Orientational epitaxy and lateral structure of the hexagonally reconstructed Pt(001) and Au(001) surfaces

We present results of synchrotron-x-ray-scattering studies of the orientational epitaxy exhibited by clean, hexagonally reconstructed Pt(001) and Au(001) surfaces. For the Pt(001) surface, a high-symmetry direction of the hexagonal overlayer is aligned with a high-symmetry direction of the bulk between 1820 and 1685 K. Between 1685 and 1580 K, the relative rotation angle varies continuously from 0°to 0.75°with a one-half-power-law dependence on the reduced temperature. At 1580 K, domains with a rotation angle of 0.8°appear discontinuously, in coexistence with those with a rotation angle of 0.75°. The two rotation angles reach 0.9°and 0.75°for the continuously and discontinuously rotated components, respectively, at 300 K. At all temperatures, the overlayer is incommensurate along both directions of the surface, with weakly temperature-dependent incommensurabilities. The areal density of the Pt(001) overlayer is compressed by 8% with respect to the hexagonal (111) planes in the bulk. In addition, the extent of translational order within the surface layer decreases with decreasing temperature. The Au(001) surface exhibits a strongly discontinuous rotational transformation at 980 K and there is coexistence between rotated and unrotated domains, in agreement with previous measurements. Rotated domains appear at a rotation angle of 0.8°and their number grows with decreasing temperature at the expense of unrotated domains. Our measurements reveal the existence of additional favored rotation angles: one of 0.9°and one that varies smoothly from 0°to 0.5°. The relative domain populations depend on temperature. A mean-field theory of rotational transformations, which accounts for the continuous rotational behavior of the Pt(001) surface, is presented, and it is shown that there are no corrections to mean-field behavior from fluctuations for a rotational transformation.