7  Lattice Dynamics II

NoteLearning Objectives

• Derive the dispersion relation of the monatomic linear chain and interpret the role of the first Brillouin zone.
• Compute the group velocity and identify the long-wavelength sound limit.
• Derive the acoustic and optical branches of the diatomic linear chain.
• Interpret zone-center and zone-boundary eigenvectors in terms of in-phase and out-of-phase motion.
• Build the bridge from discrete allowed \(q\)-values to the continuum limit and the vibrational density of states.