ON THE DOYLE-TURNER REPRESENTATION OF THE OPTICAL-POTENTIAL FOR RHEED CALCULATIONS

The approximate representation of the atomic potential in the form of a set of Gaussian exponential terms has long been recognized as the most convenient method for carrying out many-beam calculations of reflection high-energy electron diffraction (RHEED) intensities. Smith and Burge [Acta Cryst, 15 (1962) 182] and later Doyle and Turner [Acta Cryst. A 24 (1968) 390] (hereafter referred as DT) used Gaussian fitting to represent the scattering factor of a number of elements. However, until recently the coefficients of the DT expansion were only known for the real part of the crystal potential. In this paper, we show how the DT parameters can be introduced and calculated for the imaginary part of the potential. A set of the DT coefficients is given in tabulated form which provides an accurate approximation to the imaginary part of the potential arising from thermal motion of atoms. These coefficients correspond to the same set of values of the Debye-Waller factor as those used by Radi [Acta Cryst. A26 (1970) 41], Our analysis shows that in most cases the real space behaviour of the imaginary part of the potential differ substantially from the often assumed hypothesis Im U(r) = constant x Re U(r), and this difference appears to have a considerable effect on the RHEED intensities calculated using a many-beam approach. Comparison of our calculations with the results obtained recently by other authors suggests that there exist some additional processes of diffuse scattering affecting elastic RHEED intensities. Computer programs used for carrying out calculations of the DT parameters are available upon request.