Cluster decomposing for Green functions and thermodynamic potential of a system of electrons and phonons of a disordered crystal

The cluster expansion for two-time retarded Green's functions and thermodynamic potential of disordered crystal with the account of the electron-phonon and electron-electron interactions is obtained The electronic states of a system are described in the many-band tight-binding model. The calculations are based on a diagram technique for the temperature Green's functions. The coherentpotential approximation is chosen as the zero single-site approximation in this method of cluster expansion. As shown, the contributions of the scattering of elementary excitations on clusters decrease with increasing the number of sites in a cluster on some small parameters. In the one-band model, the analytic evaluations of the influence of electron-phonon interaction on the electron energy spectrum of the ordered alloy are made The possibility of application of the obtained results for the description of influence of strong electron correlations on the electronic structure and properties of transition-metals' alloys with narrow energy bands is shown on the example of Fe-Ti alloy.