Crystallography of the Tetragonal → Monoclinic Transformation in Zirconia

The tetragonal to monoclinic (t → m) transformation in zirconia occurs through two paths ; transformation along path I has two Bain strains that involve shearing of a rectangular face of the tetragonal unit cell, and shearing of the square base corresponds to path II. The monoclinic variants resulting from each of the three Bain strains can form 12 twins, and four of the twins corresponding to path II are neither of type I nor of type II. Habit planes do not exist for the transformation along path I, whereas transformation along path II has : (±0.8139, ±0.3898, -0.4309) t , (±0.6489, ±0.6271, -0.4309) t , (±0.7804, ±0.4530, -0.4309) t .