transformation twinning
A martensite plate has a problem to solve. The shear that creates it would, on its own, leave the plate the wrong shape to fit the untransformed crystal around it, causing enormous strain. Transformation twinning is nature's fix: inside the plate the new crystal is split into thin, alternating slabs that are mirror images of each other (twins), and this fine twinning cancels out the awkward part of the shape change while keeping the new structure everywhere.
This is the lattice-invariant shear: an extra, internal shear that does not change the crystal structure (each twin band is the same phase, just re-oriented) but adjusts the overall shape so the habit plane stays undistorted. It is called lattice-invariant precisely because it leaves the lattice type unchanged — it only re-partitions orientation. The plate ends up as a stack of nanometre-to-micrometre twin lamellae; alternatively the accommodation can be done by fine slip instead of twinning, but in many martensites it is twinning you see under the electron microscope.
Transformation twinning is the secret of the shape-memory effect. In a shape-memory alloy the martensite forms as self-accommodating twin variants that produce almost no overall shape change; bending the cold alloy just moves the twin boundaries (detwinning), and heating reverts everything to the single high-symmetry parent — so the object springs back to its remembered shape. The twins are mobile, low-energy interfaces, which is why the whole process is reversible.
Bend a length of NiTi shape-memory wire in its cold (martensitic) state into a new shape and you are really just pushing its fine internal twin boundaries — growing the favourable twin variant (detwinning), not truly plastically destroying the crystal. Heat it and the material returns to a single high-symmetry parent, the twins vanish, and the wire remembers and springs back to its original shape.
Transformation twinning (lattice-invariant shear): alternating mirror twins inside a plate cancel the shape misfit and keep the habit plane invariant — the basis of shape memory.
The lattice-invariant shear of transformation twinning does NOT change the crystal structure — each twin band is the same phase, only re-oriented; it adjusts the overall shape so the habit plane stays invariant, and the shape-memory effect rests on these mobile twin boundaries.