The tight-binding method of modelling materials lies between the very accurate, very expensive, ab initio methods and the fast but limited empirical methods. When compared with ab initio methods, tight-binding is typically two to three orders of magnitude faster, but suffers from a reduction in transferability due to the approximations made; when compared with empirical methods, tight-binding is two to three orders of magnitude slower, but the quantum mechanical nature of bonding is retained, ensuring that the angular nature of bonding is correctly described far from equilibrium structures. Tight-binding is therefore useful for the large number of situations in which quantum mechanical effects are significant, but the system size makes ab initio calculations impractical. In this paper we review the theoretical basis of the tight-binding method, and the range of approaches used to exactly or approximately solve the tight-binding equations. We then consider a representative selection of the huge number of systems which have been studied using tight-binding, identifying the physical characteristics that favour a particular tight-binding method, with examples drawn from metallic, semiconducting and ionic systems. Looking beyond standard tight-binding methods we then review the work which has been done to improve the accuracy and transferability of tight-binding, and moving in the opposite direction we consider the relationship between tight-binding and empirical models.

https://iopscience.iop.org/article/10.1088/0034-4885/60/12/001/pdf

Tight-binding modelling of materials

We describe a method for performing density-functional calculations for topologically disordered condensed matter. This method combines the recursion and the linear-muffin-tin-orbital (LMTO) methods, and uses the tight-binding representation. In the present version, the LMTO matrix elements are evaluated in the atomic-sphere approximation (ASA). Various levels of approximation for the ASA Hamiltonian, such as the two-center tight-binding one, are systematically derived and tested. The method is applied to crystalline bcc Fe and to amorphous ${\mathrm{Fe}}_{80}$${\mathrm{B}}_{20}$. Charge self-consistency is only treated for the average Fe and the average B atoms. The Fe-B bonding is found to be covalent. A Stoner theory is derived and used to describe the ferromagnetism. The structures of our density of states for ferromagnetic ${\mathrm{Fe}}_{80}$${\mathrm{B}}_{20}$ agree in detail with reliable photoemission data.

Electronic-structure calculations for amorphous solids using the recursion method and linear muffin-tin orbitals: Application to Fe80B20.

Publisher Summary The term “invar” stands for alloys showing minimum thermal expansion coefficients (maximum spontaneous volume magnetostriction) in certain ranges of composition and temperatures. Invar effect originates from investigations by Ch.E. Guillaume who found that ferromagnetic fcc FeNi alloys at concentrations around Fe 65 Ni 35 show almost constant thermal expansion as a function of temperature in a wide range around room temperature. According to his results, the linear thermal expansion coefficient α = (1/ l )/(d l /d T ) of Fe 65 Ni 35 Invar at 300 K is about 1.2 × 10 -6 K -1 , thus an order of magnitude smaller than in the pure components Fe and Ni and even smaller than in a Pt–10% Ir alloy, the material used for the prototype meter. The chapter summarizes the magnetic phase diagrams of the most important binary and ternary alloy systems showing moment–volume instabilities in general and Invar or Elinvar behavior in special composition ranges. Besides the magnetic-transition temperatures, Curie temperatures T C for ferromagnetic (FM) transitions, Neel temperatures T N for antiferromagnetic (AF) transitions, and T f for spin glass (SG) or re-entrant spin glass (RSG) like transitions, the diagrams contain information about the structural phases occurring in the systems.

Chapter 3 Invar: Moment-volume instabilities in transition metals and alloys

Overall features of magnetism in amorphous transition metals have been investigated on the basis of a finite-temperature theory of the local-environment effect. It is shown that the simple ferromagnetism of Fe, Co, and Ni is drastically changed by structural disorder; amorphous transition metals form spin glasses (SG's) for compositions near amorphous Fe (6.7\ensuremath{\lesssim}N\ensuremath{\lesssim}7.35), ferromagnets for compositions near amorphous Co (7.35\ensuremath{\lesssim}N\ensuremath{\lesssim}9.0), and paramagnetisms for compositions near amorphous Ni (9.0\ensuremath{\lesssim}N\ensuremath{\lesssim}10.0) where N is the number of d electrons. The SG is accompanied by formation of local ferromagnetic clusters for N\ensuremath{\gtrsim}7.2, and shows reentrant behavior at the ferromagnetic boundary N\ensuremath{\approxeq}7.35. The ferromagnetism in amorphous transition metals is shown to be well explained by the main-peak position in the noninteracting densities of states. It is found that structural disorder enhances the Curie temperatures (${\mathit{T}}_{\mathit{C}}$) in the range 7.9\ensuremath{\lesssim}N\ensuremath{\lesssim}8.5 as compared with bcc and fcc structures. These results explain recent experimental data for the SG in Fe-rich amorphous alloys and the high ${\mathit{T}}_{\mathit{C}}$ in amorphous Co-Y alloys, but they are quite different from the early picture obtained for amorphous transition-metal--metalloid alloys.

Magnetism in amorphous transition metals.

A recently developed tight-binding-bond approach for the calculation of interatomic forces in disordered materials is extended to amorphous transition-metal--metalloid alloys. It is shown that the interaction of the transition-metal d electrons with the metalloid p electrons leads to strong covalent bonding forces that are reflected in a pronounced nonadditivity of the pair interactions. The structure of the amorphous alloys is modeled by a simulated molecular-dynamics quench. Results for Fe-B, Ni-B, Fe-P, and Ni-P glasses are in good agreement with diffraction experiments. It is shown that the covalent bonding forces lead to a chemical and topological order similar to that postulated in stereochemically defined models based on the packing of trigonal prismatic units. The molecular-dynamics simulations also predict a medium-range order (concentration fluctuations on a scale of 15--20 \AA{}) in agreement with the existing small-angle scattering data.

Structural modeling of transition-metal–metalloid glasses by use of tight-binding-bond forces

Itenerant magnetic properties of amorphous metallic systems: Numerical studies of the Fe-B alloys

Itinerant magnetic properties of amorphous metallic systems II: Magnetic moment distribution in the Fe-B alloys and the magnetism of amorphous Fe

Electronic properties of glassy metals, including transport properties, are studied by numerical calculations for realistic structural models. For the Fe1-xBx and Cu1−Zrx system results are presented for total and partial densities of states and the electrical resistivities. For Cu0.65Zr0.35 also the Hall constant is calculated. The results agree with recent experiments. The projections of the densities of states on the B-p-bands give the possibility to distinguish between different structural models with similar radial distribution function.



Fur realistische Strukturmodelle metallischer Glaser werden elektronische Eigenschaften und elektronische Transporteigenschaften numerisch berechnet. Fur Fe1−xBx werden Ergebnisse fur die totalen und partiellen Zustandsdichten und die Widerstande vorgestellt. Fur Cu0.65Zr0.35 wird erstmals die Hallkonstante numerisch berechnet. Alle Ergebnisse stimmen gut mit Experimenten uberein. Die Projektionen der Zustandsdichten auf die B-p-Bander gestatten es, zwischen verschiedenen Strukturmodellen zu unterscheiden, die ahnliche radiale Verteilungsfunktionen besitzen.

Electronic properties of glassy metals

Calcul, a l'aide de l'approximation des liaisons fortes autocoherente, des proprietes magnetiques de Fe 1−x B x et Fe 1−x Zr x Hg

https://hal.archives-ouvertes.fr/jpa-00228812/document

ITINERANT MAGNETISM OF AMORPHOUS Fe-BASED ALLOYS

Electronic properties of glassy metallic alloys

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