This paper provides a clear and simple group theory description of deformation in shape memory alloys (SMAs) from DO3 austenite to 18R martensite. The 24 elements in the point group of austenite P24 correspond to 24 martensite habit plane variants. After one pair of vectors (the normal vector of the habit plane and the corresponding shape strain vector) are obtained, the other 47 pairs (including the inverse pairs) can be produced by operations of P24 and inverse through centre on the original pair. As point group P4 is a subgroup of P24, operations of P4 and on one pair of vectors results in 8 pairs of vectors, which belong to the same basal plane. Point group P2 is a regular subgroup of P24. Phase transformation eigenstrain C is invariant in the operation of group P2. There are 12 elements in L12, which is the left co-set of P2 in P24, and they correspond to 12 different phase transformation eigenstrains in 18R Martensite. The point group S4 is also a subgroup of P24, and stands for the self-accommodation group in 18R Martensite. 4 pairs of vectors in this self-accommodation group S4 cluster along direction i1-i2/2. All 48 pairs of vectors can be generated by applied left co-set operations and on these clustered pairs.
Zhu, J., & Liew, K. M. (2003). Description of deformation in shape memory alloys from DO3 austenite to 18R martensite by group theory. Acta Materialia, 51(9), 2443-2456. https://doi.org/10.1016/S1359-6454(02)00604-3