Thermodynamic equilibrium of a crystalline sphere in a fluid

Abstract

A treatment is given of the thermodynamic equilibrium of a crystalline sphere immersed in a fluid under the assumptions that the surface free energy and surface stress are isotropic and that the sphere is in a homogeneous state of hydrostatic stress. The treatment extends previous work and includes, for the sphere/fluid system, a thermodynamic treatment of surface stress, a derivation of a Gibbsian adsorption equation, a systematic discussion of the solution of the two surface equations resulting from two independent surface variations, and expressions for the work of nucleation and nucleus (sphere) composition. The most interesting theoretical result is that, for fixed temperature and chemical potentials (uniform throughout the system), the state of matter in the sphere differs, in general, from that of bulk of the same phase. For example, the composition in the sphere is not given, in general, by the parallel tanget construction using bulk free energy curves; the necessary correction is provided. Again, an expression is rederived for the difference between a given chemical potential in the sphere and in bulk crystal, holding fixed the temperature, pressure, and composition of the crystal; the chemical potential difference is traceable to a difference in the defect concentration.