Determination of Lattice Parameters by the Kossel and Divergent X-Ray Beam Techniques

Abstract

The principal aim of this article is to develop in a clear and orderly manner a general relationship and show how it can be used to determine with a high degree of precision lattice parameters of tetragonal and hexagonal as well as cubic crystals. The introduction and extensive use of electron-probe microanalyzers provides a ready-made means of obtaining both Kossel and divergent X-ray beam patterns which could previously be produced only with specially constructed X-ray tubes. The present ease of their production as well as the continuing need for precise lattice parameters for the study of many problems associated with crystallized solids has stimulated a renewed interest in these two techniques. As has been recently shown by several experimental results limited to cubic crystals, these techniques are capable of giving lattice parameters with the same degree of precision as those obtained by the more classical means. The development of the general relationship is preceded by a brief historical review, a discussion of the relative merits of the methods, a short description of the nature of the diffraction patterns, and the geometrical conditions necessary for realizing precision parameter measurements. In conclusion, the advantages and disadvantages of the Kossel and divergentbeam methods compared with those of the classical powder techniques are enumerated and discussed.