The multiple scattering theory of phonons in mass disordered lattices |
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Authors: | V Čápek |
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Institution: | (1) Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, Praha 2, Czechoslovakia |
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Abstract: | A version of the multiple scattering theory previously applied to the electronic problem of substitutional alloys is completed and modified in order to handle the problem of vibrations of general mass-disordered crystal lattices. The Born series is expressed in terms describing the scattering corrections to the appropriate effective medium. A new physical interpretation of the effective medium condition is given and the total partial summation of the Born series for the full scattering T-matrix is completed to the infinite order. The T-matrix is thus re-expressed in terms corresponding to resonant “ping-pong” scattering of renormalized phonons on all possible clusters of scattering centres. Confining to clusters of only limited number of scattering centres yields a set of successive approximations. The one-centre approximation for cubic crystals complies with the Taylor's selfconsistent procedure. A simple illustrative example in the two-centre approximation is solved and discussed. |
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