Geometrical Model of Polymorphous Transformations in Titanium and Zirconium

A geometrical model of transformation of a body-centered cubic lattice of α-phase into a hexagonal close-packed lattice of α-phase is developed with the aim of explaining the special features of the crystal geometry of formation of martensite phases in titanium and zirconium and in alloys based on them. The transformation is described as mutual reconstruction of coordination polyhedra of the cubic and hexagonal lattices through an intermediate configuration of the crystal structure of ω-phase. In the language of algebraic geometry the transition is implemented as reconstruction of an 11-atom cluster that represents a union of three octahedra around a common edge into an 11-atom cluster composed of 11 tetrahedra united over faces. Experimentally observed orientation relations and habit planes at α → ω and β → α transformations are describable by elements of the structure of the mentioned clusters.