Hinderks D, Kohl H. Calculation of inelastic scattering processes of relativistic electrons in oriented crystals.
Ultramicroscopy 2014;
151:101-106. [PMID:
25499690 DOI:
10.1016/j.ultramic.2014.11.030]
[Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2014] [Revised: 11/27/2014] [Accepted: 11/28/2014] [Indexed: 11/16/2022]
Abstract
The inelastic scattering of electrons in oriented crystals has been used to determine the positions of atoms within a crystal, to obtain site-dependent electron energy loss spectra and, more recently, to obtain an energy loss signal corresponding to the circular dichroism in X-ray absorption spectroscopy. The theoretical approaches currently used for the description of these processes are based on the nonrelativistic Schrödinger equation. Nowadays many experiments, however, are conducted with incident energies of 200 or 300 keV. Therefore it is indispensable to use a relativistic description for such processes based on the Dirac equation. Using the Coulomb gauge it is shown, that the fully relativistic cross sections for plane wave scattering are given by the modulus square of a sum of two terms: one describing the electrostatic interactions similar to the nonrelativistic theory plus one additional term describing the interaction of the specimen with the magnetic field produced by the incident electron. In crystals both terms can interfere leading to large deviations from nonrelativistic theory.
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