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We derive an analytical expression for the chemical potential of disordered binary alloys using a reciprocal space approach. The main characteristic of the formalism is that it does not limit the effective radius of atomic interaction and correlations in the system. The lattice displacements caused by atomic size mismatch can be naturally introduced into this formalism. A comparison with results from Monte Carlo simulations shows very good agreement. The new analytical expression for the chemical potential can be widely applied, e.g., for the calculation of phase diagrams as well as surface segregation profiles in nanoconfined systems.