Statistical error analysis of surface-structure parameters determined by low-energy electron and positron diffraction: Data errors.

Abstract

An error-analysis procedure that gives statistically significant error estimates for surface-structure parameters extracted from analyses of measured low-energy electron and positron diffraction (LEED and LEPD) intensities is proposed. This procedure is applied to a surface-structure analysis of Cu(100) in which experimental data are simulated by adding Gaussian-distributed random errors to the calculated intensities for relaxed surface structures. Quantitative expressions for the variances in the surface-structural parameters are given and shown to obey the expected scaling laws for Gaussian errors in the experimental data. The procedure is shown to describe rigorously parameter errors in the limit that the errors in the measured intensities are described by uncorrelated Gaussian statistics. The analysis is valid for structure determinations that are of sufficient quality to admit errors that have magnitudes within the region of convergence of a linear theory that relates perturbations of diffracted intensities to perturbations in structural parameters. It is compared with previously proposed error-estimation techniques used in LEED, LEPD, and x-ray intensity analyses.