The Piezoelectric Potential of a Screw Dislocation in a Cubic Medium

An exact and closed-form solution is found for the electric potential generated by a screw dislocation in a cubic piezoelectric medium. The governing equations for the antiplane elastic deformation coupled with the in-plane electric field are formulated in terms of the elastic displacement and the electric potential, and a general solution is obtained. The complex logarithm function is exploited to find the electric potential around the screw dislocation. It is found that the equipotential lines are straight lines passing through the dislocation which is a singular point. Two cubic piezoelectric crystals (Bismuth Germanate and Bismuth Germanium Oxide) are used to illustrate the angular variation of the electric potential around the dislocation. It is concluded that a two-term Fourier series representation is an excellent approximation for Bismuth Germanate, but it is not good enough for Bismuth Germanium Oxide.