Anisotropic lattice distortions in random alloys from first-principles theory

High-Throughput Screening of All-d-Metal Heusler Alloys for Magnetocaloric Applications

Due to their versatile composition and customizable properties, A2BC Heusler alloys have found applications in magnetic refrigeration, magnetic shape memory effects, permanent magnets, and spintronic devices. The discovery of all-d-metal Heusler alloys with improved mechanical properties compared to those containing main group elements presents an opportunity to engineer Heusler alloys for energy-related applications. Using high-throughput density-functional theory calculations, we screened magnetic all-d-metal Heusler compounds and identified 686 (meta)stable compounds. Our detailed analysis revealed that the inverse Heusler structure is preferred when the electronegativity difference between the A and B/C atoms is small, contrary to conventional Heusler alloys. Additionally, our calculations of Pugh ratios and Cauchy pressures demonstrated that ductile and metallic bonding are widespread in all-d-metal Heuslers, supporting their enhanced mechanical behavior. We identified 49 compounds with a double-well energy surface based on Bain path calculations and magnetic ground states, indicating their potential as candidates for magnetocaloric and shape memory applications. Furthermore, by calculating the free energies, we propose that 11 compounds exhibit structural phase transitions and suggest isostructural substitutions to enhance the magnetocaloric effect.

Design of Laves phase-reinforced compositionally complex alloy

Topologically close-packed (TCP) phases such as Laves phases are usually considered to harm the mechanical properties of classical superalloys for high-temperature applications. However, if an optimal fraction and size are designed, this situation can completely change for some compositionally complex alloys (CCA). Based on existing studies on austenitic or ferritic steels, we propose in this paper a design strategy aimed at exploiting the role of the Laves phase in defining the mechanical properties of wrought CCAs at elevated temperatures. We demonstrate its efficiency by applying it to the design and production of a new Laves phase-reinforced CCA and present the results of their experimental and theoretical investigation. The results show that a new Laves phase-reinforced CCA can have fine-grained microstructures, lower density, and superior mechanical strength at elevated temperatures while maintaining workability. These new alloys show promising properties compared to existing CCA wrought alloys and actual Ni-based superalloys.

Anderson transition in stoichiometric Fe2VAl: high thermoelectric performance from impurity bands

Discovered more than 200 years ago in 1821, thermoelectricity is nowadays of global interest as it enables direct interconversion of thermal and electrical energy via the Seebeck/Peltier effect. In their seminal work, Mahan and Sofo mathematically derived the conditions for ’the best thermoelectric’—a delta-distribution-shaped electronic transport function, where charge carriers contribute to transport only in an infinitely narrow energy interval. So far, however, only approximations to this concept were expected to exist in nature. Here, we propose the Anderson transition in a narrow impurity band as a physical realisation of this seemingly unrealisable scenario. An innovative approach of continuous disorder tuning allows us to drive the Anderson transition within a single sample: variable amounts of antisite defects are introduced in a controlled fashion by thermal quenching from high temperatures. Consequently, we obtain a significant enhancement and dramatic change of the thermoelectric properties from p-type to n-type in stoichiometric Fe₂VAl, which we assign to a narrow region of delocalised electrons in the energy spectrum near the Fermi energy. Based on our electronic transport and magnetisation experiments, supported by Monte-Carlo and density functional theory calculations, we present a novel strategy to enhance the performance of thermoelectric materials.

The mathematical conditions for the best thermoelectric is well known but never realised in real materials. Here, the authors propose the Anderson transition in a narrow impurity band as a physical realisation of this seemingly unrealisable scenario.

Thermodynamics and Magnetism of SmFe12 Compound Doped with Co and Ni: An Ab Initio Study

Ni-doped Sm(Fe1−xCox)12 alloys are investigated for their magnetic properties. The Sm(Fe,Co)11M1 compound (M acts as a stabilizer) with the smallest (7.7 at.%) rare-earth-metal content has been recognized as a possible contender for highly efficient permanent magnets thanks to its significant anisotropy field and Curie temperature. The early transition metals (Ti-Mn) as well as Al, Si, and Ga stabilize the SmFe12 compound but significantly decrease its saturation magnetization. To keep the saturation magnetization in the range of 1.4–1.6 T, we suggest replacing a certain amount of Fe and Co in the Sm(Fe1−xCox)12 alloys with Ni. Ni plays the role of a thermodynamic stabilizer, and contrary to the above-listed elements, has the spin moment aligned parallel to the spin moment of the SmFe12 compound, thereby boosting its saturation magnetization without affecting the anisotropy field or Curie temperature.

Using first-principles calculations to predict the mechanical properties of transmuting tungsten under first wall fusion power-plant conditions

Tungsten and tungsten alloys are being considered as leading candidates for structural and functional materials in future fusion energy devices. The most attractive properties of tungsten for the design of magnetic and inertial fusion energy reactors are its high melting point, high thermal conductivity, low sputtering yield and low long-term disposal radioactive footprint. Yet, despite these relevant features, tungsten also presents a very low fracture toughness, mostly associated with inter-granular failure and bulk plasticity, that limits its applications. Significant neutron-induced transmutation happens in these tungsten components during nuclear fusion reactions, creating transmutant elements including Re, Os and Ta. Density functional theory (DFT) calculations that allow the calculation of defect and solute energetics are critical to better understand the behavior and evolution of tungsten-based materials in a fusion energy environment. In this study, we present a novel computational approach to perform DFT calculations on transmuting materials. In particular, we predict elastic and plastic mechanical properties (such as bulk modulus, shear modulus, ductility parameter, etc) on a variety of W-X compositions that result when pure tungsten is exposed to the EU-DEMO fusion first wall conditions for ten years.

Alloying effect on the order-disorder transformation in tetragonal FeNi

Tetragonal ([Formula: see text]) FeNi is a promising material for high-performance rare-earth-free permanent magnets. Pure tetragonal FeNi is very difficult to synthesize due to its low chemical order-disorder transition temperature ([Formula: see text] K), and thus one must consider alternative non-equilibrium processing routes and alloy design strategies that make the formation of tetragonal FeNi feasible. In this paper, we investigate by density functional theory as implemented in the exact muffin-tin orbitals method whether alloying FeNi with a suitable element can have a positive impact on the phase formation and ordering properties while largely maintaining its attractive intrinsic magnetic properties. We find that small amount of non-magnetic (Al and Ti) or magnetic (Cr and Co) elements increase the order-disorder transition temperature. Adding Mo to the Co-doped system further enhances the ordering temperature while the Curie temperature is decreased only by a few degrees. Our results show that alloying is a viable route to stabilizing the ordered tetragonal phase of FeNi.

Tests on the Accuracy and Scalability of the Full-Potential DFT Method Based on Multiple Scattering Theory

We investigate a reduced scaling full-potential DFT method based on the multiple scattering theory (MST) code MuST, which is released online (https://github.com/mstsuite/MuST) very recently. First, we test the accuracy by calculating structural properties of typical body-centered cubic (BCC) metals (V, Nb, and Mo). It is shown that the calculated lattice parameters, bulk moduli, and elastic constants agree with those obtained from the VASP, WIEN2k, EMTO, and Elk codes. Second, we test the locally self-consistent multiple scattering (LSMS) mode, which achieves reduced scaling by neglecting the multiple scattering processes beyond a cut-off radius. In the case of Nb, the accuracy of 0.5 mRy/atom can be achieved with a cut-off radius of 20 Bohr, even when small deformations are imposed on the lattice. Despite that the calculation of valence states based on MST exhibits linear scaling, the whole computational procedure has an overall scaling of about O(N1.6), due to the fact that the updating of Coulomb potential scales almost as O(N2). Nevertheless, it can be still expected that MuST would provide a reliable and accessible way to large-scale first-principles simulations of metals and alloys.

Strain localisation and failure at twin-boundary complexions in nickel-based superalloys

Twin boundaries (TBs) in Ni-based superalloys are vulnerable sites for failure in demanding environments, and a current lack of mechanistic understanding hampers the reliable lifetime prediction and performance optimisation of these alloys. Here we report the discovery of an unexpected γ″ precipitation mechanism at TBs that takes the responsibility for alloy failure in demanding environments. Using multiscale microstructural and mechanical characterisations (from millimetre down to atomic level) and DFT calculations, we demonstrate that abnormal γ″ precipitation along TBs accounts for the premature dislocation activities and pronounced strain localisation associated with TBs during mechanical loading, which serves as a precursor for crack initiation. We clarify the physical origin of the TBs-related cracking at the atomic level of γ″-strengthened Ni-based superalloys in a hydrogen containing environment, and provide practical methods to mitigate the adverse effect of TBs on the performance of these alloys.

Coherent twin boundaries in nickel-based superalloys are vulnerable sites for alloy failure in demanding environments. Here, the authors show that the abnormal γ″ precipitation mechanism at twin boundaries is responsible for pronounced strain localisation and subsequent failure.

Pressure effect on the order-disorder transformation in L10 FeNi

The ordered phase of the FeNi system is known for its promising magnetic properties that make it a first-class rare-earth free permanent magnet. Mapping out the parameter space controlling the order-disorder transformation is an important step towards finding growth conditions that stabilize the [Formula: see text] phase of FeNi. In this work, we study the magnetic properties and chemical order-disorder transformation in FeNi as a function of lattice expansion by utilizing ab initio alloy theory. The largest volume expansion considered here is 29% which corresponds to a pressure of [Formula: see text] GPa. The thermodynamic and magnetic calculations are formulated in terms of a long-range order parameter, which is subsequently used to find the ordering temperature as a function of pressure. We show that negative pressure promotes ordering, meaning that synthetic routes involving an increase of the volume of FeNi are expected to expand the stability field of the [Formula: see text] phase.

Thermodynamics and Magnetism of YCo5 Compound Doped with Fe and Ni: An Ab Initio Study

YCo5 permanent magnet exhibits high uniaxial magnetocrystalline anisotropy energy and has a high Curie temperature. These are good properties for a permanent magnet, but YCo5 has a low energy product, which is notably insufficient for a permanent magnet. In order to improve the energy product in YCo5, we suggest replacing cobalt with iron, which has a much bigger magnetic moment. With a combination of density-functional-theory calculations and thermodynamic CALculation of PHAse Diagrams (CALPHAD) modeling, we show that a new magnet, YFe3(Ni1-xCox)2, is thermodynamically stable and exhibits an improved energy product without significant detrimental effects on the magnetocrystalline anisotropy energy or the Curie temperature.

Unprecedented non-hysteretic superelasticity of [001]-oriented NiCoFeGa single crystals

Superelasticity associated with the martensitic transformation has found a broad range of engineering applications^1,2. However, the intrinsic hysteresis³ and temperature sensitivity⁴ of the first-order phase transformation significantly hinder the usage of smart metallic components in many critical areas. Here, we report a large superelasticity up to 15.2% strain in [001]-oriented NiCoFeGa single crystals, exhibiting non-hysteretic mechanical responses, a small temperature dependence and high-energy-storage capability and cyclic stability over a wide temperature and composition range. In situ synchrotron X-ray diffraction measurements show that the superelasticity is correlated with a stress-induced continuous variation of lattice parameter accompanied by structural fluctuation. Neutron diffraction and electron microscopy observations reveal an unprecedented microstructure consisting of atomic-level entanglement of ordered and disordered crystal structures, which can be manipulated to tune the superelasticity. The discovery of the large elasticity related to the entangled structure paves the way for exploiting elastic strain engineering and development of related functional materials.

Yield strength and misfit volumes of NiCoCr and implications for short-range-order

The face-centered cubic medium-entropy alloy NiCoCr has received considerable attention for its good mechanical properties, uncertain stacking fault energy, etc, some of which have been attributed to chemical short-range order (SRO). Here, we examine the yield strength and misfit volumes of NiCoCr to determine whether SRO has measurably influenced mechanical properties. Polycrystalline strengths show no systematic trend with different processing conditions. Measured misfit volumes in NiCoCr are consistent with those in random binaries. Yield strength prediction of a random NiCoCr alloy matches well with experiments. Finally, we show that standard spin-polarized density functional theory (DFT) calculations of misfit volumes are not accurate for NiCoCr. This implies that DFT may be inaccurate for other subtle structural quantities such as atom-atom bond distance so that caution is required in drawing conclusions about NiCoCr based on DFT. These findings all lead to the conclusion that, under typical processing conditions, SRO in NiCoCr is either negligible or has no systematic measurable effect on strength.

Phase Stability in U-6Nb Alloy Doped with Ti from the First Principles Theory

First-principles calculations within the density-functional-theory (DFT) approach are conducted in order to explore and explain the effect of small amounts of titanium on phase stability in the U-6Nb alloy. During rapid quenching from high to room temperature, metastable phases α′ (orthorhombic), α″ (monoclinic), and γ0 (tetragonal) can form, depending on Nb concentration. Important mechanical properties depend on the crystal structure and, therefore, an understanding of the effect of impurities on phase stability is essential. Insights on this issue are obtained from quantum-mechanical DFT calculations. The DFT framework does not rely on any material-specific assumptions and is therefore ideal for an unbiased investigation of the U-Nb system.

Development of a CALPHAD Thermodynamic Database for Pu-U-Fe-Ga Alloys

The interaction of actinides and actinide alloys such as the δ-stabilized Pu-Ga alloy with iron is of interest to understand the impurity effects on phase stability. A newly developed and self-consistent CALPHAD thermodynamic database is presented which covers the elements: Pu, U, Fe, Ga across their whole composition and temperature ranges. The phase diagram and thermodynamic properties of plutonium-iron (Pu-Fe) and uranium-iron (U-Fe) systems are successfully reassessed, with emphasis on the actinide rich side. Density functional theory (DFT) calculations are performed to validate the stability of the stoichiometric (Pu,U)6Fe and (Pu,U)Fe2 compounds by computing their formation enthalpies. These data are combined to construct the Pu-U-Fe ternary phase diagram. The thermodynamic assessment of Fe-Ga is presented for the first time and application to the quaternary Pu-U-Fe-Ga system is discussed.

Effects of Alloying Elements on the Stacking Fault Energies of Ni58Cr32Fe10 Alloys: A First-Principle Study

Ni58Cr32Fe10-based alloys, such as Alloy 690 and filler metal 52 (FM-52), suffer from ductility dip cracking (DDC). It is reported that decreasing the stacking fault energy (SFE) of these materials could improve the DDC resistance of Alloy 690. In this work, the effects of alloying elements on the stacking fault energies (SFEs) of Ni58Cr32Fe10 alloys were studied using first-principle calculations. In our simulations, 2 at.% of Ni is replaced by alloy element X (X=Al, Co, Cu, Hf, Mn, Nb, Ta, Ti, V, and W). At a finite temperature, the SFEs were divided into the magnetic entropy (SFEmag) and 0 K (SFE0) contributions. Potentially, the calculated results could be used in the design of high-performance Ni58Cr32Fe10-based alloys or filler materials.

Colossal Elastocaloric Effect in Ferroelastic Ni-Mn-Ti Alloys

Energy-efficient and environment-friendly elastocaloric refrigeration, which is a promising replacement of the conventional vapor-compression refrigeration, requires extraordinary elastocaloric properties. Hitherto the largest elastocaloric effect is obtained in small-size films and wires of the prototype NiTi system. Here, we report a colossal elastocaloric effect, well exceeding that of NiTi alloys, in a class of bulk polycrystalline NiMn-based materials designed with the criterion of simultaneously having large volume change across phase transition and good mechanical properties. The reversible adiabatic temperature change reaches a strikingly high value of 31.5 K and the isothermal entropy change is as large as 45  J kg^{-1} K^{-1}. The achievement of such a colossal elastocaloric effect in bulk polycrystalline materials should push a significant step forward towards large-scale elastocaloric refrigeration applications. Moreover, our design strategy may inspire the discovery of giant caloric effects in a broad range of ferroelastic materials.

Density Functional Theory description of the order-disorder transformation in Fe-Ni

The thermodynamic ordering transformation of tetragonal FeNi system is investigated by the Exact Muffin-Tin Orbitals (EMTO) method. The tetragonal distortion of the unit cell is taken into account and the free energy is calculated as a function of long-range order and includes the configurational, vibrational, electronic and magnetic contributions. We find that both configurational and vibrational effects are important and that the vibrational effect lowers the predicted transformation temperature by about 480 K compared to the value obtained merely from the configurational free energy. The predicted temperature is in excellent agreement with the experimental value when all contributions are taken into account. We also perform spin dynamics calculations for the magnetic transition temperature and find it to be in agreement with the experiments. The present research opens new opportunities for quantum-mechanical engineering of the chemical and magnetic ordering in tetrataenite.

Generalized stacking fault energy of carbon-alloyed paramagnetic [Formula: see text]-Fe

Generalized stacking fault energy (GSFE) is an important parameter for understanding the underlying physics governing the deformation mechanisms in face-centred cubic (fcc) materials. In the present work, we study the long-standing question regarding the influence of C on the GSFE in austenitic steels at paramagnetic state. We calculate the GSFE in both [Formula: see text]-Fe and Fe-C alloys using the exact muffin-tin orbitals method and the Vienna Ab initio Simulation Package. Our results show that the GSFE is increased by the presence of interstitial C, and the universal scaling law is used to verify the accuracy of the obtained stacking fault energies. The C-driven change of the GSFE is discussed considering the magnetic contributions. The effective energy barriers for stacking fault, twinning and slip formation are employed to disclose the C effect on the deformation modes, and we also demonstrate that the magnetic structures as a function of volume explain the effect of paramagnetism on the C-driven changes of the stacking fault energies as compared to the hypothetical non-magnetic case.

Space partitioning of exchange-correlation functionals with the projector augmented-wave method

We implement a Becke fuzzy cells type space partitioning scheme for the purposes of exchange-correlation within the GPAW projector augmented-wave method based density functional theory code. Space partitioning is needed in the situation where one needs to treat different parts of a combined system with different exchange-correlation functionals. For example, bulk and surface regions of a system could be treated with functionals that are specifically designed to capture the distinct physics of those regions. Here, we use the space partitioning scheme to implement the quasi-nonuniform exchange-correlation scheme, which is a useful practical approach for calculating metallic alloys on the generalized gradient approximation level. We also confirm the correctness of our implementation with a set of test calculations.

Elastic Properties of FeCr20Ni8Xn (X = Mo, Nb, Ta, Ti, V, W and Zr) Austenitic Stainless Steels: A First Principles Study

Austenitic stainless steels suffer from intergranular corrosion and stress corrosion cracking when exposed to elevated temperature (500–800 °C). Under these environments, Cr-carbides and Cr-carbontrides precipitate at the grain boundaries, which results in the formation of Cr-depleted zone. In practice, alloying elements could be added into austenitic stainless steels to modify the precipitation processes. Besides the precipitation processes, the elastic properties of the iron matrix would be influenced. Using the exact muffin-tin orbitals (EMTO) method, the solute effects on the elastic properties of FeCr20Ni8 austenitic stainless steels were studied. Based on the simulated shear modulus (G) and bulk modulus (B), we proposed a design map for FeCr20Ni8 based alloys, aiming to provide a basis for the design of high-performance austenitic stainless steels.

Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems

Great progress has been made in recent years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean-field theory and the Coherent Potential Approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Unlike the average effective medium-based methods mentioned above, typical medium-based methods properly capture the states localized by disorder. The typical medium dynamical cluster approximation not only provides the proper order parameter for Anderson localized states, but it can also incorporate the full complexity of Density-Functional Theory (DFT)-derived potentials into the analysis, including the effect of multiple bands, non-local disorder, and electron-electron interactions. After a brief historical review of other numerical methods for disordered systems, we discuss coarse-graining as a unifying principle for the development of translationally invariant quantum cluster methods. Together, the Coherent Potential Approximation, the Dynamical Mean-Field Theory and the Dynamical Cluster Approximation may be viewed as a single class of approximations with a much-needed small parameter of the inverse cluster size which may be used to control the approximation. We then present an overview of various recent applications of the typical medium dynamical cluster approximation to a variety of models and systems, including single and multiband Anderson model, and models with local and off-diagonal disorder. We then present the application of the method to realistic systems in the framework of the DFT and demonstrate that the resulting method can provide a systematic first-principles method validated by experiment and capable of making experimentally relevant predictions. We also discuss the application of the typical medium dynamical cluster approximation to systems with disorder and electron-electron interactions. Most significantly, we show that in the limits of strong disorder and weak interactions treated perturbatively, that the phenomena of 3D localization, including a mobility edge, remains intact. However, the metal-insulator transition is pushed to larger disorder values by the local interactions. We also study the limits of strong disorder and strong interactions capable of producing moment formation and screening, with a non-perturbative local approximation. Here, we find that the Anderson localization quantum phase transition is accompanied by a quantum-critical fan in the energy-disorder phase diagram.

Impact of Chemical Fluctuations on Stacking Fault Energies of CrCoNi and CrMnFeCoNi High Entropy Alloys from First Principles

Medium and high entropy alloys (MEAs and HEAs) based on 3d transition metals, such as face-centered cubic (fcc) CrCoNi and CrMnFeCoNi alloys, reveal remarkable mechanical properties. The stacking fault energy (SFE) is one of the key ingredients that controls the underlying deformation mechanism and hence the mechanical performance of materials. Previous experiments and simulations have therefore been devoted to determining the SFEs of various MEAs and HEAs. The impact of local chemical environment in the vicinity of the stacking faults is, however, still not fully understood. In this work, we investigate the impact of the compositional fluctuations in the vicinity of stacking faults for two prototype fcc MEAs and HEAs, namely CrCoNi and CrMnFeCoNi by employing first-principles calculations. Depending on the chemical composition close to the stacking fault, the intrinsic SFEs vary in the range of more than 150 mJ/m 2 for both the alloys, which indicates the presence of a strong driving force to promote particular types of chemical segregations towards the intrinsic stacking faults in MEAs and HEAs. Furthermore, the dependence of the intrinsic SFEs on local chemical fluctuations reveals a highly non-linear behavior, resulting in a non-trivial interplay of local chemical fluctuations and SFEs. This sheds new light on the importance of controlling chemical fluctuations via tuning, e.g., the annealing condition to obtain the desired mechanical properties for MEAs and HEAs.

Phase-transition assisted mechanical behavior of TiZrHfTax high-entropy alloys

Recent developments of high-entropy alloys with high strength and high ductility draw attention to the metastability-engineering strategy. Using first-principle theory, here we demonstrate that reducing the Ta level in the refractory TiZrHfTa_x system destabilizes the body-centered cubic (bcc) phase and leads to the appearance of the hexagonal close-packed (hcp) phase embedded in the bcc matrix. The alloying-induced features of the elastic parameters for the cubic and hexagonal structures are mapped out in details, and strong sensitivity to the crystal lattice and chemistry is revealed. Results show softening of the bcc matrix with decreasing Ta concentration which ensures ductile behavior. However, the elastically nearly isotropic hcp precipitates possess enhanced resistance against shear which promotes strengthening of the TiZrHfTa_x dual-phase system. The present atomic-level insight provides strong evidence to the experimental observation, and emphasizes the significance of quantum-design for advanced multi-phase high-entropy alloys with excellent strength-ductility combinations.

Quantum-mechanical analysis of effect of alloying elements on ε-martensite start temperature of steels

With regard to the transformation mechanism of austenitic high manganese steel, the prediction of the ε-martensite start temperature is a critical consideration in alloy design. Evaluation of the ε-martensite start temperature makes it possible to predict the microstructure and to understand the phase transformation occurring during deformation. Here we use the quantum mechanical calculation of random alloys to understand the physics for ε-martensitic transformation in steels. We could find the linear relationship between the measured ε-martensite start temperatures and the crystal structure stability for various compositions. We also could estimate the effect of several alloying elements. It is expected that the effect of decreasing the temperatures for the same amount of alloying elements addition will be larger moving farther from Group VIII. By creating a free-energy model that reflects the temperature effect, we were able to calculate the average driving force required for the ε-martensitic transformations.

Physical mechanism of δ-δ'-ε phase stability in plutonium

Based on first-principle calculations, we have systematically explored the nature of the elastic stability and the δ-δ′-ε phase transitions in pure Pu at high temperature. It is found that, both the electron-phonon coupling and the spin fluctuation effects tend to decrease the tetragonal elastic constant (C′) of δ-Pu, accounting for its anomalous softening at high temperature. The lattice thermal expansion together with the electron-phonon coupling can stiffen C′ of ε-Pu, promoting its mechanical stability at high temperature. The δ-ε transition is calculated to take place around 750–800 K, and is dominated by the phonon vibration. The δ′ intermediate phase is realized around 750 K mainly because of the thermal spin fluctuation.

First Principles Theory of the hcp-fcc Phase Transition in Cobalt

Identifying the forces that drive a phase transition is always challenging. The hcp-fcc phase transition that occurs in cobalt at ~700 K has not yet been fully understood, although early theoretical studies have suggested that magnetism plays a main role in the stabilization of the fcc phase at high temperatures. Here, we perform a first principles study of the free energies of these two phases, which we break into contributions arising from the vibration of the lattice, electronic and magnetic systems and volume expansion. Our analysis of the energy of the phases shows that magnetic effects alone cannot drive the fcc-hcp transition in Co and that the largest contribution to the stabilization of the fcc phase comes from the vibration of the ionic lattice. By including all the contributions to the free energy considered here we obtain a theoretical transition temperature of 825 K.

Stacking fault energy of face-centered cubic metals: thermodynamic and ab initio approaches

The formation energy of the interface between face-centered cubic (fcc) and hexagonal close packed (hcp) structures is a key parameter in determining the stacking fault energy (SFE) of fcc metals and alloys using thermodynamic calculations. It is often assumed that the contribution of the planar fault energy to the SFE has the same order of magnitude as the bulk part, and thus the lack of precise information about it can become the limiting factor in thermodynamic predictions. Here, we differentiate between the interfacial energy for the coherent fcc(1 1 1)/hcp(0 0 0 1) interface and the 'pseudo-interfacial energy' that enters the thermodynamic expression for the SFE. Using first-principles calculations, we determine the coherent and pseudo-interfacial energies for six elemental metals (Al, Ni, Cu, Ag, Pt, and Au) and three paramagnetic Fe-Cr-Ni alloys. Our results show that the two interfacial energies significantly differ from each other. We observe a strong chemistry dependence for both interfacial energies. The calculated pseudo-interfacial energies for the Fe-Cr-Ni steels agree well with the available literature data. We discuss the effects of strain on the description of planar faults via thermodynamic and ab initio approaches.

Exchange-Correlation Catastrophe in Cu-Au: A Challenge for Semilocal Density Functional Approximations

Semilocal density functional approximations occupy the second rung of the Jacob's ladder model and are thus expected to have certain limits to their applicability. A recent study [Y. Zhang, G. Kresse, and C. Wolverton, Phys. Rev. Lett. 112, 075502 (2014)] hypothesizes that the formation energy, being one of the key quantities in alloy theory, would be beyond the grasp of semilocal density functional theory (DFT). Here, we explore the physics of semilocal DFT formation energies and shed light on the connection between the accuracy of the formation energy and the ability of a semilocal approximation to produce accurate lattice constants. We demonstrate that semilocal functionals designed to perform well for alloy constituents can concomitantly solve the problem of alloy formation energies.

Ab initio calculations of mechanical properties of bcc W-Re-Os random alloys: effects of transmutation of W

To examine the effect of neutron transmutation on tungsten as the first wall material of fusion reactors, the elastic properties of W_1-x-y  Re _x  Os _y (0  ⩽  x, y  ⩽  6%) random alloys in body centered cubic (bcc) structure are investigated systematically using the all-electron exact muffin-tin orbitals (EMTO) method in combination with the coherent-potential approximation (CPA). The calculated lattice constant and elastic properties of pure W are consistent with available experiments. Both Os and Re additions reduce the lattice constant and increase the bulk modulus of W, with Os having the stronger effect. The polycrystalline shear modulus, Young's modulus and the Debye temperature increase (decrease) with the addition of Re (Os). Except for C ₁₁, the other elastic parameters including C ₁₂, C ₄₄, Cauchy pressure, Poisson ratio, B/G, increase as a function of Re and Os concentration. The variations of the latter three parameters and the trend in the ratio of cleavage energy to shear modulus for the most dominant slip system indicate that the ductility of the alloy enhances with increasing Re and Os content. The calculated elastic anisotropy of bcc W slightly increases with the concentration of both alloying elements. The estimated melting temperatures of the W-Re-Os alloy suggest that Re or Os addition will reduce the melting temperature of pure W solid. The classical Labusch-Nabarro model for solid-solution hardening predicts larger strengthening effects in W_1-y  Os _y than in W_1-x  Re _x . A strong correlation between C' and the fcc-bcc structural energy difference for W_1-x-y  Re _x  Os _y is revealed demonstrating that canonical band structure dictates the alloying effect on C'. The structural energy difference is exploited to estimate the alloying effect on the ideal tensile strength in the [0 0 1] direction.

Ab initio investigation of competing antiferromagnetic structures in low Si-content FeMn(PSi) alloy

The antiferromagnetic structures of a low Si-content FeMn(PSi) alloy were investigated by first principles calculations. One possible antiferromagnetic structure in supercell along the c-axis was revealed in FeMnP0.75Si0.25 alloy. It was found that atomic disorder occupation between Fe atom on 3f and Mn atoms on 3g sites is responsible for the formation of antiferromagnetic structures. Furthermore the magnetic competition and the coupling between possible AFM supercells along the c and a-axis can promote a non-collinear antiferromagnetic structure. These theoretical investigations help to deeply understand the magnetic order in FeMn(PSi) alloys and benefit to explore the potential magnetocaloric materials in Fe2P-type alloys.

Impact of magnetic fluctuations on lattice excitations in fcc nickel

The spin-space averaging formalism is applied to compute atomic forces and phonon spectra for magnetically excited states of fcc nickel. Transverse and longitudinal magnetic fluctuations are taken into account by a combination of magnetic special quasi random structures and constrained spin-density-functional theory. It turns out that for fcc Ni interatomic force constants and phonon spectra are almost unaffected by both kinds of spin fluctuations. Given the computational expense to simulate coupled magnetic and atomic fluctuations, this insight facilitates computational modeling of magnetic alloys such as Ni-based superalloys.

From soft to hard magnetic Fe-Co-B by spontaneous strain: a combined first principles and thin film study

In order to convert the well-known Fe-Co-B alloy from a soft to a hard magnet, we propose tetragonal strain by interstitial boron. Density functional theory reveals that when B atoms occupy octahedral interstitial sites, the bcc Fe-Co lattice is strained spontaneously. Such highly distorted Fe-Co is predicted to reach a strong magnetocrystalline anisotropy which may compete with shape anisotropy. To probe this theoretical suggestion experimentally, epitaxial films are examined. A spontaneous strain up to 5% lattice distortion is obtained for B content up to 4 at%, which leads to uniaxial anisotropy constants exceeding 0.5 MJ m(-3). However, a further addition of B results in a partial amorphisation, which degrades both anisotropy and magnetisation.

Thermal surface free energy and stress of iron

Absolute values of surface energy and surface stress of solids are hardly accessible by experiment. Here, we investigate the temperature dependence of both parameters for the (001) and (110) surface facets of body-centered cubic Fe from first-principles modeling taking into account vibrational, electronic, and magnetic degrees of freedom. The monotonic decrease of the surface energies of both facets with increasing temperature is mostly due to lattice vibrations and magnetic disorder. The surface stresses exhibit nonmonotonic behaviors resulting in a strongly temperature dependent excess surface stress and surface stress anisotropy.

Ab initio-predicted micro-mechanical performance of refractory high-entropy alloys

Recently developed high-entropy alloys (HEAs) consisting of multiple principal elements represent a new field of metallurgy and have demonstrated appealing properties for a wide range of applications. Using ab initio alloy theory, we reveal the alloying effect on the elastic properties and the ideal tensile strength (ITS) in the [001] direction of four body-centered cubic (bcc) refractory HEAs based on Zr, V, Ti, Nb, and Hf. We find that these HEAs show high elastic anisotropy and large positive Cauchy pressure, suggesting good extrinsic ductility. Starting from ZrNbHf, it is found that the ITS decreases with equimolar Ti addition. On the other hand, if both Ti and V are added to ZrNbHf, the ITS is enhanced by about 42%. An even more captivating effect is the ITS increase by about 170%, if Ti and V are substituted for Hf. The alloying effect on the ITS is explained by the d-band filling. An intrinsic brittle-to-ductile transition is found in terms of the failure mode under uniaxial tension. These investigations suggest that intrinsically ductile HEAs with high ideal strength can be achieved by controlling the proportion of group four elements to group five elements.

Generalized stacking fault energies of alloys

The generalized stacking fault energy (γ surface) provides fundamental physics for understanding the plastic deformation mechanisms. Using the ab initio exact muffin-tin orbitals method in combination with the coherent potential approximation, we calculate the γ surface for the disordered Cu-Al, Cu-Zn, Cu-Ga, Cu-Ni, Pd-Ag and Pd-Au alloys. Studying the effect of segregation of the solute to the stacking fault planes shows that only the local chemical composition affects the γ surface. The calculated alloying trends are discussed using the electronic band structure of the base and distorted alloys.Based on our γ surface results, we demonstrate that the previous revealed 'universal scaling law' between the intrinsic energy barriers (IEBs) is well obeyed in random solid solutions. This greatly simplifies the calculations of the twinning measure parameters or the critical twinning stress. Adopting two twinnability measure parameters derived from the IEBs, we find that in binary Cu alloys, Al, Zn and Ga increase the twinnability, while Ni decreases it. Aluminum and gallium yield similar effects on the twinnability.

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.

Elastic properties of fcc Fe-Mn-X (X = Cr, Co, Ni, Cu) alloys studied by the combinatorial thin film approach and ab initio calculations

The elastic properties of fcc Fe-Mn-X (X = Cr, Co, Ni, Cu) alloys with additions of up to 8 at.% X were studied by combinatorial thin film growth and characterization and by ab initio calculations using the disordered local moments (DLM) approach. The lattice parameter and Young's modulus values change only marginally with X. The calculations and experiments are in good agreement. We demonstrate that the elastic properties of transition metal alloyed Fe-Mn can be predicted by the DLM model.

Magnetic properties of Mn2NiSn shape memory alloy

In this paper, we present the magnetic properties of the inverse Heusler Mn2NiSn alloy computed by ab initio density functional theory (DFT) calculations in order to understand the large magnetic moments observed in experiments in contrast to smaller values obtained in previous ab initio calculations. Our results show that the magnetization in this system is quite sensitive to volume and atomic ordering in the sublattices. The observed variations in the magnetizations are explained from the features in the electronic structures of the Mn d-bands. We conclude that the symmetry of lattice sites and the alloying with Ni atoms are responsible for a high magnetic moment for a range of volumes. This opens a possible route to realize a large magnetization, a requirement for shape memory properties in magnetic alloys, in similar systems with an inverse Heusler structure.

Magnetic properties and temperature-dependent half-metallicity of Co2Mn(Ga(1-x)Z(x)) (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).

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 L1(2) 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, C(11) and C(12) decrease, whereas C(44) 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.

Phonon dispersions in random alloys: a method based on special quasi-random structure force constants

In an attempt to obtain reliable first-principles phonon dispersions of random alloys, we have developed a method to calculate the dynamical matrix, with respect to the wavevector space of the ideal lattice, by averaging over the force constants of a special quasi-random structure. Without additional approximations beyond standard density functional theory, the present scheme takes into account the local atomic position relaxations, the composition disorder, and the force constant disorder in a random alloy. Numerical results are presented for disordered Cu(3)Au, FePd, and NiPd and good agreement between the calculations and the inelastic neutron scattering data is observed.

Effect of temperature on the elastic anisotropy of pure Fe and Fe0.9Cr0.1 random alloy

The elastic properties of pure iron and substitutionally disordered 10 at. % Cr Fe-Cr alloy are investigated as a function of temperature by using first-principles electronic-structure calculations by the exact muffin-tin orbitals method. The temperature effects on the elastic properties are included via the electronic, magnetic, and lattice expansion contributions. We show that the degree of magnetic order in both pure iron and Fe(90)Cr(10) alloy mainly determines the dramatic change of the elastic anisotropy of these materials at elevated temperatures. The effect of lattice expansion is found to be secondary but also very important for quantitative modeling.

Phase Stability and Elasticity of TiAlN

We review results of recent combined theoretical and experimental studies of Ti_1−xAl_xN, an archetypical alloy system material for hard-coating applications. Theoretical simulations of lattice parameters, mixing enthalpies, and elastic properties are presented. Calculated phase diagrams at ambient pressure, as well as at pressure of 10 GPa, show a wide miscibility gap and broad region of compositions and temperatures where the spinodal decomposition takes place. The strong dependence of the elastic properties and sound wave anisotropy on the Al-content offers detailed understanding of the spinodal decomposition and age hardening in Ti_1−xAl_xN alloy films and multilayers. TiAlN/TiN multilayers can further improve the hardness and thermal stability compared to TiAlN since they offer means to influence the kinetics of the favorable spinodal decomposition and suppress the detrimental transformation to w-AlN. Here, we show that a 100 degree improvement in terms of w-AlN suppression can be achieved, which is of importance when the coating is used as a protective coating on metal cutting inserts.

First-principles atomistic study of surfaces of Fe-rich Fe-Cr

The surface properties of Fe-rich ferromagnetic Fe-Cr alloys are investigated using a first-principles quantum-mechanical method. In dilute alloys, the surfaces are dominated by Fe, whereas the Cr-containing surfaces become favorable when the bulk Cr concentration exceeds the limit of ∼ 10 atomic per cent. The abrupt change in the surface behavior is the consequence of complex competing magneto-chemical interactions between the alloying atoms. Considering the quantities of various features: equilibrium surface profiles, chemical potentials, segregation energies, surface energies, magnetic moments, mixing energies and pair interactions, within a wider range of bulk and surface concentrations enables us to build a comprehensive picture of the physics of Fe-Cr surfaces. Using the present achievements many previously controversial results can now be merged into a consistent model of Fe-rich Fe-Cr alloys.