Eutectic and peritectic equilibria in coherent binary alloys

Abstract

This work extends the Cahn--Larché thermodynamic framework to binary alloys in which two coherent solid phases coexist with an incoherent liquid and investigates how coherency strain energy modifies classical eutectic and peritectic equilibria. We derive equilibrium conditions for three-phase coexistence that include an elastic energy term dependent on the molar fractions of the solid phases and apply them to model binary eutectic and peritectic systems. We find that coherency stress transforms the eutectic point into a finite three-phase equilibrium field spanning a continuous range of compositions and temperatures. In contrast, coherency stress in peritectic systems progressively destabilizes the two-solid equilibrium without generating a stable three-phase field and can suppress the peritectic reaction entirely. This asymmetry is governed by the geometric relationship between the stress-free compositions of the phases: when the liquid composition lies between those of the two solids (eutectic configuration), the liquid serves as a thermodynamic buffer against the coherency penalty on the solid--solid pair; when it lies outside (peritectic configuration), no such mechanism is available. These results demonstrate that coherency stress can fundamentally alter three-phase equilibria involving a liquid and suggest that such effects may be significant in systems with large coherent misfits.

Figures (5)

• Figure 1: Gibbs free energy curves at three representative temperatures relative to the eutectic temperature in the stress-free system ($T_E$) obtained with various coherency magnitudes, $\mathcal{W}$, expressed in terms of the reference free energy parameter of the solid phases ($b=b_\alpha=b_\beta$).
• Figure 2: Phase equilibria maps for various coherency magnitudes, $\mathcal{W}$, expressed in terms of the reference free energy parameter of the solid phases ($b=b_\alpha=b_\beta$).
• Figure 3: Gibbs free energy curves at three representative temperatures relative to the peritectic temperature in the stress-free system ($T_P$) obtained with various coherency magnitudes, $\mathcal{W}$, expressed in terms of the reference free energy parameter of the solid phases ($b=b_\alpha=b_\beta$).
• Figure 4: Phase equilibria maps for various coherency magnitudes, $\mathcal{W}$, expressed in terms of the reference free energy parameter of the solid phases ($b=b_\alpha=b_\beta$).
• Figure 5: Assessment of predicted effects for a realistic eutectic system exemplified by Cu--Ag: (a) phase diagram and parabolic approximations of the Gibbs free energies with deviations from the common tangent corresponding to (b) realistic lattice misfit of 1% and (c) its theoretical upper bound 5%. The common tangent for $\alpha+\beta$ is shown as a dashed line in (b,c).