Measurement of step and kink energies and of the step-edge stiffness from island studies on Pt(111)

Abstract

By using temperature-variable scanning tunneling microscopy, we studied two-dimensional vacancy islands on Pt(111) between 593 and $713\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Due to the difference in the step free energies of $A$ and $B$ steps, the equilibrium shape of the vacancy islands has a threefold symmetry. From the analysis of the equilibrium shape of the vacancy islands, we calculate the angular dependence of the step free energy on Pt(111). The absolute values for the step free energies per atom of $A$ and $B$ steps are determined from the equilibrium shape fluctuations to be ${\ensuremath{\beta}}_{A}=348\ifmmode\pm\else\textpm\fi{}16\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$/atom and ${\ensuremath{\beta}}_{B}=300\ifmmode\pm\else\textpm\fi{}14\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$/atom, respectively. Furthermore, we derive the temperature dependence of the step-edge stiffness $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\beta}}$ with ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\beta}}}_{A}$ between 510 and $453\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$/atom and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\beta}}}_{B}$ between 1974 and $1104\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$/atom in the temperature range considered. From the stiffness, we obtain the kink formation energies for $A$ and $B$ steps, ${\ensuremath{\epsilon}}_{A}=143\ifmmode\pm\else\textpm\fi{}9\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ and ${\ensuremath{\epsilon}}_{B}=206\ifmmode\pm\else\textpm\fi{}9\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$, respectively.