Melting Behavior of Mackay Icosahedral Gold Cluster
                  from Molecular Dynamics Simulations

* Introduction

   * Recent interest on gold nanoclusters and gold nanorods.

   * Experimental and simulating results for gold nanoclusters and
     gold nanorods.

   * Melting behavior of gold nanorods requires deeper understanding of
     the facets acting in nano size.

   * The simulating and experimental results for infinite fcc <111> facets.

   * Our conclusion of Mackay icosahedral gold cluster melting behavior.


* Methods

   * Andersen Thermostat and constant temperature molecular dynamics, glue
     potential, cell index method.

   * Bond orientational order parameters.

   * Surface geometrical analysis:
       * Surface atom discrimination -- cone algorithm.
       * Bond curvature and local curvature calculations.
       * Surface atom distribution (atomic clouds) and averaging.

   * Atom mobility analysis:
       * Mean squared displacement and diffusion coefficients.
       * Interlayer diffusion.
       * Ellipsoid surface atom movement representation.


* Results

   * Mackay icosahedral structure with central atom missing.

   * Caloric curve and melting temperature, superheating.

   * Surface and interior bond order parameters.

   * Mean squared displacement and diffusion coefficients.

   * Interlayer diffusion.

   * Bond curvature distribution.

   * Ellipsoid surface atom movement representation.

   * Average equilibrium shapes.

   * Results of other sizes.


* Conclusion

   * Slow cooling procedure leads gold cluster with thousands of atoms to
     Mackay icosahedral structure.

   * Due to small size, at high temperature, the shape fluctuates vibrately
     to form atomic clouds, so that the instantaneous configuration is always
     more faceted than the average. Our simulation verified the fluctuations 
     are distributed around an equilibrium shape at each temperature.

   * With increasing temperature, vertex atoms start to diffuse first,
     the edge atoms diffuse at a little higher temperature, rounding
     the vertices and edges.

   * Although surface atoms diffuse at lower temperature, the surface structure
     is softened only about 100K below melting temperature. No surface melting
     prior to bulk melting.

   * There is a faceting (or equivalently roughening) of the fcc <111> surface
     of the cluster, that takes place as a finite size effect, and tracks
     the melting transition, occuring just below the melting.

   * The only difference of melting behavior between Mackay icosahedral gold
     cluster and infinite fcc <111> surface is caused by the increased
     mobility of vertex and edge atoms.