  In this paper we improve the understanding of the cofactor conditions, which
are particular conditions of geometric compatibility between austenite and
martensite, that are believed to influence reversibility of martensitic
transformations. We also introduce a physically motivated metric to measure how
closely a material satisfies the cofactor conditions, as the two currently used
in the literature can give contradictory results. We introduce a new condition
of super-compatibility between martensitic laminates, which potentially reduces
hysteresis and enhances reversibility. Finally, we show that this new condition
of super-compatibility is very closely satisfied by Zn45Au30Cu25, the first of
a class of recently discovered materials, fabricated to closely satisfy the
cofactor conditions, and undergoing ultra-reversible martensitic
transformation.
