Lattice parameter engineering for reversible martensitic materials using simplified cofactor conditions

Abstract

Cofactor conditions (CCs) provide a geometric criterion for achieving highly compatible austenite/twinned martensite interfaces and have served as a guiding principle for the design of highly reversible martensitic materials. However, their standard ten- sorial form obscures the direct connection between crystallographic lattice parameters and compatibility. In this work, we reformulate the CCs in the eigenspace of the trans- formation stretch tensor. The resulting expressions reduce the compatibility problem to algebraic relations involving the principal stretches and the crystallographic twin axes. Simplified conditions are derived for both Type I/II and Compound 1/2 twins. We find that, for Type I/II twins, once the middle-eigenvalue condition λ2 = 1 is imposed, the remaining conditions reduce to sets of paired curves in the (λ1, λ3) eigenvalue space, while for Compound twins, the conditions lead to admissible domains, revealing a broader compatibility design window than the curve-like conditions associated with Type I/II twins. We further specialize the formulation to cubic to tetragonal, cubic to orthorhombic, and cubic to monoclinic I/II transformations, thereby establishing explicit links between lattice parameters, eigenvalues, and compatibility. The analysis suggests two main conclusions: (i) cubic to monoclinic transformations provide additional design freedom through the monoclinic angle, offering a promising route to simultaneously achieve low hysteresis and large transformation strain; and (ii) Compound twins provide an important design pathway because they occupy finite admissible regions rather than isolated solution curves.

25 pages