Temperature-dependent surface relaxations of Ag(111)

The temperature-dependent surface relaxation of Ag(lll) is calculated by de nsity-functional theory. At a given temperature, the equilibrium geometry i s determined by minimizing the Helmholtz free energy within the quasiharmon ic approximation. To this end, phonon dispersions all over the Brillouin zo ne are determined from density-functional perturbation theory. We find that the top-layer relaxation of Ag(lll) changes from an inward contraction (-0 .8%) to an outward expansion (+6.3%) as the temperature increases from T=0 K to 1150 K, in agreement with experimental findings. Also, the calculated surface phonon dispersion curves at room temperature are in good agreement with helium-scattering measurements. The mechanism driving this surface exp ansion is analyzed, and the physical picture developed by Narasimhan and Sc heffler is essentially confirmed. [S0163-1829(99)00502-0].