By adding a suitably defined elastic energy term to the free energy, a new free energy
function is obtained which, over a limited composition range, has all the properties of a
thermodynamic potential for coherent processes. It may be used for instance to obtain the
coherent phase diagram by the ordinary method of common tangents, and in this paper it is
used to examine the coherent nucleation in isotrpic solids, expecially in the vicinity of the
limit of metastability, where such nucleation is not classical.