A number of solid materials are known to undergo transformation to other `more stable' phases. Frequently, these transformations proceed through a solution phase with which each of the solid phases attempts to be in equilibrium. The analysis of these transformations is presented in terms of the formalism of two population balances. Kinetic and thermodynamic explanations are provided for these transformations. It is demonstrated that this population-balance approach allows one to include a nucleation step for either phase, and to generate model simulations for a multitude of vessel geometries. In addition, a postulate is set forth to explain why, in some cases, the more stable phase evolves apparently without the appearance of the precursor `metastable' phase. Lastly, we show that a recent analysis is a special case of this more formal treatment.