Competition between invariant habit plane and compatible junction plane in TiNb-based shape memory alloy

The invariant plane (IP) condition at a habit plane (HP) and the kinematic compatibility (KC) condition at a junction plane (JP) are quantitatively evaluated by the geometrically nonlinear theory of martensite and the origin of the twin orientation relationship (OR) at a JP is revealed in a β titanium shape memory alloy. Exact twin OR at a JP is impossible among the habit plane variants (HPVs). A nonzero rotation is necessary to maintain the compatibility at a JP between the HPVs. The fully compatible HPV cluster in which IP at a HP and KC at a JP are maintained simultaneously is impossible in this alloy. However, it was found that twin OR and KC can be maintained simultaneously. The preferentially observed HPV clusters in transmission electron microscopy are the clusters with a smaller rotation to maintain KC at a JP.

► Kinematic compatibility (KC) among martensite variants in Ti-Nb-Al is evaluated.
► Rotation Q is necessary to keep KC at any junction plane (JP).
► The rotation Q is equivalent to the rotation to form the exact twin-relationship.
► The JP preferentially observed in experiment is the JP with the smaller Q.
► We propose two preferential JPs with {1 1 1} type I and 〈2 1 1〉 type II twin in Ti-Nb-Al.