Electron Theory: Crystallography Basics

This lecture introduces key notions of crystallography relevant to electron theory, covering the Wigner-Seitz cell, reciprocal lattice, and Brillouin zones. The Wigner-Seitz cell is a primitive cell containing one atom, with examples like a cube, cuboctahedron, and rhombododecahedron. The reciprocal lattice is the Fourier-transform of the real space lattice, with examples for bcc and fcc lattices. The reciprocal lattice vectors correspond to lattice points in reciprocal space, forming lattice planes. The Brillouin zones are the Wigner-Seitz cells in reciprocal space, with areas indicative of diffraction planes. The lecture explores the importance of lattice planes in diffraction phenomena and the behavior of electron waves when interacting with Brillouin zone surfaces.