Neutron Brillouin scattering in dense fluids P. Verkerk (Delft University) on behalf of the FINGO (France, Italy, Netherlands, Germany, Ontario) collaboration.

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Thermal neutron scattering is a typical microscopic probe for investigating dynamics and structure in condensed matter. In contrast, light (Brillouin) scattering with its three orders of magnitude larger wavelength is a typical macroscopic probe. In a series of experiments using the improved small-angle facility of IN5 a significant step forward is made towards reducing the gap between the two. For the first time the transition from the conventional single line in the neutron spectrum scattered by a fluid to the Rayleigh-Brillouin triplet known from light-scattering experiments is clearly and unambiguously observed in the raw neutron data without applying any corrections.

Since its very beginning thermal neutron scattering has been an invaluable tool in the development of theories for the dynamics and structure of fluids. The reason is that the wavelength as well as the energy perfectly match the structure and dynamics of a fluid on a microscopic scale. In contrast, light scattering and in particular Brillouin scattering is a typical macroscopic probe suitable for the investigation of hydrodynamics.

Our aim is the understanding of thermodynamics and hydrodynamics on the basis of the molecular-interaction forces. Therefore, our present understanding of fluids would be further enhanced if we had a probe for investigating the transition from the microscopic to the macroscopic region. In contrast to SANS there is an upper limit to the wavelength of the neutrons which may be used, because their energy must be sufficiently large to permit interaction with the dynamic processes in the fluid. For observation of propagating modes, like for instance phonons, the neutron velocity v must be larger than the sound velocity c_s. In fluids c_s ranges from about 400 ms^-1 for rare gases to about 5000 ms^-1 for molten lithium, so, the minimum neutron energy is about 4 meV in the first case and about 400 meV in the second case.

In the hydrodynamic regime the wavelength l_d of the density fluctuations in the fluid that interact with the scattered radiation (usually light) is large compared with the mean free path l (we regard the fluid for a moment as a collection of moving and colliding hard spheres). Because l_d = 2p /Q with Q the momentum transfer in the scattering event, the hydrodynamic regime is approached if Ql << 1, which can be realised either by increasing the wavelength of the incident radiation or by measuring at very small scattering angles. As stated before, the first possibility does not work for neutrons if we want to obtain information on the dynamics.

Obviously, in a small-angle experiment very good angular resolution is mandatory. In the hydrodynamic limit the spectrum of scattered radiation consists of the Rayleigh-Brillouin triplet. The width of the peaks is proportional Q² and the position of the inelastic Brillouin peaks is proportional to Q, so with decreasing scattering angle increasingly good energy resolution is required. This can only be achieved at the cost of a considerable reduction in count rate and, therefore, neutron Brillouin-scattering requires the world's most intense neutron sources. To the best of our knowledge two instruments are available today for such experiments: IN5 at ILL for thermal and cold neutrons and PHAROS for hot neutrons at the spallation source of the Neutron Scattering Center, Los Alamos National Laboratory. A third instrument is under construction at the cold source of the Hahn-Meitner Institute, Berlin.

Egelstaff et al. used IN5 modified with a temporarily installed position-sensitive detector with time-of-flight analysis for the first time in an experiment on nitrogen at room temperature. An international team was then set up involving groups from France, Italy, the Netherlands, Germany, and Ontario, hence called FINGO (Latin for "I invent"), to further develop the technique and applications of neutron Brillouin scattering. A few more experiments were done on argon and krypton before the small-angle facility was improved during the reactor shut-down with a permanently installed position-sensitive detector and a vacuum flight-path.

In April 1996 FINGO used the new facility in a series of experiments on high-density krypton at room temperature and on liquid argon (using ⁸⁶Kr and ³⁶Ar for pure coherent scattering). We used an incident wavelength of 5 Å (3.3 meV), resulting in an energy resolution for the scattered neutrons of 0.13 meV FWHM. Figs. 1 and 2 present the result for ⁸⁶Kr at room temperature and 800 bar, only corrected for background and container scattering. The sound dispersion is very clearly visible as well as the increasing damping with increasing wave-vector. In Fig. 3 we compare the fully corrected (except for resolution) data for Q = 0.085 Å^-1 with the hydrodynamic Rayleigh-Brillouin triplet folded with the experimental resolution.

Figure 1 (left): Contour map (produced by the LAMP software) of the scattered neutron spectrum for krypton at room temperature and 800 bar after correction for background and container scattering.

Figure 2 (right): Same data as Fig. 1, now plotted as function of wave vector Q and energy transfer DE in order to show the limits of the kinematic region. The hydrodynamic sound velocity is 572 ms^-1 or 3.81 Å meV.

Although Ql = 0.02, which was expected to be well within the hydrodynamic range, the experimental data still deviate considerably from pure hydrodynamics.

This surprising result deserves further analysis; comparison with similar experiments on argon may shed new light on the relation between the interparticle interactions and the transport coefficients.

Reasonable agreement with the experiment may however, be obtained by using the hydrodynamic model but with transport coefficients used as fitting parameters (see Fig. 3). 

The members of FINGO are or have been Fabrizio Barocchi and Ubaldo Bafile (Florence), James Youden, Chris Benmore and Peter Egelstaff (Guelph, Ontario), Hannu Mutka (ILL) and Jens Suck (ILL / Chemnitz), Leo de Graaf, Barry Mos and Peter Verkerk (Delft).

Figure 3: Experimental S(Q,w) (not corrected for resolution) at Q = 0.085 Å^-1 (green dots with error bars) compared with the hydrodynamic Rayleigh-Brillouin triplet if the parameters are determined from the experimental thermodynamic and transport coefficients (blue) and if the parameters are fitted (red).