$\beta$ orientation reconstruction and shear deformation calculation in hcp-bcc-hcp phase transformation

We introduce a cluster-based technique to automate pixel-wise reconstruction of $\beta$ orientations from parent $\alpha$ orientations over large, indexed regions. This approach provides a valuable tool for analyzing problems that require historical information about current $\alpha$ microstructures, such as investigating variant selection mechanisms during the $\alpha \to \beta \to \alpha$ transformation. Additionally, we present a method for calculating deformation gradient variants associated with phase transformations between hcp ($\alpha$) and bcc ($\beta$) phases based upon a series of frame rotations and shape transformations. This method streamlines the integration of transformation kinematics into continuum-based models by enabling convenient computation of the deformation gradient governing the transformation.