Revisiting the cofactor conditions: Elimination of transition layers in compound domains

The paper studies how to remove “transition layers” at interfaces when a material contains compound domains during martensitic phase transformations. It extends classical cofactor conditions by building a comprehensive theoretical framework for which interfaces can be compatible. The authors emphasize a key requirement: a commutation property among martensitic variants. They derive necessary and sufficient “extreme compatibility conditions” that enable simultaneous elimination of transition layers at phase interfaces for both Type I/II and compound laminates, across all volume fractions. They apply the theory to cubic-to-orthorhombic and cubic-to-monoclinic II transformations and explicitly derive the conditions. The theory predicts new zero-elastic-energy microstructures, including stress-free inclusions and distinctive martensitic cluster patterns, and discusses the possibility of supercompatibility in non-conventional twins observed in NiMnGa. Overall, the results are presented as guidance for rational design of next-generation shape memory alloys with optimized functional properties, by enabling stress-free interfaces that support nucleation in both directions.