Phases, phase equilibria and phase rules in low-dimensional systems

TL;DR

This paper develops a unified thermodynamic framework for describing phases and phase transformations across one, two, and three-dimensional systems, including interfaces and line defects, with generalized phase rules and thermodynamic relations.

Contribution

It introduces a rigorous, unified approach to thermodynamics applicable to all dimensionalities, extending phase rules and relations to interfaces and line defects.

Findings

Derived adsorption and coexistence equations for lines and interfaces.

Established generalized phase rules for 1D, 2D, and 3D systems.

Predicted maximum number of coexisting phases in low-dimensional systems.

Abstract

We present a unified approach to thermodynamic description of one, two and three dimensional phases and phase transformations among them. The approach is based on a rigorous definition of a phase applicable to thermodynamic systems of any dimensionality. Within this approach, the same thermodynamic formalism can be applied for the description of phase transformations in bulk systems, interfaces, and line defects separating interface phases. For both lines and interfaces, we rigorously derive an adsorption equation, the phase coexistence equations, and other thermodynamic relations expressed in terms of generalized line and interface excess quantities. As a generalization of the Gibbs phase rule for bulk phases, we derive phase rules for lines and interfaces and predict the maximum number of phases than may coexist in systems of the respective dimensionality.