Anomalously Large Thermal Expansion at the (0001) Surface of Beryllium without Observable Interlayer Anharmonicity

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Abstract
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.