Decomposition of the transformation displacement field

Abstract

The displacement field of a phase transformation is studied from a modification of the O-lattice theory. A methodology is provided for analysing the possible long-range strain shear field caused by migration of an interface. The singular value decomposition method is applied to establish a two-way association between a displacement vector and its associated point(s) in a crystal lattice. The displacement lattice (D lattice) is introduced; it serves as a convenient framework for the description of the long-range strain field. The D lattice is shown to be related to the O lattice by a reciprocal theorem. The magnitude of the long-range strain shear field j ₁ is examined with variations of the interface orientation and the local translation displacement between crystals. For a given habit plane, the condition for j ₁ to reach a minimum value requires that the translation vector should not contain any component that can be accommodated by dislocations in the interface. The minimum j ₁ is related to the interfacial energy of the habit plane and the strain energy in opposite fashions. The analysis of j ₁ can offer a useful basis for examining the coupled effect of these different energies on the development of the habit plane and orientation relationship in a phase transformation.