Physics / advanced
Periodic structure and lattice vibrations
Develop reciprocal-space reasoning from diffraction and crystal geometry to phonon dispersions, thermal response, and anharmonic effects.
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Module 01 advanced
Periodic structure and lattice vibrations
Develop reciprocal-space reasoning from diffraction and crystal geometry to phonon dispersions, thermal response, and anharmonic effects.
- 01
Bravais lattices and crystal bases
Separate translational geometry from the atomic motif, distinguish primitive and conventional cells, and count atoms without confusing lattice points with basis sites.
25 min - 02
Reciprocal lattices and Brillouin zones
Construct reciprocal vectors with an explicit 2π convention, fold wavevectors consistently, and define the Brillouin zone as a reciprocal Wigner–Seitz cell.
26 min - 03
Laue and Bragg diffraction conditions
Derive reciprocal-vector selection from coherent scattering, relate it to Bragg geometry, and separate geometrically allowed peaks from nonzero measured intensities.
26 min - 04
Structure factors and extinction rules
Compute coherent basis amplitudes, derive centring absences, and distinguish exact symmetry cancellations from weak peaks caused by chemical contrast or form factors.
27 min - 05
Monoatomic and diatomic chain phonons
Derive harmonic chain dispersions with explicit cell-length and mass conventions, check acoustic limits, and identify the origin of a diatomic optical branch.
29 min - 06
Three-dimensional dynamical matrices
Assemble mass-weighted harmonic force constants, interpret eigenvalues as squared frequencies, and enforce translational sum rules without confusing eigenvectors with physical displacements.
29 min - 07
Acoustic and optical phonon branches
Count lattice branches from primitive-cell degrees of freedom, interpret low-wavevector motion and polarization, and separate optical branch labels from optical activity.
27 min - 08
Debye and Einstein heat-capacity models
Normalize phonon densities of states, derive quantum heat-capacity limits, and distinguish Debye acoustic scaling from the single-frequency Einstein approximation.
29 min - 09
Anharmonicity and thermal expansion
Derive a weak-asymmetry shift in mean bond length, relate volume-dependent phonons to expansion, and distinguish quasiharmonic thermodynamics from full anharmonic dynamics.
29 min - 10
Phonon scattering and thermal transport
Connect heat-carrying phonon populations to group velocity and lifetime, distinguish normal and Umklapp scattering, and quantify the limits of a simple kinetic conductivity estimate.
29 min