Describing the morphology of 2H martensite using group theory part I: Theory

This paper is devoted to a clear and simple group theory description of the morphology and microstructure (including the orientation relationships among lattice correspondence variants, habit plane variants and the self-accommodation diamond) of 2H martensite in shape memory alloys (SMAs). There are 24 elements in point group ℘ ₂₄ of DO ₃ austenite, and they correspond to 24 habit plane variants. These 24 habit plane variants form a cubic group. Martensite point group ℘ ₄ is a subgroup of ℘ ₂₄ and 4 habit plane variants that, correspond to ℘ ₄ and form a correspondence variant dominant group. A cubic group can be divided into six correspondence variant dominant groups that correspond to six elements of ℒ ₆ - the left co-set of ℘ ₄ in ℘ ₂₄. The point group ℒ ₄ is also a subgroup of ℘ ₂₄ and is a self-accommodation group in 2H martensite. 4 normal directions of habit plane variants in self-accommodation group ℒ ₄ cluster together along one [110] direction. A cubic group can be divided into six self-accommodation equivalent classes, which correspond to six self-accommodation martensite diamonds. There are 4 different cubic groups in 2H martensite. Thus, there are 96 martensite habit plane variants that correspond to 192 normal habit plane directions and 48 phase transformation eigenstrains.