Efficient calculation of phase coexistence and phase diagrams: application to a binary phase-field crystal model

Abstract

We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems. In particular, this involves the determination of lines of phase coexistence related to first order phase transitions and the continuation of triple points. To illustrate the method we apply it to a binary Phase-Field-Crystal model for the crystallisation of a mixture of two types of particles. The resulting phase diagram is determined for one- and two-dimensional domains. In the former case it is compared to the diagram obtained from a one-mode approximation. The various observed liquid and crystalline phases and their stable and metastable coexistence are discussed as well as the temperature-dependence of the phase diagrams. This includes the (dis)appearance of critical points and triple points. We also relate bifurcation diagrams for finite-size systems to the thermodynamics of phase transitions in the infinite-size limit.

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• Suppression of coarsening and emergence of oscillatory behavior in a Cahn-Hilliard model with nonvariational coupling
• Jerky active matter: a phase field crystal model with translational and orientational memory
• Perspective: New directions in dynamical density functional theory
• Localized states in passive and active phase-field-crystal models
• Coexistence of uniform and oscillatory states resulting from nonreciprocity and conservation laws
• Complex-tensor theory of simple smectics
• Derivation and analysis of a phase field crystal model for a mixture of active and passive particles
• Theory of Nonequilibrium Multicomponent Coexistence
• Exploring Bifurcations in Bose-Einstein Condensates via Phase Field Crystal Models
• Theory of Nonequilibrium Coexistence with Coupled Conserved and Nonconserved Order Parameters
• Motility-induced crystallization and rotating crystallites