Microstructures and properties of high-entropy alloys

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

First-principles band theory, properly augmented by topological considerations, has provided a remarkably successful framework for predicting new classes of topological materials. This Colloquium discusses the underpinnings of the topological band theory and its materials applications.

Colloquium : Topological band theory

Since the discovery of superconductivity above 30 K by Bednorz and M\"uller in the La copper oxide system, the critical temperature has been raised to 90 K in Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ and to 110 and 125 K in Bi-based and Tl-based copper oxides, respectively. In the two years since this Nobel-prize-winning discovery, a large number of electronic structure calculations have been carried out as a first step in understanding the electronic properties of these materials. In this paper these calculations (mostly of the density-functional type) are gathered and reviewed, and their results are compared with the relevant experimental data. The picture that emerges is one in which the important electronic states are dominated by the copper $d$ and oxygen $p$ orbitals, with strong hybridization between them. Photon, electron, and positron spectroscopies provide important information about the electronic states, and comparison with electronic structure calculations indicates that, while many features can be interpreted in terms of existing calculations, self-energy corrections ("correlations") are important for a more detailed understanding. The antiferromagnetism that occurs in some regions of the phase diagram poses a particularly challenging problem for any detailed theory. The study of structural stability, lattice dynamics, and electron-phonon coupling in the copper oxides is also discussed. Finally, a brief review is given of the attempts so far to identify interaction constants appropriate for a model Hamiltonian treatment of many-body interactions in these materials.

Electronic structure of the high-temperature oxide superconductors

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

Complete Solution of the Korringa-Kohn-Rostoker Coherent-Potential-Approximation Equations: Cu-Ni Alloys

The authors considered the coherent potential approximation (CPA) for a substitutionally disordered alloy crystal potential which is of the nonoverlapping muffin-tin form. The authors simplified the KKR-CPA theory using the atomic sphere approximation (ASA) of Andersen (1975). In its new form the fundamental equations of the theory can be solved numerically. The computational effort is not particularly large on the scale of modern bandstructure calculations. As an illustration of the authors' method they calculated the Bloch spectral functions and the partially averaged local density of states for a number of alloy potentials designed to represent paramagnetic CucNi1-c alloys. Where comparison is possible the authors found good agreement with previous calculations. Their results are also consistent with various experimental data.

https://iopscience.iop.org/article/10.1088/0305-4608/8/12/008/pdf

The atomic sphere approximation to the KKR-CPA: electronic structure of paramagnetic CucNi1-c alloys

Calculations of the L alpha soft X-ray emission spectra of Cu-Ni alloys using the muffin-tin form of the coherent potential approximation (KKR-CPA) are presented. The transition matrix elements are determined exactly within the KKR-CPA, and lifetime broadening is included. The results of new experiments on the L alpha spectra are also reported and combined with X-ray photoemission measurements of the core state binding energies, so that the relative positions of the Cu and Ni emission bands may be determined. Good agreement between theory and experiment is found, confirming the KKR-CPA description of the local densities of states in Cu-Ni alloys. Striking non rigid-band behaviour is observed. It is suggested that soft X-ray studies of the type the authors describe should be a useful probe of alloy potential functions.

Soft X-ray emission and the local densities of states in Cu-Ni alloys

The electronic structure of La2CuO4 and YBa2Cu3O7 has been evaluated within the local density approximation, using the LMTO-ASA method. The calculated lattice parameter for the La-based oxide is within 1% of the experimental value. Theoretical photoemission and inverse photoemission spectra (XPA and BIS) are presented. The spectra are dominated by the emission from the Cu sites and show a Cu d band strongly affected by the bonding with the O p levels.

http://iopscience.iop.org/article/10.1088/0305-4608/17/7/006/pdf

Electronic structure of La-Cu and Y-Ba-Cu oxides: ground-state properties and photoemission spectra

The authors used the atomic sphere approximation (ASA) to implement the Korringa-Kohn-Rostoker-coherent potential approximation (KKR-CPA) program in order to investigate the electronic structure of AgcPd1-c alloys. In contrast with previous tight-binding calculations and in agreement with experiments the authors find that there is a split-off impurity band in the Pd-rich as well as the Ag-rich alloys. This reflects the fact that random hybridisation and random overlap played an important role in their calculation while they have been neglected in previous work. In addition to the averaged density of states and the specific heat they discuss the evolution of the individual bands and their lifetimes with changing concentration in terms of the Bloch spectral functions.

W M Temmerman

Papers

Complete Solution of the Korringa-Kohn-Rostoker Coherent-Potential-Approximation Equations: Cu-Ni Alloys

The atomic sphere approximation to the KKR-CPA: electronic structure of paramagnetic CucNi1-c alloys

Soft X-ray emission and the local densities of states in Cu-Ni alloys

Electronic structure of La-Cu and Y-Ba-Cu oxides: ground-state properties and photoemission spectra

On the electronic structure of AgcPd1-c alloys