Internal Friction and Defect Interaction in Germanium: Theoretical

A model has been constructed in which small vibrations of dislocation line segments cause displacements in the point-imperfection distributions surrounding the dislocations. The energy lost through the motions of the point imperfections is observed as mechanical damping. The motion of the dislocations is obtained from the theory of Koehler. The Cottrell potential is taken as the interaction between dislocations and point defects.It is shown from the high-frequency expansion of the theoretical energy dissipation that the dependence of the dissipation on strain, frequency, and temperature is essentially the same as that of the normal anelastic relaxation effect, in agreement with the experimental observations. It is further shown that the magnitude of the effect is such as to support the hypothesis that the lattice vacancy, present in a concentration of approximately 10¹⁰/cm³, is the point defect which interacts with dislocations, giving rise to the observed vibrational energy loss. In turn, using the numbers derived from the vacancy hypothesis, it is shown that the cutoff for the purely elastic dislocation potential is several atom spacings from the dislocation line.