CONTINUOUS ORDER-DISORDER PHASE-TRANSITIONS OF THE P(2X2) AND (ROOT-3X-ROOT-3)R30-DEGREES SUPERSTRUCTURES OF SULFUR ON RU(001) - EFFECTIVE CRITICAL EXPONENTS AND FINITE-SIZE EFFECTS

Critical properties of the two-dimensional order-disorder phase transi tions of the p(2 x 2) and the (square-root 3 x square-root 3)R30-degre es superstructures of sulfur chemisorbed on Ru(001) were determined by spot-profile analysis using high-resolution low-energy electron diffr action. Both transitions are continuous, as evident from the power-law behavior observed for 0.01 less-than-or-equal-to absolute value of t less-than-or-equal-to 0.1 (t = T/T(c) - 1) and from the values obtaine d for the criticial exponents. For smaller absolute value of t the pha se transitions are finite-size rounded by an interaction of the supers tructure domains with steps (average distance between steps approximat ely 275 angstrom). The values of the effective exponents beta of the o rder parameter, nu of the correlation length, gamma of the susceptibil ity and the exponent eta [only determined for p(2x2)] fall close to th e values theoretically predicted for the four-state and three-state Po tts universality classes, respectively. Deviations of experimental val ues from Potts values, found for beta and gamma, are attributed to cor rections to scaling which in part might be specific to the lattice gas . Additional experiments on vicinal surfaces with higher step densitie s show that pinning of the superstructure domains at monoatomic steps limits the correlation length to values below the average terrace widt h. The finite-size-induced effects are quantitatively compatible with predictions from finite-size scaling theory.