Wulff shapes and the critical nucleus for a triangular Ising lattice

V. A. Shneidman; R. K. Zia

doi:10.1103/physrevb.63.085410

Wulff shapes and the critical nucleus for a triangular Ising lattice

V. A. Shneidman, R. K. Zia

Physics

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

Equilibrium Wulff shapes and interfacial energies of two-dimensional "crystals" on a triangular lattice are considered. Asymptotic approximations are constructed for both the shapes and energies in the limit T→0 where crystals are close to perfect hexagons, and the limit T→T_c (critical temperature) where crystals have near-circular shapes. The intermediate temperature region is studied numerically, and accurate interpolating approximations are proposed. The relevance of the study to the nucleation problem is discussed.

Original language	English (US)
Article number	085410
Pages (from-to)	854101-854107
Number of pages	7
Journal	Physical Review B - Condensed Matter and Materials Physics
Volume	63
Issue number	8
DOIs	https://doi.org/10.1103/physrevb.63.085410
State	Published - 2001

All Science Journal Classification (ASJC) codes

Electronic, Optical and Magnetic Materials
Condensed Matter Physics

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10.1103/physrevb.63.085410

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abstract = "Equilibrium Wulff shapes and interfacial energies of two-dimensional {"}crystals{"} on a triangular lattice are considered. Asymptotic approximations are constructed for both the shapes and energies in the limit T→0 where crystals are close to perfect hexagons, and the limit T→Tc (critical temperature) where crystals have near-circular shapes. The intermediate temperature region is studied numerically, and accurate interpolating approximations are proposed. The relevance of the study to the nucleation problem is discussed.",

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AB - Equilibrium Wulff shapes and interfacial energies of two-dimensional "crystals" on a triangular lattice are considered. Asymptotic approximations are constructed for both the shapes and energies in the limit T→0 where crystals are close to perfect hexagons, and the limit T→Tc (critical temperature) where crystals have near-circular shapes. The intermediate temperature region is studied numerically, and accurate interpolating approximations are proposed. The relevance of the study to the nucleation problem is discussed.

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Wulff shapes and the critical nucleus for a triangular Ising lattice

Abstract

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