Description of polymorphic transformations of Ti and Zr in the framework of the algebraic geometry

A geometric model for the transformation of a body centered cubic (bcc) lattice into a hexagonal close packed (hcp) lattice has been developed. The transformation is described as the mutual reconstruction of coordination polyhedra of bcc and hcp lattices through an intermediate configuration coinciding with the crystal structure of the ω-phase. On the language of the algebraic geometry the transformation is effected as the transformation of the 11-atomic fragment of the {3, 4, 3} polytope into the 11-atomic fragment of the {3, 3, 5} polytope. It was found that the orientation relations and habit planes of both α ↔ ω and β ↔ α transformations which have been reported for Ti and Zr are determined by the structural elements of these fragments.