My knowledges of faceting and roughening are mainly from the textbook: "Principles of condensed matter physics", P.M. Chaikin & T.C. Lubensky.
1) From the configurations and the distributions of bond curvatures and local curvatures, we can conclude that qualitatively the icosahedral gold cluster go through a roughening (faceting) transition before complete melting.
2) By visual examination of the configurations, beginning at 600K, the atoms around vertices begin to diffuse. The diffusion area becomes larger with increasing temperature. At 1000K, most atoms (including edge and some facet atoms) travel 2-3 atom distances. However, there are still some atoms remain in the original positions. Those atoms seems to be on the largest facets.
3) Although surface atoms diffuse from 600K to 1000K, surface bond order parameters don't change much.
1) I don't know if faceting and roughening transitions are defined including the influence of thermal fluctuations. If not, thermal fluctuations blur the results and should be excluded from the statistics.
2) The characteristics of faceting transition are smoother
corners and edges, and smaller facets, until no angle discontinuities at and
above roughening transition temperature TR.
By visual examination of the sampled configurations, up to 1000K there
still exist facets, edges and corners for each spontaneous configuration,
although they fluctuate a lot from configuration to configuration.
How can we quantitatively characterize faceting? (Can bond curvatures
or local curvatures do that?)
3) The textbook uses sine-Gordon Hamiltonian to define the roughening temperature TR. Should we try to understand and calculate sine-Gordon Hamiltonian for our cluster?
4) Is it possible that at 1000K, the surface atoms diffuse on the surface and between layers, but the surface structure remain unchanged? Can we say it is surface melting?