Anharmonicity

Abstract: The physical mechanisms which can produce second-order dielectric polarization are discussed on the basis of a simple extension of the theory of dispersion in ionic crystals. Four distinct mechanisms are described, three of which are related to the anharmonicity, second-order moment, and Raman scattering of the lattice. These mechanisms are strongly frequency dependent, since they involve ionic motions with resonant frequencies lower than the light frequency. The other mechanism is related to electronic processes of higher frequency than the light, and, therefore, is essentially flat in the range of the frequencies of optical masers. Since this range lies an order of magnitude higher than the ionic resonances, the fourth mechanism may be the dominant one. On the other hand, a consideration of the linear electro-optic effect shows that the lattice is strongly involved in this effect, and, therefore, may be very much less linear than the electrons. It is shown that the question of the mechanism involved in the second harmonic generation of light from strong laser beams may be settled by experiments which test the symmetry of the effect. The electronic mechanism is subject to further symmetry requirements beyond those for piezoelectric coefficients. In many cases, this would greatly reduce the number of independent constants describing the effect. In particular, for quartz and KDP there would be a single constant.

Abstract: The zero-temperature equation of state of metals, in the absence of phase transitions, is shown to be accurately predicted from zero-pressure data. Upon appropriate scaling of experimental pressure-volume data a simple universal relation is found. These results provide further experimental confirmation of the recent observation that the total-binding-energy---versus---separation relations for metals obey a universal scaling relation. Important to our results is a parameter $\ensuremath{\eta}$, which is a measure of the anharmonicity of a crystal. This parameter is shown to be essential in predicting the equation of state. A simple formula is given which predicts the zero-temperature derivative of the bulk modulus with respect to pressure.

Abstract: A new kind of localized mode is proposed to occur in a pure anharmonic lattice. Its localization properties are similar to those of a localized mode for a force-constant defect in a harmonic lattice. These modes, which are thermally generated like vacancies but with much smaller activation energies, may appear at cryogenic temperatures in strongly anharmonic solids such as quantum crystals as well as in conventional solids.