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Old and new aspects in lattice-dynamical theory

An overview of the basics of theoretical lattice dynamics is presented. Starting from the classical formulation, a tutorial description of the evolution of the lattice-dynamical theories is reported. After a brief summary of the mostly used phenomenological models, the modern concepts of first-principles lattice dynamics are introduced, paying special attention to the methods based on the density-functional theory. Among these methods, the perturbative ab initio approach is highlighted. Furthermore, the application of this formalism to some cases of general interest is shown. In particular, we report on the controversy about the origin of a peak in the second-order Raman spectrum of diamond, on the phonon spectrum of the wurtzite nitrides and on the temperature-induced phase transitions in tin.