Pedagogical Problems in Lattice Dynamics

Pedagogical Problems in Lattice Dynamics presents a simplified approach to advanced problems in lattice dynamics. The basic concepts of lattice dynamics, viz, nature of lattice vibrations, elastic wave propagation and occurrence of phase transitions, are brought through pedagogical problems employing perfect lattices. The inclusion of defects in various configurations, and the characteristics of localized, gap and inband modes are illustrated with suitable examples. The dynamics of molecular crystals, involving translational and librational modes are discussed using specific one dimensional molecular lattice. Vibrations in pure and defect induced molecular lattices have been worked out presenting extensive illustrations of the modes and their properties.. The nature of lattice vibrations, their polarization characteristics in centrosymmetric and noncentric lattices have been studied. The occurrence of pure and quasi modes in typical ionic crystals and elliptic/circular polarizations in quartz has also been pointed out. The book includes a brief discussion on the propagation of elastic waves in piezo electric crystals and the consequent changes in pure mode directions. The Madelung constants in several crystals are presented in view of their utility in assessing phase transitions and lattice stability.