Abstract

X-ray standing waves (XSW) are used to measure the structure of the $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ to $(3\ifmmode\times\else\texttimes\fi{}3)$ low-temperature phase transition for the $\frac{1}{3}$ monolayer Sn/Ge(111) surface. A three-dimensional direct-space imaging approach, based on the summation of several $\mathrm{hkl}$ XSW-measured Fourier coefficients, is demonstrated. At room temperature, the Sn atoms are found to occupy the ${T}_{4}$-adsorption sites with one-third of the Sn atoms 0.45 \AA{} higher than the remaining two-thirds. The $(3\ifmmode\times\else\texttimes\fi{}3)$ phase has no significant change in the XSW-measured structural parameters. This is consistent with an order-disorder-type phase transition.

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