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CHARACTERIZATION METHODS. 60 X-RAY AND NEUTRON SCATTERING X-ray and neutron scattering are valuable techniques for the determination of an unknown atomic structure of a material, even in cases of highly disordered systems like amorphous phases. As seen by electron microscopy, a nanocrystalline material consists of crystalline grains that are separated by grain boundaries of about 0.5 to 1 nm thickness (around two to four nearest-neighbor atomic distances). The volume fraction of such an interfacial component changes with grain size and is about 0.3 to 0.6, for example, for a mean grain diameter of 5 nm. X-ray diffraction curves for a nanocrystalline sample therefore will be composed of a part that originates from the crystalline grains, with their well-known structure, and a significant part that originates from atoms located in the boundary regions. Even if it is assumed that the local atomic structure of these grain boundaries is similar to that of more extended grain boundaries, it may be expected that the aggregate of all the different boundaries in a nanophase material (i.e., the interfacial component of the structure) will exhibit an aggregate structure that is apparently different from known solid-state structures. This expectation is based on the fact that a nanophase material consists of a high number-density of different interfaces (about 1019 per cm3 for a grain size of 5 nm) with atomic structures strongly depending on the misorientation of the adjacent grains. A recent x-ray study (Zhu et al., 1987) of nanocrystalline iron with 4-to 6-nm grain sizes has indicated that no preferred interatomic distances like those found in a crystalline or amorphous structure occur in the best-fit interfacial structure (i.e., all interatomic distances appear to occur with similar probabilities, except those forbidden because of interatomic penetration). Hence, according to this x-ray study, the interfacial component (i.e., the sum of all boundaries of this nanophase material) represents an aggregate solid-state structure without long-range or short-range order. Further support for this view comes from a recent EXAFS study of nanocrystalline metals (Haubold et al., 1988). The local atomic structures of individual nanocrystalline interfaces, however, are likely to manifest ordered structural units as known from grain boundaries in normal polycrystalline materials. This has recently been shown to be the case for nanophase TiO2 by Raman spectroscopy (Melendres et al., 1989). The actual local atomic nature of nanophase boundaries needs to be further elucidated in general, and atomic resolution electron microscopy on nanophase materials can be expected to facilitate such an elucidation. Beyond such studies of atomic structure, x-ray and neutron small-angle scattering can also be useful tools for the study of grain-and pore-size distributions and grain boundry characteristics, particularly as a function of sintering temperatures, as shown by recently completed small-angle scattering investigations (Epperson et al., 1989; Wallner et al., 1989). Because of the likelihood of random orientation of crystallites in some three-dimensional nanostructures, the use of single-crystal techniques is of
CHARACTERIZATION METHODS. 61 dubious value. The Rietveld powder profile technique should be extended to handle these types of problems. Because of its general applicability to multiphase systems and the possibility of extension to include determinations of both grain size and inhomogeneous strain, this technique offers the potential of being a central tool in the study of atomic arrangements in three-dimensional nanostructures. With the use of high-resolution diffractometers on high-intensity synchrotron sources, even milligram sizes of samples can be measured. The technique can be easily extended to monitor the influence of time, temperature, and pressure on the atomic arrangements in the nanostructure. Because the x-ray technique averages over significant volumes of material, it offers a complementary tool to STEM and other atomic-imaging techniques. A different approach must be employed when the study of lamellar nanostructures using x-ray scattering is being considered. Low-angle x-ray diffraction is a powerful tool for the analysis of layer structure in periodic multilayers, particularly for those that are largely or completely amorphous. A theory for the scattering of x-rays from such periodic amorphous or largely amorphous arrays has been developed. It incorporates all of the results of the full dynamical theory of x-ray scattering (which in general is needed to make the correct first approximation to the analysis of the x-ray scattering from many multilayer systems), including absorption, extinction (i.e., depletion of the incident beam intensity), and multiple scattering. In addition, this theory provides the only systematic basis for handling the case of nonperiodic finite number of layers (John Keem, 1989, private communication). Information concerning the interfacial atomic arrangements is contained in the higher-order low-angle scattering peaks and interpeak scattering. At this time there has been no detailed analysis of this type of data and correlation of the results to real-space models for the interfacial atomic arrangements as obtained from a theoretical model or an empirical model constructed with the aid of Scanning Transmission Electron Microscopy (STEM). This is an area ripe for further study for its own value and for the value of development as a tool for others to use in the characterization of their nanostructures. Extended x-ray absorption fine structure (EXAFS) technology is well suited for the study of highly dispersed particles 2 nm in diameter that are typically outside the detection capability of conventional x-ray diffraction (XRD) or transmission electron microscopy (Sinfelt et al., 1984). EXAFS yields information about local atomic structure, including nearest-neighbor distances and the number of atoms coordinated to the metal of interest. EXAFS has been used to determine the average particle size, to identify particle morphology (hemisphere versus raft), to identify the distribution of atoms in bimetallic and multimetallic clusters (segregation of one component to the surface), to identify the interaction of catalyst particles with the support, and to identify the oxidation states of metals or promoters. In addition,
