Inelastic Ultraviolet Scattering from High Frequency Acoustic Modes in Glasses C. Masciovecchio, 1 A. Gessini, 1 S. Di Fonzo, 1 L. Comez, 2 S. C. Santucci, 1,2 and D. Fioretto 2,3 1 Sincrotrone Trieste, Area Science Park, 34012 Basovizza Trieste, Italy 2 Dipartimento di Fisica and INFM, Universit di Perugia, I-06123, Perugia, Italy 3 INFM-CRS Soft, Universita ` di Roma La Sapienza, P. A. Moro 2, 00185 Roma, Italy (Received 3 February 2004; published 17 June 2004) The dynamic structure factor of vitreous silica and glycerol has been measured as a function of temperature and of the momentum transfer up to Q  0:105 nm 1 using a novel experimental technique, the inelastic ultraviolet scattering. As in the case of Brillouin light scattering and ultrasonic measurements, the temperature dependence of the acoustic attenuation shows a plateau below the glass transition whose amplitude scales as Q 2 . Moreover, a slight temperature dependence of attenuation has been found in vitreous silica at about 130 K, which seems to be reminiscent of the peak measured at lower Qs. These two findings strongly support the idea that anharmonicity is responsible for sound attenuation at ultrasonic and hypersonic frequencies. Finally, we demonstrate that the attenuation mechanism should show a change of regime between 0.105 and 1 nm 1 . DOI: 10.1103/PhysRevLett.92.247401 PACS numbers: 78.35.+c, 07.60.Rd, 62.80.+f, 63.50.+x The nature of acoustic excitations and of the acoustic absorption is a central issue in the physics of glasses and, more generally, of disordered materials [1]. The acoustic absorption of glasses is strongly enhanced compared to crystals and a broad absorption maximum occurs in many systems at temperatures higher than 10 K. The peak intensity scales as the momentum transfer Q, while the high temperature side, almost constant with temperature, exhibits a quadratic Q dependence [2]. This behavior is well documented up to Q  0:04 nm 1 , typical of Brillouin light scattering (BLS) experiments [3,4]. A Q 2 dependence of attenuation has been also widely discussed in the 1–10 nm 1 range investigated by inelas- tic x-ray scattering (IXS) [5] and by numerical calcula- tions [6–8], up to a region where a Q 4 behavior is found, possibly due to Rayleigh scattering of acoustic waves [9,10]. At even higher Qs a region of strong scatter- ing is eventually observed as the Ioffe-Regel limit is reached [9]. Different models have been proposed to account for these experimental findings. The interpretation of the sound absorptions in terms of Debye relaxation alone is questionable because unrealistic distributions of relaxa- tion times have to be assumed especially at high tempera- ture and Q where the maximum of absorption tends to degenerate into a shoulder [2]. A model has been recently proposed suggesting that anharmonicity, i.e., the cou- pling of acoustic modes with thermal vibrations, can induce sound attenuation at ultrasonic and hypersonic frequencies, explaining both the T independence of at- tenuation above the peak and the Q 2 behavior [11]. The validity of this model is supposed not to extend up to IXS frequencies, being limited to the so-called Akiezer re- gime [12], below  100 GHz. The Q 2 behavior in the THz region, obtained also in harmonic simulations of the glass, has been attributed to the topological disorder [5–8]. A crossover regime in the attenuation mechanism can be thus inferred between Q  0:04 and Q  1 nm 1 [3]. In this critical region little data on sound attenuation of glasses can be found, obtained by a picosecond optical technique (POT) [13], and these data seem to be incon- sistent with BLS results [3]. In the present Letter we report an inelastic ultraviolet scattering (IUVS) study on the damping of acoustic waves in two prototypical glasses: vitreous silica and glycerol. This novel technique is used to gain informa- tion on the dynamic structure factor of the investigated glasses in the mesoscopic Q range from 0.078 to 0:105 nm 1 , never investigated before by scattering techniques. The experiment was performed at the new IUVS beam line at the Elettra Synchrotron light laboratory in Trieste. This instrument allows one to work both with undulator and UV laser sources. In the first case the incident radia- tion can be tuned from 240 to 110 nm. The undulator radiation must be monochromatized and, for this pur- pose, an 8 m Czerny-Turner normal incidence monocro- mator is used [14]. The laser is a 488 nm single mode 95 second harmonic generator Lexel Ar  laser whose frequency is doubled by an intracavity system equipped with nonlinear beta barium borate single crystals. Independent of the configuration chosen, the beam is focused onto the sample to a spot size of about 200  200 m 2 . The incident flux on the sample is  10 13 photons=s when operating with synchrotron radia- tion and  10 17 photons=s in the laser mode. A spherical mirror collects the scattered radiation over a solid angle of 40  40 mrad 2 close to backscattering and sends it onto the entrance slit of a 8 m Czerny-Turner spectrograph used to energy analyze the signal coming from the probe [14]. The photons are detected by a 13:5 m pixel charge- coupled device detector that allows one to collect the inelastic spectrum in one single shot, thus avoiding long-lasting monochromator scans of the diffraction PHYSICAL REVIEW LETTERS week ending 18 JUNE 2004 VOLUME 92, NUMBER 24 247401-1 0031-9007= 04=92(24)=247401(4)$22.50  2004 The American Physical Society 247401-1