Computation of Diffuse Intensities in Alloys

Diffuse intensities in alloys are measured by a variety of techniques, such as x ray, electron, and neutron scattering. Above a structural phase-transformation boundary, typically in the solid-solution phase where most materials processing takes place, the diffuse intensities yield valuable information regarding an alloy's tendency to order. This has been a mainstay characterization technique for binary alloys for over half a century. Although multicomponent metallic alloys are the most technologically important, they also pose a great experimental and theoretical challenge. For this reason, a vast majority of experimental and theoretical effort has been made on binary systems, and most investigated “ternary” systems are either limited to a small percentage of ternary solute (say, to investigate electron-per-atom effects) or they are pseudo-binary systems. Thus, for multicomponent alloys the questions are: how can you interpret diffuse scattering experiments on such systems and how does one theoretically predict the ordering behavior? This article discusses an electronic-based theoretical method for calculating the structural ordering in multicomponent alloys and understanding the electronic origin for this chemical-ordering behavior. This theory is based on the ideas of concentration waves using a modern electronic-structure method. Thus, examples show how the electronic origin behind the unusual ordering behavior in a few binary and ternary alloy systems that were not understood prior to the authors, work were determined. From the start, the theoretical approach is compared and contrasted to other complimentary techniques for completeness. In addition, some details are given about the theory and its underpinnings. Importantly, for the more general multicomponent case, in the context of concentration waves how to extract more information from diffuse-scattering experimental data is described. For binary or multicomponent alloys, the atomic short-range order (ASRO) in the disordered solid-solution phase is related to the thermally induced concentration fluctuations in the alloy. Such fluctuations in the chemical site occupations are the (infinitesimal) deviations from a homogeneously random state, and are directly related to the chemical pair correlations in the alloy. Thus, the ASRO provides valuable information on the atomic structure to which the disordered alloy is tending. Importantly, the ASRO can be determined experimentally from the diffuse scattering intensities measured in reciprocal space either by x rays, neutrons, or electrons. However, the underlying microscopic or electronic origin for the ASRO cannot be determined from such experiments, only their observed indirect effect on the order. Therefore, the calculation of diffuse intensities in high-temperature, disordered alloys based on electronic density-functional theory and the subsequent connection of those intensities to its microscopic origin(s) provides a fundamental understanding of the experimental data and phase instabilities. These are the principal themes that are emphasized in this article. Keywords: diffuse intensities; alloys; principles; data analysis; initial interpretation; multicomponent alloys; atomic short range order; DFT hamiltonian; polarization