THERMODYNAMICS OF PARTICLE COARSENING

The coarsening of precipitate particles during the heat treatment of alloys depends both on the diffusivity of the surrounding phase and on the concentration differences given by the Gibbs-Thomson equation, both of which depend on the solution thermodynamics of the surrounding phase. However, it is now known that thermodynamic terms cancel in the theory; therefore coarsening is independent of solution behavior. The equations that confirm this prediction for multicomponent systems are derived and discussed. In addition, it is shown for ternary and higher order systems that a generalized form of the Gibbs-Thomson equation gives a vector that is normal to the matrix-precipitate phase diagram boundary.