Orientation Relationships in Precipitation Systems

Based on a survey of the literature on orientation relationships in precipitation systems a unified view of all the kno"rn relationships in b~c/hcp and bee/fcc systems is presented. Within each set of crystal systems, orientation relationships are closely connected by small fixed rotations whose magnitude depends only on crystal symmetries. Close parallels exist between the two sets of crystal systems, bee/fcc and bcc/hcp. The regularities observed in the literature survey lead to the hypothesis that precipitate and matrix tend to be related by an invariant line strain. The relative rotation of the tv;·o lattices predieted by this hypothesis is determined as a function of the lattice para,neter ratio and is consistent with a large number of experimental studies. In the analysis of simple non--coherent precipitate morphologies the criterion of directional mismatch is demonstrated to be superior to the commonly used planar mismatch criterion. The precipitate morphology sensitively reflects variations in orientation relationships. Morphologies of coherent and equilibrium semicoherent precipitates are governed by more complex criteria but are also dominated by basically crystallographic requirements. INTRODUCTION The orientation relationship (OR) between two phases of different crystal structure is important because it has a strong bearing on