Quantitative studies of two-dimensional first- and second-order phase transitions by integrating diffraction methods

Using low-energy electron diffraction (LEED), we show for two classes of systems, which are representative for second- and first-order phase transitions in adsorbed layers, that quantitative properties of phase transitions can be studied also by using integrated diffracted intensities, turning the instrument to low resolution in two-dimensional reciprocal space, k_∥. For the continuous order-disorder phase transitions of several atomic adsorption systems, critical properties have been studied by determination of the critical exponents α (of the specific heat) and η, the anomalous critical dimension, in the limit k_∥ξ ≫ 1. We performed systematic tests of the conditions under which these exponents can be determined reliably from the diffracted intensity of superstructure beams. In first-order phase transitions, scaling laws characterize specific mechanisms driving the transitions. As an example of two-dimensional first-orderphase transitions, the transitions between a two-dimensional (2D) gas and the 2D solid of the first monolayer have been studied for the noble gases Ar, Kr and Xe on a NaCl(100) surface in quasi-equilibrium with the three-dimensional (3D) gas phase. Using linear temperature ramps, we show that the widths of the hysteresis loops of these transitions as a function of the heating rate, r, scale with a power law ∝r^x with x between 0.4 and 0.5 depending on the system. The hysteresis loops for different heating rates are similar. The island area of the condensed layer was found to grow initially with a time dependence ∝t⁴. These results are in agreement with a model of growth-controlled hysteresis, which predicts x = 0.5 and hysteresis loop similarity.