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On the theory of lattice vibrations in mixed crystals. The connection between the REI model, ATA, and CPA
Author(s) -
Böttger H.
Publication year - 1976
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220770217
Subject(s) - coherent potential approximation , lattice vibration , connection (principal bundle) , lattice (music) , hierarchy , mathematics , vibration , born approximation , mathematical physics , physics , mathematical analysis , quantum mechanics , geometry , electronic structure , scattering , phonon , acoustics , economics , market economy
For an isotopically disordered one‐dimensional model of a mixed crystal a hierarchy of equations for conditionally averaged Green functions is derived. A definite single‐site approximation leads to the random element isodisplacement model (REI‐model). This approximation is shown to be equivalent to a somewhat modified average t ‐matrix approximation (ATA) and, for a self‐consistent formulation, to a somewhat modified coherent potential approximation (CPA).