Stability and Symmetry Breaking in Metal Nanowires III: Nonlinear Stability and Structural Dynamics...
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Transcript of Stability and Symmetry Breaking in Metal Nanowires III: Nonlinear Stability and Structural Dynamics...
Stability and Symmetry Breaking in Metal Nanowires III:Nonlinear Stability and Structural Dynamics
Capri Spring School on Transport in Nanostructures, March 30, 2007
Charles Stafford
1. Structural dynamics: surface self-diffusion
•Consider axisymmetric shapes R(z,t).
•Structural dynamics → surface self-diffusion of atoms:
•Born-Oppenheimer approx. → chemical potential of a surface atom:
.
•Model ionic medium as an incompressible fluid:
J. Bürki, R. E. Goldstein & CAS, PRL 91, 254501 (2003)
Propagation of a surface instability:Phase separation
↔
Evolution of a random nanowire to a universal equilibrium shape
J. Bürki, R. E. Goldstein & CAS, PRL 91, 254501 (2003)
→ Explains nanofabrication technique invented by Takayanagi et al.
Thinning of a nanowire: Kink formation & propagation
J. Bürki, cond-mat/0611070
Thinning driven by sink of atomsat left end of wire,
i) Rapid initial movement:
ii) Constant asymptotic speed:
Fabrication of a gold nanowire using an electron microscope
Courtesy of K. Takayanagi, Tokyo Institute of Technology
Model thermal fluctuations via stochastic Ginzburg-Landau field theory based on semiclassical energy functional.
2. Stochastic GL theory of thermal fluctuations
Lifetime of a metal nanocylinder
•Neumann b.c.’s at wire ends.
•Lifetime limited by nucleation of surface kinks at ends.
J. Bürki, CAS & D. L. Stein, PRL 95, 090601 (2005)
Lifetime of a metal nanocylinder
Universal activation barrier to nucleate a surface kink in a long wire:
J. Bürki, CAS & D. L. Stein, PRL 95, 090601 (2005)
Lifetimes for Na nanocylinders:
Parameters for various metals: