Role of Anharmonicity
Figure shows the dependence of the frequencies of the anharmonic local
modes on their amplitudes. In each case as the amplitude of the mode
increases, its frequency move farther away from the top of the phonon
band, Wm, and the mode becomes more
localized.
In the region of small amplitude, the frequencies of the two
local modes with different parities are almost identical and coincide
with the frequency of the envelope soliton of the continuum
approximation. A further increase in amplitude (or anharmonicity
parameter) separates these modes from the envelope soliton region, and
both odd and even parity anharmonic local modes become distinguishable
elementary vibrations.
When the eigenvectors of the local modes are used as initial
conditions for molecular dynamics (MD) simulations, there is excellent
agreement between the simulated frequencies (circles) and the analytic
results (solid curves) shown in Figure.
Last modified: August 12, 1997