Unusually Large Thermal Expansion of Ag(111)

We investigate the thermal behavior of the (111) surface of silver, using phonon frequencies obtained from ab initio total energy calculations, and anharmonic effects treated within a quasiharmonic approximation. Our results reproduce the experimental observation of a large and anomalous increase in the surface thermal expansion at high temperatures [P. Statiris et al., 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).