VOLUME 81, NUMBER 17                   P H Y S I C A L R E V I E W L E T T E R S                             26 OCTOBER 1998

Comment on "High Frequency Dynamics of Glass
Forming Liquids at the Glass Transition"

  In a recent Letter, Masciovecchio et al. reported
inelastic x-ray scattering spectra, I Q, v , of organic
glass-forming liquids at temperatures T near their glass-
transition temperatures Tg [1]. They conclude that
soundlike modes are supported by these materials in
their glass and liquid forms at spatiotemporal scales well
within the microscopic realm. This conclusion challenges
the present understanding of glasses and supercooled
liquids, and, in particular, it conflicts with established
views on their thermal properties. These portray thermal
conduction at high T (or also high v) as taking place in a
strong phonon-scattering regime in which the "plane-wave
picture" that heat is carried by long-wavelength phonons
is neither necessary nor adequate.
  To illustrate the difficulty in reconciling the position
in [1] with standard teaching, one may consider, e.g.,           FIG. 1. (right) Raman spectra of glassy and crystalline OTP
estimates of the phonon mean free path in glassy glycerol,       at 6 K. Calculated dispersion curves (left) [4].
a material studied in [1]. Using the dominant phonon
approximation and experimental values of the thermal
conductivity, specific heat, and ultrasound velocity at T  
100 K [2], one finds for both longitudinal and transverse        like plane waves. The same observations apply to glyc-
phonons an estimate comparable to molecular dimensions,          erol, for which data similar to Fig. 1 are also available [5].
  # 8 Ĺ. In fact, the universal strong phonon scattering           An exercise that seems worth undertaking would be
in glasses reaches a Ioffe-Regel limit,     l, already at        to perform a study similar to that in [1], at T values
lower v and corresponding lower T [3]. Beyond this               comparable and below those of the thermal conductivity
limit, acousticlike excitations are nonpropagating, and their    "plateau." At these low temperatures, phonon-scattering
range is typically a few Ĺ. On the opposite, data on             mechanisms are far less severe than those operative at
glycerol at the same T taken from Fig. 3 of [1], when            temperatures explored in [1] and thus enable one to analyze
interpreted in terms of well-defined sound waves, lead to        sound propagation in terms of well-founded concepts.
an estimate     75 Ĺ, 1 order of magnitude above the one
predicted from thermodynamics.                                   F. Javier Bermejo,1 Gabriel J. Cuello,1 Eric Courtens,2
                                                                 René Vacher,2 and Miguel A. Ramos3
  The difficulty with [1] results from the assignment of a        1Consejo Superior de Investigaciones Cienti´ficas
soundlike character to intensities measured up to very high        Serrano 123, E-28006 Madrid, Spain
v. To illustrate this, Fig. 1 displays experimental Raman         2Laboratoire des Verres, UMR 5587 CNRS
spectra in the relevant v range for glassy and crystalline         Université de Montpellier II
o-terphenyl (OTP), another material studied in [1]. In the         F-34095 Montpellier Cedex 5, France
crystal, there are a large number of peaks at v , 20 meV.         3Departamento de Fi´sica de la Materia Condensada, C-III
These are assigned to at least 45 Raman-active modes [4].          Universidad Autónoma, E-28049 Madrid, Spain
Their dispersion curves are drawn in Fig. 1 for a particu-
lar high-symmetry direction. The glass spectrum, super-          Received 10 March 1998                [S0031-9007(98)07493-6]
posed to the crystal one, covers a very similar range of v.      PACS numbers: 63.10.+a, 61.10.Eq, 63.50.+x, 78.70.Ck
The dispersion curves of the crystal show that the three
acoustic modes have an upper bound at v   2.5 meV                 [1] C. Masciovecchio et al., Phys. Rev. Lett. 80, 544 (1998).
(see [4] for more details). It is unjustified to assign all       [2] M. Grimsditch and N. Rivier, Appl. Phys. Lett. 58, 2345
the vibrational dynamics of the glass below 20 meV just               (1991); Q. W. Zou et al., (unpublished); G. E. Gibson and
to "sound modes" that would reach frequencies far larger              W. F. Giauque, J. Am. Chem. Soc. 45, 93 (1923).
than those of the crystal. When this is pursued, an appar-        [3] A. C. Anderson, in Amorphous Solids: Low Temperature
                                                                      Properties, edited by W. A. Phillips (Springer, Berlin,
ent "dispersion relation" results from a plot of a frequency          1981), Chap. 5.
describing the center of gravity of the spectra versus Q.         [4] A. Criado et al., Mol. Phys. 82, 787 (1994).
Such a plot is not the dispersion curve of a well-defined         [5] F. J. Bermejo et al., Phys. Rev. B 53, 5259 (1996);
mode. It is only a device to describe averaged data, with-            J. Dawidowski et al., Phys. Rev. E 53, 5079 (1996); G. J.
out any particular implication that one deals with anything           Cuello et al., Phys. Rev. B 57, 8254 (1998).



                   0031-9007 98 81(17) 3801(1)$15.00             © 1998 The American Physical Society                       3801