Temperature dependent surface relaxations of Ag(111)

TL;DR

This study uses density-functional theory to analyze how the surface relaxation of Ag(111) varies with temperature, revealing a transition from contraction to expansion consistent with experiments.

Contribution

It provides a detailed temperature-dependent analysis of Ag(111) surface relaxation using first-principles calculations, including phonon dispersions and free energy minimization.

Findings

Surface relaxation changes from contraction to expansion with temperature.

Calculated phonon dispersion matches helium scattering data.

Surface expansion mechanism is elucidated.

Abstract

The temperature dependent surface relaxation of Ag(111) is calculated by density-functional theory. At a given temperature, the equilibrium geometry is determined by minimizing the Helmholtz free energy within the quasiharmonic approximation. To this end, phonon dispersions all over the Brillouin zone are determined from density-functional perturbation theory. We find that the top-layer relaxation of Ag(111) 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 expansion is analyzed.