Dislocation-loop-length distribution and frequency-dependent damping for small impurity concentrations

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Abstract
For calculating effects such as Granato-Lücke dislocation damping, a distribution function for loop lengths of dislocation bowing out under an external stress is needed. Koehler's equation for a statistical distribution of pinning points ignores the nodes of the dislocation network. This means that it becomes inapplicable for small concentrations of impurity pinning points. In this paper a new equation is derived which takes into account a statistical distribution of pinning points and equally spaced nodes. A second equation with the vibrational entropy allowed for will hold only approximately. Both equations are applicable for all impurity concentrations down to zero. Granato-Lücke frequency-dependent internal friction, and the modulus defect as calculated from the first equation, are compared to that calculated from Koehler's distribution. A distribution of network lengths may easily be included.

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