Experimental and theoretical investigation of nonequilibrium acoustic phonon dynamics in praseodymium-doped fluorides

Due to the relative simplicity of the energy levels in $\rm LaF\sb3:Pr\sp{3+}$ this system has been the source of many investigations involving vibrational dynamics. Previous studies have included energy transfer between interstitial sites in PrF$\sb3$ due to thermal phonons (Hamilton et al, 1977), and frequency dependence measurements of the anharmonic lifetimes of acoustic phonons in $\rm LaF\sb3:Pr\sp{3+}$ (Tolbert et al, 1990). It is the object of this dissertation to further these investigations and to explore the theoretical nature of vibrational quanta surrounding a defect site.

In particular, two experimental investigations are reported. The first investigation examines stimulated energy transfer between an interstitial and stoichiometric site, in PrF$\sb3$, employing Defect Induced One Phonon Absorption of far infrared radiation (FIR). By direct stimulation of the transfer mechanism and by detailed modeling, an upper limit of $(1.9\pm0.2)\times10\sp6$ s$\sp{-1}$ to the transfer rate was obtained. The second investigation uses a plasma switching technique to generate ultrafast FIR pulses and thus go beyond the limited temporal resolution of the previous investigations performed by Tolbert et al. This work examines the frequency dependence of the anharmonic decay rate of high frequency acoustic phonons ranging between 55 cm$\sp{-1}$ and 113 cm$\sp{-1}$ in $\rm LaF\sb3:Pr\sp{3+}.$ A measurable deviation from the isotropic dispersionless model was found. The frequency dependence of the anharmonic decay rate was fitted to an exponent of $6.4\pm0.3,$ whereas the isotropic dispersionless model predicts an $\omega\sp5$ dependence.

Finally, the nature of vibrational states surrounding a defect site, and the effect of these states on the anharmonic decay rate are discussed. A theory describing the gradual relaxation of momentum conservation due to broken translational symmetry is presented, and the resulting effects on the anharmonic interactions of various vibrational modes is explored.