Geodesic
Statistical theory of diffusion. Application to a~vacancy in a~linear chain of atoms
Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 2, pp. 265-277

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The model for a vacancy in a lattice consists of a linear chain of the atoms, which contains one vacant site, together with a substrate potential. For this model the diffusion coefficient of vacancy is studied on the basis of the Kubo's expression for the transport coefficient. In deriving one a lattice distortion around the vacancy and massdifference scattering are taken into account. Two mechanisms of the transition the atom in the neighbouring vacant site is considered: the Orbach-type process at high temperatures which lead to the Arrhenius-type expression (the classical picture) and the tunnel transition at low temperatures. The phonon scattering is described by means of the $t$-matrix and Green function method. 
@article{TMF_1975_24_2_a13,
     author = {Yu. A. Kashlev},
     title = {Statistical theory of diffusion. {Application} to a~vacancy in a~linear chain of atoms},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {265--277},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1975_24_2_a13/}
}
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Yu. A. Kashlev. Statistical theory of diffusion. Application to a~vacancy in a~linear chain of atoms. Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 2, pp. 265-277. http://geodesic.mathdoc.fr/item/TMF_1975_24_2_a13/