Multiple scattering of electrons in solids and molecules: A cluster-model approach

Abstract

A method for the simulation of electron scattering and diffraction in solids and molecules within the cluster approach is presented with explicit applications to photoelectron diffraction, electron scattering in molecules, and low-energy electron diffraction. No approximations are made beyond the muffin-tin model, and, in particular, an exact representation of the free-electron Green function is used. All multiple-scattering paths are accounted for up to an order of scattering that ensures convergence. The method relies upon a convenient separation of the free-electron Green function in rotation matrices and translations along the z axis, which greatly reduces the computation time and storage demand. The evaluation of the multiple-scattering expansion is implemented using the fully convergent recursion method, which permits one to perform an iterative refinement of the final-state wave function, as expressed in the basis set of spherical harmonics attached to each atom of the cluster. Examples are offered in which the direct multiple-scattering expansion and the more elaborated simultaneous relaxation method fail to converge, whereas the recursion method leads to convergence. The computation time needed by the resulting computer program of electron diffraction in atomic clusters to determine the self-consistently scattered wave function is proportional to N 2 (l max ϩ1) 3 , where N is the number of atoms in the cluster and l max is the maximum angular momentum for which the scattering phase shifts take non-negligible values. Within this method it is possible to establish that in practical cases NϾ1000 might be needed for a convergence of the cluster size, although the angular averaging inherent in many experiments may reduce this. The recursion method was also modified to reduce the effort in computing angular distributions of photoelectrons and low-energy diffracted electrons, which now require negligible time for each angle of emission once the wave function has been determined for a given electron energy. Angle and energy distributions of core-level photoemission, elastic scattering of electrons from a free molecule, and low-energy electron diffraction in large-unit-cell surfaces are calculated.

X-ray photoelectron diffraction study of Cu(111): Multiple scattering investigation

“…The cluster-model approach of the EDAC code [4] used here to simulate the XPD experiment is based on the muffin-tin potential approximation [13]. EDAC evaluates the MSC expansion using a fully convergent recursion method.…”

“…[4] and references therein). It is the aim of this paper to perform an as complete as possible comparison of Cu(1 1 1) surface XPD measurements with the MSC simulations using the EDAC (electron diffraction in atomic clusters) computer code [4]. Therefore, this study serves to verify to what degree state of the art EDAC multiple scattering simulations are able to reproduce full-hemispherical XPD patterns.…”

Direct evidence for ferroelectric polar distortion in ultrathin lead titanate perovskite films

“…Non-centro-symmetric position of oxygen atoms First, considering oxygen as the emitter atom, fully automated computer code for calculating electron diffraction in atomic clusters (EDAC) via multiple scattering [31], based on the muffin-tin potential approximation [32] was used to calculate the XPD pattern. Fig.…”

Observation and resonant x-ray optical interpretation of multi-atom resonant photoemission effects in O1semission from NiO

“…To further illustrate the potential influence of PD on such energy scans, we show in Fig. 1(d) multiple-scattering PD calculations for a cluster of 250 atoms representing a NiO(100) surface, making use of the recently developed EDAC program 25 . The modulations predicted here are substantial, and we have indicated the energy range of the broad scan in Fig.…”

“…To assess the second possibility, we have again carried out multiple scattering photoelectron diffraction calculations with the EDAC program 25 , this time for a cluster of 450 atoms representing a Ni(100) surface. Multiple scattering up to 25 th order was included to insure convergence, and the calculations were averaged over the expected analyzer acceptance solid angle.…”