Disorders real-self-energy

The Green function, Gij ui) is defined as the Fourier transform of G K,lj) as indicated above. Similarly, the real-space counterparts of G(K,w) and S(K,o)) can also be defined by Eq. (6), completing the loop of self-consistent equations to be solved for the self-energy. These real-space quantities, defined over the sites of a finite cluster of sites, can be used to provide an exact treatment of the disorder in the cluster. Thus, the Green function G satisfies the expression, (using operator notation and suppressing the energy parameter from now on)... 

Nor is the methodology exhaustive in terms of experimental data, as required of a proper alloy theory. Indeed, it produces results that are known to be contrary to the behavior of physical systems. For example, it yield a self-energy that is real whereas the dispersion in the experimental spectra of disordered alloys suggests a complex quantity. Because the method lacks scientific foundation, its generalization to incorporate a broader spectrum of physical reality is unjustified. 

Real surfaces will generally also have defects analogous to those occurring in the bulk. As the temperature of an initially ideal surface is increased a certain amount of thermal disorder in the form of vacancies, interstitials and self adsorbed ions (and their complexes) will occur due to the balancing effect of the entropy contribution. The formation energies and entropies (vibrational) associated with such defects will be different from the corresponding bulk values and hence their densities will vary with depth into the crystal. Since ionic defects are of prime importance for conduction in many ionic crystals the properties of individual surface point defects are of fundamental interest in assessing surface conductance contributions. 

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