We present a closed and consistent model for growth phenomena of binary systems. Starting with the free energy of mixtures, a mean-field description of the material is derived that accounts for morphological as well as compositional evolution, which are strongly coupled to each other. The derived phase-field model describes surface effects, e.g. surface diffusion and anisotropic surface tension, as well as codiffusion in the evolving bulk phase. The model leads to a set of nonlinear partial differential equations of high order, which are solved simultaneously using adaptive finite elements and used to analyse the interplay of growth, surface and compositional dynamics. The external driving force is a mass flux from a fluid or vapour phase which allows to control the growth process.