Fluctuation spectroscopy of step edges on Pt(111) and Pd(111)

Abstract

By step fluctuation spectroscopy, using low-energy electron microscopy (LEEM), we investigate step energies and relaxation on clean Pt(111) and Pd(111) surfaces at temperatures above half the melting temperature ${T}_{m}$. Some effort has been expended to develop accurate procedures for analyzing fluctuations observed as video recordings. The average step stiffnesses are about $210\phantom{\rule{0.3em}{0ex}}\mathrm{meV}∕\mathrm{nm}$ and $265\phantom{\rule{0.3em}{0ex}}\mathrm{meV}∕\mathrm{nm}$ for Pt and Pd, weakly temperature dependent, and in each case fairly isotropic with mainly a sixfold angular variation. Consequently, the step free energies are highly isotropic. At the lower temperatures, the relaxation rates of fluctuations with wave vector, $q$, vary as ${q}^{3}$. This is the unambiguous signature of step relaxation by surface diffusion over the terraces. It affords accurate determinations of the surface mass diffusion coefficients ${\mathrm{D}}_{s}=5(\ifmmode\times\else\texttimes\fi{}{2}^{\ifmmode\pm\else\textpm\fi{}1})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}(\ensuremath{-}1.2\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕{k}_{B}T)\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}∕\mathrm{s}$ for Pt(111) and ${\mathrm{D}}_{s}=3(\ifmmode\times\else\texttimes\fi{}{2.5}^{\ifmmode\pm\else\textpm\fi{}1})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}(\ensuremath{-}{1.1}_{5}\ifmmode\pm\else\textpm\fi{}{0.1}_{5}\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕{k}_{B}T)\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}∕\mathrm{s}$ for Pd(111). At more elevated temperatures the measured rates vary approximately as ${q}^{2}$ in both cases. This corresponds to the surface process being short-circuited by a faster flow of bulk vacancies. Known bulk diffusion coefficients for Pt and Pd are consistent with this interpretation. An effective procedure is developed to separate bulk and surface contributions. There is the appearance of universality in the fluctuation processes, which approximates as an homologous dependence on $T∕{T}_{m}$. It is observed for Pt(111) at $1400\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and above that neighboring steps react to form multisteps that retain capillary characteristics. The stiffnesses of multisteps formed from up to five associated steps have been determined by fluctuation spectroscopy and are employed to discuss the energetics of multistep formation. Clear evidence is found that the multistep free energy contains important contributions from internal degrees of freedom. The kinetics of multistep fluctuations are explained by the same diffusion coefficient ${\mathrm{D}}_{s}$ determined from single steps.