The arrangement of atoms around an edge dislocation in copper has been calculated by a variational method using a central-force approximation. The pairwise interaction between discrete atoms was represented by a Morse potential function. In the calculation of the complete dislocation, the atoms were not permitted to relax in a direction parallel to the dislocation line. This prevented dissociation. Linear-elasticity theory is found to break down inside a core radius of 9 Å for a complete $〈112〉$ dislocation [$\mathrm{Burgers}\mathrm{vector}=\left(\frac{a_0}{2}\right)〈110〉$, where $a_0$ is the lattice constant]. The corresponding core energy is 0.65 eV per {112} plane. If the core is replaced by a cylindrical hole of radius $r_{\mathrm{eh}}$ (the equivalent hole radius), the inside of which is hollow and outside of which linear-elastic theory holds at all points, this radius is 0.8 Å. The complete dislocation was found to have a width of 13 Å (i.e., about five Burgers vectors). The core region is found to be neither hollow nor like a liquid. If the atoms are permitted to relax in a direction parallel to the dislocation line, the dislocation spontaneously dissociates into two Heidenreich-Shockley partials; and this process involves no activation energy. A stacking fault of infinite extent has an energy of 30 erg ${\mathrm{cm}}^{-2\mathrm{}}$ for the potential and truncation used in the calculation. Certain precautions must be taken to ensure that the separation distance of the partials is the same as the distance given by elastic theory. Several different potential forms were used in the calculations of stacking-fault energy. The stacking-fault energy is found to be critically dependent upon the form of the interatomic potential. For the pseudopotential for aluminum given by Harrison, the stacking-fault energy is approximately 250 erg ${\mathrm{cm}}^{-2\mathrm{}}$.

• Received 18 September 1964

DOI:https://doi.org/10.1103/PhysRev.145.465