Schwingungsverhalten von Zwischengitteratomen

The vibrational behaviour of crystals with point defects, especially with self-interstitials, is discussed with particular emphasis on defect-induced resonant and localised modes. For low-frequency resonant modes, an analytical expression for the Green's function of the defect is derived starting from a method due to Krumhansl and Matthew. The Green's function has the form of the Green's function of an onedimensional oscillator with an effective force constant f$^{eff}$, an effective mass M$^{eff}$ and a velocity-dependent damping determined by f$^{eff}$ and M$^{eff}$. Simple approximations for these effective quantities are given. The vibrational properties of self-interstitials in the octahedral and 100-dumbbell configuration in a fee lattice are treated in detail. For simple forceconstant-models the local frequency spectra are calculated for both configurations showing that the interstitial only vibrates with high-frequency localised modes and with low-frequency resonant modes. Furthermore the influence of the resonant modes on physical properties such as the change of elastic constants of phonon dispersion curves and of specific heat is discussed