On the Strong Composition Dependence of the Martensitic Transformation Temperature and Heat in Shape Memory Alloys.

General derivation of the well-known Ren-Otsuka relationship, 1αdTodx=-αβ (where To, x , α and β(>0) are the transformation temperature and composition, as well as the composition and temperature coefficient of the critical shear constant, c ', respectively) for shape memory alloys, SMAs, is provided based on the similarity of interatomic potentials in the framework of dimensional analysis. A new dimensionless variable, tox=ToxTmx, describing the phonon softening (where T m is the melting point) is introduced. The dimensionless values of the heat of transformation, Δ H , and entropy, Δ S , as well as the elastic constants c ', c 44 , and A=c44c' are universal functions of t o ( x ) and have the same constant values at t o (0) within sub-classes of host SMAs having the same type of crystal symmetry change during martensitic transformation. The ratio of dtodx and α has the same constant value for all members of a given sub-class, and relative increase in c ' with increasing composition should be compensated by the same decrease in t o . In the generalized Ren-Otsuka relationship, the anisotropy factor A appears instead of c ', and α as well as β are the differences between the corresponding coefficients for the c 44 and c ' elastic constants. The obtained linear relationship between h and t o rationalizes the observed empirical linear relationships between the heat of transformation measured by differential scanning calorimetry (DSC) ( Q A ⟶ M ) and the martensite start temperature, M s .