Technical Notes - Interaction of Dislocations and Long-Range Order

IT has been pointed out by Cottrell' and Fisher that long-range order would produce superdis-locations, consisting of two partial dislocations separated by an out-of-phase region. The mutual repulsion of the partial dislocations is balanced by the surface tension of the out-of-phase domain boundary joining the dislocations (Fig. 1). The calculation of the equilibrium spacing of the dislocations has yet to be made. The argument uses the Bragg and Williams theory of long-range order." The metal under consideration is the A-B, body-centered type, such as ß brass. The slip system is taken to be [Ill], (110). Since nearest-neighbor interactions are considered, only the atoms position in the two (110) planes adjoining the slip plane have to be labeled. Corner sites are called a and a' in the top and bottom (110) planes, respectively. Similarly ß and ß are the body-centered sites. Thus, a and ß and 0 and a sites are nearest neighbors. Assume that the bottom plane moves and the top plane is fixed during slip; the atoms in a and ß sites exchange sites but atoms in a and ß sites remain fixed. Fraction of A atoms in a sites, for example, is given by fa and fa. for the un-slipped and slipped condition, respectively. Similarly number of A atoms in the a sites is given by n, and n'a for the unslipped and slipped condition, respectively. As the dislocation moves into the ordered region the change in number of A-A bonds is given by