Syllabus

• Brief History, crystals, primitive translation vectors, basis, Wigner-Seitz primitive cell, Lattice types in 3-D and 2-D, Diamond and Zinc blende structures.
• X-ray, electron, and neutron diffraction, Periodicity of crystals/electron density, reciprocal lattice vectors, Ewald construction, elastic scattering, Bragg result and diffraction conditions, Structure factor, atomic form factor, thermal effects, Debey-Waller factor.
• Van der Waals bonding, fluctuating dipolar interactions using quantum mechanics and polarizability arguments leading to 6th power potential, Lennard-Jones Potential and repulsive interactions.
• Ionic bonding, cohesive energy, Madelung constant and its evaluation.
• Covalent bonding, H2 molecule example, Heitler-London approach, antisymmetry of wavefunctions, singlet/triplet states, Hybridization, σ-bonding, promotional and overlap energy, sp2 and sp3 examples.
• Phonons and crystal vibrations, classical equations of atomic motion, Hooke's law formalism, longitudinal and transverse modes, traveling and standing wave solutions, ω vs. k dispersion relations, Brillouin zones, wave packets, group velocity, phase velocity, long-wavelength limits, sound waves, multiple atoms per unit cell, optical and acoustical phonon branches, Phonon dispersion examples for Pb, Na, Si, phonon momentum, Stokes and anti-Stokes processes, Neutron scattering measurements used to determine ω vs. k.
• Thermal properties of phonons, quantum mechanics approach, Harmonic oscillator, Hamiltonian, energy quantization of mode ω(k), Zero-point energy, Boltzmann statistics, Planck distribution function, Normal mode enumeration, density of states for phonons, Einstein and Debey models, Heat capacity, Dulong and Petit value, Anharmonic terms in crystal potential, thermal expansion, thermal resistivity of phonon gas, Umklapp processes.
• Quantum theory of free electron gas, metallic bonding, Drude assumption, Schrodinger Equation and solutions to "particle in a box", 1-D, 2-D, and 3-D metals, Born Von Karman periodic boundary conditions, Fermi Energy, average electron energy, density of states, Fermi-Dirac distribution, chemical potential, temperature dependence of chemical potential and electronic energy, electronic contribution to specific heat of metals.
• Electrical conductivity, resistivity, Ohm's Law, Hall effect, Hall coefficient, magnetoresistance.
• Electrons in a weak Periodic potential, E vs. k dispersion, crystal momentum k, conditions for Bragg reflection of electrons; formation of band gap, Perturbation theory and degeneracy problem at Brillouin zone boundary, Bloch's theorem, Fourier analysis of Schrodinger equation and "central equation", Energy levels near intersection of Bragg planes, reduced-, extended-, and repeated-zone schemes.
• Semiconductors, direct and indirect fundamental bandgap, valence and conduction bands, optical excitation, electrons and holes, parabolic band approximation and effective mass tensor, sp3 hybridization revisited, s and p-like band dispersions, Si, Ge and GaAs band structure and dispersion, spin-orbit interaction, addition of angular momentum, fcc and bcc brillouin zones and high-symmetry directions.

Bibliography