• transformations;
  • invariant line analysis;
  • precipitation;
  • habit planes;
  • orientation relationships

Several phenomenological crystallographic theories, including the invariant line model, O-line analysis and Δg parallelism rules, have been proposed and then successfully applied to the interpretation of crystallographic features for most face-centred cubic/body-centred cubic precipitation systems. However, the application of these methods requires the use of extra criteria and multiple rotations. A simplified invariant line analysis is proposed in this paper, to simplify the above theories from the well known confusions of additional criteria and multiple rotation around specific axes. One-step rotation dispenses with extra criteria or any input orientation relationship and so can deduce an invariant line when a Burgers vector is parallel to the habit plane. This simplified analysis makes the application of the theory more understandable, where it anticipates the invariant line, the habit plane, the orientation relationship between the matrix and the precipitate, and the distance between dislocations for which the Burgers vector is not inclined. The predictions are simplified, highly efficient and coincide well with experimental observations from lath-shaped precipitates in Cu–Cr and Ni–Cr alloys, as well as with the theoretical results obtained by O-line theory and Δg parallelism rules.