The formal theory of surface dislocations has been applied to the f.c.c.-b.c.c, interfaces defined by (111) F II (110)B. With the Bain correspondence between the two lattices, various theoretical models and experimental results on these interfaces have been analyzed. The results of the analysis suggest that preferred interface orientations can be explained on the basis that they are those of minimum or near-minimum Burgersvector contents. This concept leads to an improved criterion for comparing the elastic component of interfacial energies. The limitations of geometrical models for predicting low-energy interfaces are discussed.
IntroductionIn this paper, we describe f.c.c.-b.c.c, boundaries in terms of the formal geometrical theory of surface dislocations (Bilby, Bullough & de Grinberg, 1964), of which the 0-lattice theory (Bollmann, 1970) may be considered to be a quantized version (Christian, 1976). We also discuss the extent to which criteria such as 'best fit' are successful in predicting observed interface orientations. Particular emphasis is given to experimental results from the copper-chromium agehardening alloy system (Hall, Aaronson & Kinsman, 1972;Weatherly, Humble & Borland, 1979) for which the theory of Bollmann (1974)
c, interfaceThe Burgers vector content B of an interface between two phases designated by the subscripts + and -can be defined through the formulawhere p is a vector in the interface and S+ and 5_ are the deformations carrying the reference lattice, in which B and p are expressed in the final orientations of the (+) and (-) lattices respectively. If we choose the (+) lattice to be the reference lattice, which is transformed into the (-) lattice by the deformation $, the formula becomes
B = (I--S-m) p. (2)If we suppose that the misfit in the interface defined by (2) i where vx~,and v is a unit vector normal to the boundary. The form of (2) demonstrates that if p is fixed in length and none of the three eigenvalues of S is equal to unity, then the locus of all points B defined through the equation is the surface of an ellipsoid. The principal axes of the ellipsoid can be determined by application of Lagrange multipliers to the function f(p)= ~ BiB ii