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Monte Carlo Simulation of Melting and Lattice Relaxation of the (111) Surface of Silver

It is experimentally observed and theoretically proved that the distance between topmost layers of a metal surface has a contraction. However, well-known potentials such as Lennard-Jones and Morse potentials lead to an expansion of the surface inter-layer distance. Such simple potentials therefore cannot be used to study metal surface relaxation. In this paper, extensive Monte Carlo simulations are used to study the silver (111) surface with both the Gupta potential (GP) and the Embedded Atom Method (EAM) potential. Our results of the lattice relaxation at the (111) surface of silver show indeed a contraction for both potentials at low temperatures in agreement with experiments and early theories. However at higher temperatures, the EAM potential yields a surface melting at $\simeq 700$ K very low with respect to the experimental bulk melting at $\simeq 1235$ K while the GP yields a surface melting at $\simeq 1000$ K closer to the bulk one. In addition, we observe with the EAM potential an anomalous thermal expansion, i. e. the surface contraction becomes a surface dilatation with respect to the bulk, at $\simeq 900$ K. The Gupta potential does not show this behavior.We compare our results with different experimental and numerical results.