First-principles study of the thermal expansion of Be(10(1)over-bar0)

We present a first-principles study of the thermal expansion of Be(10 (1) over bar0) surface, within the quasiharmonic approximation (QHA). The maximum temperature studied (T=700 K) is well below melting and QHA is adequate in this regime. Many layers are involved in the thermal relaxation of this surface, and in order to apply QHA to this complex system we developed a method for the efficient computation of the third-order derivatives of the total energy in a metallic system using the density-functional perturbation theory . Computer codes for this method are made available on the web. We find that as the temperature increases the short interlayer spacings near the surface contract and the long interlayer spacings expand. The mechanism leading to this behavior is disclosed and compared with that for Mg(10 (1) over bar0) and Al(110) surfaces, where a similar effect was previously observed.