Transport theory at the nanoscale. II. Interface dynamics for film growth

Conditions for surface nucleation and growth of a film are determined in a diffuse interface model. A method is given, derived from a Fokker-Planck equation for the nonequilibrium particle distribution, which links atomic and mesoscopic events in a rheological description similar to the classical continuum theory of fluid flow. Film nucleation and growth are modeled by the spatially inhomogeneous continuous evolution of the instantaneous density profile which measures the average number of particles or molecules at given time and position. It is shown how an alteration in the distribution of particles in the vicinity of the boundary between parent and product phases induces transient film growth and damped vibrations at the surface. The method is general but as an illustration, the condensation of a simple classical fluid on cooling is considered in detail.