VOLUME 78, NUMBER 5 P H Y S I C A L R E V I E W L E T T E R S 3 FEBRUARY 1997 Comment on "Transition from Normal to Fast quencies well above hydrodynamic sound while retaining Sound in Liquid Water" a phase velocity substantially below that of hydrodynamic sound comes as a mere consequence of fitting the spec- In a recent Letter, Sette et al. [1] claim to have de- trum of excitations within the 10­40 meV range with only tected the origin of some transition from normal to fast one spectral function (the experimental densities of states sound in liquid water by means of inelastic scattering of show at least three peaks [4]) and in no way can be in- x rays. Such a result is adduced from measurements of terpreted in terms of "coupling" between modes [1] or the the I Q, v (uncorrected by the atomic form factors and existence of some "mesoscopic" domain in ice and water the large multiphonon contribution) spectral response of [7] where sound propagation becomes decoupled from the liquid water and hexagonal ice. elastic properties of the media (i.e., a common value of The data exemplify the progress achieved in instrument 3200 6 100 m s22 is found for the phase velocity in wa- development, registered within an astoundingly short lapse ter at 21 ±C, 4 ±C, and ice at 220 ±C, whereas the hydrody- of time (i.e., for comparison see [2]). However, the namic sound velocity goes from 1500 to 1420 m s21 conclusions hinge on several assertions on the dynamics and 4000 m s21 for the same three temperatures). of Ih ice which run counter to the experience accumulated It then seems clear that what is being sampled contains over years, as well as on a rather simplified procedure a large contribution of higher-lying modes which because for data reduction and analysis. Consequently the main of its highly localized nature become effectively decoupled results of such a Letter should be qualified in its essence from the dramatic changes in the elastic properties of the for reasons that are explained below. sample occurring upon crossing the freezing transition. The microscopic dynamic response of a polycrystalline If what is sampled and assigned as a LA mode were molecular solid is substantially complicated by the orien- of mostly acoustic origin, the stationary condition of the tational averaging of the different and numerous crystal sound waves would have caused a strong bend of the modes (up to 21 in ice Ih) which leads to an average "dispersion" curve leading to a vanishing (or at least rather dynamic structure factor S Q, v avg showing features small) group velocity at the Brillouin zone boundary, that which represent envelopes over modes, and consequently is, Q 0.75 Ć21 [8]. the frequency corresponding to their maxima cannot be directly assigned as the one corresponding to a well de- J. L. Martinez, F. J. Bermejo, A. Criado, and M. Alvarez fined crystal excitation. To see this, one can compare the Consejo Superior de Investigaciones CientiŽficas S Q, v Serrano 123, E-28006 Madrid, Spain avg of a polycrystalline model of ice shown in Fig. 2 of [3] with those reported for ice in Fig. 4 of [1], and realize their proximity once the different ratios of peak in- S. M. Bennington tensities due the disparate character of the two techniques ISIS Pulsed Neutron Facility to sample the dynamics is accounted for. Since the char- Rutherford Appleton Laboratory Chilton, Didcot, Oxon OX11, 0QX, United Kingdom acter of individual modes is known, it can be verified that the quantities vmax Q of peak maxima in S Q, v avg Received 9 July 1996 [S0031-9007(96)02087-X] encompass a wide mixture of polarizations and therefore PACS numbers: 61.10.Eq, 63.50.+x, 78.70.Ck cannot be interpreted in terms of a well defined physical frequency, but have to be considered as a valid means to describe the data only. Therefore, the assignment of [1] F. Sette, G. Ruocco, M. Krisch, C. Masciovecchio, R. transverse-optic (TO) or longitudinal-acoustic (LA) char- Verbeni, and U. Bergmann, Phys. Rev. Lett. 77, 83 (1996). acter to the polarizations of both peaks in I Q, v does [2] F. Sette, G. Ruocco, M. Krisch, U. Bergmann, C. Masciovecchio, V. Mazzacurati, G. Signorelli, and R. not seem to be justified. It also runs counter to neutron Verbeni, Phys. Rev. Lett 75, 850 (1995). scattering work [4] where the lowest frequency feature, [3] A. Criado, F. J. Bermejo, M. GarciŽa-Hernandez, and J. L. which corresponds to the strongest peak in the density of MartiŽnez, Phys. Rev. E 47, 3516 (1993). states and shows basically no isotopic effect (i.e., repre- [4] D. D. Klug, E. Whalley, E. C. Svensson, J. H. Root, and sents the feature where the collective effects are strongest), V. F. Sears, Phys. Rev. B 44, 841 (1991). was characterized as dominantly transverse acoustic (TA). [5] B. Renker, Phys. Lett. 30A, 493 (1969); in Physics and Also it opposes the measurement of Renker [5] on ice- Chemistry of Ice, edited by E. Whalley et al. (Royal Soc. Ih single crystals, where it is shown that the frequency of Canada, Ottawa, 1973), p. 82. the LA mode at the zone boundary never exceeds some [6] F. J. Bermejo, M. Alvarez, S. M. Bennington, and R. 19.5 meV, whereas the peak frequencies shown in Fig. 4 Vallauri, Phys. Rev. E 51, 2250 (1995). of [1] are significantly above such a figure 30 meV . [7] G. Ruocco, F. Sette, U. Bergmann, M. Krisch, C. Masciovecchio, V. Mazzacurati, G. Signorelli, and R. The steep behavior of the vmax Q corresponding to the Verbeni, Nature (London) 379, 521 (1996). higher-frequency peak comes as a consequence of the ori- [8] C. Kittel, Introduction to Solid State Physics (Wiley, New entational averaging of intensities corresponding to modes York, 1986), Chap. 5. See also F. W. de Wette and with rather different polarizations [5,6]. Its rise up to fre- A. Rahman, Phys. Rev. 176, 784 (1968). 0031-9007 97 78(5) 975(1)$10.00 © 1997 The American Physical Society 975