title: Phases, phase equilibria, and phase rules 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.
authors.affiliation: Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA.
authors.forename: T
authors.initials: T
authors.lastname: Frolov
authors.affiliation: Department of Physics and Astronomy, MSN 3F3, George Mason University, Fairfax, Virginia 22030, USA.
authors.forename: Y
authors.initials: Y
authors.lastname: Mishin