Displacive phase transition at the 5/3 monolayer of Pb on Ge(001)

At a coverage of 5/3 monolayer (ML), Pb adsorbed on Ge(001) forms a ground phase displaying a ((2 1)(0 6))s ymmetry. This phase undergoes two reversible phase transitions ((2 1)(0 6))<->((2 1)(0 3))<->(2x1) at the critical temperatures T(c1)similar to 178 K and T(c2)similar to 375 K, respectively. We investigated the behavior of the relevant order parameters at the critical temperatures by means of He and in-plane x-ray diffraction (HAS and XRD, respectively). Both phase transitions at the critical temperature put in evidence a clear order-disorder behavior, in agreement with the universality class expected for the corresponding symmetry group transformation. The low-temperature transition yields the critical exponent of the two-dimensional (2-D) Ising universality class, whereas the three-state Potts' critical exponents are found for the high-temperature transition. By out-of-plane XRD measurements, the low-temperature phase transition is observed to be accompanied by a static surface distortion at room temperature. A complementary HAS study of the temperature evolution of the surface charge corrugation reveals that the complete ((2 1)(0 6))<->((2 1)(0 3)) transition is of the displacive type. On the contrary, the high-temperature phase transition does not show any change of the surface corrugation up to its irreversible decomposition, thus pointing to a pure order-disorder character.