Determination of Composition of Solid Solutions Using X-Ray Diffraction Techniques

Abstract

Although ordinarily a qualitative tool, x-ray diffraction techniques can be particularly powerful when dealing with continuous solid solutions. The very properties of the atoms that allow them to form these solutions often make it difficult to distinguish between them by chemical means. Even most physical analytical techniques have difficulty distinguishing among a physical mixture, a solid solution or a mixture of the two. This paper will be limited to substitutional solid solutions, where only two constituents are being altered. The principle behind the techniques to be discussed is based on the differences in effective atomic radii between the solvent atom and the substituting atom which results in an expansion or contraction of the lattice which is directly measurable. Several methods will be described which are particularly suited for investigating continuous solid solutions obeying Vegard’s Law. When Vegard’s Law is not obeyed, these methods can be suitably adjusted. Some of these methods can be extremely precise, permitting a determination of relative composition to 1 part in 10⁹.