THE EXPANSION OF TENSOR-LEED IN CARTESIAN COORDINATES

At present the direct approach in LEED structure analysis has the primary disadvantage of being limited to structural models located within 0.1 angstrom of an arbitrarily chosen reference structure. This limitation is a consequence of the use of the simplest form of the Tensor-LEED approximation, which is linear in the atomic displacements and thus allows the direct inversion of LEED IV spectra. However, the implementation of the method for larger displacements and the potential new applications to thermal disorder, require that the more accurate, second-order Tensor-LEED approximation, be recast into a power series of the atomic coordinates. In this paper it is shown that the coefficients of such a power series expansion can be derived from the first-order Tensor-LEED approximation by evaluating simple recurrence relations. In addition, we develop a new way of shifting the origin of coordinates by using the full second-order Tensor-LEED approximation. Taking into account terms including up to fifth powers of the atomic displacements, the new scheme is shown to be valid for atomic displacements of up to 0.2 angstrom perpendicular and 0.4 angstrom parallel to the surface, for the case of Ni(100) c(2 x 2)-O at normal incidence. Although this result corresponds to a restricted range of validity as compared to the full second-order approximation, it is suggested to cover the whole range of Tensor-LEED by a limited number of calculations at shifted origin. Thus the resulting scheme for calculating LEED intensities as a polynomial is as powerful as the original second-order Tensor-LEED and allows for new applications as suggested in the direct approach.