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Neutron Scattering of Clathrate and Semiclathrate Hydrates

1.1. Introduction

Neutron scattering is a standard tool when dealing with the microscopic properties of the condensed matter at the atomic level. This comes from the fact that the neutron matches with the distances and energy scales, and thus with the microscopic properties of most solids and liquids. Neutrons, with wavelengths in the order of angstroms, are capable of probing molecular structures and motions and increasingly find applications in a wide array of scientific fields, including biochemistry, biology, biotechnology, cultural heritage materials, earth and environmental sciences, engineering, material sciences, mineralogy, molecular chemistry, solid state and soft matter physics.

The striking features of neutrons can be summarized as follows. Neutrons are neutral particles. They interact with other nuclei rather than with electronic clouds. They have (de Broglie) wavelengths in the range of interatomic distances. They have an intrinsic magnetic moment (a spin) that interacts with the unpaired electrons of magnetic atoms. Their mass is in the atomic mass range. They carry, thus, similar energies and momentum than those of condensed matter, and more specifically of gas hydrates.

As gas hydrates are mainly constituted of light elements (H, O, C, etc.), in situ neutron scattering appears as a technique particularly suited to their study. In the case of diffraction (i.e. structural properties), while the identification of these light atoms by X-ray diffraction requires the presence of heavy atoms and is therefore extremely complicated, neutron diffraction (NP) is highly sensitive to them due to the interaction of the neutrons with nuclei rather than with electron clouds. Moreover, most of the matter is "transparent" to neutron beams. Such a feature provides advantages for studying gas hydrates when a heavy sample environment is required (e.g. high pressure, low temperature). For instance, X-ray powder diffraction studies are usually restricted to small sample volumes, as large sample volumes would be associated with a strong absorption and unwanted scattering from the pressure cell. Neutron techniques allow studies of bulk processes in situ in representative volumes, hence with high statistical precision and accuracy [STA 03, HEN 00, GEN 04, FAL 11]. Furthermore, although alteration of some types of ionic clathrate hydrates (or semiclathrates), such as the splitting of the tetra-alkylammonium cations into alkyl radicals [BED 91, BED 96], by X-ray irradiation has been reported, neutrons do not damage sample.

Finally, future developments in gas hydrate science will be based on the understanding, at a fundamental level, of the factors governing the specific properties of gas hydrates. In this respect, the investigation of gas hydrate dynamics is a prerequisite. At a fundamental level, host-guest interactions and coupling effects, as well as anharmonicity, play an important role. These phenomena take place over a broad timescale, typically ranging from femtoseconds to microseconds. Investigating the dynamics (intramolecular vibrations, Brownian dynamics, etc.) of gas hydrates thus requires various complementary techniques, such as NMR or Raman spectroscopy, and indeed inelastic and quasi-elastic neutron scattering (QENS), especially when it comes to encapsulating light elements such as hydrogen or methane in water-rich structures.

In this chapter, the recent contributions of neutron scattering techniques in gas hydrate research are reviewed. After an introduction to neutron scattering techniques and theory, an overview of the accessible information (structural and dynamical properties) by means of neutron scattering is provided. Then, selected examples are presented, which illustrate the invaluable information provided by neutron scattering. Some of these examples are directly related to existing or possible applications of gas hydrates.

1.2. Neutron scattering

Both nuclear and magnetic neutron interactions are weak: strong but at very short length scale for the nuclear interaction and at larger scale for the magnetic interaction. In that respect, the probed sample can be considered as transparent to the neutron beam. This highly non-destructive character combined with the large penetration depth, both allowed because of the weak scattering, is one of the main advantages of this probe.

Nuclear scattering deals with nuclear scale interaction and hence presents no wave vector dependent form factor attenuation allowing to offer high momentum transfers for diffraction or specific techniques such as deep inelastic neutron scattering (also known as neutron Compton scattering).

Neutron spectroscopic techniques range from the diffraction of large objects using small-angle scattering, usually made with long incident wavelengths (cold neutrons), to direct imaging through contrast variation (neutron tomography), usually made with short wavelengths (hot neutrons) and going through ordinary diffraction and inelastic scattering in the intermediate wavelength range.

In that respect, neutron scattering complements without necessarily overlapping the other available spectroscopic techniques such as nuclear magnetic resonance (NMR). If one naturally thinks about X-ray for structure determination, neutrons are very competitive for inelastic scattering and even essential for magnetic scattering both in the diffraction and inelastic modes.

The main drawback that contrasts with the numerous advantages comes from the intrinsic relative flux limitation of neutron sources, and thus, this type of spectroscopy can only be performed at dedicated large-scale facilities.

1.2.1. A basic ideal scattering experiment

In a generic experiment (Figure 1.1), a beam of monochromated neutrons with single energy (Ei) is directed on a sample. The scattered neutrons are collected along direction (angles ? and ?) and analyzed by energy difference with the incident energy by using a detector, covering a solid angle ?O of the sphere, which measures the analyzed neutron intensity. The measured intensity in the solid angle spanned by the detector and in a final energy interval ?Ef in this simple gedanken experiment reads:

where F stands for the incident flux at the incident energy and ? is the efficiency of the detector. The quantity between the identified terms is the double differential scattering cross-section, a surface per unit of energy, which characterizes the interaction of the neutron with the sample or the surface that the sample opposes to the incident beam. Since the intensity has the dimension of count/s, the double differential scattering cross-section can be seen as the ratio of the scattered flux in the given detector per unit energy over the incident flux.

Figure 1.1. Sketch of an ideal scattering experiment. An incident neutron beam of monochromatic energy Ei and wave vector ki is scattered with energy Ef and wave vector kf. For a color version of this figure, see www.iste.co.uk/broseta/hydrates1.zip

1.2.2. Neutron scattering theory

The mathematical development of the neutron scattering technique comes from the more general scattering theory. The interaction of the neutron with a single nucleus is first examined and then the generalization of the theory for an assembly of scatterers is developed. From scattering theory to its application to neutron scattering, the aim is to convince that the scattering of neutrons by the nuclei or by the spins of an ensemble of atoms provides information on the structure and motions of the atoms, i.e. information on the sample under investigation at the atomic level.

To study the scattering of a single neutron by one nucleus of the sample at the atomic level, one has to consider the incoming neutron as a plane wave, whose square modulus gives the probability of finding the neutron at a given position in space (this probability is a constant for a plane wave). Considering a point-like interaction between the neutron plane wave and the nucleus, the nucleus size in interaction being far smaller than the neutron wavelength and atomic distances, the scattered neutron wave is then described as an isotropic spherical wave whose intensity is proportional to 1/r and the strength of the interaction between the neutron and the nucleus of interest, called the scattering length b.

The scattering length b is specific (and tabulated, see [SEA 92]) to each nucleus and does not vary with the atomic number in a correlated way. It can be positive, meaning repulsive interaction, negative (attractive) and can be complex and energy dependent, which means that the target can absorb the neutron (absorption proportional to the incident wavelength in the thermal neutron range).

Going from the scattering by a single nucleus to the scattering by a macroscopic assembly of nuclei as found in a condensed medium is a matter of properly summing all scattered waves under well-defined approximations, which are generally fulfilled in neutron scattering experiments.

The first obvious approximation is that the scattered waves are weak and thus leave the incident plane wave unperturbed over the coherence volume. This allows retaining only the first term of the Born series of the Lipmann-Schwinger equation. This simplification is known as the Born approximation.

For the sample (but not for the...