Order-disorder transition driven by dynamical effects between the Sn/Ge(111)-($3\times3$) and $(\sqrt{3}\times\sqrt{3})R30^{\circ}$ phases

A dynamical origin for the Sn/Ge(111) room temperature phase has been revealed by the accurate structural determination of the ($3\times3$) and $(\sqrt{3}\times\sqrt{3})R30^{\circ}$ Sn/Ge(111) phases using surface x-ray diffraction experiments. Basically, two well distinct Sn sites are present in both phases, which build in a vertical corrugation of $\sim$0.49 \AA at the Sn layer. The temperature evolution of the width and intensity of the diffraction beams exhibits an order-disorder phase transition behavior, with little change in the magnitude of the atomic displacements. Hence, the room temperature Sn/Ge(111) phase is the result of a vertical flipping of the Sn adatoms.