Soft Report - Dipartimento di Fisica - Sapienza

High-frequency dynamics of v-GeO 2The effect of disorder on the density fluctuations is atopic with so many unsolved aspects that measuringthe dynamics at THz frequencies in simple glassesremains a class of demanding experiments. Severalattempts have been made to experimentally identifythe nature of the excitations in the mesoscopic region,as well as the origin of the excess of states in thedensity of states (DOS) which gives rise to the BosonPeak (BP). Inelastic x-ray scattering (IXS) experimentsat THz frequency were carried out in several glassesand evidence for the existence of phonon-likeexcitations was found [1,2]. A recent contribution camefrom the observation of two excitations in the currentspectra of v-SiO 2 on IXS data and the persistence ofpropagating sound waves up to Q values close thepseudo-Brillouin-zone edge [2]. The experimentalfindings were complemented by the results of MolecularDynamics Simulations (MD) [3]. This work [4] isdedicated to the investigation of the high frequencydynamics of v-GeO 2 carried out by exploiting four INSspectrometers operated over complementarykinematics ranges with different energy resolutions. Insuch a way, access to a wide kinematics range with aresolution adequate to resolve the inelastic featuresunder investigation was obtained. Brillouin peaks, welldefined and resolved from the tails of the elastic peak,are clearly apparent from the spectra independently ofany model or data treatment. Increasing Q, the peakposition shifts towards higher which reveals, beyondany doubt, the propagating character of this excitation.At low Q, besides the inelastic peak associated to thesound mode, both theoretical and numerical studiespredict a second dispersing excitation in the dynamicresponse function, suggesting the existence of atransverse-like dynamics (Fig. 1).1000 IN1 0.3 Å -1The whole set of the present neutron data in v-GeO 2 isconsistent with the picture of propagating vibrationalexcitations, namely a first mode which shows aremarkable dispersion, beyond which it merges into abroad inelastic bump roughly centred at ∼30 meV, anda second mode characterized by much lower excitationenergies and a much less pronounced dispersion. Weassign a longitudinal acoustic character to the firstmode and a transverse acoustic nature to the secondmode, whose flattening at large Q could contribute tothe excess of vibrational states typical of the high-Q BP.The visibility of a transverse excitation in theintrinsically longitudinal density fluctuation spectra of adisordered system can be justified by the mixingphenomenon: the polarization character of thevibrations, which is well defined at low Q, becomesmore and more ill-defined at larger Q. At highfrequency the transverse dynamics acquires alongitudinal symmetry component, observable by INSmeasurements. To give further ground to the presentinterpretation, we carried out a MD simulation on v-GeO 2 using 680 molecules in a cubic box correspondingto the density ρ=3.6 g cm -3 , interacting through a VanBeest-type potential. Longitudinal and transversecurrent spectra were obtained from the simulations andthey reproduce the vibrational features observed in theexperimental spectra. The dispersion relationsassociated to the different modes are shown in fig 2together with the results of MD. In conclusion we foundclear presence of two well defined peaks with anassociated dispersion, which were assigned to the highfrequency counterpart of the LA and TA modes. Thecomparison between experimental and simulateddispersion curves supported the hypothesis that thequasi-transverse acoustic modes contribute to the BP.60500S(Q, ω) [a.u.]01000 0.5 Å -15001000 IN8 0.65 Å -1500010000-30 -20 -10 0 10 20 305000-30 -20 -10 0 10 20 3080 IN3 0.75 Å -1604020080 2.0 Å -16040200-10 -5 0 5 10ω [meV]0.8 Å -1Fig. 1 Selection of INS spectra of v-GeO 2 at 300 K.Spectra show a well defined high frequency-peakdispersing in q. the low two panels show a lowfrequencyexcitation, masked in the upper spectra.Dashed lines represent the spectrometer resolutions.ω [meV]402000 2 4Q [Å -1 ]Fig. 2. Dispersion relations of v-GeO 2 as resulted fromthe fitting of the neutron data are compared with themain maximum of the simulated L (higher branch) andT (lower branch) current spectra (open triangles). Thedashed lines are the L and T sound velocity.References[1] O. Pilla et al. Phys. Rev. Lett.85, 2136 (2000).[2] B. Ruzicka et al. Phys. Rev. B 69, 100201(2004).[3] O. Pilla et al., J. Phys. Cond. Mat. 16, 8519 (2004).[4] L. E. Bove, Europhys. Lett., 71 (4), 563 (2005).Authors:S. Caponi (a), A. Fontana (a), L. E. Bove (b)(a) Dipartimento di Fisica and INFM-CRS Soft,Università di Trento, Trento, Italy; (b) CRS-SOFT Unitàdi Perugia.63SOFT Scientific Report 2004-06