The Determination of Stacking Fault Energy by the Tetrahedron Method

Abstract

At present there are three methods for obtaining values of the stacking fault energy y of face-centred cubic (f.c.c.) materials by direct observation of dislocationstacking fault configurations in the electron microscope. These are based on measurements of extended three-fold dislocation nodes (e.g. Whelan 1958;Brown and ThOlen 1964), faulted dipole configurations (e.g. Haussermann and Wilkens 1966; Steeds 1967), and triangular Frank dislocation loops and stacking fault tetrahedra (e.g. Silcox and Hirsch 1959;Loretto, Clarebrough, and Segall 1965). The main advantages of the third method over the other two are that it is applicable to materials of a very wide range of stacking fault energy and involves only simple length measurements of defects that are easily recognized. However, it has suffered from the disadvantage that the values of y deduced from these measurements relied on an incomplete theory. The present authors have reconsidered this problem and, subject to the limitations of isotropic linear elasticity, have taken into account the major variables that may affect the values of y. It is the purpose of this note to present the results of this theory in a form in which values of y may easily be obtained from measurements of Frank dislocation loops and stacking fault tetrahedra without the resources of a large digital computer.Loretto, Clarebrough, and Segall (1965) have shown that triangular Frank dislocation loops and stacking fault tetrahedra are formed in f.c.c. metals and alloys when these are plastically deformed. Their experiments indicated that a dislocation mechanism was responsible for the formation of the triangular Frank loops and that all the stacking fault tetrahedra were formed by the dissociation of these in the manner originally suggested by Silcox and Hirsch (1959). Thus, by observing the size of the largest tetrahedron and the smallest Frank loop in a given plastically deformed material, it is possible to determine the critical edge length lc above which the transformation of loops to tetrahedra is energetically unfavourable.Several authors (Czjzek, Seeger, and Mader 1962; Jossang and Hirth 1966;Humble, Segall, and Head 1967) have computed the energy balance between triangular Frank loops and stacking fault tetrahedra as a function of defect size, but they have considered only the terms in the dislocation interaction energy and stacking fault energy. We have recently reformulated the problem considering the total energy of the defect (Humble and Forwood 1968). This formulation includes terms such as the kinetic energy of the moving Shockley dislocations T, the energy dissipated to the crystal lattice fL, and the work done by the stress W, as well as terms in the interaction energy Etd and fault energy E ty • The potential energy of a crystal containing the defect Etd + Ety -W was plotted as a function of dissociation, * Manuscript