VOLUME 80, NUMBER 3 P H Y S I C A L R E V I E W L E T T E R S 19 JANUARY 1998 High Frequency Dynamics of Glass Forming Liquids at the Glass Transition C. Masciovecchio,1 G. Monaco,2 G. Ruocco,2 F. Sette,1 A. Cunsolo,1 M. Krisch,1 A. Mermet,1 M. Soltwisch,3 and R. Verbeni1 1European Synchrotron Radiation Facility, B.P. 220 F-38043 Grenoble, Cedex France 2Universitá di L'Aquila and Istituto Nazionale di Fisica della Materia, I-67100, L'Aquila, Italy 3Institut für Experimentalphysik, Freie Universitat Berlin, D-14195 Berlin, Germany (Received 14 May 1997) The dynamic structure factor of the glass formers glycerol, o-terphenyl, and n-butyl-benzene has been studied by inelastic x-ray scattering across the liquid-glass transition. Data taken at selected temperatures in the 1 8 nm21 momentum transfer (Q) range show a propagating soundlike mode in both liquid and glass phases. The energy of this mode, studied at fixed Q ( 2 nm21) on a fine temperature grid, shows a cusp behavior in a region either comparable or higher than the macroscopic structural arrest temperature Tg. This suggests the existence of a correlation between the glass structure and the arrest taking place at the molecular scale. [S0031-9007(97)05023-0] PACS numbers: 63.10.+a, 61.10.Eq, 63.50.+x, 78.70.Ck The study of the high frequency density fluctuations In this Letter, we study the high frequency dynamics in glass forming liquids has received great attention, and in the glass transition region, and present measurements one of its aims is to improve our understanding on the of the S Q, v in three glass forming systems: glycerol microscopic mechanisms responsible for the liquid-glass (GLY), o-terphenyl (OTP), and n-butyl-benzene (NBB). transition. Whether the liquid-glass transition must be In all these systems, we find a propagating longitudinal col- considered as a classical phase transition is, in fact, a still lective dynamics in a temperature range extending from the highly debated topic. For example, the glass transition glass to the liquid phase well above Tg, and up to Q trans- temperature Tg, associated to the macroscopic structural fers approaching the inverse of the interparticle separation. arrest, cannot be considered as a critical transition tem- This result confirms and generalizes previous findings ob- perature because there are quantities showing anomalous tained in a molecular liquid as water [5], and in other behaviors at temperatures different from Tg: among others, glasses as SiO2, glycerol, and LiCl:6H2O [6]. Specifically, the time scale dependence of the structural relaxations, and it shows that this dynamics is the high frequency continu- the ergodicity of the system. Similarly, an order parameter ation of the acoustic branch detected with ultrasound and in the classical sense has not yet been identified, and there Brillouin light scattering techniques. Moreover, at a given are properties that depend on the cooling rate. These issues Q, we find that the temperature dependence of the excita- have been the object of many theoretical models, extending tion frequency, V Q, T , is more pronounced in the liquid from thermodynamic descriptions of the transition [1] to than in the glass, and has a cusplike behavior at a tem- pure dynamical approaches as the mode coupling theory perature Tx which we infer to be higher than Tg. We as- (MCT) [2]. sociate this behavior to the liquid-glass transition at the The dynamics of the density fluctuations is addressed investigated frequencies, which manifests in a change of by the experimental determination of the dynamic structure the collective dynamics likely to be due to the freezing factor, S Q, v . Laser light scattering experiments address of the microscopic diffusional processes. The common the collective properties in the long wavelength limit, behavior among the considered systems may lead us to giving important information on the coupling between the speculate on a more general origin of this property, and sound waves and the structural relaxation processes [3]. therefore to its validity also for other glass formers. At the level of intermolecular time and length correlations, The experiment has been carried out at the very high en- traditionally, these determinations should be the domain of ergy resolution IXS beam line (BL21-ID16) at the Euro- neutron spectroscopies. The inelastic neutron scattering pean Synchrotron Radiation Facility. The incident x-ray techniques, however, due to kinematic limitations, are not beam is obtained by the combination of a cryogenically easily applied to study collective excitations in disordered cooled Si(111) double crystal monochromator and a very systems. On the contrary, they are successfully used to high energy resolution backscattering monochromator op- determine the nonergodicity factor from the quasielastic erating at the Si(11 11 11) reflection [7]. The scattered scattering energy region, and the excitations at large Q [4]. photons are collected by a spherical silicon crystal ana- As shown by recent works on liquids and glasses [5,6], lyzer, also operating at the Si(11 11 11) back-reflection [8]. the neutron kinematic limitations can now be overcome The monochromatic beam has an energy of 21 748 eV using inelastic x-ray scattering (IXS) with meV energy and an intensity of 2 3 108 photons s. The total en- resolution. ergy resolution, determined from the elastic scattering of a 544 0031-9007 98 80(3) 544(4)$15.00 © 1998 The American Physical Society VOLUME 80, NUMBER 3 P H Y S I C A L R E V I E W L E T T E R S 19 JANUARY 1998 Plexiglas sample at the maximum of its static structure factor, is 1.5 meV full width at half maximum. The mo- mentum transfer, Q 2k0 sin us 2 , with k0 the wave vector of the incident photon and us the scattering angle, is selected between 1 and 8 nm21 by rotating a 7 m long analyzer arm in the horizontal scattering plane. The to- tal Q resolution has been set to 0.2 0.4 nm21 for Q # . 2 nm21. Energy scans are done by varying the rela- tive temperature between the monochromator and analyzer crystals. Each scan has taken about 1300, and each Q, T - point spectrum has been obtained from the average of two to five scans depending on the sample temperature. The data have been normalized to the intensity of the inci- dent beam. The three high purity, anhydrous glass-former samples have been distilled in vacuum before loading the sample cell in an argon glove box. According to Angell's definition [9], glycerol is an "intermediate" glass former, while o-terphenyl and n-butyl-benzene are "fragile." To avoid crystallization of the undercooled liquids, the cell has been made out of a pyrex-glass tube [4 (10) mm in- ner (outer) diameter and 20 mm length], capped with two diamond single crystals disks, 1 mm thick, to reduce un- desired scattering signals. In the Q-v region of interest, empty cell measurements gave the flat electronic detector background of 0.6 counts min (Eurisys-Mesures EPX-R). The cell length was chosen to be comparable to the x-ray photoabsorption length, and multiple scattering was neg- ligible. The samples temperatures were changed with a typical 1 deg K min rate, and no spectral changes were ob- served among different scans at the same temperature, or approaching the selected temperature from either above or below. The IXS spectra were measured at different Q, T points. The Q dependence was studied in the 1 8 nm21 Q region at the selected temperatures of 145, 175, 242, FIG. 1. IXS spectra of glycerol (GLY) at 292 K and at the indicated Q values. The data (±), shown with the error bars, and 292 K in glycerol, and of 156, 223, 328, and 405 K are superimposed to the fit (solid line) as explained in the text. in o-terphenyl. At the Q value of 2 nm21 in GLY, and The dashed (dotted) lines represent the quasielastic (inelastic) of 2.5 nm21 in OTP and NBB, we studied the tempera- contributions to the total fits. The data are normalized to the ture evolution of the IXS spectra from 70 K, i.e., well central peak intensity, corresponding to 250, 400, 650, 900, and inside the glass phase for the three systems, up to 2T 900 counts for Q 1 to 5 nm21. The typical counting time g. was 300 s point. The inset reports the values of V ( ) and Examples on the typical Q dependence of the IXS spectra G (±) as derived from the fit. are reported in Fig. 1(a) for liquid glycerol at T 292 K (Tg 186 K). The panel shows that the inelastic signal Here Ic Q and I Q are, respectively, the intensities of disperses with Q in a very similar fashion as previously the central peak and of the inelastic contribution, V Q , reported for glycerol glass, and in other glasses [6]. The G Q , and Gc Q refer to the central frequency and to the data obtained for o-terphenyl at T 328 K (Tg 243 K) energy widths of the side and central lines, and n v is show a similar behavior. the Bose factor. The spectrum is fitted to the convolution The energy position and the width of the excitations has of F Q, v with the instrument resolution function using been determined modeling the spectra with the function standard x2 minimization. The arbitrary choice of the F Q, v , which consists of a Lorentzian for the quasielas- DHO is made because it contains the basic features of the tic scattering, and a damped harmonic oscillator (DHO) inelastic part of the S Q, v of a disordered system, and [10] for the two side peaks: allows us to determine the spectroscopic parameters and G their Q, T dependencies independently of specific theories F Q, v I c Q c Q 1 n v 1 1 I Q v2 1 G [11] as demonstrated on other real and simulated systems c Q 2 [5,6,12]. vG Q 2V Q 3 . (1) The individual contributions to a typical fit are shown V Q 2 2 v2 2 1 G Q 2v2 by the dashed and dotted lines in Fig. 1. The inset reports 545 VOLUME 80, NUMBER 3 P H Y S I C A L R E V I E W L E T T E R S 19 JANUARY 1998 the values obtained for V Q and G Q . The full set represents the maximum of the longitudinal current cor- of parameters derived from the fits and the Q and T de- relation function in the DHO model of the S Q, v , ex- pendencies of the corresponding dispersion curves will be hibits a clear temperature dependence with a slope change discussed elsewhere [13]. We emphasize here the disper- in a temperature region not far from Tg. A quantitative sion of the excitation energies, and, therefore, the propa- description of this observation is obtained using the val- gating nature of the collective dynamics in these liquids ues of V Q, T at temperatures below Tg, i.e., well inside up to Q values comparable to Qm 2, where Qm is the po- the glass phase, and at high temperatures, i.e., well inside sition of the first maximum in the static structure factor. the liquid phase, to estimate two linear functions. The Similarly, this indicates that the dynamics in the liquid whole set of data is then well represented by these two phase is similar to that of the glass. linear relations that cross each other at a temperature indi- Selected IXS spectra of glycerol, taken at Q 2 nm21 cated as Tx. The best fit to the high- and low-temperature and at the indicated T values, give in Fig. 2 an example of the temperature dependence of the excitations. Using the same fitting procedure as for the data reported in Fig. 1, we derived the temperature dependence of V Q, T and G Q, T at the considered Q values. These relations are reported in Figs. 3(a)­3(c) for the three samples. In this figure, we also indicate the Tg's for each glass former. The temperature behaviors are quite similar for the three samples. The parameter G Q, T , related to the energy spread of the excitation, has a monotonic behavior in the considered temperature region within its statistical deter- mination. On the contrary, the parameter V Q, T , which FIG. 3. Temperature dependence of the V Q, T and the G Q, T derived from the fits at the indicated Q values for glycerol (GYL), o-terphenyl (OTP), and n-butyl-benzene. The error bars correspond to 61s statistical error. The full lines are the best fits to the points in the low- and high-temperature regions; they cross at the indicated temperatures Tx. The FIG. 2. IXS spectra of GLY at Q 2 nm21 and at the dashed lines indicate the limits of the 61s prediction bands. indicated temperatures. The symbols are as in Fig. 1, and the The uncertainty on each Tx, indicated by the horizontal bar, counts on the maxima in 300 s are 300, 350, 400, 400, and is derived from the intersection of the prediction bands. The 400 counts for T 75 to 349 K. glass-transition temperature Tg is also indicated. 546 VOLUME 80, NUMBER 3 P H Y S I C A L R E V I E W L E T T E R S 19 JANUARY 1998 points is reported in Fig. 3, together with their 61s pre- persistence of propagating collective excitations in the diction bands. With this procedure, we derive Tx and its whole liquid-glass transition temperature region; (ii) we error from the crossing of the two fits. We find that the derived a characteristic temperature Tx, which is higher values of Tx are in a range systematically above the glass than, or comparable to the macroscopic structural arrest transition temperatures Tg. In the case of glycerol, Tx temperature Tg, depending on the fragility of the glass 300 6 20 K is definitively higher than Tg, while in OTP, [9]. Tx, therefore, may mark the microscopic liquid-glass Tx 270 6 25 K is only slightly above Tg. In NBB transition. This study, more generally, demonstrates a (Tx 180 6 40 K) Tx and Tg have comparable values strong correlation between the liquid-glass transition and within an uncertainty larger than in the other two systems. the high frequency dynamics, and opens intriguing ques- The much steeper change of the excitation energy in the tions that may shed new interest on the microscopic pro- liquid phase ends at Tx. We suggest, therefore, that in cesses associated to the glass transition. the considered high frequency limit, Tx marks the micro- We acknowledge J. F. Legrand for useful discussions, scopic transition between two different dynamical regimes, H. Müller and F. Salhi for the samples preparation, and respectively, characteristic of the glass and liquid phases. B. Gorges and J. F. Ribois for technical assistance. In view of the considered Q-v region, this transition can then be interpreted as the freezing of the diffusional de- grees of freedom at the molecular level. If these findings would be confirmed in other glass forming systems, one could speculate on the existence of a general behavior of [1] D. Kivelson et al., Physica (Amsterdam) 219A, 27 (1995). the excitation frequencies above and below T [2] U. Bengtzelius, W. Götze, and A. Sjolander, J. Phys. C x. Finally, we observe that the ratio T 17, 5915 (1984). x Tg is 1 in NBB, [3] G. Li, W. M. Du, J. Hernandez, and H. Z. Cummins, Phys. 1.1 in OTP, and 1.6 in GLY, indicating a correlation Rev. E 48, 1192 (1993); Y. X. Yan, L. T. `Cheng, and between this ratio and the fragility of the glass. A similar K. A. Nelson, J. Chem. Phys. 88, 6477 (1988); W. T. correlation has been found in many glass formers for the Grubbs and R. A. MacPhail, J. Chem. Phys. 100, 2561 ratio Tc Tg [14], where Tc is the MCT critical tempera- (1994). ture marking the microscopic transition from a nonergodic [4] W. Knaak, F. Mezei, and B. Farago, Europhys. Lett. 7, to an ergodic system. It will be of great interest to evaluate 529 (1988). the possibility to identify the T [5] F. Sette et al., Phys. Rev. Lett. 75, 850 (1995); G. Ruocco x determined by the present IXS with the MCT T et al., Nature (London) 379, 521 (1996); F. Sette et al., c. We note, however, that there is a possible important disagreement between our results and Phys. Rev. Lett. 77, 83 (1996). the MCT predictions for the ergodicity parameter, f [6] C. Masciovecchio et al., Phys. Rev. Lett. 76, 3356 (1996); 1 2 c2 P. Benassi et al., Phys. Rev. Lett. 77, 3835 (1996). 0 c2 . In fact, if one identifies c with our V Q, T [7] R. Verbeni et al., J. Synchrotron Radiat. 3, 62 (1996). Q, and assumes that c0, the zero frequency sound veloc- [8] C. Masciovecchio et al., Nucl. Instrum. Methods Phys. ity, does not have anomalies around Tc, our results would Res., Sect. B 111, 181 (1996). indicate for f a temperature dependence below Tx oppo- [9] C. A. Angell, in Relaxation in Complex Systems, edited site to the theoretical predictions. This can be reconciled by K. L. Ngai and G. B. Wright (NRL, Washington, DC, considering that the identification of V Q, T Q with c 1984), p. 3. can be incorrect because of structural effects inducing the [10] B. Fak and B. Dorner, Institute Laue Langevin Report bending of the V-Q dispersion relation and/or dynamical No. 92FA008S, 1992. effects as the high frequency tail of a relaxation process. [11] Qualitatively similar results are obtained using other A detailed study on the determination of c model functions as Lorentzians and Gaussians. from the whole dispersion curve and on the issue whether other relaxation [12] M. Sampoli, G. Ruocco, and F. Sette, Phys. Rev. Lett. 79, processes are activated in the considered temperature and 1678 (1997), and references therein. [13] G. Monaco, C. Masciovecchio, G. Ruocco, and F. Sette, momentum transfer region will be the subject of a forth- Phys. Rev. Lett. (to be published). coming publication [13]. [14] A. P. Sokolov, A. Kisliuk, D. Quitmann, A. Kudlik, In conclusion, we have shown in three glass forming and A. Rössler, J. Non-Cryst. Solids 172­174, 138 systems that (i) in the high frequency limit, there is the (1994). 547