Mathematics Colloquium

---

Highly Irregular Microstructures and TN Configurations

Speaker: John Ball, Heriot-Watt University and Maxwell Institute for Mathematical Sciences, Edinburgh

Location: Warren Weaver Hall 1302

Date: Monday, December 8, 2025, 3:45 p.m.

Synopsis:

Remarkable martensitic microstructures are observed in the alloy Ti76Nb22Al2, which undergoes a cubic to orthorhombic transformation with six martensitic variants Ui = UTi > 0 having middle eigenvalue  2(Ui) = 1, thus allowing exact interfaces between the high temperature cubic austenite phase and the low temperature orthorhombic martensite phase. The unusual microstructure arises from the fact that the 12 matrices in the set of martensitic energy wells S6i =1 SO(3)Ui which are compatible with the undistorted austenite, i.e. which are rank-one connected to 1, are pairwise incompatible. The talk will explain the underlying theory and describe attempts to understand the observed microstructures by studying gradient Young measures, exact gradients and TN-congurations supported on these 12 incompatible matrices. This is joint work with Tomonari Inamura and Francesco Della Porta.