| Date: | Wed, 05 Apr 2006 |
| From: | Chris Rycroft |
| Subject: | Simple Person's Applied Math Seminar - Thursday, 5pm, 2-139 |
Hi all,
This week at SPAMS we have Pak Wing Fok, who will be talking about
step flow models of crystal surfaces. The talk will be held at 5pm on
Thursday in 2-139, and will be followed by Italian food in the
Applied Math Common Room.
Hope to see you then,
Chris, Pak, Kevin,
The SPAMS Organizers.
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Title: Relaxation of Crystal Surfaces through Step Flow Models
Abstract: A crystal with a small miscut from a plane of symmetry
results in a surface covered by steps of atomic height. In the
absence of material deposition, crystal surfaces relax to become flat
via the motion of steps, and can develop macroscopically flat regions
called facets. For axisymmetric surface profiles, the steps are
concentric circles with radii that satisfy a system of ODEs coupled
because of step interactions. These "step-flow" ODEs have peculiar
properties associated with the rapid motion of extremal steps and the
formation of facets.
First, I will focus on predictions generated by the step-flow ODEs.
These results concern properties of step bunching and - since
crystals with an infinite number of steps have been studied
frequently in the past - the effects of finite crystal height. In
particular, I show that under certain conditions, step bunches can
always form by choosing a suitable initial step configuration. The
effect of finite crystal height is described quantitatively by
tracking the facet expansion.
I will also talk about a PDE model of surface relaxation, focusing on
the issue of boundary conditions. A boundary condition that
incorporates the discreteness of steps at the facet is implemented
and is shown to give good agreement with step-flow data for a wide
range of step-interaction parameter values.
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