Orientierungsbeziehungen

Orientierungsbeziehungen (ORs) describe the geometric relationship between the orientations of two crystalline lattices at an interface or between a parent and product phase. An OR specifies which lattice planes and crystallographic directions are parallel across the boundary, and equivalently, the misorientation needed to map one orientation onto the other. They can be described either by plane–direction correspondences (for example, certain planes in one lattice remaining parallel to planes in the other) or by a misorientation characterized by a rotation axis and angle.

In materials science ORs are particularly important for understanding phase transformations, epitaxial growth, and the formation of laminated or composite structures. A transforming material may adopt a limited set of ORs, leading to preferred habit planes and orientation textures. The most well-known examples in steel are the Kurdjumov–Sachs and Nishiyama–Wassermann orientation relationships, which relate the orientation of austenite (FCC) to that of martensite or ferrite (often BCC or BCT) during transformation. In practice, several variants can occur, depending on composition, temperature, and cooling path, so a distribution of ORs is often observed.

Quantitative description uses misorientation angles and rotation axes, or explicit plane–direction correspondences, sometimes represented with orientation relationship matrices. ORs can be determined experimentally by electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), or X‑ray diffraction.

Understanding ORs helps predict interface energies, transformation textures, and mechanical properties, and is also relevant to epitaxial growth in thin films and ceramics.