Crystalline solids neutron diffraction

To answer this question we need to consider the kind of physical techniques that are used to study the solid state. The main ones are based on diffraction, which may be of electrons, neutrons or X-rays (Moore, 1972 Franks, 1983). In all cases exposure of a crystalline solid to a beam of the particular type gives rise to a well-defined diffraction pattern, which by appropriate mathematical techniques can be interpreted to give information about the structure of the solid. When a liquid such as water is exposed to X-rays, electrons or neutrons, diffraction patterns are produced, though they have much less regularity and detail it is also more difficult to interpret them than for solids. Such results are taken to show that liquids do, in fact, have some kind of long-range order which can justifiably be referred to as a structure . 

The most important experimental task in structural chemistry is the structure determination. It is mainly performed by X-ray diffraction from single crystals further methods include X-ray diffraction from crystalline powders and neutron diffraction from single crystals and powders. Structure determination is the analytical aspect of structural chemistry the usual result is a static model. The elucidation of the spatial rearrangements of atoms during a chemical reaction is much less accessible experimentally. Reaction mechanisms deal with this aspect of structural chemistry in the chemistry of molecules. Topotaxy is concerned with chemical processes in solids, in which structural relations exist between the orientation of educts and products. Neither dynamic aspects of this kind are subjects of this book, nor the experimental methods for the preparation of solids, to grow crystals or to determine structures. 

At the time the neutron diffraction experiments were carried out it was not known that there are two forms of amorphous solid water. Consequently, although the deposition system was designed to ensure elimination of crystalline ice in the sample, neither the geometry nor the deposition rate were the same as used in the X-ray experiments of Narten, Venkatesh and Rice 7>27>. We shall argue below that although the substrate temperature used by WLR was low, their data are only consistent with diffraction from high temperature low density D20(as). 

A porous particle contains many interior voids known as open or closed pores. A pore is characterized as open when it is connected to the exterior surface of the particle, whereas a pore is closed (or blind) when it is inaccessible from the surface. So, a fluid flowing around a particle can see an open pore, but not a closed one. There are several densities used in the literature and therefore one has to know which density is being referred to (Table 3.15). True density may be defined as the mass of a powder or particle divided by its volume excluding all pores and voids. True density is also referred to as absolute density or crystalline density in the case of pure compounds. However, this density is very difficult to be determined and can be calculated only through X-ray or neutron diffraction analysis of single-crystal samples. Particle density is defined as the mass of a particle divided by its hydrodynamic volume. The hydrodynamic volume includes the volume of all the open and closed pores. Practically, the hydrodynamic volume is identified with the volume included by the outer surface of the particle. The particle density is also called apparent or envelope density. The term skeletal density is also used. The skeletal density of a porous particle is higher than the particle one, since it is the mass of the particle divided by the volume of solid material making up the particle. In this volume, the closed pores volume is included. The interrelationship between these two types of density is as follows (ASTM, 1994 BSI, 1991) ... 

These embrace X-ray diffraction, neutron diffraction and electron diffraction. The first two of these are almost entirely used in the study of crystalline solids, while electron diffraction is of most value (to inorganic chemists at least) for structure determinations of gaseous substances. X-ray diffraction has been used to obtain structural information for species in solution, and electron diffraction has applications in the... 

The classical idea of molecular structure gained its entry into quantum theory on the basis of the Born Oppenheimer approximation, albeit not as a non-classical concept. The B-0 assumption makes a clear distinction between the mechanical behaviour of atomic nuclei and electrons, which obeys quantum laws only for the latter. Any attempt to retrieve chemical structure quantum-mechanically must therefore be based on the analysis of electron charge density. This procedure is supported by crystallographic theory and the assumption that X-rays are scattered on electrons. Extended to the scattering of neutrons it can finally be shown that the atomic distribution in crystalline solids is identical with molecular structures defined by X-ray diffraction. 

Unfortunately, specialists in the field of single crystal NMR spectroscopy are not specialists in single crystal neutron diffraction, and, as with solid-state infrared spectroscopy, good experiments using both methods on the same crystalline compound are relatively rare, cf. [246, 247]. 

The best and most direct methods to observe the hydration of a macromolecule are X-ray and neutron diffraction analyses carried out at high resolution to better than 1.8 A. In the crystals of proteins, the macromolecules are heavily hydrated so that between 20Vo and 909o of the total volume are solvent. In fact, despite their well-defined crystal morphology, crystalline proteins more resemble concentrated protein solutions than the solid state. 

Using structural data obtained from neutron diffraction studies for 41 different crystalline solids, the following linear relationship was reported [70] ... 

There is, however, an alternative (but still indirect) way to view these molecules. It involves studies of crystalline solids and the use of the phenomenon of diffraction. The radiation used is either X rays, with a wavelength on the order of 10 cm, or neutrons of similar wavelengths. The result of analyses by these diffraction techniques, described in this volume, is a complete three-dimensional elucidation of the arrangement of atoms in the crystal under study. The information is obtained as atomic positional coordinates and atomic displacement parameters. The coordinates indicate the position of each atom in a repeat unit within the crystal, while the displacement parameters indicate the extent of atomic motion or disorder in the molecule. From atomic coordinates, it is possible to calculate, with high precision, interatomic distances and angles of the atomic components of the crystal and to learn about the shape (conformation) of molecules in the crystalline state. 

This review article is concerned with the structure, bonding, and dynamic processes of water molecules in crystalline solid hydrates. The most important experimental techniques in this field are structural analyses by both X-ray and neutron diffraction as well as infrared and Raman spectroscopic measurements. However, nuclear magnetic resonance, inelastic and quasi elastic neutron scattering, and certain less frequently used techniques, such as nuclear quadrupole resonance, electron paramagnetic resonance, and conductivity and permittivity measurements, are also relevant to solid hydrate research. 

Both X-ray and neutron diffraction methods are applied to determine the structure of crystalline solid hydrates. Because of the very small scattering cross-section of hydrogen atoms for X-rays it is much desirable to solve the crystal structure by means of neutron diffraction techniques. 

Various models are reported in the literature for correcting the bond lengths and angles of H2O molecules in solid hydrates for thermal motion and anharmonicity. However, as recently shown , both positive and negative terms exist, which partially compensate for each other. Therefore, data obtained by neutron diffraction do not show systematic errors larger than 3 pm and 2°, respectively, and, hence, the differences between the average water molecule in crystalline hydrates and that in the gas phase discussed above should be real. ... 

Consider now real materials with model micropores, that is to say with regular dimensions and whose pore walls consist of well-defined crystalline adsorption sites (including possible cationic sites). Such solids can be found within the realm of zeolites and associated materials such as the aluminophosphates. One can imagine the probability that a fluid adsorbed within such micropores may be influenced by the well-defined porosity and thus become itself "ordered. Such phenomena have already been highlighted with the aid of powerful but heavy techniques such as neutron diffraction and quasi-elastic incoherent neutron diffusion. The structural characterisation of several of the following systems was carried out with the aid of such techniques in collaboration with the mixed CNRS-CEA Leon Brillouin Laboratory at Saclay (France). 

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