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 is the melting point) is introduced. The dimensionless values of the heat of transformation, ΔH, and entropy, ΔS, as well as the elastic constants c', c₄₄, and A=c44c' are universal functions of t(x) and have the same constant values at t(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. 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 c₄₄ and c' elastic constants. The obtained linear relationship between h and t rationalizes the observed empirical linear relationships between the heat of transformation measured by differential scanning calorimetry (DSC) (Q^⟶) and the martensite start temperature, M.