Theory of Extended Dislocations in Symmetry Directions in Anisotropic Infinite Crystals and Thin Plates

Abstract

Formulas are given for the stress components of dislocations along the c axis and in the basal plane of hexagonal crystals, along cube edges and face diagonals of cubic crystals, and for a few other cases. From these, formulas are derived for hexagonal crystals which relate stacking fault energy to the width and orientation with respect to the Burgers vector of extended dislocations and triple partial ribbons. For materials of very low stacking fault energy the distance between partial dislocations is comparable to the thickness of the films used in thin film transmission electron microscopy. The effect of stress-free surfaces on the dislocation widths is calculated for arbitrarily oriented extended dislocations lying parallel to the single plane surface of a semi-infinite isotropic solid and for 30° extended dislocations and symmetrical, screw triple partial ribbons lying parallel to the plane surfaces of an anisotropic plate. Procedures are given for correcting the widths obtained from electron microscopy. For graphite these corrections are important for extended dislocations in very thin films and for all triple partial ribbons.