Diffraction: Determination of Atomic Structure

Abstract

Abstract Knowledge of the atomic configuration of a material is important for understanding its properties. Among various experimental techniques, the diffraction method determines the atomic positions in material structures in a straightforward way through the interference between the waves that used as the probe. This chapter provides a basic overview of diffraction methods and their applications to determine the structures of surfaces and two-dimensional atomic layers, focusing on the use of electron and positron beams. We start with the well-known Bragg equation to interpret where diffraction spots appear in a pattern, and we then extend it to a more general case by employing 2D reciprocal-lattice rods, the Ewald sphere, and the Laue condition. We introduce atomic scattering factor, refraction effect, and penetration depth to understand how information is obtained from the spot intensities. We also discuss the differences in the diffraction intensities produced by electrons, positrons, and X-rays. We describe both kinematical and dynamical diffraction theories for calculating the diffraction intensities produced by X-rays, electrons, and positrons. After showing the surface sensitivity of positrons, we review some typical examples of structural analyses (Ag/Si(111), In/Si(111), graphene/Co(0001) and graphene/Cu(111), silicene/Ag(111), and germanene/Al(111)) obtained using positron diffraction. Finally, we briefly describe future prospects for surface structure analysis using diffraction methods.