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

Sette et al. Reply: In [1] we report the dynamical struc-
ture factor for the liquid and solid phases of water mea-
sured by inelastic x-ray scattering (IXS). The data show
that (i) in the liquid, the fast sound, already observed in in-
elastic neutron scattering (INS) [2] and IXS [3], originates
from a bend up of the dispersion relation of the acoustic
excitations, V Q ; (ii) the bend up takes place when V Q 
become equivalent to the energy of a second weakly dis-
persing mode; and (iii) from the results in polycrystalline
ice, the weakly dispersive mode in the liquid is likely to be
reminiscent of the transverse phonon branch in ice Ih.
  In their Comment, Martinez et al. [4] criticize our
analysis of the ice data. The main points of our work,
however, i.e., points (i) and (ii), stay by all means undis-
putable, thanks also to the overwhelming theoretical evi-
dences [5] which are fully consistent with our experiment
and interpretation [6].                                            FIG. 1. Dispersion curves for the lowest transverse  T  and
                                                                   longitudinal  L  phonon branches in ice Ih crystals. Full circles
  With respect to the ice data, Martinez et al. claim              (squares) refer to the neutron data taken along the G-M G-K 
that (1) our analysis would be inconclusive because                direction in oriented D2O ice Ih single crystals at 90 K [6].
measurements on a polycrystal induce a severe averaging            Open circles refer to the IXS data on H2O ice Ih polycrystals
among excitations in the Brillouin zone, and the steep             measured at 253 K [1,7].
dispersion relation would be an artifact due to the mixing
of different modes. (2) Our ice data, summarized in the              In summary, we believe that the present Comment does
dispersion relation of Fig. 4 of [1], would not agree with         not add new information to the conclusions reported in [1].
previous measurements on ice single crystals [7].
  Contrary to the first point, we think that one must use          F. Sette,1 G. Ruocco,2 M. Krisch,1 C. Masciovecchio,1
the polycrystalline data to compare the high frequency             R. Verbeni,1 and U. Bergmann1
dynamics of the solid with the liquid phase [1,8], exactly           1European Synchrotron Radiation Facility
because they represent an orientational average within the            B.P. 200 F-38043 Grenoble, Cedex, France
Brillouin zone.                                                      2Universitá di L'Aquila
  Contrary to the second point, as shown in Fig. 1, the               and Istituto Nazionale di Fisica della Materia
peak positions from the INS data of Renker on D                       I-67100, L'Aquila, Italy
                                                        2O ice
Ih at T   88 K, full symbols [7,9], and our IXS data
on H                                                               Received 9 September 1996             [S0031-9007(96)02086-8]
        2O ice Ih polycrystals at T   253 K, open symbols
[1,8], are in excellent agreement. The small deviations            PACS numbers: 61.10.Eq, 63.50.+x, 78.70.Ck
can be ascribed to the temperature dependence of the force
constants.                                                          [1] F. Sette et al., Phys. Rev. Lett. 77, 83 (1996).
  In Fig. 1, the two lowest transverse  T  and longitudinal         [2] J. Teixeira, M. C. Bellissant-Funel, S. H. Chen, and
 L  branches from the IXS data are reported as a function               B. Dorner, Phys. Rev. Lett. 54, 2681 (1985).
of the absolute Q value. The T branch is not observed               [3] F. Sette et al., Phys. Rev. Lett. 75, 850 (1995).
at small Q due to well known polarization selection rules.          [4] J. L. Martinez et al., preceding Comment, Phys. Rev. Lett.
                                                                        78, 975 (1997).
The INS data, unfolded from the reduced Brillouin zone              [5] A. Rahman and F. H. Stillinger, Phys. Rev. A 10,
of the hexagonal lattice with four molecules per unit cells,            368 (1974); S. Sastry, F. Sciortino, and H. E. Stanley,
are reported in the extended zone which also corresponds                J. Chem. Phys. 95, 7775 (1991); F. Sciortino and S. Sastry,
to the reduced Brillouin zone of a tetrahedral lattice with             J. Chem. Phys. 100, 3881 (1994); U. Balucani, G. Ruocco,
two molecules per unit cell. The dynamics, in fact, with                A. Torcini, and R. Vallauri, Phys. Rev. E 47, 1677 (1993).
its force constants and selection rules, is dictated by the         [6] Form factor correction are very small in this Q range,
almost tetrahedral configuration of the oxygen atoms.                   and, in any case, they cannot affect a dispersion relation.
This is best exemplified by the negligible dependence on                Multiphonon background corrections do not make sense
the propagation directions of the phonon energies, and                  in a liquid, and what is reported in [1] is the S Q, v 
by the absence of energy gaps at the reduced Brillouin                  which is, in the present context, the only relevant dynami-
zone boundaries of the hexagonal lattice  7 8 nm21 . In                 cal variable.
                                                                    [7] B. Renker, Phys. Lett. 30A, 493 (1969); Physics and
conclusion, the consistency among the new IXS data and                  Chemistry of Ice (Royal Soc. Canada, Ottawa, 1973).
the old INS results confirms our good understanding of              [8] G. Ruocco et al., Nature (London) 379, 521 (1996).
the lattice dynamics in ice Ih without need of further              [9] P. Bosi, R. Tubino, and G. Zerbi, J. Chem. Phys. 59, 4578
theoretical models.                                                     (1973).

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