We have measured a large thermal surface expansion, 6 times larger than the bulk, on Be(0001) using low-energy electron diffraction. This observation seems to be inconsistent with previous measurements reporting negligible anharmonicity in the surface phonon modes normal to the surface. Density-functional theory calculations for the thermal expansion from the minimum in the free energy within the quasiharmonic approximation agree with the experimental observations and demonstrate that the enhanced thermal expansion is caused largely by a softening of the in-plane vibrations.[ S0031-9007(98) PACS numbers: 63.20. Ry, 68.35.Bs, 68.35.Ja Thermal expansion of a crystal is a direct manifestation of the anharmonic nature of the interatomic forces in solids. For purely harmonic interatomic potentials, the mean positions of the atoms do not change even though their vibrational amplitudes increase with temperature. Thus, an expansion upon heating is intimately related to the anharmonicity of normal modes of lattice vibrations, which, in turn, are determined by the nature of binding between the different units in the lattice. When a crystal is cleaved, a surface is formed by breaking the symmetry and reducing the coordination. This process causes larger thermal motion of the surface atoms and presumably enhanced anharmonicity in the interlayer potential. As the temperature is increased, this anharmonicity can lead to large anisotropic vibrations, surface roughening, and premelting [1].Early free energy calculations with pair potentials for the (100), (110), and (111) surfaces of Cu showed that anharmonicity and its effect on the equilibrium atomic positions (thermal expansion) and the vibrations around the equilibrium atomic positions (mean-square displacements) should be 2-3 times larger at the surface as compared to the bulk [2]. The first experimental evidence for enhanced thermal expansion of a crystal surface was reported for the Pb(110) surface [3] and then for Ni(100), Ag(111), and Cu(110) [4]. The coefficients of thermal expansion were found to be 5 to 20 times larger than in the bulk, much higher than suggested by the aforementioned theory. The assumption in all of these studies was that the enhanced thermal expansion is caused by the greatly enhanced anharmonicity of vibrations perpendicular to the surface.The first quantitative measurement of surface anharmonicity was performed on Cu(110) by Baddorf and Plummer [5] using high-resolution electron energy loss spectroscopy (HREELS). In their study, the temperature dependence of the surface phonon energies and lifetimes revealed a vibrational anharmonicity for motion normal to the surface 4-5 times greater than in the bulk. Unfortunately, there are no equivalent measurements of anharmonicity for Ag(111), Ni(100), and Pb (110) to complement the thermal expansion measurements.Recently, the density-functional theory calculations by Narasimhan and Scheffler [6] and Cho and Scheffler [7] have challenged the intuitive picture of thermal expansion. They argue that ther...