- Email: [email protected]
Light- and heavy-water dynamics
Physica B 276}278 (2000) 183}184
Light- and heavy-water dynamics夽 S. Longeville *, R.E. Lechner Technische UniversitaK t MuK nchen, Physik Department, James Franck Strasse, D-85747 Garching, Germany Laboratoire Le& on Brillouin, CE Saclay, F-91191 Gif-sur-Yvette, France Berlin Neutron Scattering Centre, Hahn-Meitner Institut Glienicker Strasse 100, D-14109 Berlin, Germany
Abstract We show "rst results of an analysis of the dynamics of water as observed by neutron scattering, based on a model common to both isotopic forms, H O and D O. Using incoherent scattering results from H O, and the liquid structure factor of D O, we show that within the framework of an approximation of decoupled motions, the H O and D O spectra can be reproduced in a broad wave-vector range with physical parameters very similar for both kinds of water. 2000 Elsevier Science B.V. All rights reserved. Keywords: Water; Time of #ight
Most of the descriptions of water dynamics obtained from neutron scattering experiments have so far been performed in the framework of microscopic dynamic models analysing incoherent neutron scattering spectra with respect to di!usive translational and rotational motions [1]. Because of a lack of practicable theoretical models describing the coherent scattering from liquids due to the same type of motions, the pertinent information carried by the pair correlation function has so far be entirely neglected. In the present contribution we attempt to overcome, at least partially, these de"ciencies by a common analysis of neutron scattering spectra from both pure light and heavy water. Relaxation processes in light-water dynamics have been quite successfully described by the study of the quasielastic incoherent neutron scattering function by Chen et al. [2] and Teixeira et al. [1]. In their approach, the authors assumed that the rotational (R(Q, t)) and
translational (¹(Q, t)) processes are not correlated and can be described as classical motions of rigid molecules. They accounted for the attenuating e!ect of vibrations by a Debye}Waller factor IQ(Q, t)"e\/6S7 R(Q, t)¹(Q, t). If in addition to decoupling of translational and rotational motions, we assume that the rotational motions of di!erent molecules are also decoupled [3], the intermediate scattering function for coherent scattering can then be written as
#
, e\ O 0G \0G R J1(Q, t) G
, e\ O 0G \0H R J2(Q) G H$G
with
J1(Q, t)" 夽
This work was supported by the Grant 03PE5TUM6 from the Bundesministeriums fuK r Bildung, Wissentschaft Forschung und Technologie and the European Commission for Experiments at BENSC with TMR contract ERBFMGECT950060. * Corresponding address. Laboratoire LeH on Brillouin, CE Saclay, F-91191 Gif-sur-Yvette, France. Tel.: #33-1-69087530; fax: #33-1-69088261. E-mail address: [email protected] (S. Longeville)
I(Q, t)"e\/6S7
? b b e\ O 0L \0K R
K L K L
and
? sin QR L , J2(Q)" b L QR L L where N is the number of molecules per volume unit and a the number of atoms per molecule. With the same
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 2 4 5 - 4
184
S. Longeville, R.E. Lechner / Physica B 276}278 (2000) 183}184
di!usion laws as used by Teixeira et al. [1] (continuous rotational di!usion [3] and translational jump di!usion [4]) and in the framework of the Vineyard [5] approximation for describing the coherent contribution of the molecular center-of-mass translation, we obtain a tractable expression to be compared with the data. Instead of employing only a Debye}Waller factor to account for the attenuating e!ect of vibrational motions, we have however added a damped-harmonic-oscillator (DHO) term to obtain the incoherent and coherent scattering functions, S1(Q, u) and S!(Q, u). The geometry of the molecule together with the measured temperature-dependent structure factor S(Q) [6] are used as input parameters in the "tting procedure. Experiments were performed on the time-of-#ight spectrometer NEAT at Hahn}Meitner Institut Berlin. For the incident wavelength a value of 5.1 As was chosen, with chopper speeds of 10 000 and 4000 rpm, corresponding to elastic resolutions of about 100 and 220 lev (FWHM), respectively. The data were collected with 388 single detectors ranging from 13 to 1373 in scattering angle; this corresponds to a wavevector range of 0.28}2.27 As \ for elastic momentum transfer. The measured time-of-#ight spectra were normalized and transformed to S(Q, u) using the NEAT software package [7]. From this the dynamic susceptibility was calculated: s (Q, u)"S(Q, u)/n (u, ¹), where n is the Bose}Einstein occupation factor. Fig. 1 shows typical susceptibility `spectraa obtained for H O and D O for Q"1.75 As \$0.04 and ¹"298 K. One can clearly observe at least two distinct contributions in the data: a wave-vector-dependent di!usive (quasi-elastic) process peaked near 0.4 meV and a contribution at higher energy
(peaked near 6 mev) accounted for by the damped harmonic oscillator term (DHO). The di!usive term has been decomposed into one translational (peak at ca. 0.3 meV) and two rotational contributions (ca. 0.5 and 1.2 meV). The DHO term has been "tted on spectra obtained at 278 K, just above the crystallisation temperature for both kinds of water. Its characteristic energy
u (Q) of about 6 meV does not seem to be temperature dependent, and the temperature evolution of the intensity is well described by the Bose}Einstein behaviour. Therefore, this DHO term was "xed and used also at higher temperature. Best "ts give a rotational di!usion coe$cient D "0.1 mev at 298 K corresponding to a character istic time of &1.09 ps very similar to the one obtained by Teixeira et al. [1]. The wave-vector dependence of the full-width at half-maximum (FWHM), C(Q), of the translational di!usion contribution in the frame of the jump di!usion model, for H O leads to a residence time of q "0.52$0.03 ps. To obtain such a value we used as input in the formula the di!usion coe$cient measured by NMR [8] at the same temperature: D "2.24; 10\ cm s\.
D Q C(Q)" . 1#D Qq In D O one observes oscillations in the translational contribution width around the value deduced from the incoherent spectra, characteristic of coherent e!ects (De Gennes' narrowing). As can be seen in Fig. 1 the quality of the re"nements is satisfactory. This is true for the wave-vector range 0.8}2.2 As \; but at lower wave-vectors an additional contribution is observable. Since the relative weight of this contribution is higher in D O than in H O, and since the static structure factor, (S(Q)), at such wave vectors is much lower than in the rest of the spectrum, it is likely to be caused by multiple scattering e!ects (MSC). Data re"nements accounting for this are in progress.
References
Fig. 1. Susceptibility spectra and re"nements for both H O and D O using the same microscopic dynamical model based at ¹"298 K.
[1] J. Teixeira, M.-C. Bellisent-Funel, S.H. Chen, A.J. Dianoux, Phys. Rev. A 31 (1985) 1913. [2] S.H. Chen, J. Teixeira, R. Nicklow, Phys. Rev. A 26 (1982) 3477. [3] V.F. Sears, Can. J. Phys. 45 (1966) 237. [4] P.A. Egelsta!, Introduction to the Liquid State, Clarendon Press, Oxford, 1967. [5] Vineyard, Phys. Rev. 119 (1960) 1150. [6] M.-C. Bellissent-Funel, L. Bosio, J. Chem. Phys. 102 (1995) 3727. [7] J. Fitter, B. Ru%eH , R.E. Lechner, NEAT software package (1999). [8] T. Dippel, Ph.D. Thesis, Max-Planck-Institut, Stuttgart, 1991.
Light- and heavy-water dynamics夽 S. Longeville *, R.E. Lechner Technische UniversitaK t MuK nchen, Physik Department, James Franck Strasse, D-85747 Garching, Germany Laboratoire Le& on Brillouin, CE Saclay, F-91191 Gif-sur-Yvette, France Berlin Neutron Scattering Centre, Hahn-Meitner Institut Glienicker Strasse 100, D-14109 Berlin, Germany
Abstract We show "rst results of an analysis of the dynamics of water as observed by neutron scattering, based on a model common to both isotopic forms, H O and D O. Using incoherent scattering results from H O, and the liquid structure factor of D O, we show that within the framework of an approximation of decoupled motions, the H O and D O spectra can be reproduced in a broad wave-vector range with physical parameters very similar for both kinds of water. 2000 Elsevier Science B.V. All rights reserved. Keywords: Water; Time of #ight
Most of the descriptions of water dynamics obtained from neutron scattering experiments have so far been performed in the framework of microscopic dynamic models analysing incoherent neutron scattering spectra with respect to di!usive translational and rotational motions [1]. Because of a lack of practicable theoretical models describing the coherent scattering from liquids due to the same type of motions, the pertinent information carried by the pair correlation function has so far be entirely neglected. In the present contribution we attempt to overcome, at least partially, these de"ciencies by a common analysis of neutron scattering spectra from both pure light and heavy water. Relaxation processes in light-water dynamics have been quite successfully described by the study of the quasielastic incoherent neutron scattering function by Chen et al. [2] and Teixeira et al. [1]. In their approach, the authors assumed that the rotational (R(Q, t)) and
translational (¹(Q, t)) processes are not correlated and can be described as classical motions of rigid molecules. They accounted for the attenuating e!ect of vibrations by a Debye}Waller factor IQ(Q, t)"e\/6S7 R(Q, t)¹(Q, t). If in addition to decoupling of translational and rotational motions, we assume that the rotational motions of di!erent molecules are also decoupled [3], the intermediate scattering function for coherent scattering can then be written as
#
, e\ O 0G \0G R J1(Q, t) G
, e\ O 0G \0H R J2(Q) G H$G
with
J1(Q, t)" 夽
This work was supported by the Grant 03PE5TUM6 from the Bundesministeriums fuK r Bildung, Wissentschaft Forschung und Technologie and the European Commission for Experiments at BENSC with TMR contract ERBFMGECT950060. * Corresponding address. Laboratoire LeH on Brillouin, CE Saclay, F-91191 Gif-sur-Yvette, France. Tel.: #33-1-69087530; fax: #33-1-69088261. E-mail address: [email protected] (S. Longeville)
I(Q, t)"e\/6S7
? b b e\ O 0L \0K R
K L K L
and
? sin QR L , J2(Q)" b L QR L L where N is the number of molecules per volume unit and a the number of atoms per molecule. With the same
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 2 4 5 - 4
184
S. Longeville, R.E. Lechner / Physica B 276}278 (2000) 183}184
di!usion laws as used by Teixeira et al. [1] (continuous rotational di!usion [3] and translational jump di!usion [4]) and in the framework of the Vineyard [5] approximation for describing the coherent contribution of the molecular center-of-mass translation, we obtain a tractable expression to be compared with the data. Instead of employing only a Debye}Waller factor to account for the attenuating e!ect of vibrational motions, we have however added a damped-harmonic-oscillator (DHO) term to obtain the incoherent and coherent scattering functions, S1(Q, u) and S!(Q, u). The geometry of the molecule together with the measured temperature-dependent structure factor S(Q) [6] are used as input parameters in the "tting procedure. Experiments were performed on the time-of-#ight spectrometer NEAT at Hahn}Meitner Institut Berlin. For the incident wavelength a value of 5.1 As was chosen, with chopper speeds of 10 000 and 4000 rpm, corresponding to elastic resolutions of about 100 and 220 lev (FWHM), respectively. The data were collected with 388 single detectors ranging from 13 to 1373 in scattering angle; this corresponds to a wavevector range of 0.28}2.27 As \ for elastic momentum transfer. The measured time-of-#ight spectra were normalized and transformed to S(Q, u) using the NEAT software package [7]. From this the dynamic susceptibility was calculated: s (Q, u)"S(Q, u)/n (u, ¹), where n is the Bose}Einstein occupation factor. Fig. 1 shows typical susceptibility `spectraa obtained for H O and D O for Q"1.75 As \$0.04 and ¹"298 K. One can clearly observe at least two distinct contributions in the data: a wave-vector-dependent di!usive (quasi-elastic) process peaked near 0.4 meV and a contribution at higher energy
(peaked near 6 mev) accounted for by the damped harmonic oscillator term (DHO). The di!usive term has been decomposed into one translational (peak at ca. 0.3 meV) and two rotational contributions (ca. 0.5 and 1.2 meV). The DHO term has been "tted on spectra obtained at 278 K, just above the crystallisation temperature for both kinds of water. Its characteristic energy
u (Q) of about 6 meV does not seem to be temperature dependent, and the temperature evolution of the intensity is well described by the Bose}Einstein behaviour. Therefore, this DHO term was "xed and used also at higher temperature. Best "ts give a rotational di!usion coe$cient D "0.1 mev at 298 K corresponding to a character istic time of &1.09 ps very similar to the one obtained by Teixeira et al. [1]. The wave-vector dependence of the full-width at half-maximum (FWHM), C(Q), of the translational di!usion contribution in the frame of the jump di!usion model, for H O leads to a residence time of q "0.52$0.03 ps. To obtain such a value we used as input in the formula the di!usion coe$cient measured by NMR [8] at the same temperature: D "2.24; 10\ cm s\.
D Q C(Q)" . 1#D Qq In D O one observes oscillations in the translational contribution width around the value deduced from the incoherent spectra, characteristic of coherent e!ects (De Gennes' narrowing). As can be seen in Fig. 1 the quality of the re"nements is satisfactory. This is true for the wave-vector range 0.8}2.2 As \; but at lower wave-vectors an additional contribution is observable. Since the relative weight of this contribution is higher in D O than in H O, and since the static structure factor, (S(Q)), at such wave vectors is much lower than in the rest of the spectrum, it is likely to be caused by multiple scattering e!ects (MSC). Data re"nements accounting for this are in progress.
References
Fig. 1. Susceptibility spectra and re"nements for both H O and D O using the same microscopic dynamical model based at ¹"298 K.
[1] J. Teixeira, M.-C. Bellisent-Funel, S.H. Chen, A.J. Dianoux, Phys. Rev. A 31 (1985) 1913. [2] S.H. Chen, J. Teixeira, R. Nicklow, Phys. Rev. A 26 (1982) 3477. [3] V.F. Sears, Can. J. Phys. 45 (1966) 237. [4] P.A. Egelsta!, Introduction to the Liquid State, Clarendon Press, Oxford, 1967. [5] Vineyard, Phys. Rev. 119 (1960) 1150. [6] M.-C. Bellissent-Funel, L. Bosio, J. Chem. Phys. 102 (1995) 3727. [7] J. Fitter, B. Ru%eH , R.E. Lechner, NEAT software package (1999). [8] T. Dippel, Ph.D. Thesis, Max-Planck-Institut, Stuttgart, 1991.