The criteria for stabilities of eutectics, solid solutions and precipitates are proposed. Based on the Thomas-Fermi-Dirac model on the boundary conditions, electron densities and chemical potentials should be equal in either side of a composite film. The optimum condition for the energy balance and the sizes of films of eutectics is given. The criteria for stabilities of eutectics, solid solutions and precipitates are proposed. Based on the Thomas-Fermi-Dirac model on the boundary conditions, electron densities and chemical potentials should be equal in either side of a composite film. The optimum condition for the energy balance and the sizes of films of eutectics is given.