Enhanced and correlated thermal vibrations of Cu(111) and Ni(111) surfaces

Abstract

Enhanced and correlated thermal vibrations are studied for Cu(111) and Ni(111) by high-resolution medium energy ion scattering (MEIS) using the ion shadowing effect. We also perform molecular dynamics (MD) simulations based on the embedded atom method (EAM). The MEIS analysis reveals a slight contraction of $0.011\ifmmode\pm\else\textpm\fi{}0.003$ and $0.007\ifmmode\pm\else\textpm\fi{}0.003\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ for Cu(111) and Ni(111), respectively, for the first interlayer distance without any surface reconstruction. The root mean square (rms) bulk thermal vibration amplitude and thermal vibration amplitudes (TVAs) of the top-layer atoms in the surface normal and lateral directions, respectively, are determined to be $0.085\ifmmode\pm\else\textpm\fi{}0.005$, ${0.141}_{\ensuremath{-}0.005}^{+0.010}$, and ${0.094}_{\ensuremath{-}0.005}^{+0.008}\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ for Cu(111) and $0.068\ifmmode\pm\else\textpm\fi{}0.005$, ${0.098}_{\ensuremath{-}0.005}^{+0.010}$, and ${0.074}_{\ensuremath{-}0.005}^{+0.008}\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ for Ni(111). We also observe strong correlations between the nearest-neighbor atoms in the [110] string and determine the correlation coefficients to be $+0.24\ifmmode\pm\else\textpm\fi{}0.05$ and $+0.20\ifmmode\pm\else\textpm\fi{}0.05$ for Cu(111) and Ni(111), respectively, for the motion perpendicular to the [110] axis. The present MEIS result is basically in agreement with the MD simulations using the EAM potential proposed by Foiles, Baske, and Daw [Phys. Rev. B 33, 7983 (1986)] rather than that approximated by Oh and Johnson [J. Mater. Res. 3, 471 (1988)].