  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).
