G. Schoeck, THE GENERALIZED PEIERLS-NABARRO MODEL, Philosophical magazine. A. Physics of condensed matter. Defects and mechanical properties, 69(6), 1994, pp. 1085-1095
In the original Peierls-Nabarro model the core structure of a dislocat
ion is determined as the solution of an integrodifferential equation.
This equation describes the balance between the forces resulting from
the deformation of two elastic half-spaces and from a one-dimensional
periodic lattice potential acting across the glide plane. A method is
described here which allows the core structure and core energy to be o
btained for a straight dislocation with arbitrary Burgers vector in an
arbitrary glide plane in a crystal of arbitrary anisotropy, for which
the displacement potential is represented by a two-dimensional Fourie
r series. This is accomplished by describing the internal displacement
s by appropriate trial functions with a set of free parameters whose v
alue is then determined by minimizing the total energy. The method is
applied to obtain the core configuration of a screw dislocation dissoc
iated in a {111} plane of a f.c.c. lattice.