Crystallite Relaxation by Confined Screw Dislocation Motion
Nanoscale lead crystallites supported on Ruthenium substrate
were prepared in unstable shapes by rapidly cooling the system from its
high temperature state. It was observed that about 30% of these crystallites
had a noncentered screw dislocation on the circular top facet. These crystallites
relax to their equilibrium state by turning of the spiral step emerging
from the screw dislocation. The turning of these spiral steps was observed
using Scanning Tunneling Microscopy. These experiments showed that when
the radius was 385 nm a single revolution took 23 minutes. As the spiral
turns the shape and rotation rate changes significantly as can be seen
in this movie of successive STM images.
We construct a model of the top surface consisting of a step
that starts the core of the dislocation and smoothly joins a circle corresponding
to the boundary of the top facet. The local motion of the step is governed
by the attachment and detachment of atoms from the step edge but the global
shapes are strongly influenced by the confinement due to the finite size
of the facet. The time dependent step shapes
predicted using a curvature driven law of motion are very similar to the
experimental shapes and the kinetic parameters are in agreement with other
experiments on the same system.
Uniformly Rotating Shapes
We also look at approximate solutions called Uniformly Rotating
Shapes (URS). These shapes have, at any given time a constant angular velocity
along the step from the core to the point where they join the circle smoothly
with a continuous first derivative. But unlike the case of a centered spiral,
the angular velocity and the total arc length from the core to the joining
point will change for solutions at different time instants. These shapes
are very close to the time dependent solution when they join the crystallite in
the upper half plane, but there are no URS that join in the other half
plane. Experiment (a), the time dependent shapes (b), and the URS (c),
are compared in this Figure.
This work has been supported by NSF-MRSEC at University
of MD, DMR #0080008.