Localized vibrations of H ^– and D ^– ions in the alkaline earth fluorides

Abstract

Measurements of the absorption spectra associated with the vibrations of H - and D - ions in CaF 2 , SrF 2 and BaF 2 have been made in the region 1 to 17 μm . The most detailed investigation has been made in CaF 2 , where, in addition to the fundamental vibrational frequency, a second harmonic and two third harmonics of the fundamental frequency have been observed. The spectra have been assigned to the localized vibrations of isolated light ions on fluorine sites. The harmonics are seen because of anharmonic effects; to a good approximation the light ions can be considered to oscillate in an anharmonic tetrahedral potential well produced by a nearly static host lattice. W eak satellite lines are observed in the immediate vicinity of the fundamental vibrational lines due to the presence of small concentrations of H – and D – ions in other lattice configurations. Broad bands occur at displacements greater than about 100 cm-1 to higher and lower frequencies from the localized vibrational lines due to combined excitation of the localized mode and lattice band modes. The temperature-dependent intensity, shift and width of the localized vibrational lines have been measured. The presence of the broad side bands and the temperature-dependent effects arise from anharmonic interactions with the band modes of lattice vibration. A simple model of the band modes leads to very satisfactory agreement between theory and observed anharmonic effects for reasonable values of the anharmonic force constants which are regarded as parameters.

Nonlinear damping and dephasing in nanomechanical systems

“…XI, we discuss the dephasing of low-frequency vibrational modes due to their coupling to thermal phonons. For high-frequency modes, where the decay of thermal phonons can be disregarded, the theory is similar to the theory of dephasing for localized vibrations in solids [52,53]. For smaller ω 0 , the decay of thermal phonons has to be taken into account.…”

“…Equation (76) has the same form as the expression for the dephasing rate of the modes localized near defects in solids [52,53]. In Refs.…”

“…Along with damping, scattering of phonons off the considered mode leads to its dephasing, i.e., loss of coherence, as was first discussed for high-frequency vibrations localized near defects in solids [52,53]. In contrast to damping, the scattering that leads to dephasing is quasielastic, the energy of the mode is not changed.…”

“…The dimensionless parameters γ (1)]. Equation (54) allows one to express the coefficients A μ in the expression for the nonlinear decay rate (53) in terms of the integral strain invariants,…”

“…The mode number μ ≡ (n,m) is a set of integers n,m 0,n + m > 0, and ζ = 1 − Equations (50), (53), and (54)- (58) give…”