Soft Report - Dipartimento di Fisica - Sapienza

Scientific Report – Non Equilibrium Dynamics and ComplexityHigh Frequency Dynamics in Disordered SystemsThe discovery that disordered materials, such asglasses and liquids, support the propagation of soundwaves in the terahertz frequency region has renewedinterest in a long-standing issue: the nature ofcollective excitations in disordered solids. From theexperimental point of view, the collective excitationsare often studied through the determination of thedynamic structure factor S(Q,ω), i.e. the timeFourier transform of the collective intermediatescatteringfunction F(Q,t) which, in turn, is the spaceFourier transform of the density self-correlationfunction. S(Q,ω) has been widely studied in the pastby the Brillouin light scattering (BLS) and inelasticneutron scattering (INS) techniques. Thesetechniques left an unexplored gap in the Q-space,corresponding to exchanged momentum approachingthe inverse of the inter-particle separation a (themesoscopic region, Q=1–10 inverse nm). This Qregion is important, because here the collectivedynamics undergoes the transition from thehydrodynamic behaviour to the microscopic singleparticleone.Investigation of S(Q,ω)in this mesoscopic region hasbecome possible recently thanks to the developmentof the IXS technique; many systems, ranging fromglasses to liquids, have been studied with thistechnique [1-8]. In addition to specific quantitativedifferences among different systems, all the systemsinvestigated show some qualitative common featuresthat can be summarized as follows:(i) Propagating acoustic-like excitations exist up to amaximum Q-value Q m (aQ m≈1–3 depending on thesystem fragility), having an excitation frequencyΩ(Q). On increasing Q there exists a positivedispersion of the sound velocity (Fig. 2).(ii) Ω(Q) versus Q shows an almost linear dispersionrelation, and its slope, in the Q0 limit, extrapolatesto the macroscopic sound velocity.(iii) The width of the Brillouin peaks, Γ(Q), follows apower law, Γ(Q)=DQ α , with α=2 within the currentlyavailable statistical accuracy (Fig. 1).(iv) The value of D does not depend significantly ontemperature, indicating that this broadening (i.e. theFig. 2: (A) Excitation energy Ω(Q) for vitreous silicafrom IXS (full dots) [2] and MD (open dots) [1].The upper curve is for the L-mode, the lower one isfor the T-mode.; (B) Apparent sound velocity from(A) defined as Ω(Q)/Q.sound attenuation) in the high-frequency region doesnot have a dynamic origin, but is due to the disorder.(v) Finally, at large Q-values, a second peak appearsin S(Q,ω) at frequencies smaller than that of thelongitudinal acoustic excitations. This peak can beascribed to the transverse acoustic dynamics, whosesignature is observed in the dynamic structure factoras a consequence of the absence of pure polarizationof the modes in a topologically disordered system.References[1] O. Pilla et al. J. of Phys. C. M. 16, 8519 (2004).[2] B. Ruzicka, et al. PRB 69, 100201 (2004).[3] T. Scopigno, et al. PRL 92, 025503 (2004).[4] R. Angelini, et al. PRB 70, 224302 (2004).[5] T. Scopigno, et al. PRL 94, 155301 (2005).[6] E. Pontecorvo et al. PRE 71, 011501 (2005).[7] T. Scopigno et al. PRL 96, 135501 (2006)[8] C. Masciovecchio et al. preprint (2006).Fig. 1: Excitation broadening (Γ) vs. excitationenegy position (Ω) square in glassy Selenium [3].AuthorsR. Angelini (a), M. Krisch (c), C. Masciovecchio (b),G. Monaco (c), Pontecorvo (a,d), G. Ruocco (a,d), B.Ruzicka (a), E. T. Scopigno (a), F. Sette (c).(a) CRSSOFT-INFM-CNR, Roma, Italy (b) Elettra, Trieste,Italy (c) ESRF, Grenoble, France (d) Dip. Di Fisica,Univ. Di Roma, Roma, Italy.SOFT Scientific Report 2004-0652