These lecture notes develop the thermal physics of solids from microscopic structure to macroscopic thermodynamic and transport behavior. Lecture 1 Fundamental Concepts of Solids begins with the basic question of what a solid is, distinguishing crystalline, polycrystalline, and amorphous matter in terms of short-range and long-range order. It also introduces the many-particle Hamiltonian of electrons and nuclei as the formal microscopic starting point and explains why thermal properties are ultimately tied to the spectrum of excitations and their statistical occupation. Lecture 2 Interatomic Bonding then connects microscopic bonding to thermal energy scales by discussing covalent, ionic, metallic, van der Waals, and hydrogen bonding, the meaning of cohesive energy, the curvature of interatomic potentials, local bond stiffness, characteristic vibrational frequencies, and the Debye temperature.
The next part of the course establishes the structural language needed for lattice dynamics and scattering. Lecture 3 Fundamentals of Crystal Structure introduces crystal structures in real space through Bravais lattices, bases, primitive and conventional cells, Wigner–Seitz cells, crystal symmetry, crystal systems, and the 14 Bravais lattices. It also discusses common elemental and binary structure types, emphasizing that the basis determines coordination, symmetry, diffraction intensities, and later the existence of optical phonons. Lecture 4 Reciprocal Space, Diffraction, and Structure Factor develops the reciprocal-space framework of periodic solids. It introduces reciprocal lattices, Brillouin zones, Bragg and Laue diffraction conditions, the Ewald construction, scattering amplitudes, atomic form factors, structure factors, systematic extinctions, Debye-Waller reduction, and the distinction between elastic and inelastic scattering.
The central part of the lecture notes develops lattice dynamics. Lecture 5 Lattice Dynamics I starts from the Born–Oppenheimer approximation and shows how nuclear motion on an electronic energy surface leads, in the harmonic approximation, to linear equations of motion for atomic displacements. Translational symmetry then reduces the real-space problem to a dynamical-matrix eigenvalue problem for each wave vector. This provides the general framework for vibrational branches and their classification into acoustic, optical, longitudinal, and transverse modes. Lecture 6 Lattice Dynamics II applies this formalism to explicit model systems. It derives dispersion relations for one-dimensional crystals with one-atomic and two-atomic bases, explains group velocity and the long-wavelength sound limit, motivates the restriction to the first Brillouin zone, and shows how acoustic and optical branches arise from in-phase and out-of-phase motion of atoms in the basis. The lecture then generalizes the branch counting to three-dimensional crystals.
The following lectures connect vibrational spectra to thermodynamics. Lecture 7 Phonons explains how finite boundary conditions quantize the allowed wave vectors and how mode counting in reciprocal space leads to the phonon density of states \(D(\omega)\). It interprets \(D(\omega)\) as a frequency histogram of vibrational modes, derives its geometric relation to constant-frequency surfaces and group velocity, and explains van Hove singularities and the role of dimensionality. Lecture 8 Heat Capacity then uses this density-of-states framework to derive the lattice heat capacity. Starting from the classical Dulong-Petit law and its failure at low temperature, it introduces quantum harmonic oscillators, Bose-Einstein phonon occupation, the phonon internal energy, the Einstein approximation, and the Debye approximation. This leads to the high-temperature Dulong-Petit limit, the low-temperature Debye \(T^3\) law, and the interpretation of the Debye temperature as a characteristic vibrational energy scale.
The later lectures show why real solids require physics beyond the harmonic approximation. Lecture 9 Anharmonicity and Thermal Expansion explains why a strictly harmonic crystal cannot thermally expand and introduces anharmonic lattice potentials. It connects anharmonicity to phonon-phonon interactions, three-phonon processes, mean atomic displacements in asymmetric potentials, free energy, pressure, the Grüneisen parameter, and the Grüneisen relation for thermal expansion. Lecture 10 Thermal Conductivity develops lattice thermal transport from both macroscopic and microscopic viewpoints. It begins with Fourier’s law and thermal diffusivity, then describes phonons as heat carriers whose thermal conductivity is controlled by heat capacity, group velocity, relaxation time, and mean free path. Boundary scattering, point defects, isotopes, alloys, normal processes, and umklapp processes are used to explain the characteristic temperature dependence of \(\kappa(T)\) in crystalline insulators and the plateau-like behavior of glasses.
Electronic contributions to thermal properties are addressed in Lecture 11 Electronic Contributions to Thermal Properties (optional). It treats the electronic heat capacity and heat conduction of metals. It begins with the Drude model and its limitations, then introduces the Sommerfeld model, Fermi-Dirac statistics, the linear-in-\(T\) electronic heat capacity, the Sommerfeld coefficient, and the low-temperature separation \(C=\gamma T+\beta T^3\) into electronic and phononic parts. It also discusses heat currents in an electron gas, coupled charge and heat transport, the Wiedemann-Franz law, and thermoelectric effects such as the Seebeck, Peltier, and Thomson effects. The remaining failures of the free-electron model motivate the need for band structure and Bloch electrons.