Related papers: Crystal Shapes and Phase Equilibria: A Common Math…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
Pathways and structural dynamics of phase transformations impact performance of materials in energy and information storage technologies. Palladium hydride ($\mathrm{PdH}_x$) nanocrystals are an ideal model system for studying…
The purpose of the study is to further investigate the classical Gibbs analysis of the heterogeneous system "stressed crystal - melt." It is demonstrated that each equilibrium configuration is stable with respect to a special class of…
The behavior of a surface energy $\mathcal F(E,u)$, where $E$ is a set of finite perimeter and $u\in L^1(\partial^* E, \mathbb R_+)$ is studied. These energies have been recently considered in the context of materials science to derive a…
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…
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…
Atom arrangement plays a critical role in determining material properties. It is, therefore, essential for materials science and engineering to identify and characterize distinct atom configurations. Currently, crystal structures can be…
A general formulation is presented to derive the equation of motion and to demonstrate thermodynamic consistency for several classes of phase field models at once. It applies to models with a conserved phase field, describing either uniform…
The phase field crystal (PFC) method has emerged as a promising technique for modeling materials with atomistic resolution on mesoscopic time scales. The approach is numerically much more efficient than classical density functional theory…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
In this article, we review the analytical and numerical approaches for computing the phase space structures in two degrees-of-freedom Hamiltonian systems that arise in chemical reactions. In particular, these phase space structures are the…
A modified phase field crystal model in which the free energy may be minimised by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where…
The dynamics of glass formation in monatomic and binary liquids are studied numerically using a microscopic field theory for the evolution of the time-averaged atomic number density. A stochastic framework combining phase field crystal free…
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.…
Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions, developing models for interface and grain boundary structures. In…
The stability of the phase difference between two white-light continua, generated from the same 180-fs pulses at 1035\,nm, is assessed by a modified Bellini-Hansch interferometer. Mutual spectral stability is studied as a function of…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
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…
Predictions of relative stabilities of (competing) molecular crystals are of great technological relevance, most notably for the pharmaceutical industry. However, they present a long-standing challenge for modeling, as often minuscule free…
We develop an innovative technique for studying inhomogeneous phases with a spontaneous broken symmetry. The method relies on the knowledge of the exact form of the free energy in the homogeneous phase and on a specific gradient expansion…