Coherent-potential approximation binary alloys

ANG AO ATA BF CB CF CNDO CPA DBA DOS FL GF HFA LDOS LMTO MO NN TBA VB VCA WSL Anderson-Newns-Grimley atomic orbital average t-matrix approximation Bessel function conduction band continued fraction complete neglect of differential overlap coherent-potential approximation disordered binary alloy density of states Fermi level Green function Flartree-Fock approximation local density of states linear muffin-tin orbital molecular orbital nearest neighbour tight-binding approximation valence band virtual crystal approximation Wannier-Stark ladder... 

We summarize below the main theoretical approaches to the binary alloy, i.e. those based on the coherent-potential approximation (CPA).156... 

In order to solve the multiple-scattering problem for the alloy, one replaces the original random alloy by an ordered lattice of effective scatterers, or the so-called effective medium. The effective medium is described by a site U (but not a sort i) dependent (complex) coherent potential. Therefore, the eflFective medium has the symmetry of the underlying crystal lattice. In the single site approximation the properties of these effective atoms have to be determined self-consistently by the condition that the scattering of electrons of real atoms embedded in the effective medium vanish on the average. For a disordered binary alloy this idea is schematically illustrated in Fig. 2. 

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