Diffraction from stepped surfaces in thermal equilibrium

We have performed Monte Carlo simulations of the diffraction from simple two-dimensional models of vicinal surfaces in order to aid interpretation of measured diffraction profiles. At low temperature, we find the sharp diffraction features predicted from the analogy of stepped surfaces with two-dimensional incommensurate phases. These sharp features vanish only near the roughening temperature of the low-index surface corresponding to the terraces between steps. If one fits experimental data having sharp diffraction features to models of step disorder which do not include the ordering influence of step wandering, one can severely overestimate the amount of disorder. We emphasize that long-range correlations in step positions are more important than the local order in step edge structure or step separations for interpreting sharp diffraction features from steps. After much theoretical effort, it has become well-established that asymptotically the height-height correlations for rough surfaces diverge logarithmically (with a prefactor having a universal component at low temperature). We show explicitly how to use diffraction data to access this behavior for stepped surfaces. In the process, we evaluate the accuracy of a popular approximate expression for the diffracted intensity.