* Corresponding author. Fax: #33-4-67-14-32-99. E-mail address: rene@ldv.univ-montp2.fr (R. Vacher) Physica B 276}278 (2000) 427}428 Brillouin scattering of neutrons and X-rays from glasses R. Vacher*, E. Courtens, M. Foret, B. Hehlen, E. Rat, H. Casalta, B. Dorner Laboratoire des Verres, Universite de Montpellier II, CNRS, F-34095 Montpellier, Cedex 5, France I.L.L., BP 156, F-38042 Grenoble, France Abstract Inelastic neutron and X-ray scattering are used to investigate high-frequency acoustic modes in glasses, in particular glassy selenium and densi"ed silica. Strong scattering takes over above a crossover frequency where the excitations loose their plane-wave character.  2000 Elsevier Science B.V. All rights reserved. Keywords: Brillouin scattering; Glasses; Phonons The nature of vibrations in glasses at frequencies high up on acoustic branches is a question of great current interest. A central issue is whether very high-frequency acoustic excitations still propagate as damped plane waves or rather experience strong scattering in relation with the structural disorder [1]. In the latter case, the acoustic vibrations loose their character of propagating plane waves above a Io!e}Regel crossover frequency,   . This question can only be addressed with spectro- scopy, i.e. Brillouin scattering (BS), requiring conserva- tion of energy  and momentum Q. The models to interpret the dynamical structure factor, S(Q,), of course di!er whether one has viscous damping or elastic phonon scattering [2]. In non-periodic materials, kinematic conditions impose severe limitations to neutron-BS (NBS) experiments. Presently, NBS can be achieved only in glasses of su$- ciently low sound velocity. Examples of spectra measured on glassy selenium (g-Se) are shown in Fig. 1. The measurements were performed on the triple-axis spec- trometer IN8 at the ILL. The frequency resolution was & 1.4 meV. At the smallest Q, the Brillouin peaks are clearly seen on the spectra. The data can be "tted equally well with two models, either the damped harmonic oscil- lator (DHO) assuming viscous damping, or the crossover model which describes S(Q,) in the presence of strong scattering [3,4]. Only by considering other physical evid- ences, in particular the plateau in the thermal conduc- tivity near 10 K, can the elastic phonon scattering mechanism be assumed to dominate. At larger Q, other contributions to S(Q,) mask the Brillouin peaks, as already seen for Q"4 nm in Fig. 1. These arise from local modes, and from Umklapp scattering where mo- mentum is exchanged partly with the "rst sharp di!rac- tion peak [5]. Both Brillouin and Umklapp signals indi- cate that sound waves are strongly scattered for energies above   &3.4 meV. The corresponding crossover wave vector is q  &3 nm [6]. In vitreous silica, measurements where NBS was asso- ciated with inelastic X-ray scattering (IXS) gave   &3.9 meV and q  &1 nm at room temperature [7]. The above crossover values in q and  are very close to the resolution limits of both NBS and IXS. In order to overcome this problem, we performed IXS from densi"ed silica glass, d-SiO  [8] at the ESRF in Grenoble. In this case we anticipated a higher crossover frequency, su$- cient to be observable with current IXS resolution. Examples of spectra are shown in Fig. 2. At small Q-values, the pro"le of the Brillouin peaks corresponds to the resolution. At Q'2.5 nm, the line width in- creases strongly. The whole set of data was "tted with the crossover model and   &9 meV was found. An important feature, observed in Fig. 2, is that S(Q,)P0 as P0. This behavior is predicted by the crossover model, as the spectrum measured at a given Q is the sum of the contributions of all modes of di!erent  at this particular Q [2]. As modes at P0 are plane 0921-4526/00/$ - see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 3 4 6 - 0