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:

Chemical potential of a surface atom

J. Bürki, R. E. Goldstein & CAS, PRL 91, 254501 (2003)

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.

What happens if we turn off the electron-shell potential?

Rayleigh instability!

Universal equilibrium shape: magic cylinder + unduloidal contacts

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:

Kink = stationary state connecting two minima

Thinning of a nanowire: Kink interactions

J. Bürki, cond-mat/0611070

Fabrication of a gold nanowire using an electron microscope

Courtesy of K. Takayanagi, Tokyo Institute of Technology

J. Bürki, R. E. Goldstein & CAS, PRL 91, 254501 (2003)

Necking of a nanowire under strain

Hysteresis: elongation vs. compression

J. Bürki, R. E. Goldstein & CAS, PRL 91, 254501 (2003)

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:

3. Conclusions

Universal equilibrium shape: magic cylinder suspended between unduloidalcontacts.

“Universal” stability:

New class of nonlinear dynamics at the nanoscale: Long-time dynamics governed by the nucleation, propagation, and interaction of surface solitons.