Julia Kundin

Phase-field crystal modeling of anisotropic material systems of arbitrary Poisson's ratio

Recently, we derived a generalized model for isotropic as well as anisotropic crystal lattice systems of arbitrary Poissons ratio within the framework of the continuum phase-field crystal (PFC) approach [R. Prieler, J. Hubert, D. Li, B. Verleye, R. Haberkern, H. Emmerich, J. Phys.: Condens. Matter 21 (2009) p.464110] and showed how its parameters can be derived from classical density functional theory [M.A. Choudhary, D. Li, H. Emmerich and H. Löwen, J. Phys.: Condens. Matter 23 (2011) p.265005]. Here, we present a general procedure to model anisotropic material systems of arbitrary Poissons ratios. In that way we can for the first time identify PFC solutions of arbitrary Poissons ratios and thereby extend the applicability of the PFC method to a larger class of material systems.

Thermodynamic consistency and fast dynamics in phase-field crystal modeling

A general formulation is presented to derive the equation of motion and demonstrate thermodynamic consistency for several classes of phase-field (PF) and PF crystal (PFC) models. It can be applied to models with a conserved and non-conserved phase-field variable, describing either locally uniform or periodic stable states, and containing slow as well as fast thermodynamic variables. The approach is based on an entropy functional formalism previously developed in the context of PF models for locally uniform states [P. Galenko and D. Jou, Phys. Rev. E 71 (2005) p.046125] and thus allows to extend several properties of the latter to PF models for periodic states, i.e., PFC models.

A study of the step-flow growth of the PVT-grown AlN crystals by a multi-scale modeling method

A kinetic Monte Carlo (KMC) model coupled with the vapor diffusion above the Al-polar (0001) surface of AlN is constructed for the physical vapor transport (PVT) growth of AlN crystals. Most of the important surface events and the vapor diffusion of Al atoms are taken into account. Based on the numerical simulations, an analytical model of the step-flow growth on the (0001) surface is attained and the time evolution of random terrace widths under homogeneous and linearly inhomogeneous vapor fluxes of Al atoms is explored. Using the KMC model and the analytical model it is found that under the growing conditions in this work the rate limiting step for the PVT growth of AlN is the supply of Al atoms due to the tiny flow of Al atoms in the vapor phase (Alg) at the steady state. The energy barriers for adsorbed AlN (AlNad) incorporated at different configurations of neighboring AlN dimers can influence the growth morphology significantly. If the adsorption rate of Alg is much slower than the rates of the surface events, the step-bunching caused by the randomness of the terrace widths can be avoided under either the homogeneous or linearly inhomogeneous flux of Alg.

Dynamic Modeling of Critical Velocities for the Pushing/Engulfment Transition in the Si-SiC System Under Gravity Conditions

An extended non-steady-state model for the interaction between a solid particle and an advancing solid/liquid interface based on the dynamic model of Catalina etxa0al. (Metall Mater Trans A 31:2559–2568, 2000) is used to calculate the critical velocities for the pushing/engulfment transition in Si-SiC system under microgravity and under normal gravity conditions. The aim of this study was to explain the abnormal behavior of the critical velocity in experiments. The simulations were carried out for two cases of the drag force formulation. The effects of the non-spherical form of the particles as well as the cluster formation were also taken into account. It is found that in the presence of the gravity force, the particles will be engulfed when the particle size exceeds a certain limit which does not depend on the choice of the drag force formulation.