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

TL;DR

This paper introduces an efficient numerical continuation method to calculate phase diagrams, including coexistence lines and triple points, applied to a binary phase-field crystal model to analyze phase behavior in one- and two-dimensional systems.

Contribution

The paper presents a novel application of numerical continuation techniques to accurately compute phase diagrams for complex thermodynamic systems, including metastable states and critical points.

Findings

Phase diagrams for binary PFC model are computed in 1D and 2D.

Comparison with one-mode approximation shows good agreement.

Identification of stable and metastable phases and their coexistence.

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.