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The Dynamics of a Crystal Lattice With Defects
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Acta Cryst approximation axes axis boundary Brillouin zone Brockhouse calculations condition continuous spectrum coordinates correlation functions corresponding cross section crystal lattice cubic crystal Debye-Waller factors dependence determined discrete frequency dislocation displacement vector eigenvalue eigenvectors elastic constants electronic elements energy equations of motion expression factor figure force constants formula Fourier frequency spectrum germanium given by equation Green's function host crystal impurity atom interaction inverse irreducible representation lattice vibrations lattice waves Lifshitz linear localized modes long-wave Maradudin 1964 molecule Mossbauer effect nearest neighbours neutrons scattered normal modes obtain optic modes perfect crystal perturbation potential perturbed crystal phonon Phys physical plane point defects Proc propagation properties quasi-local vibrations reciprocal lattice relation resonance modes rotations solution of equation spectrum band symmetry operations temperature theory total representation transform transverse unit cell values of q velocity vibration amplitude vibrational frequencies wave number wave vector wavelength x-rays zero