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,
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
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
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
C. Kittel, Introduction to Solid State Physics (Seventh Edition)