LEED crystallographic studies of the (311) surface of nickel: II. Methodology and uncertainties

The reliability indices proposed for LEED structural analyses by Zanazzi and Jona and by Pendry have been examined with data for the (311) surface of nickel. Consideration has been given to how these indices are affected by various operations and procedures including the smoothing of experimental data, the averaging of I(E) curves which are closely equivalent, the correcting of measured intensities for differences in grid transparencies, and including energy-dependent forms of V_or the multiple-scattering calculations. Simultaneously, assessments have been made of three potential procedures for estimating uncertainties in the determined surface geometrical parameters. In this regard a new measure of uncertainty (S₃) appears useful. It provides a compromise between being based entirely on the single-beam reliability index values, for the condition of minimum in the overall R, and being based entirely on geometries that minimise values of the single-beam indices.