Optical absorption and neutron scattering by lattice vibrations of incommensurate lattices

1 October 1978

journal article
research article
Published by American Physical Society (APS) in Physical Review B

Vol. 18 (7) , 3275-3281
https://doi.org/10.1103/physrevb.18.3275

Abstract

The lattice dynamics of discrete incommensurate lattices are studied numerically by linearizing the equations of motion for the Frenkel-Kontorova model (which consists of a chain of masses connected by springs sitting in a sinusoidal potential) about the equilibrium positions of the atoms, which are determined numerically. The optical-absorption and neutron scattering cross sections are studied. It is found that despite the fact that the incommensurate system lacks translational invariance (because there does not exist a unit cell), the optical-absorption and neutron scattering spectra always appear to consist of a few sharp lines, no matter how strong the coupling of the two periodic systems. The calculations should be applicable to incommensurate charge-density waves, ionic order in potassium hollandite, a one-dimensional ionic conductor, and other systems exhibiting two incommensurate periodicities.

Keywords

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