Ultrasonic-phase-velocity measurements in electron-irradiated quartz.

Abstract

Precision measurements of the ultrasonic velocity change as a function of temperature were carried out in electron-irradiated quartz (dose=1.0\ifmmode\times\else\texttimes\fi{}${10}^{20}$ e/${\mathrm{cm}}^{2}$, E=3 MeV) for two frequencies: 648 and 480 MHz. Between 0.33 and 2 K, a frequency-independent logarithmic increase of the velocity is observed. The effect is very small, but clearly indicates the presence of the resonant interaction of tunneling states with phonons. The experiment shows that tunneling states of a two-state nature are present. In addition, the effect of the relaxation process on the velocity is observed and shows that the tunneling states are of the same nature as in glasses. A comparison with neutron-irradiated quartz indicates that similar tunneling states are induced by electrons and neutrons, in spite of the different disordering processes. It is suggested that the electron-induced Frenkel pairs provide the necessary freedom for rearrangements and rotations of the tetrahedra, which can be at the origin of the tunneling states.