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Applications of Group Theory to Lattice Dynamics
Theory of the Vibrational Frequency Spectra of Solids
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A. A. Maradudin amplitude approximation atomic force constants boundary conditions Brillouin zone calculations coefficients components Consequently contribution correlation functions corresponding critical points crystal slab crystal surface cubic crystal Debye defect defined determined dielectric diffuse scattering dipole discussion disordered dispersion curves dispersion relation dynamical matrix eigenvalues eigenvectors electrons elements equations of motion evaluation expansion experimental expression free surfaces frequency spectrum given by Eq Green's function host crystal impurity atom integral interactions ionic crystals irreducible representation isotopic lattice dynamics limit linear chain localized modes macroscopic field mass mean square displacements method monatomic Montroll nearest neighbor neutron normal mode normal mode frequencies obtain one-dimensional optical modes perturbed crystal phonon Phys point group polariton reciprocal lattice result right hand side side of Eq singularities solution space group specific heat spectra surface modes temperature theoretical theory tion transformation transverse unit cell values vanishes wave vector zero