Quantitative analysis of low-energy-electron diffraction: Application to Pt(111)

A method is described for quantitative analysis of low-energy-electron diffraction (LEED) intensity-energy spectra by comparison of experimental spectra with spectra calculated using a dynamic theory of LEED. The method involves a minimization of the variance of the fit between experimental and calculated spectra as a function of the calculational variables, both structural and nonstructural, leading to determination of optimum parameter values. Correlation between the variables is taken into account. The method is applied to extensive, new experimental LEED data for Pt(111). It is shown quantitatively that the variance of the fit depends strongly on the value of a single structural variable, $d_{\perp }$, the first interlayer spacing, but weakly on the values of three nonstructural variables, $V_0$, the inner potential, $V_{\mathrm{im}}$, the absorption potential, and ${\Theta }_D$, the Debye temperature. The analysis leads to an optimum value of $d_{\perp }=2.29\mathrm{}$ Å, corresponding to a 1% expansion of the first layer spacing, with an estimated error of ±0.1 Å. This result is in good agreement with the earlier studies of Kesmodel and co-workers.