Kinematical Scattering: Bloch Wave Theory and Applications

This lecture covers the principles of kinematical scattering from a crystal lattice, focusing on the Bragg law, Laue condition, and the Ewald sphere. It introduces the concept of scattering geometry and the first Born approximation, explaining how a unit cell scatters a spherical wave modulated by the scattering angle. The lecture also discusses the deficiencies of the kinematical model and transitions into the dynamical theory using the Bloch wave approach. The instructor presents the mathematical formulations for calculating scattering intensity and the integration over the sphere at a distance from the sample. The lecture concludes with an overview of the Bloch wave theory, particularly the two-beam approximation, and how it relates to diffracted beam intensities, emphasizing the decoupling of Bloch waves into plane wave components at the bottom of the crystal thickness. This comprehensive overview provides a solid foundation for understanding the kinematical and dynamical aspects of electron diffraction in crystal lattices.