Exact Muffin-tin Orbitals Method Research Articles

Ab initioinvestigation of the elastic properties of Ni3Fe

Ab initio alloy theory, formulated within the exact muffin-tin orbitals method in combination with the coherent-potential approximation, is used to determine the elastic properties of Ni-Fe alloys with Fe:Ni ratio 1:3. The interplay between magnetic and chemical effects is investigated by computing the lattice parameters and the single-and polycrystal elastic moduli for different partially ordered structures in the ferro-and paramagnetic states. It is found that the influence of long-range chemical order on the bulk properties strongly depends on the magnetic state. The largest magnetic-order-induced changes are obtained for the chemically ordered L1(2) phase. The ferromagnetic L1(2) system possesses similar to 5.4% larger elastic Debye temperature than the paramagnetic L1(2) phase, which in turn has a similar Theta(D) as the chemically disordered face-centered cubic phase in either the ferro-or paramagnetic state. It is concluded that magnetic ordering has a substantially larger impact on the bulk parameters of Ni3Fe than chemical ordering. The calculated trends are explained based on the electronic structure of nonmagnetic, ferromagnetic, and paramagnetic ordered and disordered phases.

Modeling of Steels and Steel Surfaces Using Quantum Mechanical First Principles Methods

We describe recent progress in first principles materials modelling applied to iron alloys. First principles methods in general have proven to be an effective way of describing atomic level phenomena in solids. When applied to alloys with chemical disorder, however, the widely used supercell methods turn out to be impractical due to the vast variety of different possible configurations. This problem can be overcome using the coherent potential approximation (CPA), which enables the description of a multicomponent alloy in terms of an effective medium constructed in such a way that it represents, on the average, the scattering properties of the alloy. A bulk alloy, in the case of substitutional random alloys, can thus be described with a single atom while a slab is needed to describe surfaces. The exact muffin-tin orbitals (EMTO) method provides a first principles method that can be combined with the CPA in order to describe steels and other multicomponent alloys. We describe the EMTO-CPA method and provide examples of both bulk and surface properties that can be modelled with this method.

Ideal strength of random alloys from first principles

The all-electron exact muffin-tin orbitals method in combination with the coherent-potential appproximation has been employed to investigate the ideal tensile strengths of elemental V, Mo solids and V- and Mo-based random solid solutions. The present ideal tensile strengths, calculated assuming isotropic Poisson contraction, are 16.1, 26.7 and 37.6 GPa for bcc V in the [001], [111] and [110] directions, respectively, and 26.7 GPa for bcc Mo in the [001] direction, which are all in good agreement with the available theoretical data. When a few percent Tc is introduced in Mo, it is found that the ideal strength decreases in the [001] direction. For the V-based alloys, Cr increases and Ti decreases the ideal tensile strength in all principal directions. Adding the same concentration of Cr and Ti to V leads to ternary alloys with similar ideal strength values as that of pure V. The alloying effects on the ideal strength is explained using the electronic band structure.

Surface parameters of ferritic iron-rich Fe–Cr alloy

Using first-principles density functional theory in the implementation of the exact muffin-tin orbitals method and the coherent potential approximation, we studied the surface energy and the surface stress of the thermodynamically most stable surface facet (100) of the homogeneous disordered body-centred cubic iron–chromium system in the concentration interval up to 20 at.% Cr. For the low-index surface facets of Fe and Cr, the surface energy of Cr is slightly larger than that of Fe, while the surface stress of Cr is considerably smaller than that of Fe. We find that Cr addition to Fe generally increases the surface energy of the Fe–Cr alloy; however, an increase of the bulk amount of Cr also increases the surface stress. As a result of this unexpected trend, the (100) surface of Fe–Cr becomes more stable against reconstruction with increasing Cr concentration. We show that the observed trends are of magnetic origin. In addition to the homogeneous alloy case, we also investigated the impact of surface segregation on both surface parameters.

Magnetic properties and temperature-dependent half-metallicity of Co2Mn(Ga1−xZx) (Z=Si, Ge, Sn) from first-principles calculation

Using the first-principles exact muffin-tin orbitals method in combination with the coherent potential approximation, we investigated the magnetic properties, exchange interactions, and temperature-dependent half-metallicity of the Co2Mn(Ga1−xZx) (Z=Si, Ge, Sn) alloys. The total magnetic moment follows perfectly a previously proposed Slater–Pauling relation, i.e., μ0 = Nt − 24, with Nt being the number of valence electrons. The Co–Mn and Co1–Co2 (inter-sublattice) interactions are dominated by direct exchange, whereas the Co1–Co1 (intra-sublattice) interaction is characterized by superexchange. The Mn–Mn exchange interaction in Co2MnGa is of long-ranged RKKY-type. However, the Mn–Mn exchange interactions in Co2MnZ are relatively localized and can be attributed to superexchange. The Co–Mn, Co1–Co2 and Co1–Co1 total exchange interactions increase with x, whereas the Mn–Mn total exchange interactions show convex behavior. The calculated Curie temperature (TC) increases with x. The ability of Z to enhance TC follows the sequence of Si > Ge > Sn, in agreement with the experimental findings. The temperature dependence of the spin polarization at the Fermi level [P(T)] is investigated based on the disordered local moment model. P(T) drops abruptly at temperatures much lower than TC. At temperatures higher than 200 K, the composition with higher TC generally corresponds to larger P(T).

Effect of Nb on the Properties of Ti-Nb Random Alloys from First-Principles

The effect of Nb on the equilibrium lattice parameters and relative stability between β and ω phases of Ti1-xNbx (0 < x 0.4) random alloys as well as their mechanical properties in body-centered-cubic crystallographic phase was investigated using the exact muffin-tin orbitals method in combination with the coherent potential approximation. It has been found that the calculated lattice parameters of the β phase agree well with the experimental data. For ω phase, the value of a increases almost linearly with increasing Nb concentration, while the opposite situation presented for c/a. Both Nb addition and increasing temperature enhanced the stability of β phase relative to ω phase. The critical Nb concentration for the complete stabilization of β phase at 300 K, 673 K and 1273 K was 22 at.%, 17 at.% and 9 at.%, respectively. The polycrystalline bulk modulus B, Youngs modulus E and shear modulus G increased monotonously with Nb addition and reducing the Nb concentration below 30 at.% resulted in lower E compared to that of Ti-6Al-4V. The calculated G/B values demonstrate that the bcc Ti1-xNbx (0 < x 0.4) random alloys should be intrinsically ductile.

Ab initioinvestigation of high-entropy alloys of 3delements

Single-phase high-entropy alloys are investigated using the exact muffin-tin orbitals (EMTO) method in combination with the coherent potential approximation (CPA). Choosing the paramagnetic face-centered-cubic NiCoFeCr alloy as an example, we compare the CPA results with those obtained using the supercell (SC) method. For the equilibrium Wigner-Seitz radius and elastic properties, the single-site mean-field approximation turns out to yield consistent results with the SC approach. Next, we employ the EMTO-CPA method to study the bulk properties of CuNiCoFeCrTi${}_{x}$ ($x=0.0--0.5,1.0$) and NiCoFeCrTi high-entropy alloys. A detailed comparison between the theoretical results and the available experimental data demonstrates that ab initio theory can properly describe the fundamental properties of this important class of engineering alloys. Theory predicts NiCoFeCr and CuNiCoFeCr to be more isotropic and less ductile than the Ti-containing single-phase alloys (CuNiCoFeCrTi${}_{x}$ with $x\ensuremath{\gtrsim}0.4$ and NiCoFeCrTi).

Lattice parameters and relative stability of α″ phase in binary titanium alloys from first-principles calculations

The crystallographic structure and stability of the α″ phase relative to the α and β phases in Ti–x M (M=Ta, Nb, V, Mo) alloys are investigated by using the first-principles exact muffin-tin orbital method in combination with the coherent potential approximation. We show that, with increasing concentration of the alloying elements, the structure of the orthorhombic-α″ phase evolutes from the hcp-α to the bcc-β phase, i.e., the lattice parameters b/a and c/a as well as the basal shuffle y decreases from those corresponding to the α phase to those of the β phase. The compositional α/α″ and α″/β phase boundaries are determined by comparing the total energies of the phases. The predicted α/α″ phase boundaries are about 10.2, 10.5, 11.5, 4.5at% for Ti–V, Ti–Nb, Ti–Ta, and Ti–Mo, respectively, in reasonable agreement with experiments. The α″/β phase boundaries are higher than the experimental values, possibly due to the absence of temperature effect in the first-principles calculations. Analyzing the electronic density of states, we propose that the stability of the α″ phase is controlled by the compromise between the strength of the covalent and metallic bonds.

The effect of long-range order on the elastic properties of Cu3Au

Ab initio calculations, based on the exact muffin-tin orbitals method are used to determine the elastic properties of Cu–Au alloys with Au/Cu ratio 1/3. The compositional disorder is treated within the coherent potential approximation. The lattice parameters and single-crystal elastic constants are calculated for different partially ordered structures ranging from the fully ordered L12 to the random face centered cubic lattice. It is shown that the theoretical elastic constants follow a clear trend with the degree of chemical order: namely, C11 and C12 decrease, whereas C44 remains nearly constant with increasing disorder. The present results are in line with the experimental findings that the impact of the chemical ordering on the fundamental elastic parameters is close to the resolution of the available experimental and theoretical tools.

Effect of Re content on elastic properties of B2 NiAl from ab initio calculations

Abstract The effect of substitutional alloying of Re on elastic properties of B2 NiAl has been studied using first-principles electronic-structure calculations by the exact muffin-tin orbitals method and the coherent potential approximation. Our calculations have shown that elastic constants C 12 , C 44 and bulk modulus B of (Ni 1− x Re x )Al alloys increase with Re composition almost linearly, but concentration dependence of elastic constants C 11 , Young modulus E , shear modulus G , G / B ratio and the Cauchy pressure P C is strongly nonmonotonously and has peculiarities near the concentration x = 30 at.% Re. Analyzing the density of states and Fermi surface sections we have a direct connection between the behavior of the elastic constants of (Ni 1− x Re x )Al alloys and changes in the interatomic bonding and Fermi surface topology.

Influence of Ni on the lattice stability of Fe-Ni alloys at multimegabar pressures

The lattice stability trends of the primary candidate for Earths core material, the Fe-Ni alloy, were examined from first principles. We employed the exact muffin-tin orbital method (EMTO) combined ...

One-particle spectral function and analytic continuation for many-body implementation in the exact muffin-tin orbitals method

We investigate one of the most common analytic continuation techniques in condensed matter physics, namely the Pad\'{e} approximant. Aspects concerning its implementation in the exact muffin-tin orbitals (EMTO) method are scrutinized with special regard towards making it stable and free of artificial defects. The electronic structure calculations are performed for solid hydrogen, and the performance of the analytical continuation is assessed by monitoring the density of states constructed directly and via the Pad\'{e} approximation. We discuss the difference between the \textbf{k}-integrated and \textbf{k}-resolved analytical continuations, as well as describing the use of random numbers and pole residues to analyze the approximant. It is found that the analytic properties of the approximant can be controlled by appropriate modifications, making it a robust and reliable tool for electronic structure calculations. At the end, we propose a route to perform analytical continuation for the EMTO + dynamical mean field theory (DMFT) method.

First-principles based thermodynamic model of phase equilibria in bcc Fe-Cr alloys

The complete and accurate thermodynamic and kinetic description of any systemis crucialfor understanding and predicting its properties. A particular interest is in systemsthat are used for some practical applications and have to be constantly improved usingmodification of their composition and structure. This task can be quite accuratelysolved at a fundamental level by density functional theory methods. Thesemethods areapplied to two practically important systems Fe-Cr and TiC-ZrC.The elastic properties of pure iron and substitutionally disordered Fe-Cr alloy are investigatedas a function of temperature and concentration using first-principles electronicstructurecalculations by the exact muffin-tin orbitals method. The temperature effectson the elastic properties are included via the electronic, magnetic, and lattice expansioncontributions. It is shown that the degree of magnetic order in both pure iron andFe90Cr10 alloy mainly determines the dramatic change of the elastic anisotropy of thesematerials at elevated temperatures. A peculiarity in the concentration dependence ofthe elastic constants in Fe-rich alloys is demonstrated and related to a change in theFermi surface topology.A thermodynamic model for the magnetic alloys is developed from first principles andapplied to the calculation of bcc Fe-Cr phase diagram. Various contributions to the freeenergy (magnetic, electronic, and phonon) are estimated and included in the model. Inparticular, it is found that magnetic short range order effects are important just abovethe Curie temperature. The model is applied for calculating phase equilibria in disorderedbcc Fe-Cr alloys. Model calculations reproduce a feature known as a Nishizawahorn for the Fe-rich high-temperature part of the phase diagram.The investigation of the TiC-ZrC system includes a detailed study of the defect formationenergies and migration barriers of point defects and defect complexes involvedin the diffusion process. It is found, using ab initio atomistic simulations of vacancymediateddiffusion processes in TiC and ZrC, that a special self-diffusion mechanism isoperative for metal atom diffusion in sub-stoichiometric carbides. It involves a noveltype of a stable point defect, a metal vacancy ”dressed” in a shell of carbon vacancies.It is shown that this vacancy cluster is strongly bound and can propagate through thelattice without dissociating.

Phase stability of Ni2(Mn1−xFex)Ga: A first-principles study

Ni${}_{2}$(Mn${}_{1\ensuremath{-}x}$Fe${}_{x}$)Ga ferromagnetic shape memory alloy shows unusual composition-dependent martensitic transformation temperature (${T}_{\mathrm{M}}$), namely, ${T}_{\mathrm{M}}$ decreases with increasing $e/a$ ratio. In hope of understanding this unusual behavior, we investigated the composition dependence of the heat of formation (${H}_{\mathrm{f}}$) and shear elastic modulus (${C}^{\ensuremath{'}}$) of the cubic austenite as well as the stability of the five-layer modulated (5M) tetragonal martensite relative to the austenite, using first-principles exact muffin-tin orbital method in combination with coherent potential approximation. Our calculations demonstrated that ${H}_{\mathrm{f}}$ of the austenite increases with the Fe content $x$. ${C}^{\ensuremath{'}}$ increases slightly with $x$ up to 0.05 but decreases thereafter. The composition dependence of both ${H}_{\mathrm{f}}$ and ${C}^{\ensuremath{'}}$ cannot fully account for the trend of ${T}_{\mathrm{M}}$ against $x$ although such correlations have been proposed in literature for other Ni-Mn-Ga based alloys. The structure of 5M martensite phase of Ni${}_{2}$(Mn${}_{1\ensuremath{-}x}$Fe${}_{x}$)Ga with $0<x<0.2$ is determined by optimizing both the shear (changing $c/a$) and wavelike shuffle of atoms in (110) planes along [1$\overline{1}$0] direction adopting the experimentally determined modulation function. The energy difference $\ensuremath{\Delta}{E}_{\mathrm{AM}}$ between the austenite and 5M phases decreases with increasing $x$ up to 0.05, following the lower $\ensuremath{\Delta}{E}_{\mathrm{AM}}$ corresponding to lower ${T}_{\mathrm{M}}$ rule. However, with $x$ larger than 0.05, $\ensuremath{\Delta}{E}_{\mathrm{AM}}$ increases, against the experimental ${T}_{\mathrm{M}}\ensuremath{\sim}x$ behavior. We propose that, if taking the temperature effect and the spin-orbital coupling into account, the $\ensuremath{\Delta}{E}_{\mathrm{AM}}\ensuremath{\sim}x$ curve might be altered and may explain the unusual composition dependence of Ni${}_{2}$(Mn${}_{1\ensuremath{-}x}$Fe${}_{x}$)Ga.

Elastic properties of vanadium-based alloys from first-principles theory

The effect of Cr and Ti on the fundamental mechanical properties of V-Cr-Ti alloys has been investigated using the all-electron exact muffin-tin orbitals method in combination with the coherent-potential approximation. The static lattice constant and elastic parameters have been calculated for the body-centered-cubic V${}_{1\ensuremath{-}x\ensuremath{-}y}$Cr${}_{x}$Ti${}_{y}$ (0 \ensuremath{\le} x,y \ensuremath{\le} 0.1) random solid solution as a function of composition. Our theoretical predictions are in good agreement with the available experimental data. Alloys along the equicomposition region are found to exhibit the largest shear and Young's modulus as a result of the opposite alloying effects obtained for the two cubic shear elastic constants. The classical solid-solution hardening (SSH) model predicts larger strengthening effect in V${}_{1\ensuremath{-}y}$Ti${}_{y}$ than in V${}_{1\ensuremath{-}x}$Cr${}_{x}$. By considering a phenomenological expression for the ductile-brittle transition temperature (DBTT) in terms of Peierls stress and SSH, it is shown that the present theoretical results can account for the variations of DBTT with composition.

Site preference and effect of alloying on elastic properties of ternaryB2 NiAl-based alloys

Using the exact muffin-tin orbitals method in conjunction with the coherent potential approximation, we study the site preference of transition metal impurities X (X = Sc, Ti, V, Cr, W, Re, Co) in ...

Self-consistent supercell approach to alloys with local environment effects

We present an efficient and accurate method for calculating electronic structure and related properties of random alloys with a proper treatment of local environment effects. The method is a generalization of the locally self-consistent Green's function (LSGF) technique for the exact muffin-tin orbital (EMTO) method. An alloy system in the calculations is represented by a supercell with a certain set of atomic distribution correlation functions. The Green's function for each atom in the supercell is obtained by embedding the cluster of neighboring atoms lying within a local interaction zone (LIZ) into an effective medium and solving the cluster Dyson equation exactly. The key ingredients of the method are locality, which makes it linearly scaling with the number of atoms in the supercell, and coherent-potential self-consistency of the effective medium, which results in a fast convergence of the electronic structure with respect to the LIZ size. To test the performance and accuracy of the method, we apply it to two systems: Fe-rich bcc-FeCr random alloy with and without a short-range order, and a Cr-impurity on the Fe surface. Both cases demonstrate the importance of taking into account the local environment effects for correct description of magnetic and bulk properties.

Elastic parameters of paramagnetic iron-based alloys from first-principles calculations

The elastic properties of paramagnetic (PM) ${\mathrm{Fe}}_{1\ensuremath{-}x}{M}_{x}$ ($M$ = Al, Si, V, Cr, Mn, Co, Ni, and Rh; 0 \ensuremath{\le} $x$ \ensuremath{\le} 0.1) solid solutions in the body-centered-cubic (bcc) and face-centered-cubic (fcc) structures are investigated using the exact muffin-tin orbital density functional method in combination with the coherent-potential approximation and disordered local-magnetic-moment model. All impurities considered here enlarge or leave nearly constant the equilibrium volume of PM Fe but at the same time produce both positive and negative changes in the elastic parameters. Some of the alloying elements induce opposite effects on shear elastic parameters ${C}^{\ensuremath{'}}$ and ${C}_{44}$ of PM bcc and fcc Fe, which is discussed. With a few exceptions, we find that the alloying effects on PM bcc Fe are smaller than on PM fcc Fe. The trends in the tetragonal elastic constant ${C}^{\ensuremath{'}}$ show a general correlation with the trends obtained for the bcc-fcc lattice energy difference.

Tetragonality of carbon-doped ferromagnetic iron alloys: A first-principles study

Using density-functional theory in combination with the exact muffin-tin orbital (EMTO) method and coherent potential approximation, we investigate the alloying effect on the tetragonality of Fe-C solid solution forming the basis of steels. In order to assess the accuracy of our approach, first we perform a detailed study of the performance of the EMTO method for the Fe${}_{16}$C${}_{1}$ binary system by comparing the EMTO results to those obtained using the projector augmented wave method. In the second step, we introduce different substitutional alloying elements (Al, Cr, Co, Ni) into the Fe matrix and study their impact on the structural parameters. We demonstrate that a small amount of Al, Co, and Ni enhances the tetragonal lattice ratio of Fe${}_{16}$C${}_{1}$ whereas Cr leaves the ratio almost unchanged. The obtained trends are correlated with the single-crystal elastic parameters calculated for carbon-free alloys.

Theoretical prediction of the elastic properties of body-centered cubic Fe-Ni-Mg alloys under extreme conditions

Using density functional theory formulated within the framework of the exact muffin-tin orbital method, we investigate the elastic properties of the body-centered cubic Fe0.85Ni0.1Mg0.05 alloy in the conditions at the Earth's inner core. We demonstrate that in this system, the chemical stabilization effect of Mg is significantly larger than that of Ni. We show that the elastic properties of Fe0.85Ni0.1Mg0.05 are in good agreement with those of the Earth's inner core, as given by seismic observations. We find that the excellent mechanical properties of Fe0.85Ni0.1Mg0.05 are primarily due to Mg.