Assessment of Entropy Differences from Critical Stress Versus Temperature Martensitic Transformation Data in Cu-Based Shape-Memory Alloys

The entropy differences per unit volume (ΔS^trans) between the close-packed phases in a martensitic transformation (MT) in Cu-based shape-memory alloys are obtained from mechanical tests by measuring, as a function of temperature (T), the critical resolved stress (τ). Specifically, \(\Delta S^{\text{trans}}\) values are obtained from the slope of τ versus T plots by invoking a relation which is straightforwardly derived from the classical Clausius–Clapeyron equation, viz., \(\frac{{{\text{d}}\tau }}{{{\text{d}}T}} = - \frac{{\Delta S^{\text{trans}} }}{\gamma },\) where γ is the transformation shear strain. Motivated by the significant scatter of the so obtained \(\Delta S^{\text{trans}}\) values, the thermodynamic bases of such evaluation procedure have been revised, by accounting for the nucleation step of a martensite plate. The interface, elastic strain, and chemical contributions to the Gibbs energy of nucleation have been considered. A new expression of the type \(\frac{{{\text{d}}\tau }}{{{\text{d}}T}} = {\varvec{\Omega}} - \frac{{\Delta S^{\text{trans}} }}{\gamma }\) is obtained, where the Ω term involves the elastic properties and their temperature dependence. The new \(\tau {-} T {-} \Delta S^{\text{trans}}\) relation is used to assess the \(\Delta S^{\text{trans}}\) values corresponding to the 2H/18R and 18R/6R MTs in Cu–Al–Ni and Cu–Zn–Al alloys. The ΔS^trans values obtained by the present approach fall on a scatter band centered around the zero value.