fluids
• Dynamical density functional theory and its application to spinodal decomposition
• Phase-field crystal study of grain-boundary premelting
• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• Derivation of the phase field crystal model for colloidal solidification
• Diffusive Atomistic Dynamics of Edge Dislocations in Two Dimensions
• Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics
• Melting at dislocations and grain boundaries: A Phase Field Crystal study
• Colloidal crystal growth at externally imposed nucleation clusters
• Dynamical density functional theory for dense atomic liquids
• Modelling fluids and crystals using a two-component modified phase field crystal model

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