The temperature dependence of the inelastic neutron-scattering intensity from vitreous silica has been studied between 50 and 300 K down to frequencies of 150 GHz. Above 500 GHz one finds essentially harmonic behavior. Low-frequency anharmonic behavior can be described by a relaxational model using parameters determined from ultrasonic measurements. The dynamic structure factor shows that relaxation involves coupled rotational jumps of SiC>4 tetrahedra, with a jump width of the atoms smaller than 0.8 A. These results support the hypothesis of a common origin of low-temperature glass anomalies.PACS numbers: 63.50. +X, 62.80.+f, 78.30.Ly Although low-frequency excitations in glasses have been studied extensively over the last few years 1 "" 3 their nature remains a puzzle. In addition to sound waves, common to both glasses and crystals, glasses appear to contain three different kinds of "excess" excitations. First, infrared, 4 Raman, 5 thermal, 1,3 and inelasticneutron 3 studies show a density of harmonic modes in the range 200 GHz to 1 THz over and above the soundwave (Debye) contribution. Both heat-capacity and quantitative inelastic-neutron measurements 3 in vitreous silica, for example, give a density of states up to 8 times larger than the Debye value calculated from the measured sound velocities (up to 500 GHz). The neutron experiment also identifies the local motion involved in these excess modes as harmonic libration of coupled SiC>4 tetrahedra.Second, both Raman 5,6 and, less clearly, infrared 4 measurements below room temperature show a relaxational or quasielastic contribution to the excitation spectrum, reminiscent of states seen in acoustic studies 1,2 of thermally activated relaxation processes in a range of glasses. However, attempts to link optical and acoustic measurements by the description of relaxation with a model based on symmetric double-well potentials 5,7 have not been successful in matching both the temperature and frequency dependences of the quasielastic contributions.The third group of additional excitations comprises the tunneling or two-level states 1,8 studied in a wide range of glasses between 10 mK and 1 K. Results of thermal, acoustic, and electrical measurements have been successfully interpreted and related by theory although in most cases the microscopic nature of tunneling states is as yet unknown.The lack of any microscopic picture of low-frequency excitations has meant that no convincing synthesis of these three classes of phenomena has been possible, and each has usually been studied separately. In this Letter we report a study of quasielastic neutron scattering in vitreous silica which allows us to develop a picture of the microscopic motion involved in relaxation similar to that carried through previously 3 for excess harmonic modes. Analysis of the results using a distribution of asymmetric double-well potentials allows a consistent interpretation of all relaxation phenomena.The measurements were done on two cold-neutron time-of-flight spectrometers, the IN6 at the In...
