A variational model for epitaxial crystal growth with adatoms
Riccardo Cristoferi (Heriot-Watt University)
Thursday 17th October 14:00-15:00 Maths 311B
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,
in that it can be obtained as a gradient flow of a suitable energy.
Albeit usually neglected, adatoms (atoms freely diffusing on the surface of the crystal) seem to play a
fundamental role in the description of the behaviour of a solid-vapor interfaces.
For this reason, some years ago Fried and Gurtin introduced a system of evolution equations to describe
such a situation, where adatoms are treated as a separate variable of the problem.
Also such system of evolution equations can be seen as the gradient flow of an energy.
In this talk a first step in the programme of studying the above mentioned evolution equations from a
variational point of view is presented. In particular, the focus is on the static problem in the small mass
regime, where the elastic energy is negligible. Ground states, effective energy, and phase filed approxiamtion
suitable for numerical purposes are discussed.
The talk is based on a work in collaboration with Marco Caroccia (Scuola Normale Superiore-Università di Firenze),
and Laurent Dietrich (Lycée Fabert).