1. 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

2. 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:

3. Chemical potential of a surface atom J. Bürki, R. E. Goldstein & CAS, PRL 91, 254501 (2003)

4. Propagation of a surface instability: Phase separation ↔

5. 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.

6. What happens if we turn off the electron-shell potential? Rayleigh instability!

7. Universal equilibrium shape: magic cylinder + unduloidal contacts

8. Thinning of a nanowire: Kink formation & propagation J. Bürki, cond-mat/0611070 Thinning driven by sink of atoms at left end of wire, i) Rapid initial movement: ii) Constant asymptotic speed:

9. Kink = stationary state connecting two minima

10. Thinning of a nanowire: Kink interactions J. Bürki, cond-mat/0611070

11. Fabrication of a gold nanowire using an electron microscope Courtesy of K. Takayanagi, Tokyo Institute of Technology

12. J. Bürki, R. E. Goldstein & CAS, PRL 91, 254501 (2003) Necking of a nanowire under strain

13. Hysteresis: elongation vs. compression J. Bürki, R. E. Goldstein & CAS, PRL 91, 254501 (2003)

14. Model thermal fluctuations via stochastic Ginzburg-Landau field theory based on semiclassical energy functional. 2. Stochastic GL theory of thermal fluctuations

15. 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)

16. 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:

17. 3. Conclusions Universal equilibrium shape: magic cylinder suspended between unduloidal contacts. “Universal” stability: New class of nonlinear dynamics at the nanoscale: Long-time dynamics governed by the nucleation, propagation, and interaction of surface solitons.