Related papers: Wulff shape of equilibrium crystals
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…
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…
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…
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 rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the…
The equilibrium shape of crystals is a fundamental property of both aesthetic appeal and practical import. It is also a visible macro-manifestation of the underlying atomic-scale forces and chemical makeup, most conspicuous in…
We examine the shape of a an isolated, dislocation-free ice crystal when it is in equilibrium with the vapor phase in an isothermal closed environment, as a function of temperature. From our analysis we draw the following conclusions: 1)…
The Euler-Lagrange equation of the phase-field crystal (PFC) model has been solved under appropriate boundary conditions to obtain the equilibrium free energy of the body centered cubic crystal-liquid interface for 18 orientations at…
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…
A generalised Wulf-Kaishew theorem is given describing the equilibrium shape (ES) of an isolated 3D crystal A deposited coherently onto a lattice mismatched planar substrate. For this purpose a free polyhedral crystal is formed then…
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…
A mean field theory is developed for the calculation of the surface free energy of the staggered BCSOS, (or six vertex) model as function of the surface orientation and of temperature. The model approximately describes surfaces of crystals…
We present a computational study for the equilibrium shape of gold nanoparticles. By linking extensive quantum-mechanical calculations, based on Density-Functional Theory (DFT) to Wulff construction, we predict equilibrium shapes that are…
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…
We examine the growth of crystals from vapor. We assume that the Wulff shape is a prism with a hexagonal base. The Gibbs-Thomson correction on the crystal surface is included in the model. Assuming that the-initial crystal has an admissible…
Optimizing the free energy under a mass constraint may generate a convex crystal subject to assumptions on the potential $g(0)=0$, $g \ge 0$. The general problem classically attributed to Almgren is to infer if this is the case assuming the…
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.
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…
We study an effective model of microscopic facet formation for low temperature three dimensional microscopic Wulff crystals above the droplet condensation threshold. The model we consider is a 2+1 solid on solid surface coupled with high…
We present a new approach for predicting stable equilibrium shapes of crystalline islands on flat substrates, as commonly occur through solid-state dewetting of thin films. The new theory is a generalization of the widely used Winterbottom…