Structure determination of gaseous and amorphous substances by diffraction methods: Philosophical concepts and their implementation (A Review)

Abstract

Structure determination by diffraction methods is reviewed in terms of the philosophical and mathematical aspects of the techniques used to investigate the atomic arrangements in gaseous and amorphous substances. Both theory and experiment must be adapted to each other's limitations. This is accomplished often only after much time and study have been devoted to the problems. Some areas of application are favored by an overdeterminacy in the data, which helps to simplify the mathematical aspects of the analysis. Other areas have relatively few data compared to the number of unknown parameters. In such cases, special analytical procedures that use, for example, chemical and structural information are indispensible. Applications cover a broad range of problems and afford fundamental information to many fields of science. Structure analysis by diffraction methods is concerned with the determination of the geometric arrangements of atoms in materials. At times the resolution is not sufficient to permit the location of atoms. In such cases, the positions of aggregates of atoms are determined. The average thermal motion of the atoms also often can be described. This is achieved by an interpretation of the patterns formed by suitable incident beams that are scattered by the substances of interest. The beams commonly used for such purposes are composed of electrons, x-rays, or neutrons, giving rise to the names of the various diffraction techniques.This article concerns mainly the philosophical aspects of structure determination-i.e., concepts and problems-rather than the numerous applications. The latter can be found in other articles referred to throughout the text.BACKGROUND

Applications of freeze‐fracture replication to problems in materials and colloid science

“…The more limiting feature of scattering data is that the information provided is indirect. A scattering experiment can be described mathematically as the Fourier transform of some density, atomic number, etc., distribution in the sample (Berne and Pecora, 1976;Karle, 1977). To understand the experiments, the researcher has two options.…”

“…Unfortunately, although this second option is used almost exclusively, the physical limitations and assumptions inherent to the model can bias the interpretation of the data. Often, several conflicting models, and even unphysical models, can account for the same experimental data (Karle, 1977), especially in fluid systems with little symmetry. An important example of this has been in investigations of "middle" phase microemulsions.…”

Quantitative nanostructure characterization using atomic pair distribution functions obtained from laboratory electron microscopes

“…In these latter cases, there is still significant multiple scattering, but it should be is sufficiently incoherent that it can be treated as a background and subtracted and the resulting coherent signal can be treated kinematically. This has been discussed in detail in a number of publications [7,2,1,20]. This is used in the rapidly growing field of electron crystallography [35], and has been demonstrated in previous work of electron diffraction (ED) from glasses and amorphous materials [23,8,7,17,26], though little has been done in the way of quantitative modeling in those studies.…”