Special Quasirandom Structures Research Articles

Modeling Short-Range Order in Disordered Rocksalt Cathodes by Pair Distribution Function Analysis

Pair distribution function (PDF) analysis is a powerful technique for the characterization of short-range order (SRO) in disordered materials. Accurate interpretation of experimental PDF data is critically reliant on the development of structural models that can account for local variations in site occupancies and bond lengths. To this end, we outline an approach to model SRO using first-principles calculations based on the cluster-expansion formalism. These methods are validated on neutron scattering data from two disordered rocksalt oxyfluorides, Li1.3Mn0.4Ti0.3O1.7F0.3 and Li1.3Mn0.4Nb0.2Ti0.1O1.7F0.3. For each composition, we demonstrate that an average structure without any SRO fails to reproduce several key features in the experimental PDF. To pinpoint the origin of the suspected SRO in these materials, configurational and displacive effects were separately investigated using two disparate models. Special quasi-random structures were relaxed using density functional theory to account for local changes in bond lengths while maintaining a near-random ionic configuration. This leads to slightly improved accuracy but still misrepresents asymmetry in the first few peaks of the PDF. Monte Carlo simulations were performed to model configurational SRO on a fixed lattice, which by itself is shown to have a minimal influence on the PDF. Instead, we find that it is the bond length relaxations within environments created by SRO which controls the details of the PDF, thereby highlighting the subtle but important coupling between configurational and displacive SRO in disordered materials.

Ab initio study of the lattice distortion and the vacancy defects in multi-anion oxycarbonitride ceramics TiCNO and TiZrCNO

Multicomponent ceramics have received much attention due to the tunning physicochemical properties and the huge compositional space, while multicomponent ceramics with the mixing of multi-anion are rarely studied. In this work, the local lattice distortion and vacancy formation energy in TiCNO and TiZrCNO are systematically investigated by density functional theory calculations combining with the special quasi-random structure model. The present results show that multi-anionic mixed oxycarbonitride ceramics exhibit obvious local lattice distortion. The quantified displacive distortions of C, N, and O in TiCNO are relatively large, being in order of C < N < O, although metallic elements Ti has larger distortion than nonmetals. Within incorporative mixing of Zr in cation sublattice, the distortions of Ti, C, N, and O increase evidently, the distortion degree for nonmetal elements is still in order of C < N < O. The distortion of Ti is still the largest, whereas Zr possesses almost the smallest distortion. The electronic structure shows a close association with the degree of distortion, the larger DOS at the Fermi level corresponds to the larger distortion. The vacancy defects are further studied. Our consequences show that the vacancy formation energies of non-metal elements with large local distortions are relatively low, suggesting that the local chemical environment profoundly affects the vacancy formation energy and defect-related properties. The present study reveals the important correlation of lattice distortion with electronic structure and vacancy generation, so it is valuable to deepen the understanding of the excellent properties of multicomponent ceramics with multi-anion mixing, and develop novel multicomponent ceramics with polyanionic structures.

Composition and strain dependence of intrinsic and substitutional defect formation energies in Sn[formula omitted]Ge[formula omitted] alloys

We present a density functional theory investigation of the formation energies of intrinsic and substitutional defects in SnxGe1−x alloy as a function of both Sn composition and biaxial strain relevant to heteroepitaxial interface settings. Special quasi-random supercell structures (SQS) are used obtain the ground state energy of the initial and defect bearing SnxGe1−x alloys. Intrinsic defects considered in this study include the vacancy and [110] split Ge interstitial, while substitutional defects include the analogous [110] split Sn interstitial, as well as substitutional Sn and P. The study focuses on SnxGe1−x alloy compositions with 0%–25% Sn content and compressive and tensile strains up to 2%. The results reveal a complex coupling of strain and compositional dependence of formation energies among different types of defects. The formation energies of split [110] Ge interstitial and substitutional Sn defects decrease monotonically with increasing Sn content while the intrinsic vacancy, Sn split [110] interstitial, and substitutional P defects exhibit a minimum formation energy between 13%–19% Sn. Biaxial strain increases the formation energy of all defects by approximately 0.1 eV for an absolute strain of 1%.

Exceptional enhancement of mechanical properties in high-entropy alloys via thermodynamically guided local chemical ordering

Understanding the local chemical ordering propensity in random solid solutions, and tailoring its strength, can guide the design and discovery of complex, paradigm-shifting multicomponent alloys. First, we present a simple thermodynamic framework, based solely on binary enthalpies of mixing, to select optimal alloying elements to control the nature and extent of chemical ordering in high-entropy alloys (HEAs). Next, we couple high-resolution electron microscopy, atom probe tomography, hybrid Monte-Carlo, special quasirandom structures, and density functional theory calculations to demonstrate how controlled additions of Al and Ti and subsequent annealing drive chemical ordering in nearly random equiatomic face-centered cubic CoFeNi solid solution. We establish that short-range ordered domains, the precursors of long-range ordered precipitates, inform mechanical properties. Specifically, a progressively increasing local order boosts the tensile yield strengths of the parent CoFeNi alloy by a factor of four while also substantially improving ductility, which breaks the so-called strength-ductility paradox. Finally, we validate the generality of our approach by predicting and demonstrating that controlled additions of Al, which has large negative enthalpies of mixing with the constituent elements of another nearly random body-centered cubic refractory NbTaTi HEA, also introduces chemical ordering and enhances mechanical properties.

On the miscibility gap in tungsten-based alloys

In this work we establish an approach to model miscibility gaps of alloys using statistical physics, lattice dynamics from first-principles calculations. We carefully calculate the entropy to include all processes introducing disorder to the system, i.e., combining the electronic, phononic, and configuration entropies. Furthermore we present our algorithm for generating Special Quasirandom Structures (SQS). We model the miscibility gap in tungsten - chromium and tungsten - molybdenum systems, obtaining the agreement with the experimental data. Furthermore, we propose an enhancement for the tungsten-chromium W70Cr30 alloy with tantalum and hafnium, leading to the modified stabilization temperatures TS, where the solid solution is miscible.

First-principles calculation of Fe-Mo-Cr alloys based on special quasi-random structure

Mo element has an important effect on ferritic stainless steel. It is of great significance to study the role of the Mo element in the composition design of stainless steel alloys. In this paper, the formation energy, magnetic moment, electronic structure, mechanical and high-temperature mechanical properties of Fe-Mo binary alloys and Fe-Mo-Cr ternary alloys were obtained by density functional theory of first principles. The results showed that the formation energy increases gradually with the increase of Mo content. The alloys have a stable system when the Mo concentration is less than 3.125%. The addition of Cr increases the formation energy, but when Mo content is 3.125%, the formation energy is lower than that of Fe-Mo binary alloys. Fe atoms are ferromagnetic state and Mo atoms are anti-ferromagnetic state, there is an opposite magnetic effect between them. With the increase of Mo concentration, Mo atoms change from anti-ferromagnetic to paramagnetic. Mo atoms become paramagnetic when Mo concentration reaches 100%. Mo element has little effect on the shear modulus of the alloys. The hardness and compressive strength decrease with increasing Mo concentration. The addition of Cr atom also reduces the hardness. Fe-Mo alloys have better thermal stability when Mo concentration is 12.5%. The Cr atom significantly changes the thermodynamic properties of the alloys. The volume thermal expansion coefficient of Fe-Mo-Cr ternary alloys decreases with the increase of Mo concentration, and the highest temperature appears near the Mo concentration of 12.5∼18.75%.

Local cation ordering in compositionally complex Ruddlesden–Popper n = 1 oxides

The Ruddlesden–Popper (RP) layered perovskite structure is of great interest due to its inherent tunability, and the emergence and growth of the compositionally complex oxide (CCO) concept endows the RP family with further possibilities. Here, a comprehensive assessment of thermodynamic stabilization, local order/disorder, and lattice distortion was performed in the first two reported examples of lanthanum-deficient Lan+1BnO3n+1 (n = 1, B = Mg, Co, Ni, Cu, Zn) obtained via various processing conditions. Chemical short-range order (CSRO) at the B-site and the controllable excess interstitial oxygen (δ) in RP-CCOs are uncovered by neutron pair distribution function analysis. Reverse Monte Carlo analysis of the data, Metropolis Monte Carlo simulations, and extended x-ray absorption fine structure analysis implies a modest degree of magnetic element segregation on the local scale. Further, ab initio molecular dynamics simulations results obtained from special quasirandom structure disagree with experimentally observed CSRO but confirm Jahn–Teller distortion of CuO6 octahedra. These findings highlight potential opportunities to control local order/disorder and excess interstitial oxygen in layered RP-CCOs and demonstrate a high degree of freedom for tailoring application-specific properties. They also suggest a need for expansion of theoretical and data modeling approaches in order to meet the innate challenges of CCO and related high-entropy phases.

Prediction of lattice distortion and mechanical behavior of tetragonal phase (Bi0.2Na0.2Ba0.2Sr0.2Ca0.2)TiO3 high-entropy perovskite with A-site disorder from first-principles calculations

High-entropy perovskite ceramics have drawn widespread attention as their excellent physical properties. Herein, the high-entropy (Bi0.2Na0.2Ba0.2Sr0.2Ca0.2)TiO3 (BNBSCT) perovskite is selected as case study. The distorted structure and mechanical behavior as well as the effect of pressure are comprehensively studied through implementing first-principles calculations in conjunction with special quasi-random structure. The results reveal the atomic random distribution and size different cause serious lattice distortion within the BNBSCT structure, and the pseudo-intralayer distortion is significantly smaller than the interlayer distortion. Further studies of the mechanical properties indicate that the high-entropy BNBSCT perovskite is mechanical stable, especially larger elastic parameters imply the larger resistance against elastic deformation in comparison with Bi0.5Na0.5TiO3. Compared to the rule of mixture, the higher resistance to volume deformation and crack propagation of BNBSCT suggests the strengthening of high-entropy perovskite presumably due to lattice distortion in structure. Increasing pressure leads to decrease in lattice parameter and volume of structure, then increases the degree of lattice distortion, elastic constants and elastic moduli, as well the degree of lattice distortion. Moreover, the ductility and fracture toughness are also enhanced, though the elastic anisotropy is slightly larger. This work provides a new insight into the high-entropy perovskite under high pressure, which will contribute to the further research and application of high-entropy materials.

The effects of mixing non-metal atoms in the B1 structured transition metal carbo-nitrides on their structure and mechanical properties: HfC1-xNx

In this paper, we utilize density functional theory to explore how alloying the carbide and nitride of a group IVB transition metal affects the phase stability and mechanical properties; we place an emphasis on elastic and dislocation properties, taking the HfC-HfN system as an example. An evolutionary algorithm is used to identify the ordered carbonitrides and the enthalpies of formation are compared with special quasi-random structures to identify this system's tendency to order and form a solid solution. The variation of elastic constants with composition is examined, and the computed elastic constants are used to predict the theoretical hardness. The GSF curves for various compositions are computed to determine how alloying would affect dislocation behavior. These results show that while there may be a modest peak in elastic response, the resistance to dislocation motion does not particularly show a peak. Furthermore, the alloying of HfC with HfN reduces the resistance to slip almost universally, and helps stabilize dislocations on {111} planes through the stabilization of an intrinsic stacking fault. These results are compared to previous in-depth analysis of the HfC-TaC system, allowing for comparisons between metal and non-metal alloying strategies.

Assessing the high concentration of vacancies in refractory high entropy alloys

Accurate determination of monovacancy formation enthalpy is vital for work on diffusion, melting point determination of high temperature materials, radiation damage, and thermophysical stability of alloys. These enthalpies take on a single value in pure metals but is made more complex in concentrated solid solutions due to the local chemical environments possible around each vacancy. Herein, using first-principles density functional theory, we report the distributions of vacancy formation enthalpies in 21 equiatomic 5-component solid-solution alloys from the Hf-Mo-Nb-Ta-Ti-W-Zr system. Chemical disorder is treated using the special quasi-random structure method, and the chemical potential of vacant element is treated by approximating it to its total energy in its standard state. We find that the highest vacancy formation enthalpies belong to the MoNbTaTiW alloy (which incidentally is the most reported in literature) and the lowest belongs to HfNbTaTiZr, with other alloys in-between. We use the whole distribution of formation enthalpies to estimate the equilibrium concentration of vacancies as a function of temperature.

Elastic properties of disordered binary hcp-Fe alloys under high pressure: Effects of light elements

The effects of light elements on the elastic properties of disordered binary hcp-Fe alloys were investigated at high pressures using plane-wave density functional theory combined with the Monte Carlo special quasi-random structure method. We found that the increase in the O content in hcp-Fe had a more pronounced effect on the sound velocity than Si, S, and C. The longitudinal wave velocity was decreased by ∼ 6% with 2% O content, which was a much greater decrease than the values of 0.6% and 2% induced by the same content of Si and S, respectively, under high pressures. Compared with the other three light elements, the longitudinal wave velocity of the Fe-C alloy exhibited the most gradual decreasing with increasing C content. In addition, the effects of different O and S contents on the anisotropy of hcp-Fe alloys strongly depended on the variation in pressure, whereas the pressure only slightly affected the anisotropy of Fe-Si alloy systems.

Microstructures in Iron-rich FeSi Alloys by First-principles Phase Field and Special Quasirandom Structure Methods

Coarse grained phase morphologies of iron-rich region of FeSi alloys at 1050 K are investigated by using first-principles phase field and special quasirandom structure methods without relying on any experimental or empirical information. From the free energy comparison, we find that, for the Si concentration less than 25 at%, a solid-solution-like homogeneous phase is most stable, although a random pattern in nm scale consisting of B2 Fe4–xSix and D03 Fe3Si phases may appear at 12.5 at% Si at somewhat lower temperatures. We make a conjecture that, around 12.5 at% Si, such a random pattern in nm scale is the origin of the zero magnetostriction and low magnetic anisotropy. This solves a long-standing problem of the experimentally observed zero magnetostriction at 6.5 wt% Si. On the other hand, for the Si concentration slightly larger than 25 at%, FeSi alloys prefer two-phase coexistence of the D03 Fe3Si phase and the B2 FeSi phase. All these findings are in good accordance with the available experimental evidence.

Ab-initio study of electronic, mechanical and thermodynamic properties of β-Ti–15Nb–xSi alloys for biomaterials applications

In this paper, we used the first-principles method to investigate the structural, electronic, mechanical and thermodynamic parameters of the ternary [Formula: see text]-Ti–15Nb–xSi alloys with [Formula: see text][Formula: see text]wt.%. We have carried out theoretical computations inside the density functional theory (DFT) utilizing the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) model. The random distribution of Nb atoms in the alloy was described by using both virtual crystal approximation (VCA), special quasirandom structure (SQS) and the coherent potential approximation (CPA) techniques, in combination with first-principles plane-wave pseudopotential (PW-PP) and exact muffin-tin orbital (EMTO) methods. We determined the elastic constants as well as the bulk, shear, Young’s modulus and Poisson’s ratio. Our structural results are in good agreement with the available experimental and theoretical results for the pure structure of the titanium. In addition, we have estimated the band structure and the density of state (DOS) for the electronic computations. Our findings demonstrate that all of the compounds are metallic, stable and meet the requirements for stability. Young’s modulus of Ti–15Nb–0.6Si and Ti–15Nb–1.6Si is 86.5[Formula: see text]GPa and 15.11[Formula: see text]GPa, respectively, which are similar to Young’s moduli of human bone (10–30[Formula: see text]GPa). All calculated parameters of the alloys decreased with increasing of Si concentration except for Poisson’s ratio, anisotropy and B/G ratio. Furthermore, all of the materials investigated showed ductile nature, and Young’s modulus values are needed for further applications. Excitations from the quasi-harmonic Debye approximation’s vibrational part were applied to the 0[Formula: see text]K free energy calculated via ab-initio calculations. The influence of temperatures up to 800 K on phase stability was investigated. These findings can be utilized to help designers create alternative low-modulus alloys for biomedical applications.

Prediction of mechanical properties of AlTiCrVNb high entropy alloys with B2 ordered structure

Chemical short-range order (CSRO) is widely reported and it's certainly related to high entropy alloys (HEAs)'s mechanical properties in many different correlative researches. B2 structure ordering is usually thought to improve alloy's structural stability and strength while sacrificing the plasticity significantly. In this work, we established a B2 ordered model by the special quasi-random structure method which considering the local atomic environment (to simulate the real situation in HEAs). Depending on this model and first principles, the elements' occupancy and the B2 structure ordering are considered to explore their influence on the mechanical properties of AlTiCrVNb HEAs. The B2-type partially ordered configuration was applied to non-iso atomic ratio alloys to investigate the different influence on alloys' mechanical properties due to the changing content of Ti or Cr and the results were verified by experiment.

Incorporation and migration of xenon in uranium-plutonium mixed nitride; A density functional theory study

Actinide nitride materials are promising candidates for advanced nuclear fuels. In this work, we investigate the bulk properties of the mixed nitrides U0.75Pu0.25N and U0.5Pu0.5N, and study the incorporation and migration behaviour of the fission gas Xe. The disordered U0.75Pu0.25N and U0.5Pu0.5N structures are constructed using the special quasi-random structure method. Their lattice parameters are closer to the experimentally determined values than the corresponding ordered structures. The density of states show that Pu f states are located at lower energy than U f, consistent with the trend of increasing f orbital stability across the actinide series. The actinide vacancy formation energy (Ef) in disordered and ordered U0.5Pu0.5N is highly dependent on the chemical environment around the vacancy: it increases as the number of U atoms in the first nearest-neighbour shell (NU(1NN)) increases, but decreases as the number of U atoms in the second nearest-neighbour shell (NU(2NN)) increases. The Xe incorporation energy (Ei) is found to be independent of vacancy species, depending only on the chemical environment of the vacancy. As does Ef, Ei increases with increasing NU(1NN), while decreases with increasing NU(2NN), because the smaller the NU(1NN) and the larger the NU(2NN), the larger the vacancy steric space. The Ei of Xe and Kr are calculated to be within the ranges 4.47–6.01 eV and 3.30–4.64 eV, respectively. The Xe migration energy barrier in ordered U0.5Pu0.5N allows us to set the energy range for Xe diffusion in disordered U0.5Pu0.5N as 0.50–1.75 eV. A lower range of 0.30–1.25 eV is found for Kr diffusion.

Phase-field study of elastic effects on precipitate evolution in (Al)0.05CrFeNi

We introduce a new approach to include for high and medium entropy alloys, stress effects in a Phase-field model (PFM). The approach is applied to simulate the evolution of two-phase BCC/FCC microstructures of AlCrFeNi alloys, combining phase-field method with CALPHAD data and DFT (Density Functional Theory) calculations. The composition dependent Gibbs energies and diffusion mobilities of the BCC and FCC phase as a vital input for simulating real alloys into the PFM are calculated from the Thermo-Calc TCHEA2 and MOBHEA2 databases. The special quasirandom structures (SQS) method was used to obtain the complex multicomponent lattice structures and compute with DFT the elastic properties of the BCC and FCC phases. It is found that elastic stresses emerging due to a difference in eigenstrain between the BCC and FCC phases during a phase transformation have a significant effect on the precipitate formation. The effect of the eigenstrain induced elastic stress on the BCC precipitate shape, size and the equilibrium concentrations in the two phases are quantitatively studied. The PFM presented is one of the first attempts to simulate elastic effects on high entropy alloys(HEAs) microstructures. This work contributes to the understanding of the mechanisms of phase transformation and microstructure evolution in HEAs.

Thermodynamic assessment within the Zr–B–C–O quaternary system

AbstractThermodynamic modeling of Zr–B–C–O quaternary system is conducted within the CALPHAD framework by employing data obtained from first‐principle calculations and literature. The lower order binary B–O is assessed in this work by estimating the thermodynamic properties of stable solid phases of B2O3 and B6O and by estimating the gas and liquid phases. First‐principle calculations, in conjunction with special quasirandom structure were used to predict enthalpies of mixing for the ternary solid‐solution phase of FCC‐Zr(C, O). The calculated results were used to optimize the model parameters pertaining to the cubic phase, which is described by a two‐sublattice model. The modeled Zr–C–O ternary phase diagrams calculated at 1923 and 2273 K under ambient pressure and 4 Pa, respectively, are in agreement with experimental phase diagrams.

DFT calculations of structural, magnetic, and stability of FeNiCo-based and FeNiCr-based quaternary alloys

As the Cantor-derived medium-entropy alloys (MEAs), FeNiCoMn and FeNiCrMn quaternaries in both equiatomic and non-equiatomic compositions were investigated by density functional theory combined with the quasiharmonic Debye–Grüneisen approximation using the special-quasirandom structure model. The structural properties, magnetic properties, and thermodynamics and phase stability were explored in detail. The temperature stabilization effect of lattice vibration, configurational mixing entropy, and thermal electronic excitation was discussed. Also FeNiCoPd and FeNiCrPd quaternaries, in which Mn was replaced by Pd, were considered in the same framework in order to highlight the similarities and differences between these Mn- and Pd-MEAs. The phase stability competition between homogeneous and inhomogeneous states in terms of both size and chemical ordering was revealed for four groups of FeNiCoMn, FeNiCoPd, FeNiCrMn, and FeNiCrPd MEAs.

Models of configurationally-complex alloys made simple

We present a Python package for the efficient generation of special quasi-random structures (SQS) for atomic-scale calculations of disordered systems. Both, a Monte-Carlo approach or a systematic enumeration of structures can be used to carry out optimizations to ensure the best optimal configuration is found for given cell size and composition. We present a measure of randomness based on Warren-Cowley short-range order parameters allowing for fast analysis of atomic structures. Hence, optimal structures are found in a reasonable time for several dozens or even hundreds of atoms. Both SQS optimizations and analysis of structures can be carried out via a command-line interface or a Python API. Additional features, such as optimization towards partial ordering or independent sublattices allow the generation of atomistic models of modern complex materials. Moreover, hybrid parallelization, as well as distribution of vacancies, are supported. The output data format is compatible with ase, pymatgen and pyiron packages to be easily embeddable in complex simulation workflows. Program summaryProgram title: sqsgeneratorCPC Library link to program files:https://doi.org/10.17632/m2sb3wzcvc.1Developer's repository link:https://github.com/dgehringer/sqsgeneratorLicensing provisions: MITProgramming language: Python, C++Supplementary material:https://sqsgenerator.readthedocs.ioNature of problem: Many technological relevant materials, exhibit a crystalline disorder. Within atomistic modelling approaches such as Density Functional Theory (DFT) or Molecular Dynamics, disorder is modelled with a cell containing a (small) finite set of atoms. Such an atomic configuration is usually found by enumerating structures. However, since configurational space is growing exponentially efficient tools are needed to sample it properly.Solution method: Efficient quantification of disorder using a generalization of Warren-Cowley Short Range Order (WC-SRO) parameters [1,2]. By either a Monte-Carlo approach or systematic enumeration, optimal structures can be found. The software is distributed as a Python package offering a command line interface. Core parts are written in C++ and exhibit shared (OpenMP) and distributed (MPI) memory parallelism. For embedding into complex simulation workflows, the tool exposes a Python API to integrate into popular packages such as ase [3], pymatgen [4] or pyiron [5].

Stability and electronic properties of two-dimensional Ga2O3 and (MxGa1-x)2O3 (M = Al, Ga) alloys

The alloying of Ga2O3 monolayer with oxides of the same main group element (Al and In) is simulated by the special quasirandom structures method. The stability and electronic properties of the Ga2O3 monolayer and (MxGa1-x)2O3 monolayer alloys are systematically investigated by first-principles calculations. The (AlxGa1-x)2O3 monolayer alloy becomes more stable with the increase of Al2O3 content, but the stability of (InxGa1-x)2O3 monolayer alloy worsens with the increase of In2O3 content. The (AlxGa1-x)2O3 monolayer alloy has relatively better thermodynamic stability, which would be easily synthesized at room temperature. The orbital-projected band structure and charge density reflect that the effect of alloying Ga2O3 with Al2O3 and In2O3 on the electronic properties of materials is mainly on the conduction band. Interestingly, we find that the charge density of the VBM and CBM states for Ga2O3 monolayer and its monolayer alloys exhibit the characteristic of complete separation in real space, i.e., an abnormal carrier separation. Through the calculation of the band-gap bowings parameter, it is predicted that the band gap of the monolayer alloy can continuously be tuned in the range of 3.38 ∼ 7.02 eV. These results would shed some light on the application of the Ga2O3 monolayer and its monolayer alloys in optoelectronic devices.