Crystal Structures: Reciprocal Lattice and Brillouin Zones

This lecture introduces key concepts in crystallography, focusing on the free electron model and its modifications. It begins with an overview of the veganicide cell, explaining how it represents the space associated with each atom in a crystal lattice. The instructor details the construction of veganicide cells for various lattice types, including simple cubic, body-centered cubic, and face-centered cubic structures. The lecture then transitions to the reciprocal lattice, defining it as the Fourier transform of the real space lattice. The instructor illustrates how to construct the reciprocal lattice for a body-centered cubic crystal, highlighting the differences in symmetry between real and reciprocal spaces. The discussion includes the significance of Brillouin zones, which are crucial for understanding diffraction phenomena in crystallography. The first Brillouin zone is defined, along with its relationship to the Wigner-Seitz cell. The lecture concludes by linking these concepts to the Sommerfeld model and Bloch's modifications, setting the stage for further exploration in the series.