Interfaces

TL;DR

This paper explores the theoretical aspects of phase coexistence and equilibrium forms, covering thermodynamics, statistical mechanics, microscopic interface descriptions, and phenomena like roughening transitions and facets in crystals.

Contribution

It provides a detailed analysis of microscopic interfaces and proves the validity of the Wulff construction in a simplified two-dimensional model.

Findings

Validation of the Wulff construction for 2D interfaces

Analysis of microscopic surface tension at low temperatures

Study of roughening transition and facet formation in crystals

Abstract

Several aspects of the theory of the coexistence of phases and equilibrium forms are discussed. In section 1, the problem is studied from the point of view of thermodynamics. In section 2, the statistical mechanical theory is introduced. We consider, in particular, the description of the microscopic interface at low temperatures and the existence of a free energy per unit area (surface tension). In section 3, a proof is given of the microscopic validity of the Wulff construction in a simplified model of a two-dimensional interface. Finally, in section 4, the roughening transition and the formation of facets in an equilibrium crystal are studied. Appendices A and B concern, respectively, the first and second points of section 2, mentioned above.