Coherent Potential Approximation Calculations Research Articles

Physical properties of MnFeAl-based alloys affected by Mn content and annealing

The present study is devoted to the Mn2.4Fe0.8Al0.8 and Mn2FeAl alloys prepared by induction melting and studied in their original and subsequently annealed states. The annealing was carried out at 773 K/100 h and 1073 K/100 h in the argon atmosphere. The microstructure, phase composition, magnetic properties, and atom arrangement are followed with regard to Mn content and annealing conditions.The scanning electron microscopy completed by the energy dispersive X-ray spectroscopy and neutron activation analysis has detected single-phase alloys with compositions close to the nominal ones. Their structure, analyzed by X-ray diffraction, was found to be primitive cubic β-Mn with the lattice parameters of 0.6359(2) nm for Mn2.4Fe0.8Al0.8 and 0.6339(1) nm for Mn2FeAl. The coherent potential approximation calculations and positron annihilation spectroscopy have allowed obtaining an overview to the arrangement of Mn, Fe, and Al atoms in the β-Mn structure and formation of the open volume defects. It is shown that Mn atoms occupy predominantly 8c Wyckoff sites and remaining Mn, Fe and Al atoms occupy 12d sites in equal 1/3 proportion. The open volume defects, vacancies and vacancy clusters, occur in both alloys and both annealed states in a very low concentration. From the magnetic viewpoint, both alloys in the as-prepared state and after annealing at 773 K/100 h are paramagnetic at room temperature with transition to antiferromagnetic state at about 30-40 K. The ac susceptibility measurements have indicated spin glass nature of the Mn2FeAl alloys. The annealing at a higher temperature, 1073 K/100 h, has affected mainly Mn2.4Fe0.8Al0.8 alloy manifesting a weak ferro-/ferrimagnetic contribution at room temperature contributing to a strong magnetic ordering below 42 K.

Magnetic properties of CrFeCoNi based high entory alloy

Monte Carlo simulations are performed on three high entropy alloys: Cr0.25Fe0.25Co0.25Ni0.25, Cr0.2Fe0.2Co0.2Ni0.2Pd0.2, and Cr0.2Mn0.2Fe0.2Co0.2Ni0.2, with exchange interactions extracted from The ab initio Korringa-Kohn-Rostoker method combined with the coherent potential approximation calculations. Using finite size scaling analyses, we estimate the magnetic phase transition temperature for the four component alloy to be 108(2) K, and although the individual critical exponents are different from 3D Heisenberg universality class, the reduced exponent follows Suzuki weak universality. With the additional Palladium component, the transition temperature elevates to about 200 K. In contrast, we find no magnetic order for the five component alloy with Manganese at any finite temperatures.

Phonon dispersion of binary alloys with auxiliary coherent potential approximation

We report the auxiliary coherent potential approximation (ACPA) for calculating the phonon dispersion of three-dimensional alloys with both mass and force-constant disorders. To obtain the average spectra function of disordered alloys, the average coherent scattering structure factors are derived from the auxiliary coherent medium in single-site approximation. We provide an analytical proof of the sum rule in the auxiliary coherent medium, which ensures the analyticity of physical properties. To demonstrate the accuracy and applicability of the ACPA method, we apply the ACPA to calculate phonon dispersion of several alloys, including CuPd CuAu, PdFe, and NiPt with different disorder concentrations. We find the ACPA phonon dispersion results agree very well with the itinerant coherent potential approximation calculations and experimental measurements. The approximate separable force-constant model used in the ACPA can very well represent the first-principles disordered force constants, presenting minor or even negligible influence on the phonon dispersion of the alloy. The ACPA model features easy implementation and high computational efficiency, providing an effective method for simulating vibrational properties of realistic alloys.

Effect of proton uptake on the structure of energy levels in the band-gap of Sr-doped LaScO3: diffuse reflectance spectroscopy and coherent potential approximation calculations.

Features of the energy levels in the band-gap of La1-xSrxScO3-x/2 and the effect on those levels of proton uptake from H2 and H2O atmospheres were studied by diffuse reflectance spectroscopy and coherent potential approximation (CPA) calculations. It was shown that oxygen vacancies appearing due to acceptor doping with Sr form energy levels near the bottom of the conduction band that are strongly hybridized with the states of the nearest atoms. Excitation of electrons from the valence band to these vacancy levels gives rise to an additional absorption band which overlaps with the fundamental absorption edge. Proton incorporation from both H2 and H2O atmospheres leads to formation of proton levels below the valence band. However, during H2 uptake, electrons from hydrogen atoms occupy oxygen vacancy levels, and as a result additional absorption in the red-IR range appears due to electronic transitions from these levels to the conduction band. On the other hand, H2O uptake leads to the disappearance of oxygen vacancy levels. Experimental results obtained are similar to literature data on the optical absorption properties of some other proton-conducting perovskites, allowing the conclusion that findings from these CPA calculations on the nature of the energy levels could be extrapolated to some extent to those oxides.

Elastic constants of random solid solutions by SQS and CPA approaches: the case of fcc Ti-Al

Special quasi-random structure (SQS) and coherent potential approximation (CPA) are techniques widely employed in the first-principles calculations of random alloys. Here we scrutinize these approaches by focusing on the local lattice distortion (LLD) and the crystal symmetry effects. We compare the elastic parameters obtained from SQS and CPA calculations, taking the random face-centered cubic (fcc) Ti1−xAlx () alloy as an example of systems with components showing different electronic structures and bonding characteristics. For the CPA and SQS calculations, we employ the Exact Muffin-Tin Orbitals (EMTO) method and the pseudopotential method as implemented in the Vienna Ab initio Simulation Package (VASP), respectively. We show that the predicted trends of the VASP-SQS and EMTO-CPA parameters against composition are in good agreement with each other. The energy associated with the LLD increases with x up to and drops drastically thereafter. The influence of the LLD on the lattice constants and C12 elastic constant is negligible. C11 and C44 decrease after atomic relaxation for alloys with large LLD, however, the trends of C11 and C44 are not significantly affected. In general, the uncertainties in the elastic parameters associated with the symmetry lowering turn out to be superior to the differences between the two techniques including the effect of LLD.

Investigation of electronic structure and magnetic properties of CaCo1.86As2 within the CPA method

Recently in iron free arsenide compound CaCo2As2 a 7(1)% of vacancies on the Co sites was detected (Quirinale D G et al 2013 Phys. Rev. B 88 174420). Here we report the investigation of electronic structure and magnetic properties of CaCo1.86As2 within the coherent potential approximation (CPA). First, the CPA calculations are performed on the base of the local spin density approximation. Second, the possible role of Coulomb correlations is checked within the CPA scheme developed recently for strongly correlated systems. Then the spin–orbit coupling, which could be essential for Co, is also taken into account within the CPA calculation. The A type antiferromagnetic ground state and the value of magnetic moment obtained within the CPA approximation are in good agreement with experiment.

Effects of off-stoichiometry on the spin polarization at the Co2MnβGe0.38/MgO interfaces: X-ray magnetic circular dichroism study

We have studied the electronic and magnetic states of Mn and Co atoms at the Co${}_{2}$Mn${}_{\ensuremath{\beta}}$Ge${}_{0}.38$ (CMG)/MgO ($\ensuremath{\beta}=0.67$--1.8) interfaces, which constitute CMG/MgO/CMG magnetic tunnel junctions, by means of x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroisms (XMCDs) at the Mn and Co ${L}_{2},3$ edges and compared the deduced Co and Mn magnetic moments by the density-functional calculations with the coherent potential approximation (CPA). As the Mn content $\ensuremath{\beta}$ increased, the intensity of Mn ${L}_{2},3$ XMCD decreased, in agreement with the result of the CPA calculation, which showed the resultant reduction of charges and spin moment on Mn atoms because of the delocalization of Mn 3$d$ electrons with increasing $\ensuremath{\beta}$. The Co spin magnetic moment for all the samples increased with decreasing $\ensuremath{\beta}$, again consistent with the present calculation and the previous density-functional calculation by Picozzi et al. that the Co${}_{\mathrm{Mn}}$ antisite has a larger magnetic moment than that of Co atoms at the regular sites and reduces the spin polarization at the Fermi level and hence the tunnel magnetoresistance ratio.

Hard x-ray photoemission study of near-Heusler FexSi1−xalloys

The structural and electronic properties of epitaxial and amorphous Fe${}_{x}$Si${}_{1\ensuremath{-}x}$ alloys with $x$ $=$ 0.72 and 0.67 near the binary Heusler composition of $x$ $=$ 0.75 were determined using hard x-ray photoelectron spectroscopy (HXPS). By performing the measurements at a photon energy of 5950.3 eV, the bulk-sensitivity of the measurement is enhanced by a factor of 4--7 compared to conventional soft x-ray photoelectron spectroscopy at about 1000 keV. HXPS probes, on average, as far as 76 \AA{} into the Fe${}_{x}$Si${}_{1\ensuremath{-}x}$ samples. Via core-level spectra, it is found in the amorphous alloy that, in spite of the disordered structure that could lead to a broad distribution of chemical environments, the Si environment is mostly unique. Valence-band spectra reveal a clear distinction between the contributions of the two inequivalent Fe sites of the most highly ordered ($x$ $=$ 0.72, $D$0${}_{3}$) epitaxial sample. The valence-band spectra are compared to results of fully relativistic coherent potential approximation calculations performed in the framework of the one-step model of photoemission, which reveal details of the atomic-orbital makeup of various features, and generally exhibit good agreement with experiment.

Effect of magnetic disorder and strong electron correlations on the thermodynamics of CrN

We use first-principles calculations to study the effect of magnetic disorder and electron correlations on the structural and thermodynamic properties of CrN. We illustrate the usability of a special quasirandom structure supercell treatment of the magnetic disorder by comparing with coherent potential approximation calculations and with a complementary magnetic sampling method. The need of a treatment of electron correlations effects beyond the local density approximation is proven by a comparison of LDA+U calculations of structural and electronic properties with experimental results. When magnetic disorder and strong electron correlations are taken into account simultaneously, pressure and temperature induced structural and magnetic transitions in CrN can be understood.

The electronic structure and spin polarization of Fe3−xMnxSi and Fe3−yMnSiy alloys

First principle calculations using supercell approach and coherent potential approximation (CPA) are performed to investigate the electronic and magnetic structures of Fe3−xMnxSi and Fe3−yMnSiy alloys, where x,y=0, 0.25, 0.50, 0.75, 1.00, 1.25, 1.5, 1.75, and 2.25. Using supercell calculations we obtained a metallic behavior for x=0, 0.25, and 0.5 in Fe3−xMnxSi alloys with spin polarizations of 24%, 39%, and 93%, respectively. The behavior starts to be half-metallic at x=0.75 with a small direct band gap that increases for higher concentrations of Mn. Among the half-metallic systems, only those of L21 structure at x=1 and 2 possess indirect band gaps along Γ-X symmetry line. The change of Si concentration in Fe3−yMnSiy structures retrieve the metallic behavior for all concentrations except y=1.25 that shows a half-metallic behavior with a direct band gap of 0.27 eV. We obtained a good agreement between supercell and CPA calculations for the values of the magnetic moment and the trends of the formation energies, which reveals the validity of the supercell approach in predicting the magnetic structure and the energetics of doped Heusler alloys.

Thermoelectric Properties and Electronic Structure of Bi- and Ag-Doped Mg2Si1−x Ge x Compounds

Mg2Si1−xGex compounds were prepared from pure elements by melting in tantalum crucibles. The reaction was conducted under an inert gas in a special laboratory setup. Samples for thermoelectric measurements were formed by hot pressing. Structure and phase composition of the obtained materials were investigated by x-ray diffraction (XRD). Morphology and chemical composition were examined by scanning electron microscopy (SEM) and energy-dispersive x-ray spectroscopy (EDS), respectively. Thermoelectric properties, i.e., the Seebeck coefficient, the electrical conductivity, and the thermal conductivity, were measured in the temperature range of 500 K to 900 K. The effect of Bi and Ag doping on the thermoelectric performance of Mg-Si-Ge ternary compounds was investigated. The electronic structures of binary compounds were calculated using the Korringa–Kohn–Rostoker (KKR) method. The effects of disorder, including Ge substitution and Bi or Ag doping, were accounted for in the KKR method with coherent potential approximation calculations. The thermoelectric properties of doped Mg2Si1−xGex are discussed with reference to computed density of states as well as the complex energy band structure.

A need for high-resolution Compton scattering study of hcp metals with the use of synchrotron radiation

Compton profiles of hexagonal structure metals (Mg, Zn and Cd) were measured using high energy (662keV – 137Cs isotope gamma source) and medium resolution (0.4a.u.) Compton spectrometer in the Institute of Experimental Physics, University of Bialystok. The experimental data were compared with corresponding first principles Korringa–Kohn–Rostoker coherent potential approximation calculations (KKR-CPA).Small anisotropy of Compton profiles measured in all three metals makes the observation of fermiological features extremely difficult. We show that to achieve this goal, high-resolution experimental data are essential. Judging from the recently obtained results for a much easier case of cubic Ni75Cu25 and Ni75Co25 alloys, one needs the resolution to be below about 0.15a.u. Such an experiment can be carried out at the synchrotron radiation source only with the energy above 40keV.

Nonlocal coherent potential approximation for the paramagnetic state of the degenerate double-exchange model

The coherent potential approximation (CPA) is applied to the problem of off-diagonal disorder caused by random spin orientations in the paramagnetic (PM) state of the double-exchange (DE) model. The CPA calculations are supplemented by the variational mean-field approach for the Curie temperature ${(T}_{C}).$ Our formulation of CPA is essentially nonlocal and based on the perturbation theory expansion for the T matrix with respect to fluctuations of interatomic hopping parameters near the ``mean values'' specified by matrix elements of the self-energy for the effective medium, so that in the first order it becomes equivalent to the DE theory by de Gennes. The second-order effects, considered in the present work, are not negligible and lead to substantial reduction of ${T}_{C}$ in the one-orbital case. Even more dramatic changes are expected for the degenerate DE model, where each site of the cubic lattice is represented by two ${e}_{g}$ orbitals, which also specify the form of interatomic hoppings. Particularly, the existence of two Van Hove singularities in the spectrum of the degenerate model lead to the branching of CPA solutions, when Green's function and the self-energy become multivalued functions in certain regions of the complex plane. Different solutions can be classified by some nonlocal parameter of interatomic orbital polarization ${\mathcal{O}}_{\mathrm{NL}},$ and the multivalued behavior itself has many similarities with the phenomenon of metamagnetism with respect to ${\mathcal{O}}_{\mathrm{NL}}.$ This changes the traditional concept of the DE physics dramatically. Particularly, we predict the transition to the two-phase state (with different values of the order parameter ${\mathcal{O}}_{\mathrm{NL}})$ in the PM region below a certain temperature ${T}_{P}.$ It is followed by two consecutive magnetic transitions, which go separately in two different phases. Our scenario naturally explains the phase coexistence and the appearance of several magnetic transition points, which are frequently observed in perovskite manganites.

Impurity-semiconductor band hybridization effects on the critical temperature of diluted magnetic semiconductors

We have studied the critical temperature of Diluted Magnetic Semiconductors by means of Monte Carlo simulations and Coherent-Potential-Approximation (CPA) calculations. In our model for this syste m, the magnetic ions couple with the carriers through an antiferromagnetic exchange interaction, $J$, and an electrostatic interaction $W$. The effective impurity potential $J-W$ controls the hybridization between the magnetic impurities and the hole charge on the dopants. We find that the critical temperature depends substantially on the hole charge on the magnetic impurities. The CPA critical temperature is always lower than the obtained in the Monte Carlo simulations, although all trends in the simulation results are reproduced in the CPA calculations. Finally we predict the existence of pockets of phase segregation instability close to the carriers band edges.

Fermi surface incommensurate nestings and phase equilibria in Cu-Pd alloys

The Cu-Pd phase diagram shows two low-temperature ordered phases corresponding to $B2$ and ${L1}_{2}$ superlattices or, regardless of the site occupation, to bcc and fcc geometrical arrangements. We show how the phase equilibria between these intermetallic compounds can be understood by introducing a hypothetical bcc random-alloy phase and a three-step transformation from $B2$ to random bcc to random fcc to ${L1}_{2}.$ The two order-disorder transformations, $B2$ to random bcc and random fcc to ${L1}_{2},$ analyzed in the framework of the concentration wave-functional theory, appear to be ruled by the sizes of the relevant Fermi surface (FS) nesting vectors in the two random-alloy systems. The transformation between the bcc and fcc solid solution phase is studied by first-principles Korringa-Kohn-Rostoker and coherent-potential approximation calculations, and it is shown to be influenced by electronic topological transitions occurring in the same systems. Our analysis points out the preeminent role played by the lattice-incommensurate FS nesting vectors that in both the random-alloy systems, give rise to frustrated concentration waves. The location of the $B2\ensuremath{-}{L1}_{2}$ coexistence at $T=0$ appears to be determined by the condition that the concentration waves of the fcc and bcc random alloys are equally frustrated.

Electrical conductivity of finite metallic systems: Disorder

The electrical conductivity of finite, three-dimensional clusters containing up to 201 atoms on an fcc lattice was calculated using a combination of density functional theory, multiple-scattering theory, and the Kubo-Greenwood equation. Isolated clusters and clusters embedded in a medium determined by the coherent-potential approximation (CPA) were investigated. Densities of states and electrical resistivities were calculated for various situations: varying numbers of configurations used for the configurational average, varying energies, different alloys, different cluster sizes, and, finally, two cluster types, namely, spherical and rectangular clusters. Cluster calculations were compared to CPA calculations based on the same alloys. From this comparison a criterion was derived when a representation of an infinite medium by finite clusters is expected to yield good results for the conductivity.

NMR probe of pseudogap characteristics inFe2+xV1−xAl

We report the results of a ${}^{51}\mathrm{V}$ nuclear magnetic resonance (NMR) study of ${\mathrm{Fe}}_{2+x}{\mathrm{V}}_{1\ensuremath{-}x}\mathrm{Al},$ near the ordered composition with $x=0,$ at temperatures between 4 and 500 K. All compositions are found to be metallic or semimetallic, though electrical resistivity has indicated a metal-insulator transition at $x=0.$ The low-temperature NMR relaxation rates for stoichiometric $(x=0)$ and nonstoichiometric $(x=0.10$ and $\ensuremath{-}0.05)$ compounds follow a Korringa law, associated with a finite density of carriers at the Fermi level. High-temperature relaxation rates for $x<~0$ go over to a semiconductorlike activated form, providing information about the gap structure near the Fermi energy. The results are consistent with pseudogap features identified by recent band-structure calculations, although with smaller energy splittings. We analyze pseudogap changes vs composition, and compare the band-filling behavior to a recent coherent potential approximation calculation.

Hole distribution andTcsuppression inY1−xPrxBa2Cu3O7

A model Hamiltonian, which includes the components of the ${\mathrm{CuO}}_{2}$ planes, ${\mathrm{CuO}}_{3}$ chains, and the Pr-O hybridization, is considered to describe the electronic structure of ${\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{Pr}}_{x}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}.$ We make the coherent-potential approximation calculation for the Hamiltonian to present the variation of the distribution of the holes against the Pr concentration. The results show that the hole transfer is mainly from the $\mathrm{pd}\ensuremath{\sigma}$ band to the $p\ensuremath{-}f$ hybridization band, and a small reduction of the holes residing on the ${\mathrm{CuO}}_{3}$ chains is caused by the Pr doping. A metal-nonmetal transition around $x=0.5$ can be obtained according to our calculation. We present a quantitative interpretation for the ${T}_{c}$ suppression in terms of the combination of hole-transfer and magnetic scattering effects. Moreover, the enhancement of the magnetic pair breaking due to the presence of a normal-state pseudogap is also considered. Consequently, we give a satisfactory explanation of ${T}_{c}$ suppression for the whole Pr-doping region.

Raman scattering on α-Sn: Dependence on isotopic composition

The frequencies, widths, and shapes of the one-phonon Raman spectra of isotopically enriched and highly isotopically disordered $\ensuremath{\alpha}$-Sn samples have been measured. The isotopically enriched samples show a frequency inversely proportional to the square root of the mass, in agreement with the harmonic approximation, and a linewidth inversely proportional to the mass, in agreement with perturbative calculations of anharmonic effects (Fermi's golden rule). The disordered samples show a higher Raman frequency and broader linewidth than expected from their average masses. We attribute the additional shift and broadening to disorder effects and show that it agrees well with calculations based on the coherent potential approximation (CPA). The Raman lines of the disordered samples displayed a shoulder on the low-energy side that is reproduced by a spectral function based on the CPA calculations.

Planar fault energies and sessile dislocation configurations in substitutionally disordered Ti-Al with Nb and Cr ternary additions

Abstract Variations in planar fault energies, generated by changes in alloy composition, can influence thermally activated processes which govern plasticity in intermetallic alloys. Predicting variations in defect energy as a function of alloy composition would aid both alloy design and the interrogation of models of yield stress. In this paper, layered Korringa-Kohn-Rostoker coherent potential approximation calculations are reported for the superlattice intrinsic stacking fault (SISF) and antiphase-boundary (APB) energies in binary and ternary Ti-Al alloys. The planar fault energies were calculated over a range of alloy composition: (Ti1−xAlx)1−y My with 0·48 ≤ × ≤ 0·51, 0·00 ≤ y ≤ 0·02 and M = Cr, NB. For the Ti-rich alloys, ternary additions up to 4at.% were also considered. APB (010) energies were calculated for the binary alloy while the SISF and APB (111) energies were calculated for all the binary and ternary alloys. The compositions Ti50Al50 and (Ti50Al50)1−yCry have the maximum defect energies for this range of alloy compositions. Cr additions appear to have little influence on the defect energies of the Ti-rich alloys, while slightly reducing the APB (111) in the Al-rich alloys. The defect energies for the Nb alloys are reduced relative to the binary alloys, with the fault energies increasing monotonically with increasing Al concentration. The variation in defect energies, both trends and magnitude, are used with anisotropic elasticity theory to estimate the forces needed to produce two possible 〈101]{111} superdislocation glide barriers. Also, the anisotropic elastic energy of the nonplanar equilibrium superdislocations are compared. The formation of 〈101] {111} superdislocations with portions on cross-slip octahedral planes is favoured over cross-slip onto the cube plane for conservative estimates of the planar fault energies and applied stress. These results suggest that alloy designers can expect only moderate improvements in the high-temperature yield stress, because of the formation of 〈101] {111} superdislocation barriers, with changes in alloy composition.