CHIRAL MELTING OF THE SI(113)(3X1) RECONSTRUCTION

We report the results of synchrotron X-ray scattering studies of the d isordering of the Si(113) (3x1) reconstruction. A continuous commensur ate-solid to incommensurate-fluid transformation at T-c = 950 +/- 40 K is observed. At the transformation, the reconstructed layer becomes u niaxially incommensurate along the cubic (1(1) over bar0$)-direction ( x-direction). It remains commensurate along the (33(2) over bar)-direc tion (y-direction). Critical scattering shows power-law behavior over nearly two decades of reduced temperature with exponents <(beta)over b ar> = 0.66 +/- 0.05 for the incommensurability (epsilon), v(x) = 0.65 +/- 0.07 for the inverse correlation length in the incommensurate dire ction (kappa(x)), v(y) = 1.06 +/- 0.07 for the inverse correlation len gth in the commensurate direction (kappa(y)), and y = 1.56 +/- 0.13 fo r the susceptibility (chi). Below T-c the variation of the square of t he order parameter, proportional to the peak intensity at the commensu rate position (I-0), varies with an exponent 2 beta = 0.22 +/- 0.04. I t is noteworthy that the correlation lengths in the disordered phase s cale anisotropically, i.e. v(x)=v(y), and that the collected exponents do not conform to those of any previously measured universality class . Two universal constants of the transformation have also been measure d. The ratio of the incommensurability and the inverse correlation len gth along the incommnensurate direction in the disordered phase is fou nd to be independent of temperature, i.e. <(beta)over bar> = v(x), con sistent with predictions for a new two-dimensional chiral melting univ ersality class, and to have the value w(0) = 1.6 +/- 0.2. Also, the hy perscaling ratio R(s) = chi kappa(x) kappa(y)/I0Vr, where V-r is the t wo-dimensional resolution volume, is independent of the reduced temper ature, consistent with the derived hyperscaling relationship v(x) + v( y) = y + 2 beta. According to the hypothesis of two-scale-factor unive rsality, R(s) is a universal constant, which we find takes the value R (s) = 0.07 +/- 0.03. These results are discussed in the context of pro posed phase diagrams of two-dimensional threefold-degenerate uniaxial overlayers where the chirality, or difference in free energy of light and heavy domain walls, is varied. A comparison is made to recent LEED measurements of the (3 x 1)-to-disordered transformations of Si and G e.