Remarkable martensitic microstructures are observed in the alloy  Ti76Nb22Al2 , which undergoes a cubic to orthorhombic transformation with six martensitic variants Ui=UTi greater than 0 having middle eigenvalue λ2(Ui) very close to 1. Assuming that λ2(Ui)=1 there are exactly 12 matrices in the set of energy wells ⋃6i=1SO(3)Ui that are rank-one connected to 1. This set of 12 matrices has no rank-one connections.  We attempt to understand the observed microstructures by studying gradient Young measures, exact gradients and TN-configurations supported on these 12 matrices. This is joint work with Tomonari Inamura and Francesco Della Porta.