Equilibria configurations for epitaxial crystal growth with adatoms
Dr. Riccardo Cristoferi, Heriot-Watt University, Edinbourgh
Sala conferenze IMATI-CNR, Pavia – Martedì 8 Gennaio 2019 h.15:00
Abstract. Surface diffusion is one of the most important mechanisms driving crystal growth. When bulk diffusion is much faster than the surface one, the evolution of the profile of the crystal is described by the so called Einstein-Nernst relation. According to this law, the normal velocity of the profile is related to the chemical potential. This evolution equation has a variational flavor: indeed it can be obtained as a gradient flow of a suitable energy.
When studying solid-vapor interfaces, the usually neglected effect of adatoms seems to play a fundamental role. These are atoms freely diffusing on the surface of the crystal. Some years ago Fried and Gurtin introduced a system of evolution equations to model such a situation in the regime where elastic energy is negligible. Also such system of evolution equation can be seen as the gradient flow of a surface energy.
In this talk a first step in the programme of studying the above mentioned evolution equations is presented. In particular, the following topics for the static problem are addressed: regular critical points, existence and uniqueness of minimizers and relaxation of the energy functional in a suitable topology, as well as a phase-field approximation.
The talk is based on a work in collaboration with Marco Caroccia (Scuola Normale Superiore-Università di Firenze) and Laurent Dietrich (Lycée Fabert).