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A Model for the Thermal Expansion of Ag(111) and other Metal Surfaces

We develop a model to study the thermal expansion of surfaces, wherein phonon frequencies are obtained from ab initio total energy calculations. Anharmonic effects are treated exactly in the direction normal to the surface, and within a quasiharmonic approximation in the plane of the surface. We apply this model to the Ag(111) and Al(111) surfaces, and find that our calculations reproduce the experimental observation of a large and anomalous increase in the surface thermal expansion of Ag(111) at high temperatures [P. Statiris, H.C. Lu and T. Gustafsson, Phys. Rev. Lett. 72, 3574 (1994)]. Surprisingly, we find that this increase can be attributed to a rapid softening of the in-plane phonon frequencies, rather than due to the anharmonicity of the out-of-plane surface phonon modes. This provides evidence for a new mechanism for the enhancement of surface anharmonicity. A comparison with Al(111) shows that the two surfaces behave quite differently, with no evidence for such anomalous behavior on Al(111).