The stacking-fault tetrahedron

Abstract

From symmetry arguments it is concluded that what is called a stacking-fault tetrahedron is really a self-inclusion in which a portion of the same crystal is shifted by 1/4 〈111〉 relative to the enclosing matrix. The included crystal has fewer atoms than would have been required to fill the hole in the matrix crystal with perfect material, and this is a way of accommodating clusters of vacancies. Symmetry shows that, for this shift, the energy is at an extremum and that the form of the inclusion must conform to the point group 43m (tetrahedral). This is a simpler model than the usual description, and even the unrelaxed version has lower energy for small sizes. For intermediate sizes it would relax to the same description as the relaxed version of the defect as conventionally described, and at large sizes the stacking-fault tetrahedra are unstable with respect to the formation of Frank loops.