Phase equilibria in alloys to a great extent are governed by the ordering behavior of alloy species. One of the important goals of alloy theory is therefore to be able to simulate these kinds of phenomena on the basis of first principles. Unfortunately, it is impossible, even with present day total energy software, to calculate entirely from first principles the changes in the internal energy caused by changes of the atomic configurations in systems with several thousand atoms at the rate required by statistical thermodynamics simulations. The time-honored solution to this problem that we shall review in this paper is to obtain the configurational energy needed in the simulations from an Ising-type Hamiltonian with so-called effective cluster interactions associated with specific changes in the local atomic configuration. Finding accurate and reliable effective cluster interactions, which take into consideration all relevant thermal excitations, on the basis of first-principles methods is a formidable task. However, it pays off by opening new exciting perspectives and possibilities for materials science as well as for physics itself. In this paper we outline the basic principles and methods for calculating effective cluster interactions in metallic alloys. Special attention is paid to the source of errors in different computational schemes. We briefly review first-principles methods concentrating on approximations used in density functional theory calculations, Green's function method and methods for random alloys based on the coherent potential approximation. We formulate criteria for the validity of the supercell approach in the calculations of properties of random alloys. The generalized perturbation method, which is an effective and accurate tool for obtaining cluster interactions, is described in more detail. Concentrating mostly on the methodological side we give only a few examples of applications to the real systems. In particular, we show that the ground state structure of Au3Pd alloys should be a complex long-period superstructure, which is neither DO22 nor DO23 as has been recently predicted.

http://iopscience.iop.org/article/10.1088/0034-4885/71/4/046501/pdf

Configurational thermodynamics of alloys from first principles : effective cluster interactions

Using density-functional theory calculations combined with recent local-energy and local-stress schemes, we studied the effects of Si segregation on the structural, mechanical and magnetic properties of the Σ3(1 1 1) and Σ11(3 3 2) Fe GBs formed by rotation around the [1 1 0] axis. The segregation mechanism was analyzed by the local-energy decomposition of the segregation energy, where the segregation energy is expressed as a sum of the following four terms: the local-energy change of Si atoms from the isolated state in bulk Fe to the GB segregated state, the stabilization of replaced Fe atoms from the GB to the bulk, the local-energy change of neighboring Fe atoms from the pure GB to the segregated GB and the local-energy change of neighboring Fe atoms from the system of an isolated Si atom in the bulk Fe to the pure bulk Fe. The segregation energy and value of each term greatly depends on the segregation site and Si concentration. The segregation at interface Fe sites with higher local energies in the original GB configurations naturally leads to higher segregation-energy gains, while interface sites with lower local energies can lead to larger energy gains if stronger Si-Fe interactions occur locally in the final segregated configurations. The high Si concentration reduces the segregation-energy gain per Si atom due to the local-energy increases of Si atoms neighboring to each other or through the reduction in the number of stabilized Fe atoms per Si atom as observed in a Si dimer in bulk Fe. In the Si-segregated GBs, Si-Fe bonds enhance local Young's moduli and tend to suppress the interface weakening, while the GB adhesion is slightly reduced. And Fe atoms contacting Si atoms have reduced magnetic moments, due to Si-Fe sp-d hybridization interactions.

http://iopscience.iop.org/article/10.1088/0953-8984/26/35/355005/pdf

Si segregation at Fe grain boundaries analyzed by ab initio local energy and local stress

Gadolinium is a nearly ideal soft-magnetic material. However, one cannot take advantage of its properties at temperatures higher than the room temperature where Gd loses the ferromagnetic ordering. By using high-purity bulk samples with grains ~200 nm in size, we present proof-of-concept measurements of an increased Curie point (TC) and spontaneous magnetization in Gd due to hydrogenation. From first-principles we explain increase of TC in pure Gd due to the addition of hydrogen. We show that the interplay of the characteristic features in the electronic structure of the conduction band at the Fermi level in the high-temperature paramagnetic phase of Gd and “negative” pressure exerted by hydrogen are responsible for the observed effect.

Magnetic ordering temperature of nanocrystalline Gd: enhancement of magnetic interactions via hydrogenation-induced "negative" pressure.

The cohesive properties of Ni-Sn intermetallics (stable, metastable, and virtual), hitherto unexplored by density-functional theory (DFT) methods, are reported. Specifically, the total energies and cohesive properties of Ni, Sn, and 27 Ni-Sn intermetallics are calculated from first-principles, using ultrasoft pseudopotentials (USPP) and both local-density approximation (LDA) and generalized-gradient approximation (GGA) for the exchange-correlation functional. Among the intermetallics considered, the ground-state structures are consistent with experimental observations; however, not all of them are registered in the equilibrium-phase diagram. An important result of this systematic study, using both USPP-LDA and USPP-GGA, is that oC20-NiSn4 is predicted to be the ground-state structure. Only recently, this phase has been observed as a product of the interfacial reaction in Ni/Sn diffusion couples. In addition, we find that the thermodynamic stability of a tetragonal phase, tP10-NiSn4, is very similar to that of oC20-NiSn4. The elastic stability of both tP10-NiSn4 and oC20-NiSn4 is confirmed by calculating their single-crystal elastic constants. The calorimetric data for the enthalpy of formation of stable intermetallics show an agreement that is better for those calculated with USPP-LDA than those calculated with USPP-GGA. In general, the experimental lattice parameters of stable and metastable phases are found to lie between those calculated using USPP-LDA and those calculated using USPP-GGA; however, in several cases, the values calculated using USPP-GGA agree to within 1 pct of the experimental data. The Ni3Sn2(ht) ⇌ Ni3Sn2(lt) transformation is discussed in terms of supergroup-subgroup relations. The bonding between the Ni and the Sn is discussed based on the analyses of the density of states (DOS) and the charge densities.

https://link.springer.com/content/pdf/10.1007%2Fs11661-008-9682-3.pdf

First-Principles Calculation of Phase Stability and Cohesive Properties of Ni-Sn Intermetallics

The structural, electronic and magnetic properties of Fe100−xGax alloys are studied computationally in the composition range up to x≤ 31.25 at.% and experimentally about 27 at.%. Ga content. Using ...

Phase diagram of magnetostrictive Fe-Ga alloys: insights from theory and experiment

We calculate the electronic structure, magnetic moments, and ordering energies of highly magnetostrictive Fe1−xGax alloys from first-principles in the composition range up to x=0.25. The coherent potential approximation was used to treat effects of chemical disorder. Given an underlying bcc lattice in whole range compositions investigated, the DO3 type of ordering is found to have a lower energy than A2- and B2-type structures. We find that ordering energies strongly depend on the state of magnetic order such that thermal magnetic disorder strongly favors chemical ordering (DO3 and B2). The values of the magnetic moments of Fe on different sublattices of ordered structures are found to have a distinctive dependency on the Ga concentration. By taking into account the results of earlier fully relativistic and full potential calculations of magnetostriction for ordered stoichiometric Fe3Ga compounds and available experimental phenomenology, our results for disordered alloys suggest an eventually more complex...

Magnetism and structural ordering on a bcc lattice for highly magnetostrictive Fe-Ga alloys: A coherent potential approximation study

Using the first-principles calculations based on the coherent potential approximation, we study the electronic structure, magnetic moments and the bulk modulus of FeX alloys with IVB group elements (X = Si,Ge,Sn) in the Fe-rich concentration range (x = 0.0?0.25), which form a stability region of bcc-related phases. In agreement with experiment, our calculations reproduce well a peculiar non-monotonous behaviour of the bulk modulus in Fe?Si alloys with increasing Si concentration. Such a dependence is found for all bcc-related disordered and partially ordered Fe?Si phases A2, B2 and D03, which is in contrast with an earlier suggestion that the non-monotonous bulk modulus behaviour is related to partial ordering in Fe?Si. In addition, our results predict a similar behaviour in Fe?Ge and Fe?Sn alloys. It is shown that the observed behaviour of the bulk modulus is entirely related to the changes of the magnetic properties with chemical composition.

https://iopscience.iop.org/article/10.1088/0953-8984/18/29/009/pdf

Magnetism and origin of non-monotonous concentration dependence of the bulk modulus in Fe-rich alloys with Si, Ge and Sn: a first-principles study

We use the first-principles magnetic force theorem embodied in the Korringa‐ Kohn‐Rostoker method to calculate pair magnetic exchange interactions in pure hexagonal close packed (hcp) Gd metal in the ferromagnetic as well as in the paramagnetic state with disordered local 4f-moments. It is found that the exchange interactions between the localized 4f-moments, in particular also distant ones, depend on the state of magnetic disorder. Such a dependence is a consequence of the electronic structure changes of the conduction band that mediates the interaction between the local moments. The magnetic ordering temperature has been calculated using a Monte Carlo simulation technique and the results are compared with mean-field based studies.

https://iopscience.iop.org/article/10.1088/0953-8984/19/32/326218/pdf

Magnetic exchange interactions in the paramagnetic state of hcp Gd

Site-preferences and local spin-polarization of transition metal solute atoms in B2 type Ni–Al alloys

The strong dependence of the magnetic properties of the alloy VAu4 upon the degree of chemical order has been a subject of intense experimental studies and controversial theoretical interpretations. In the framework of density functional theory using the coherent potential approximation embodied in the Korringa-Kohn-Rostoker method, we perform first principles calculations of VAu4 varying the degree of atomic chemical order from a disordered fcc alloy to the fully ordered MoNi4-type structure. In contrast to the conventional point of view, partially also based on earlier first principles studies of the ordered structure, our results suggest a localized character of the vanadium moments rather than being weakly itinerant. Moreover, we find that in the fully ordered alloy an antiferromagnetic state is more stable than the ferromagnetic. This finding leads to a significant revision of the earlier descriptions of magnetism in VAu4, which were based either on itinerant or local moment pictures. Investigating fcc Au-V alloys richer in vanadium, we also study the role of local environment effects on the stabilization of the magnetic moments at the V atoms and advocate a ferrimagnetic character of the experimentally observed state with a small spontaneous magnetization.

T. Khmelevska

Papers

Magnetism and structural ordering on a bcc lattice for highly magnetostrictive Fe-Ga alloys: A coherent potential approximation study

Magnetism and origin of non-monotonous concentration dependence of the bulk modulus in Fe-rich alloys with Si, Ge and Sn: a first-principles study

Magnetic exchange interactions in the paramagnetic state of hcp Gd

Site-preferences and local spin-polarization of transition metal solute atoms in B2 type Ni–Al alloys

Dependence of magnetism of VAu4 alloy on the state of chemical order : A first principles study