### Abstract

*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 |
---|---|

Pages (from-to) | 2443-2456 |

Number of pages | 14 |

Journal | Acta Materialia |

Volume | 51 |

Issue number | 9 |

DOIs | |

State | Published - 23 May 2003 |

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### Cite this

_{3}austenite to 18R martensite by group theory.

*Acta Materialia*,

*51*(9), 2443-2456. DOI: 10.1016/S1359-6454(02)00604-3

}

_{3}austenite to 18R martensite by group theory'

*Acta Materialia*, vol 51, no. 9, pp. 2443-2456. DOI: 10.1016/S1359-6454(02)00604-3

**Description of deformation in shape memory alloys from DO _{3} austenite to 18R martensite by group theory.** / Zhu, Jiujiang; Liew, K. M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Description of deformation in shape memory alloys from DO3 austenite to 18R martensite by group theory

AU - Zhu,Jiujiang

AU - Liew,K. M.

PY - 2003/5/23

Y1 - 2003/5/23

N2 - 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.

AB - 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.

U2 - 10.1016/S1359-6454(02)00604-3

DO - 10.1016/S1359-6454(02)00604-3

M3 - Article

VL - 51

SP - 2443

EP - 2456

JO - Acta Materialia

T2 - Acta Materialia

JF - Acta Materialia

SN - 1359-6454

IS - 9

ER -

_{3}austenite to 18R martensite by group theory. Acta Materialia. 2003 May 23;51(9):2443-2456. Available from, DOI: 10.1016/S1359-6454(02)00604-3