a ferroelastic transition

A ferroelastic transition is a structural change in which the crystal spontaneously develops a strain — it distorts to a lower-symmetry shape all by itself on cooling — and, crucially, that strain can point in more than one equivalent direction, so the crystal breaks up into regions (domains) that are strained differently but are mirror-related copies of one another. What makes it ferro is that you can switch a domain from one strain state to another by applying mechanical stress, exactly as a ferromagnet's domains switch under a magnetic field. The strain-versus-stress curve even shows a hysteresis loop.

The parent phase is more symmetric; on cooling through the transition the symmetry lowers (a group-subgroup step) in a way that lets the unit cell distort — say a cubic cell becoming tetragonal, which can stretch along x, y, or z. Each choice is a ferroelastic variant, and a real crystal contains several, separated by domain walls (often mirror-plane twin boundaries). Push on the crystal and the walls move: the favourably-oriented variant grows at the expense of the others, so the crystal can be poled mechanically. Many of these transitions are displacive and soft-mode driven; some are simultaneously ferroelectric (both strain and polarisation switch).

Ferroelasticity is one branch of the broader family of ferroic transitions (ferroelastic to strain, ferroelectric to polarisation, ferromagnetic to magnetisation), all of which arise when a symmetry-lowering transition creates several equivalent domain states. Ferroelastic and coupled ferroelectric materials (like the perovskite lead zirconate titanate, PZT) are the basis of piezoelectric sensors and actuators; shape-memory alloys are essentially ferroelastic. Structurally, the key lesson is that a spontaneous strain plus multiple switchable variants is the signature.