Crystalline solids have a highly ordered and repeating arrangement of atoms or molecules, while non-crystalline solids have a more random and disordered structure.
The three types of crystal lattices are primitive, body-centered, and face-centered. These lattices differ in the positions of the lattice points and the number of atoms contained in each unit cell.
The Brillouin zone is a region in reciprocal space that represents all the possible wave vectors of the electrons in a crystal. It is an important concept in solid state physics as it helps in understanding the behavior of electrons in a crystal lattice.
Band theory states that the energy levels of electrons in a solid form continuous bands, with a band gap between the valence and conduction band. Conductors have overlapping valence and conduction bands, allowing electrons to move freely and thus conduct electricity. Insulators have a large band gap, making it difficult for electrons to move, while semiconductors have a smaller band gap, allowing some electrons to move and conduct electricity under certain conditions.
The Fermi surface is a boundary in reciprocal space that separates the filled and empty energy levels of a material at absolute zero temperature. It is important in determining the electronic properties of a material, such as its electrical and thermal conductivity, as it represents the available energy states for electrons to occupy and participate in electronic processes.