Chiral melting of the Si(113)(3×1) reconstruction

We report the results of synchrotron X-ray scattering studies of the disordering of the Si(113) (3×1) reconstruction. A continuous commensurate-solid to incommensurate-fluid transformation at T_c = 950±40 K is observed. At the transformation, the reconstructed layer becomes uniaxially incommensurate along the cubic (110)-direction (x-direction). It remains commensurate along the (332)-direction (y-direction). Critical scattering shows power-law behavior over nearly two decades of reduced temperature with exponents β̄= 0.66±0.05 for the incommensurability (ε), ν_x = 0.65±0.07 for the inverse correlation length in the incommensurate direction (κ_x), ν_y = 1.06±0.07 for the inverse correlation length in the commensurate direction (κ_y), and γ = 1.56±0.13 for the susceptibility (χ). Below T_c the variation of the square of the order parameter, proportional to the peak intensity at the commensurate position (I₀), varies with an exponent 2β = 0.22±0.04. It is noteworthy that the correlation lengths in the disordered phase scale anisotropically, i.e. ν_x ≠ ν_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 measured. The ratio of the incommensurability and the inverse correlation length along the incommensurate direction in the disordered phase is found to be independent of temperature, i.e. β̄ = ν_x, consistent with predictions for a new two-dimensional chiral melting universality class, and to have the value w₀ = 1.6±0.2. Also, the hyperscaling ratio R_s = χκ_xκ_y/I₀V_r, where V_r is the two-dimensional resolution volume, is independent of the reduced temperature, consistent with the derived hyperscaling relationship ν_x + ν_y = γ + 2β. According to the hypothesis of two-scale-factor universality, 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 proposed 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 (3×1)-to-disordered transformations of Si and Ge.