## Abstract

This paper provides a clear and simple group theory description of deformation in shape memory alloys (SMAs) from

*DO*_{3}austenite to 18*R*martensite. The 24 elements in the point group of austenite P_{24}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 P_{24}and inverse through centre on the original pair. As point group P_{4}is a subgroup of P_{24}, operations of P_{4}and on one pair of vectors results in 8 pairs of vectors, which belong to the same basal plane. Point group P_{2}is a regular subgroup of P_{24}. Phase transformation eigenstrain**C**is invariant in the operation of group P_{2}. There are 12 elements in L_{12}, which is the left co-set of P_{2}in P_{24}, and they correspond to 12 different phase transformation eigenstrains in 18R Martensite. The point group S_{4}is also a subgroup of P_{24}, and stands for the self-accommodation group in 18*R*Martensite. 4 pairs of vectors in this self-accommodation group S_{4 }cluster along direction i_{1}-i_{2}/2. All 48 pairs of vectors can be generated by applied left co-set operations and on these clustered pairs.Original language | English |
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Pages (from-to) | 2443-2456 |

Number of pages | 14 |

Journal | Acta Materialia |

Volume | 51 |

Issue number | 9 |

DOIs | |

Publication status | Published - 23 May 2003 |

Externally published | Yes |

## Keywords

- Eigenstrain
- Group theory
- Shape memory alloys
- Phase transformation

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