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, <i>x</i>, α and β(>0) are the transformation temperature and composition, as well as the composition and temperature coefficient of the critical shear constant, <i>c</i>', 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 <i>T_m</i> is the melting point) is introduced. The dimensionless values of the heat of transformation, Δ<i>H</i>, and entropy, Δ<i>S</i>, as well as the elastic constants <i>c</i>', <i>c</i>₄₄, and A=c44c' are universal functions of <i>t_o</i>(<i>x</i>) and have the <b>same constant</b> values at <i>t_o</i>(0) within sub-classes of host SMAs having the same type of crystal symmetry change during martensitic transformation. The ratio of dtodx and <i>α</i> has the same constant value for all members of a given sub-class, and relative increase in <i>c</i>' with increasing composition should be compensated by the same decrease in <i>t_o</i>. In the generalized Ren-Otsuka relationship, the anisotropy factor <i>A</i> appears instead of <i>c</i>', and α as well as β are the differences between the corresponding coefficients for the <i>c</i>₄₄ and <i>c</i>' elastic constants. The obtained linear relationship between h and <i>t_o</i> rationalizes the observed empirical linear relationships between the heat of transformation measured by differential scanning calorimetry (DSC) (<i>Q^A</i>^⟶<i>M</i>) and the martensite start temperature, <i>M_s</i>.