The Crystal Lattice

Kristallstruktur; Gitterbaufehler;

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The goal of this text is to describe and analyze peculiarities in the classical and quantum dynamics of a crystal as a spatially periodic structure. Both traditional questions - such as the spectrum of vibrations, the idea of phonon gas and dislocations - and new aspects - for instance, the theory of quantum crystals, solitons in 1D crystals and the dislocation theory of the melting of 2D crystals - are discussed. The author gives an explanation of a set of phenomena which entered into solid state physics during the last few decades, and argues that the crystal properties are sensitive to the dimension of the crystal and its defect structure, and also depend slightly on whether the periodic structure consists of atoms, electrical dipoles, or magnetic moments (spins). Attention is also focused on dislocation mechanics as a basis of theory of plasticity, and the numerous technological applications of crystal materials.