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Neutron brillouin scattering in liquid 36Ar
ELSEVIER
Physiea B 234-236 (1997) 308-310
Neutron Brillouin scattering in liquid 36Ar B. M o s a'*, P. V e r k e r k a, U. Baffle b, C. B e n m o r e c, J.-B. S u c k d, F. B a r o c c h i e, J. C o o k f, K. A n d e r s o n f alnterfacultair Reactor Instituut, Delft University of Technology, 2629 JB Delft, The Netherlands bCNR Istituto Elettronica Quantistica, 1-50127 Firenze, Italy CDepartment of Physics, University of Guelph, ON, NIG2W1, Canada alnstitut filr Physik, T.U. Chemnitz-Zwickau, D-09107 Chemnitz, Germany eDipartimento di Fisica, Universith di Firenze, 50125 Firenze, Italy flnstitut Laue-Langevin, Grenoble, B.P. 156, 38042 Grenoble, France
Abstract We have measured S(k, to) in liquid 36Ar at three thermodynamic states along the coexistence line. We observe well-defined propagating density fluctuations, but the damping is stronger than according to linearized hydrodynamics.
Keywords: Brillouin scattering; Liquids; Phonon dispersion; Small-angle neutron scattering
1. Introduction At small wave vector k (kl < 0.1 with 1 the mean free path in a corresponding hard spheres fluid) the dynamic structure factor S(k, o~) of a fluid can be calculated from the Navier-Stokes relations, resulting in the well known Rayleigh-Brillouin triplet
speed of sound and bs = [(y - 1)a + FJ/c~. If kl is of order 1, generalised hydrodynamics is valid, i.e. the transport properties are k-dependent.
2. Experiment and results
[I]: S(ko~) =
[(y ~7 m -
S(k)
ak 2 1 Fsk 2 + ( ~ -4- csk)b,k 1)O)2 + a2k4 + 2 (co + c~k)2 + F2k 4
1 Fsk2--(~--c~k)b~k 1 + 2" (m - csk) 2 q- F~k 4 J with y the specific heat ratio, a the thermal diffusivity, F~ the sound damping factor, c~ the adiabatic
* Corresponding author.
The experiment was performed on IN5 (Institut Laue-Langevin) and is a continuation of earlier experiments [2, 3]. In order to reduce background scattering the aluminium sample container has two single-crystal sapphire windows (slab geometry) perpendicular to the incident neutron beam, with a space of 1 mm in between. 36Ar has no incoherent scattering: acoh = 77.9 b, aabs = 5.2 b at 0.18 nm. The three thermodynamic states along the gas-liquid coexistence line are given in Table 1 together with relevant thermophysical properties. In these states the forward neutron scattering fraction is 2.3%, 3.4% and 7.5% respectively (taking the value of S(0) into account).
0921-4526/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PII S 0 9 2 1 - 4 5 2 6 ( 9 6 ) 0 0 9 6 7 - 2
B. Mos et aL / Physica B 234-236 (1997) 308-310
The multidetector of IN5, at 3.66 m from the sample position, consists of a matrix of 64 x 64 elements of 1 cm 2, encoded into 2 cm wide rings. The incident wavelength is 0.5 nm and the useful detector range 1.4°-8.2 °, corresponding with reduced wave number regions kl of 0.014-0.080, 0.016-0.093 and 0.020-0.12 respectively [4]. Measurements with empty cell and cadmium slabs were made for background determination. For the determination of resolution the windows of the empty sample cell were covered with two 1 mm vanadium slabs. Absolute normalisation was performed with a methane measurement at a pressure of 2.77 bar and room temperature in the same sample cell comparing the scattered intensity with Griffing's model [5]. Computer simulations indicate that multiple scattering is almost energy independent in the relevant energy transfer window of - 1.9 to + 1.7 meV, so it is eliminated by subtraction of a constant contribution. The data are fully corrected except for resolution, normalised absolutely and transformed to (k-e)) space. The results are compared with the Navier-Stokes expression convoluted with the resolution function (FWHM 0.13 meV) using: (1) the hydrodynamic values of Table 1 for the thermophysical parameters; (2) fitting the parameters. For k = 0.85 nm -1 the results are given in Fig. 1 and Table 2. The short-wavelength sound modes are clearly visible, but the damping is considerably stronger than according to linearized hydrodynamics. Also,
Table 1 Thermophysical properties of 36Ar at the thermodynamic states of the experiment. The speed of incident neutrons is 0.7912nmps -I [7, 8] Pressure P 105 Pa 20 Temperature T K 119.6 Density n n m - 3 17.7 Mean free path l n m - ~ 0.042 Specific heat ratio 7 ( = Cp/Cv) 2.81 Thermal diffusivity a nm 2 ps 1 0.0566 Adiabatic speed of sound 0.636 Cs nm p s - 1 Sound damping factor 0.117 Fs nm 2 p s - ~ S(0) 0.197
38 129.4 16.5 0.049 3.21 0.0485 0.557
43 140.6 14.6 0.063 4.26 0.0328 0.429
0.112
0.102
0.310
0.752
309
0.8
0.6 . ~ ,
"-
0.8t'.\'\ "" ",,
!
!
"N'x,
0
O. 15
0.30
0.45
0.61
¢o/ ps "~
Fig. 1. Experimental S(k, eg) (symbols with error bars) of liquid argon along the coexistence curve for (from top to bottom) 120 K, 17.7 nm-3; 129 K, 16.5 nm-3; 141 K, 14.6 nm -3, Dashed lines: linearized hydrodynamics; solid lines: least squares fits; arrows: position of the inelastic peak.
Table 2 Thermophysical properties derived from fitting the measurements n nm -3 7 cs n m p s 1 Fs nm z p s - ~ S(k = 0.85 n m - 2)
17.7 1.9 0.64 0.54 0.29
16.5 2.2 0.56 0.26 0.36
14.6 4.6 0.43 0.34 0.70
the ratio of the intensity of the central elastic peak and the inelastic peak deviates from linearized hydrodynamics as in krypton at room temperature and comparable densities [6]. For kl even as small 0.04 hydrodynamics is not valid. This is in contrast to argon at room temperature and lower densities [-7].
Acknowledgements B.M. and P.V. thank NWO (Nederlandse Organisatie voor Wetenschappelijk Onderzoek) and
310
B. Mos et al. / Physica B 234-236 (1997) 308-310
CNRS (Centre National de la Recherche Scientifique) for their financial support.
References [1] R.D. Mountain, Rev. Mod. Phys. 38 (1966) 205. [2] P.A. Egelstaff, G. Kearley, J.-B. Suck and J.P.A. Youden, Europhys. Lett. 10 (1989) 37. [31 U. Baffle,P. Verkerk, F. Barocchi, L.A. de Graaf, J.-B. Suck and H. Mutka, Phys. Rev. Lett. 65 (1990) 2394.
[4] F.H. Ree and W.G. Hoover, J. Chem. Phys. 46 (1967) 4181. [5] G.W. Grifffng, Phys. Rev. 124 (1961) 5. [6] U. Baffle, C. Benmore, P.A. Egelstaff, B. Mos, J.-B. Suck, P. Verkerk, K. Andersen, F. Baroeehi and J. Cook, these Proceedings (ECNS '96), Physica B 234-236 (1997). [7] R.B. Stewart, R.T. Jacobson, J.H. Becker, J.C.J. Teng, P.K.K. Mui and J.V. Sengers (eds.), Proc. 8th Symp. Thermophysical Properties (American Society of Mechanical Engineers, New York, 1982). [8] V.A. Rabinovich, A.A. Vasserman, V,I. Nedostup and L.S. Veksler, Thermophysical Properties of Neon, Argon, Krypton, and Xenon (Hemisphere, Washington, 1988).
Physiea B 234-236 (1997) 308-310
Neutron Brillouin scattering in liquid 36Ar B. M o s a'*, P. V e r k e r k a, U. Baffle b, C. B e n m o r e c, J.-B. S u c k d, F. B a r o c c h i e, J. C o o k f, K. A n d e r s o n f alnterfacultair Reactor Instituut, Delft University of Technology, 2629 JB Delft, The Netherlands bCNR Istituto Elettronica Quantistica, 1-50127 Firenze, Italy CDepartment of Physics, University of Guelph, ON, NIG2W1, Canada alnstitut filr Physik, T.U. Chemnitz-Zwickau, D-09107 Chemnitz, Germany eDipartimento di Fisica, Universith di Firenze, 50125 Firenze, Italy flnstitut Laue-Langevin, Grenoble, B.P. 156, 38042 Grenoble, France
Abstract We have measured S(k, to) in liquid 36Ar at three thermodynamic states along the coexistence line. We observe well-defined propagating density fluctuations, but the damping is stronger than according to linearized hydrodynamics.
Keywords: Brillouin scattering; Liquids; Phonon dispersion; Small-angle neutron scattering
1. Introduction At small wave vector k (kl < 0.1 with 1 the mean free path in a corresponding hard spheres fluid) the dynamic structure factor S(k, o~) of a fluid can be calculated from the Navier-Stokes relations, resulting in the well known Rayleigh-Brillouin triplet
speed of sound and bs = [(y - 1)a + FJ/c~. If kl is of order 1, generalised hydrodynamics is valid, i.e. the transport properties are k-dependent.
2. Experiment and results
[I]: S(ko~) =
[(y ~7 m -
S(k)
ak 2 1 Fsk 2 + ( ~ -4- csk)b,k 1)O)2 + a2k4 + 2 (co + c~k)2 + F2k 4
1 Fsk2--(~--c~k)b~k 1 + 2" (m - csk) 2 q- F~k 4 J with y the specific heat ratio, a the thermal diffusivity, F~ the sound damping factor, c~ the adiabatic
* Corresponding author.
The experiment was performed on IN5 (Institut Laue-Langevin) and is a continuation of earlier experiments [2, 3]. In order to reduce background scattering the aluminium sample container has two single-crystal sapphire windows (slab geometry) perpendicular to the incident neutron beam, with a space of 1 mm in between. 36Ar has no incoherent scattering: acoh = 77.9 b, aabs = 5.2 b at 0.18 nm. The three thermodynamic states along the gas-liquid coexistence line are given in Table 1 together with relevant thermophysical properties. In these states the forward neutron scattering fraction is 2.3%, 3.4% and 7.5% respectively (taking the value of S(0) into account).
0921-4526/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PII S 0 9 2 1 - 4 5 2 6 ( 9 6 ) 0 0 9 6 7 - 2
B. Mos et aL / Physica B 234-236 (1997) 308-310
The multidetector of IN5, at 3.66 m from the sample position, consists of a matrix of 64 x 64 elements of 1 cm 2, encoded into 2 cm wide rings. The incident wavelength is 0.5 nm and the useful detector range 1.4°-8.2 °, corresponding with reduced wave number regions kl of 0.014-0.080, 0.016-0.093 and 0.020-0.12 respectively [4]. Measurements with empty cell and cadmium slabs were made for background determination. For the determination of resolution the windows of the empty sample cell were covered with two 1 mm vanadium slabs. Absolute normalisation was performed with a methane measurement at a pressure of 2.77 bar and room temperature in the same sample cell comparing the scattered intensity with Griffing's model [5]. Computer simulations indicate that multiple scattering is almost energy independent in the relevant energy transfer window of - 1.9 to + 1.7 meV, so it is eliminated by subtraction of a constant contribution. The data are fully corrected except for resolution, normalised absolutely and transformed to (k-e)) space. The results are compared with the Navier-Stokes expression convoluted with the resolution function (FWHM 0.13 meV) using: (1) the hydrodynamic values of Table 1 for the thermophysical parameters; (2) fitting the parameters. For k = 0.85 nm -1 the results are given in Fig. 1 and Table 2. The short-wavelength sound modes are clearly visible, but the damping is considerably stronger than according to linearized hydrodynamics. Also,
Table 1 Thermophysical properties of 36Ar at the thermodynamic states of the experiment. The speed of incident neutrons is 0.7912nmps -I [7, 8] Pressure P 105 Pa 20 Temperature T K 119.6 Density n n m - 3 17.7 Mean free path l n m - ~ 0.042 Specific heat ratio 7 ( = Cp/Cv) 2.81 Thermal diffusivity a nm 2 ps 1 0.0566 Adiabatic speed of sound 0.636 Cs nm p s - 1 Sound damping factor 0.117 Fs nm 2 p s - ~ S(0) 0.197
38 129.4 16.5 0.049 3.21 0.0485 0.557
43 140.6 14.6 0.063 4.26 0.0328 0.429
0.112
0.102
0.310
0.752
309
0.8
0.6 . ~ ,
"-
0.8t'.\'\ "" ",,
!
!
"N'x,
0
O. 15
0.30
0.45
0.61
¢o/ ps "~
Fig. 1. Experimental S(k, eg) (symbols with error bars) of liquid argon along the coexistence curve for (from top to bottom) 120 K, 17.7 nm-3; 129 K, 16.5 nm-3; 141 K, 14.6 nm -3, Dashed lines: linearized hydrodynamics; solid lines: least squares fits; arrows: position of the inelastic peak.
Table 2 Thermophysical properties derived from fitting the measurements n nm -3 7 cs n m p s 1 Fs nm z p s - ~ S(k = 0.85 n m - 2)
17.7 1.9 0.64 0.54 0.29
16.5 2.2 0.56 0.26 0.36
14.6 4.6 0.43 0.34 0.70
the ratio of the intensity of the central elastic peak and the inelastic peak deviates from linearized hydrodynamics as in krypton at room temperature and comparable densities [6]. For kl even as small 0.04 hydrodynamics is not valid. This is in contrast to argon at room temperature and lower densities [-7].
Acknowledgements B.M. and P.V. thank NWO (Nederlandse Organisatie voor Wetenschappelijk Onderzoek) and
310
B. Mos et al. / Physica B 234-236 (1997) 308-310
CNRS (Centre National de la Recherche Scientifique) for their financial support.
References [1] R.D. Mountain, Rev. Mod. Phys. 38 (1966) 205. [2] P.A. Egelstaff, G. Kearley, J.-B. Suck and J.P.A. Youden, Europhys. Lett. 10 (1989) 37. [31 U. Baffle,P. Verkerk, F. Barocchi, L.A. de Graaf, J.-B. Suck and H. Mutka, Phys. Rev. Lett. 65 (1990) 2394.
[4] F.H. Ree and W.G. Hoover, J. Chem. Phys. 46 (1967) 4181. [5] G.W. Grifffng, Phys. Rev. 124 (1961) 5. [6] U. Baffle, C. Benmore, P.A. Egelstaff, B. Mos, J.-B. Suck, P. Verkerk, K. Andersen, F. Baroeehi and J. Cook, these Proceedings (ECNS '96), Physica B 234-236 (1997). [7] R.B. Stewart, R.T. Jacobson, J.H. Becker, J.C.J. Teng, P.K.K. Mui and J.V. Sengers (eds.), Proc. 8th Symp. Thermophysical Properties (American Society of Mechanical Engineers, New York, 1982). [8] V.A. Rabinovich, A.A. Vasserman, V,I. Nedostup and L.S. Veksler, Thermophysical Properties of Neon, Argon, Krypton, and Xenon (Hemisphere, Washington, 1988).