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Capri Spring School on Transport in Nanostructures, March 30, 2007

Charles Stafford. Stability and Symmetry Breaking in Metal Nanowires III: Nonlinear Stability and Structural Dynamics. Capri Spring School on Transport in Nanostructures, March 30, 2007. 1. Structural dynamics: surface self-diffusion. Consider axisymmetric shapes R(z,t).

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Capri Spring School on Transport in Nanostructures, March 30, 2007

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  1. Charles Stafford Stability and Symmetry Breaking in Metal Nanowires III:Nonlinear Stability and Structural Dynamics Capri Spring School on Transport in Nanostructures, March 30, 2007

  2. 1. Structural dynamics: surface self-diffusion • Consider axisymmetric shapes R(z,t). • Structural dynamics → surface self-diffusion of atoms: • Model ionic medium as an incompressible fluid: • Born-Oppenheimer approx.→chemical potential of a surface atom: .

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

  5. Evolution of a random nanowire to a universal equilibrium shape → Explains nanofabrication technique invented by Takayanagi et al. J. Bürki, R. E. Goldstein & CAS, PRL 91, 254501 (2003)

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

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

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

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

  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 Lifetimes for Na nanocylinders: Universal activation barrier to nucleate a surface kink in a long wire: Parameters for various metals: J. Bürki, CAS & D. L. Stein, PRL 95, 090601 (2005)

  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.

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