Temperature dependence of x-ray photoelectron diffraction from copper: Surface and bulk effects

Abstract

The temperature dependence of x-ray photoelectron diffraction (XPD) effects in azimuthal distributions of Cu 2${p}_{3/2}$ and Cu 3p core-level intensities from a clean copper (001) surface has been measured in the range from 298 to 1010 K and for two polar angles of emission relative to the surface of theta=7\ifmmode^\circ\else\textdegree\fi{} (highly surface sensitive) and theta=45\ifmmode^\circ\else\textdegree\fi{} (more bulk sensitive). Measurements have been performed with typical angular resolutions of \ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}4\ifmmode^\circ\else\textdegree\fi{}--6\ifmmode^\circ\else\textdegree\fi{}, although some data obtained with a much higher resolution of \ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}0.6\ifmmode^\circ\else\textdegree\fi{} are also discussed. Very-high-angular-resolution azimuthal scans of Cu 2${p}_{3/2}$ intensity for theta values near 45\ifmmode^\circ\else\textdegree\fi{} show much more fine structure and sensitivity to polar-angle variation than analogous results obtained at lower angular resolution.The diffraction-produced anisotropies as measured by \ensuremath{\Delta}I/${I}_{\mathrm{max}}$=(${I}_{\mathrm{max}}$-${I}_{\mathrm{min}}$)/ $_{\mathrm{max}}$ undergo a much greater relative decrease with increasing temperatures at theta=7\ifmmode^\circ\else\textdegree\fi{} than at theta=45\ifmmode^\circ\else\textdegree\fi{}. Single-scattering cluster (SSC) calculations including Debye-Waller factors predict very well the observed diffraction patterns and their qualitative temperature dependence, as well as the variation of anisotropy with temperature at theta=7\ifmmode^\circ\else\textdegree\fi{}. At theta=45\ifmmode^\circ\else\textdegree\fi{}, theory significantly underestimates the decrease in anisotropy with temperature, probably due to multiple scattering effects occurring for emission along low-index directions with a high density of scattering atoms. Double scattering calculations were performed to estimate these effects and they are compared to experiment and the results of SSC calculations. The effective surface Debye temperatures as deduced from theory and experiment at theta=7\ifmmode^\circ\else\textdegree\fi{} are 202 and 240 K for Cu 2${p}_{3/2}$ and Cu 3p emission, respectively, in good agreement with prior determinations. Finally, the Cu 2${p}_{3/2}$ XPD data for theta=7\ifmmode^\circ\else\textdegree\fi{} gave no evidence for short-range surface melting effects on Cu(001) at temperatures up to T/${T}_{\mathrm{melting}=0.74}$.