Frequency vs. Amplitude

The figure shows the IGM frequency verses the amplitude for the two structures under investigation. The left sets of data are for zinc blende and the right sets are for the fcc lattice. These results indicate that the Td symmetry site appears to support more anharmonicity in the sense that for a given vibrational amplitude the frequency of the IGM drops farther into the forbidden gap and has a larger elastic lattice distortion around the IGM center [compare the eigenvectors shown in previous figures].
The frequency of an intrinsic gap mode as a function of normalized amplitude, a/d. The left set of data are for the zinc blende and the right set for the fcc lattice. The numerical solutions of the time-independent nonlinear equations are represented by the solid lines for the [111] and by dashed lines for the [110] crystal direction. The result of MD simulations are given by the open diamonds for the [111] direction and by open circles for the [110] direction.
The general behavior of the IGM frequency versus amplitude shown in the figure is similar for both structures - with increasing mode amplitude the frequency drops farther into the gap. An amplitude threshold is evident. An IGM which has its frequency about 5% below the bottom of the optics band (corresponding to the middle regions of the curves in the figure) has the longest lifetime of ~200-250 vibrational periods. If its frequency drops farther into the forbidden gap (~10%) the mode's lifetime decreases to ~100 periods. At the opposite small amplitude limit its lifetime again decreases (~40 periods) presumably because of the size effect for the 216-ion cluster under investigation or due to the strong coupling between the IGM and the nearby plane waves.

In both systems the elastic distortion associated with the IGM has lower symmetry than the corresponding point group symmetry of the crystal. To recover the full crystal point group symmetry for this perfect crystal it must be possible with a different set of initial conditions to rotate the IGM about the equilibrium lattice site. To test this idea we have examined IGM excitations along the three different crystal directions. Although a stable IGM mode does not appear for initial excitation along the [100] direction, the dashed lines and open circles in the figure demonstrate that for both point group symmetries a [110] directed mode can occur. These sets of data support the idea of an interchange of the IGM vibration direction as would be expected, for example, with hindered rotational motion of the excitation about the lattice site. This concomitant low frequency component of the IGM may provide new experimental ways to excite and identify these nonlinear excitations.

Last modified: April 12, 1997