On the difference between the misorientation dependences of the energies of tilt and twist boundaries

Abstract

It is shown in this paper that the strain energy associated with tilt and twist boundaries, respectively, evaluated as the elastic energy of corresponding dislocation networks, depends on the misorientation, ..delta..theta, differently in each case. In particular, if all the terms of the order ..delta..theta/sup 2/ and higher have been neglected, this dependence has the generally accepted form (see e.g. (12)) ..gamma.. = ..gamma../sub o/ + B..delta..theta(A - 1n..delta..theta) in the former case, while in the latter case ..gamma.. = ..gamma../sub o/ + B..delta..theta(A + C..delta..theta - 1n..delta..theta) (A, B and C are constants). The reason lies simply in the different nature of these boundaries: the tilt boundary contains only one set of dislocations while the twist boundary contains two sets of dislocations forming a square grid. The interaction of a dislocation with the grain boundary, which is evaluated when deriving the strain energy, consists in the case of a twist boundary of interactions with both dislocations parallel and perpendicular to it, while only interactions with parallel dislocations are involved in the case of a tilt boundary. This difference is then responsible for the above differences in the functional forms of the misorientation dependence of the boundary energy.