Dynamics on Curved Surfaces

Benasque: August 12, 2005

Mark Bowick, Andreas Bausch, Peter Lipowsky, Jan Meinke and David Nelson

Particle DynamicsBausch et al, Nat. Mat. 4 (2005) 407

cond-mat/0506366

Glide Dynamics

• Modeling dislocation glide by a Langevin equation with potential energy

21( )

2 DU y k y

22 1 Dk tB

D

k Ty e

k

leads to

This yields 0 21 /glide BD k T a s

and2lim B

tD

k Ty

k

with21 /D Bk k T a

Peierls Potential

A histogram of the glide coordinates gives us

tot B( ) / 2tot 0

1( ) with ( ) cos(2 /a)

2U y k T

DN y e U y k y U y

Long-distance diffusion

0 /renglideD D I I

( ) /p BU y k TdyI e

a

0 2/ 8 0.1 /renglideD D a s

with

3d Structures

Bausch and Bowick, cond-mat/0506741

Interstitials

Summary

• Grain boundary scars seen experimentally

• Dynamics of colloidal particles and dislocation defects directly measurable

• Elastic response of lattice and short and long-distance diffusion constant for dislocation glide both measured

• Peierls potential determined

• 3D structure determined