Phase equilibrium in two-phase coherent solids

Abstract

Phase equilibrium in a two-phase stressed coherent solid is analyzed using the thermodynamic equilibrium conditions directly. Subject to the constraints of constant temperature and external pressure, a bulk alloy composition is chosen and the corresponding volume fractions and phase compositions that satisfy the equilibrium conditions are obtained. We demonstrate unequivocally that, unlike fluids, a number of equilibrium states (combinations of volume fractions and phase composition) may exist that yield energy minima for a given temperature, pressure, and alloy composition and that these multiple metastable states may lead to a nonuniqueness in the observed physical state of the system. In addition, we show that discontinuous jumps in precipitate volume fraction both between 0 and 1 as well as jumps within the range 0 to 1 are possible with a smooth variation in alloy composition. These results are a consequence of the elastic energy, and thus the system energy, being a function of the volume fraction when two phases coexist as coherent solids. As it is difficult to display these effects on a coherent phase diagram, the concept of a phase stability diagram is introduced for both displaying and analyzing the equilibrium conditions in coherent solids. The influence of elastic inhomogeneity and the form of the free energy curves as a function of composition in the absence of stress on phase equilibrium are examined.