Overall composition dependences of coherent equilibria

The criterion for coherent equilibria is investigated. The expressions of driving force considering elastic energy for further formation of infinitesimal amount of one phase from the other in the two-phase coherent system are obtained. Zero driving force is shown to be a useful thermodynamic criterion for coherent equilibria, which not only has a clear physical meaning, but also is really convenient in coherent equilibria calculations. The coherent equilibrium equations are derived to directly demonstrate that the equilibrium compositions of phases in coherent equilibria depend on the overall alloy composition. In particular, the influence of the deviation of lattice parameter from Vegard’s law on the coherent spinodal, the field lines and the equilibrium compositions of coherent miscibility gap is examined in a regular binary solution. The calculated results show that even small deviation of lattice parameter from Vegard’s law can make the equilibrium compositions strongly dependent on the overall alloy composition. Therefore, the deviation of lattice parameter from Vegard’s law should be carefully considered in the calculation of coherent phase diagrams of the realistic systems.