Amorphous solids structural information

The use of X-ray diffraction from crystalline samples can result in a complete three-dimensional crystal structure of a molecule, but requires a single crystal suitable for proper diffraction (see Section 3.3). X-ray absorption spectroscopy (XAS) can yield limited molecular structural information on noncrystalline (amorphous) solid... 

In amorphous solids there is a considerable disorder and it is impossible to give a description of their structure comparable to that applicable to crystals. In a crystal indeed the identification of all the atoms in the unit cell, at least in principle, is possible with a precise determination of their coordinates. For a glass, only a statistical description may be obtained to this end different experimental techniques are useful and often complementary to each other. Especially important are the methods based on diffraction experiments only these will be briefly mentioned here. The diffraction pattern of an amorphous alloy does not show sharp diffraction peaks as for crystalline materials but only a few broadened peaks. Much more limited information can thus be extracted and only a statistical description of the structure may be obtained. The so-called radial distribution function is defined as ... 

As noted earlier, the diffraction of X-rays, unlike the diffraction of neutrons, is primarily sensitive to the distribution of 00 separations. Although many of the early studies 9> of amorphous solid water included electron or X-ray diffraction measurements, the nature of the samples prepared and the restricted angular range of the measurements reported combine to prevent extraction of detailed structural information. The most complete of the early X-ray studies is by Bon-dot 26>. Only scanty description is given of the conditions of deposition but it appears likely his sample of amorphous solid water had little or no contamination with crystalline ice. He found a liquid-like distribution of 00 separations at 83 K, with the first neighbor peak centered at 2.77 A. If the pair correlation function is decomposed into a superposition of Gaussian peaks, the area of the near neighbor peak is found to correspond to 4.23 molecules, and to have a root mean square width of 0.50 A. 

In this section we attempt to piece together, self-consistently, the robust information contained in the results described earlier. For this purpose we regard the predictions of the several theoretical models as hints to be selected and followed up in conjunction with experimental data. Our goal, of course, is the construction of a conjecture concerning the structures of amorphous solid and liquid water. 

The most direct source of structural information, the diffraction studies, provides strong evidence for predominantly tetrahedral ordering of a molecule and its nearest neighbors, both in amorphous solid and liquid H2O. Other, weaker but still direct, structural evidence comes from the ratio of separations of nearest neighbor and next nearest neighbor 00 pairs in liquid water, the ubiquity of tetrahedral ordering in the several crystalline ices, and the statistical geometry of simulated water. 

NMR and EPR techniques provide unique information on the microscopic properties of solids, such as symmetry of atomic sites, covalent character of bonds, strength of exchange interactions, and rates of atomic and molecular motion. The recent developments of nuclear double resonance, the Overhauser effect, and ENDOR will allow further elucidation of these properties. Since the catalytic characteristics of solids are presumably related to the detailed electronic and geometric structure of solids, a correlation between the results of magnetic resonance studies and cata lytic properties can occur. The limitation of NMR lies in the fact that only certain nuclei are suitable for study in polycrystalline or amorphous solids while EPR is limited in that only paramagnetic species may be observed. These limitations, however, are counter-balanced by the wealth of information that can be obtained when the techniques are applicable. 

Besides structure, X-ray diffraction gives a host of other valuable information. For example, powder diffraction, especially with counter diffractometers, has been widely used for phase identification, quantitative analysis of a mixture of phases, particle size analysis, characterization of physical imperfections (the last two being obtainable from line broadening) and in situ studies of reactions. In the case of amorphous solids, X-ray... 

Traditionally, X-ray absorption edge measurements have been used to determine oxidation states of metals in complex materials. The extended X-ray absorption fine structure (EXAFS), on the other hand, provides structural information such as bond distances and coordination numbers even with powdered samples, crystalline or amorphous, the fine structure essentially resulting from short-range order around the absorbing atom. The technique is also useful for studying solid surfaces (SEXAFS). The observation of fine structure beyond the K-absorption edges of materials dates back to... 

O and N shieldings more difficult to interpret and to model, but it also suggests that the shieldings of these elements can potentially give valuable information on the long-range structure of amorphous solids. 

The glass transition temperature Tg is one of the most important structural and technical characteristics of amorphous solids. The correlations of Tg of linear polymers with their chemical composition, molecular weight, rigidity and symmetry of chains, as well as some other characteristics of macromolecules are well documented 57,58) Thg information on networks is much poorer. At present, for networks there exists mainly one parameter in structure-Tg correlations. It is the concentration of crosslinks — a parameter which is very insufficient, since in networks there are chemical crosslinks of different functionality (connectivity) which are distinguished by their molecular mobility. This means that the topological aspect of the network structure should be taken into account in the Tg analysis. Another difficulty connected with Tg determination of polymers lies in vitrification occurring during polymer formation (Sect. 6). 

Solid-state nuclear magnetic resonance (NMR), a canonical technique of chemistry and physics, possesses many versatile features such as, for example, elemental specificity and local structural, electronic, and motional sensitivity. In particular, NMR can characterize samples in most types of condensed matter, be it liquid or solid, single crystal or amorphous. Given adequate sensitivity it has, therefore, the unique ability of providing metal surface and adsorbate electronic and structural information on a molecular level and allows one to access motional information of adsorbate over a time range unattainable by any other single spectroscopic technique. In addition, solid-state NMR is nondestructive, technically versatile. 

Glass, rubber, and many plastics are amorphous solids. Recent studies have shown that glass may have some structure. When X-ray diffraction is used to study glass, there appears to be no pattern to the distribution of atoms. When neutrons are used instead, an orderly pattern of silicate units can be detected in some regions. Researchers hope to use this new information to control the structure of glass for optical applications and to produce glass that can conduct electricity. 

The EXAFS spectrum [10] (Figure 6.6.) shows the variation of absorption with energy in the region up to about 1 keV beyond the absorption edge. This typically ripple-like pattern is analysed mathematically to produce a radial distribution function [10] (Figure 6.7.) which provides information about the local structure. The technique is particularly useful for the study of amorphous solids such as glasses. EXAFS is more sensitive to structural disorder than XRD. 

The ordered mesoporous materials (or crystalline mesoporous materials) such as MCM-41 (MCM stands for Mobil composite of matter), MCM-48 and SBA-15 (SBA stands for University of California, Santa Barbara) are a new generation of materials that are different from nonordered (amorphous) mesoporous materials. They are amorphous and not ordered at the atomic level from a classical crystallographic view point, but their regular channels or pores are ordered at the nanometer level. Because of this, these materials have certain characteristics of crystalline solids. Their structural information can be obtained by diffraction methods and other structural analysis techniques. The discovery of periodic mesoporous structures is a major advance in composite organic-inorganic materials synthesis. 

This chapter has concentrated on crystalline materials. X-ray diffraction can also furnish structural information about amorphous and semi-amorphous solids, even though the structure is much more diffuse. 

---