VOLUME 82, NUMBER 4 PHYSICAL REVIEW LETTERS 25 JANUARY 1999 Experimental Determination of the Structural Relaxation in Liquid Water A. Cunsolo, 1 G. Ruocco, 2 F. Sette, 1 C. Masciovecchio, 1 A. Mermet, 1 G. Monaco, 2 M. Sampoli, 3 and R. Verbeni 1 1 European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, Cedex France 2 Universitá di L’Aquila and Istituto Nazionale di Fisica della Materia, I-67100, L’Aquila, Italy 3 Universitá di Firenze and Istituto Nazionale di Fisica della Materia, I-50139, Firenze, Italy (Received 10 August 1998) The transition from normal to fast regimes of the longitudinal sound velocity has been studied by inelastic x-ray scattering in liquid water as a function of momentum transfer (1 12 nm 21 ) and temperature (260 – 570 K), using pressure (0 – 2 kbar) to keep the density at r  1 gcm 3 . As in many glass-forming liquids also in water this transition is induced by the structural (a) relaxation. The relaxation time t, however, when close to the melting point, is 2 orders of magnitude shorter than in glass formers. The activation energy, deduced from the Arrhenius behavior of t, suggests that such relaxation is associated to the rearrangement of the local structure induced by the hydrogen bond. [S0031-9007(98)08332-X] PACS numbers: 63.50. + x, 61.10.Eq, 78.70.Ck The investigation of large wave vector excitations in liquid water has shown the existence of a positive dispersion in the velocity of sound. This dispersion has been inferred in the pioneering computational [1] and experimental [2] studies of the dynamic structure factor, SQ, E, and has been recently assessed by inelastic x-ray scattering (IXS) [3,4]. Using IXS, the transition of the longitudinal sound velocity from the adiabatic value, c 0  1500 ms, to a value more than twice larger, c `  3200 ms, was studied at T  5 ± C. Here, the transition is observed for the acousticlike excitation with wave vector Q t  2 nm 21 and energy ¯ hV t  3 meV [4,5]. This sound velocity dispersion is qualitatively similar to that observed in glass-formimg liquids. There, the transition between the two dynamic regimes is determined by the coupling of the propagating density fluctuations with the dynamics of the structural rearrangements of the particles in the liquid. The complex dynamics of such a rearrangement can be described by a relaxation process with a characteristic time t . The transition takes place when the condition V t t  1 is fulfilled. In glass-forming liquids t has a very steep temperature dependence; its typical values are in the nanosecond range when close to the melting point and dramatically increases near the calorimetric glass transition temperature T g [6]. This relaxation process (a process) has a cooperative nature and the density fluctuations are differently influenced in the two opposite frequency limits: the system has a solidlike elastic behavior for vt ¿ 1, and a viscous one for vt ø 1. One could speculate that also in liquid water the physical mechanism responsible for the dispersion of the sound velocity is an a relaxation process. Contrary to glass formers, however, in water the existence of a liquid to glass transition, predicted to be in the 130–140 K region, has not yet been firmly established. The situation is even more involved as extrapolation of experiments made at T . 245 K and molecular dynamics simulations seem to indicate the presence of a relaxation time that diverges at T  230 K [7]. A further quantitative difference is found in the characteristic time, which in water is in the picosecond range at the liquid to crystal transition, corresponding to a value much faster than in glass formers. The experimental characterization of the a process is typically obtained by the determination of the dispersion of the sound velocity as a function of T and at a constant Q transfer value. At the inflection point (“t ”) of such an “S”-shaped curve the condition V t Q, T t T  1, with VQ, T   c app Q, T Q, is fulfilled. In glass- forming liquids, this condition is met by Brillouin light scattering (BLS) measurements close to melting, and by ultrasonic (US) methods close to T g . Indeed, the typical frequencies allowed by these two techniques are such that V t Q, T t T  1 is met for values of t in the 100 ps (BLS) and 1 ms (US) ranges. In the case of water, as a consequence of the small value of t close to melting, the BLS cannot access the relevant excitations energy region, although, in the highly supercooled liquid, it was possible to detect by BLS a deviation of c o towards a higher value, i.e., towards c ` [8]. The complete determination of the S-shaped curve as a function of either T or Q requires, however, the use of IXS [4]. In this Letter, we report on an IXS study of the tem- perature dependence of the transition from normal to fast sound in liquid water in the T  260 570 K and Q  1 12 nm 21 regions. In order to emphasize the ther- mal effects and to minimize the modification of the hy- drogen bond dynamics due to large variations of the excluded volume, the density was kept in the range r  0.94 1.07 gcm 3 . This was obtained adjusting the pres- sure in the 0–2 kbar range. The existence of a relaxation process is demonstrated by the observation that the tran- sition takes place at increasing Q values with increasing temperatures. The associated time scale extends into the subpicosecond region with increasing temperature. The analogy with the glass-formers phenomenology implies 0031-9007 99  82(4)  775(4)$15.00 © 1999 The American Physical Society 775