The modern version of the KKR (Korringa–Kohn–Rostoker) method represents the electronic structure of a system directly and efficiently in terms of its single-particle Green's function (GF). This is in contrast to its original version and many other traditional wave-function-based all-electron band structure methods dealing with periodically ordered solids. Direct access to the GF results in several appealing features. In addition, a wide applicability of the method is achieved by employing multiple scattering theory. The basic ideas behind the resulting KKR-GF method are outlined and the different techniques to deal with the underlying multiple scattering problem are reviewed. Furthermore, various applications of the KKR-GF method are reviewed in some detail to demonstrate the remarkable flexibility of the approach. Special attention is devoted to the numerous developments of the KKR-GF method, that have been contributed in recent years by a number of work groups, in particular in the following fields: embedding schemes for atoms, clusters and surfaces, magnetic response functions and anisotropy, electronic and spin-dependent transport, dynamical mean field theory, various kinds of spectroscopies, as well as first-principles determination of model parameters.

https://iopscience.iop.org/article/10.1088/0034-4885/74/9/096501/pdf

Calculating condensed matter properties using the KKR-Green's function method—recent developments and applications

High-entropy alloys are a class of materials that contain five or more elements in near-equiatomic proportions1,2. Their unconventional compositions and chemical structures hold promise for achieving unprecedented combinations of mechanical properties3–8. Rational design of such alloys hinges on an understanding of the composition–structure–property relationships in a near-infinite compositional space9,10. Here we use atomic-resolution chemical mapping to reveal the element distribution of the widely studied face-centred cubic CrMnFeCoNi Cantor alloy2 and of a new face-centred cubic alloy, CrFeCoNiPd. In the Cantor alloy, the distribution of the five constituent elements is relatively random and uniform. By contrast, in the CrFeCoNiPd alloy, in which the palladium atoms have a markedly different atomic size and electronegativity from the other elements, the homogeneity decreases considerably; all five elements tend to show greater aggregation, with a wavelength of incipient concentration waves11,12 as small as 1 to 3 nanometres. The resulting nanoscale alternating tensile and compressive strain fields lead to considerable resistance to dislocation glide. In situ transmission electron microscopy during straining experiments reveals massive dislocation cross-slip from the early stage of plastic deformation, resulting in strong dislocation interactions between multiple slip systems. These deformation mechanisms in the CrFeCoNiPd alloy, which differ markedly from those in the Cantor alloy and other face-centred cubic high-entropy alloys, are promoted by pronounced fluctuations in composition and an increase in stacking-fault energy, leading to higher yield strength without compromising strain hardening and tensile ductility. Mapping atomic-scale element distributions opens opportunities for understanding chemical structures and thus providing a basis for tuning composition and atomic configurations to obtain outstanding mechanical properties. In high-entropy alloys, atomic-resolution chemical mapping shows that swapping some of the atoms for larger, more electronegative elements results in atomic-scale modulations that produce higher yield strength, excellent strain hardening and ductility.

Tuning element distribution, structure and properties by composition in high-entropy alloys.

On the basis of a spin-polarised density functional description of the electrons, the authors develop a 'mean-field' theory of magnetic phase transitions in metals. The one-electron-like finite-temperature Schrodinger equation is solved, formally, for random orientations of local moments and the corresponding grand potential is used in a statistical mechanics of the spin configurations. This latter, in the mean-field approximation, requires the knowledge of the electronic grand potential averaged over various ensembles of such 'spin' configurations. These averages are carried out with the help of the Korringa-Kohn-Rostoker coherent-potential-approximation (KKR CPA) method for dealing with electrons in random potential fields. Then, the whole procedure is made self-consistent on the average. The theory determines the local moment mu , the Curie temperature TC, and the susceptibility chi (q,T) in addition to the electronic structure at finite temperatures without adjustable parameters. The authors illustrate the explicit calculations for iron. The local moment is found to be 1.9 mu B above TC, and the preliminary estimate of Tc is 1250K.

https://iopscience.iop.org/article/10.1088/0305-4608/15/6/018/pdf

A first-principles theory of ferromagnetic phase transitions in metals

Publisher Summary This chapter presents the formalism and applications of cluster expansions to the problem of ab initio calculations of thermodynamic properties of crystalline alloys. The success of the method owes much to the parallel developments of statistical and quantum mechanical methods and, of course, to the availability of powerful computational hardware and software. The technique of orthogonal expansions in cluster functions has revolutionized the treatment of configurationally disordered systems. In addition to offering the most rational and general state-of-order description of alloys, cluster methods provide the rigorous and essential link between quantum and statistical mechanical aspects of first-principles thermodynamic calculations. Cluster functions constitute a complete orthonormal set. This basis set produces a rigorous cluster algebra that is used for systems containing an arbitrary degree of configurational order (or disorder). Cluster methods are, in principle, ideally suited for calculating alloy phase equilibria.

Cluster Approach to Order-Disorder Transformations in Alloys

The ANNNI model — Theoretical analysis and experimental application

On the basis of a new first-principles, electronic model for the forces driving clustering and short-range order in metallic alloys, it is argued that observed concentration-dependent peaks in the x-ray and electron diffuse scattering intensities are due to parallel sheets of flat Fermi surface. The positions of the peaks are directly related to the spanning vector k/sub 0/.

G. M. Stocks

Papers

Concentration waves and Fermi surfaces in random metallic alloys