EXPERIMENTAL-DETERMINATION OF THE PHASE-TRANSITION CRITICAL EXPONENT-ALPHA AND EXPONENT-ETA BY INTEGRATING METHODS

Integrating methods in low-energy electron diffraction-turning the ins trument to low resolution in k(parallel to)-can reliably be used to st udy critical properties of continuous two-dimensional phase transition s and to determine critical exponents alpha and eta. We performed syst ematic tests of the conditions under which an energylike power depende nce of the diffracted intensity of superstructure beams can be observe d in order-disorder phase transitions of adsorbed atomic layers belong ing to three- and four-state Potts universality classes. As experiment al examples, we studied the systems p(2 x 2)- and (root 3 x root 3)R30 degrees-S/Ru(0001) and (2 x 2)-2H/Ni(111). We show that above T-c the condition for an energylike singularity, K-I xi much greater than 1 ( K-I: radius of integration in k space, xi: correlation length) is alre ady reached at K-I xi > 3, whereas below T-c effective exponents alpha are already obtained for K-I xi < 1. Therefore, in the temperature ra nge below T-c this method to determine alpha turns out to be particula rly easy to apply, and we concentrate on the determination of alpha be low T-c in this study. Values of alpha of 0.67 +/- 0.04 and 0.40 +/- 0 .05 were obtained for four-state Potts and three-state Potts systems, respectively. The latter value indicates small crossover effects to th e critical behavior of the peak intensity. These studies were then fur ther extended to the order-disorder transition of p(2 x 2)-O/Ni(111), which is weakly first order, and to the effects of oxygen impurities i n the system (2 x 2)-2H/Ni(111). We further show that in the limit k x i much greater than 1 the exponent eta can be determined from the k(pa rallel to) dependence of integrated ring intensities around positions of superstructure beams. With the systems mentioned, we demonstrate th at the limit of a leading term of critical scattering which is indepen dent of temperature can be reached by carrying out measurements going through the order-disorder phase transitions. Values of eta of 0.27 +/ - 0.10 and of 0.30 +/- 0.10 were obtained for the four-state and the t hree-state Potts systems, in close agreement with theoretical expectat ions.