Order-disorder c(4 X 2)-(2 X 1) transition on Ge(001): An in situ x-ray scattering study

Using in situ x-ray diffraction, we have studied the order-disorder phase transition on the Ge(001) surface by measuring the temperature dependence of a superlattice reflection specific to the c(4\ifmmode\times\else\texttimes\fi{}2) low-temperature phase. The results indicate that the transition corresponds to a two-dimensional phase transition with anisotropic interaction energies along and perpendicular to the dimer rows that form the (2\ifmmode\times\else\texttimes\fi{}1) surface. Due to pinning of the c(4\ifmmode\times\else\texttimes\fi{}2) domains by defects, we are unable to observe any universal critical behavior. The results indicate that the number of buckled dimers involved in the c(4\ifmmode\times\else\texttimes\fi{}2) reconstruction is conserved through the transition. This implies that above room temperature the (2\ifmmode\times\else\texttimes\fi{}1) surface consists of a random array of buckled dimers.