Invariant-Plane and Invariant-Line Deformation Criteria and Their Application to Interface Crystallography

Simple geometrical approaches to interface crystallography based on the invariant-plane and invariant-line deformation criteria have been overviewed. Using matrix algebra, the mathematical implications of these criteria are first discussed. To elucidate the physical meaning and the applicability of the invariant-plane deformation criterion, the re-formulation procedure of the phemonemological crystallographic theories of martensitic transformations using the infinitesimal-deformation approach is surveyed. As the application of the invariant-line deformation criterion, epitaxial relationships between deposit thin-film crystals and substrate crystals are analyzed. It has been demonstrated that these simple geometrical criteria are very useful in explaining various features of the crystallography of interfaces.