Related papers: Defining shapes of 2D-crystals with undefinable ed…
According to the Wulff construction the shape of the equilibrium crystal is determined by the surface tension considered as a function of the interface orientation. We present some (conjectured) approximate solutions and some rigorous…
This chapter discusses the equilibrium crystal shape (ECS) from a physical perspective, beginning with a historical introduction to the Wulff theorem. It takes advantage of excellent prior reviews, particularly in the late 1980's, recapping…
The shape of an equilibrium crystal is obtained, according to the Gibbs thermodynamic principle, by minimizing the total surface free energy associated to the crystal-medium interface. To study the solution to this problem, known as the…
Crystal morphologies are important for the design and functionality of devices based on low-dimensional nanomaterials. The equilibrium crystal shape (ECS) is a key quantity in this context. It is determined by surface energies, which are…
The present work revisits the classical Wulff problem restricted to crystalline integrands, a class of surface energies that gives rise to finitely faceted crystals. The general proof of the Wulff theorem was given by J.E. Taylor (1978) by…
Geometrical constructions, such as the tangent construction on the molar free energy for determining whether a particular composition of a solution, is stable, are related to similar tangent constructions on the orientation-dependent…
We present two-dimensional crystallization results in the square lattice for finite particle systems consisting of two different atomic types. We identify energy minimizers of configurational energies featuring two-body short-ranged…
We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-constant elastic energy in terms of topological invariants.…
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…
We use surface tension to distinguish between phases with isotropic internal structure from phases which are microscopically anisotropic. There are many interesting open problems, especially in two dimensions, and in phase coexistence.
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
We study the stability of closed, not necessarily smooth, equilibrium surfaces of an anisotropic surface energy for which the Wulff shape is not necessarily smooth. We show that if the Cahn Hoffman field can be extended continuously to the…
The finite size and interface effects on equilibrium crystal shape (ECS) have been investigated for the case of a surface free energy density including step stiffness and inverse-square step-step interactions. Explicitly including the…
Here, we propose a comprehensive first-principle atomistic approach to predict the Wulff-Kaischew equilibrium shape of crystals heterogeneously integrated on a dissimilar material. This method uses both reconstructed surface and interface…
The calculation of the discrete atomistic energy of a crystal near the continuum limit encounters difficulties caused by the geometric discrepancy between the continuum region occupied by the body, and the discrete collection of lattice…
Surface energies for different GaAs surface orientations have been calculated as a function of the chemical potential. We use an energy density formalism within the first-principles pseudopotential density-functional approach. The…
The topology and the geometry of a surface play a fundamental role in determining the equilibrium configurations of thin films of liquid crystals. We propose here a theoretical analysis of a recently introduced surface Frank energy, in the…
Topological spin textures emerging in magnetic materials usually appear in crystalline states. A long-standing dilemma is whether we should understand these emergent crystals as gathering particles or coupling waves, the answer of which…
Quantum states naturally represent symmetry groups, though often in a projective sense. Intriguingly, the projective nature of crystalline symmetries has remained underexplored until very recently. A series of groundbreaking theoretical and…
It is shown theoretically that a one-dimensional crystal with time reversal symmetry is characterized by a Z_{2} topological invariant that predicts the existence or otherwise of edge states. This is confirmed experimentally through the…