Special Quasirandom Structures Research Articles

Optimized Design of Quinary High-Entropy Transition Metal Carbide Ceramics Based on First Principles

In this paper, we developed models for 21 quinary high-entropy transition metal carbide ceramics (HETMCCs), composed of carbon and the transition metals Ti, Zr, Mo, V, Nb, W, and Ta, employing the Special Quasirandom Structures (SQS) method. We investigated how the transition metal elements influence lattice distortion, mixing enthalpy, Gibbs free energy of mixing, and the electronic structure of the systems through first-principles calculations. The calculations show that 21 systems can form a stable single phase, among which (TiMoVNbTa)C5, (ZrMoNbWTa)C5, and (MoVNbWTa)C5 exhibit superior stability. The formation energy and migration energy of carbon vacancies in systems with strong single-phase stability were calculated to predict their radiation resistance. The formation energy of carbon vacancies is closely related to the types of surrounding transition metal elements, with values ranging between the maximum and minimum formation energies observed in binary transition metal carbides (TMCs). The range of migration energy for carbon vacancies is wider than that observed in TMCs, which can hinder their long-range migration and enhance the radiation resistance of the materials.

Theoretical insights into the ultrahigh piezoelectric performance of (BiFeO3)n/(BaTiO3)n (n = 1–5) superlattices

Perovskite structures have attracted extensive attention in microelectromechanical systems and nanoelectromechanical systems devices due to the high piezoelectric response and the low dielectric constant. The piezoelectric and dielectric properties of the tetragonal BiFeO3/BaTiO3 superlattices grown along the c-axis direction are investigated using density functional theory (DFT) and density functional perturbation theory. The calculated results demonstrate that the (BiFeO3)n/(BaTiO3)n (n = 1–5) superlattices exhibit a profoundly increased piezoelectric response compared to their bulk structures. The (BiFeO3)2/(BaTiO3)2 possesses the highest piezoelectric d33 of 697 pC/N among known lead-free perovskite systems. Furthermore, the (BiFeO3)2/(BaTiO3)2 superlattice possesses a low dielectric ɛ33, and its d33 at 2% tensile strain is 16 times larger than that of an unstrained equilibrium structure. This demonstrates that biaxial tensile strain significantly enhances the piezoelectric response. Combining the special quasirandom structure method with DFT, the structures of a 0.5BiFeO3–0.5BaTiO3 solid solution are predicted, and its calculated d33 is 58 pC/N, which is much smaller than that of a (BiFeO3)2/(BaTiO3)2 superlattice. The results suggest that the (BiFeO3)2/(BaTiO3)2 superlattice might be a potential candidate for nonvolatile random access memory, transducers and actuators, and nanoscale electronic devices.

Software Tools for Integrating Special Quasirandom Structures and the Cluster Variation Method into the CALPHAD Formalism

Software Tools for Integrating Special Quasirandom Structures and the Cluster Variation Method into the CALPHAD Formalism

Vacancy formation free energy in concentrated alloys: Equilibrium vs. random sampling

Special Quasi-random Structures (SQSs) are often used to model disordered alloys in small simulation cells. Yet, SQS-based sampling yields defect formation energies that do not match the equilibrium values, for instance measured in atomic Monte Carlo simulations, due to the lack of chemical short-range order in random samples. In this paper, our approach to computing chemical potentials in alloys through random sampling techniques is extended to the computation of vacancy formation free energies. By rigorous thermodynamic derivation, we show that vacancy formation free energies computed from randomly sampled local chemical environments must be corrected to ensure its consistency between various available calculations. Indeed, irrespective of the choice of the species being replaced by a vacancy, we should arrive at the same value of the vacancy formation free energy. We propose a simple way to compute this correction term, and compare the outcome with equilibrium Monte Carlo results and with approximations found in the literature.

Influence of local cation order on the electronic structure and optical properties of cation-disordered semiconductor AgBiS2

Abstract Site disorder exists in some practical semiconductors and can significantly impact their intrinsic properties both beneficially and detrimentally. However, the uncertain local order and structure poses a challenge for both experimental and theoretical research. Especially, it hinders the investigation of the effects of the diverse local atomic environments resulting from the site disorder. In this study, we employ the special quasi-random structure method to perform first-principles research on the connection between local site disorder and electronic/optical properties, using the cation-disordered AgBiS2 (rock salt phase) as an example. We predict that cation-disordered AgBiS2 has a bandgap ranging from 0.6 to 0.8 eV without spin-orbit coupling and that spin-orbit coupling reduces this by approximately 0.3 eV. We observe the effects of local structural features in the disordered lattice, such as the one-dimensional chain-like aggregation of cations that results in the formation of doping energy bands near the band edges, the formation and broadening of band-tail states, and the disturbance in the local electrostatic potential, which significantly reduces the bandgap and stability. The influence of these ordered features on the optical properties is confined to alterations in the bandgap and does not markedly affect the joint density of states or optical absorption. Our study provides a research roadmap for exploring the electronic structure of site-disordered semiconductor materials, suggests that the ordered chain-like aggregation of cations is an effective way to regulate the bandgap of AgBiS2, and provides insight into how variations in local order associated with processing can affect properties.

Effect of B and Hf doping on vacancy defects in AlCrMoNbZr high entropy alloy: A first principles study

The AlCrMoNbZr high entropy alloy (HEA) has potential applications as a high-performance cladding coating material. Here, we report the results about the vacancy defects in AlCrMoNbZr HEA using first-principle calculations. We have explored the variations in bulk and vacancy defect properties due to different local chemical environments in AlCrMoNbZr HEA with and without B/Hf doping, using both supercell and special quasi-random structures (SQS) techniques. Vacancy formation energy (VFE) is analyzed in accordance with the statistical distribution across three systems. The VFE exhibits a broad range of values and is characterized by a normal distribution. It is also significantly influenced by the type of doping atoms and the type of vacancy. Specifically, B doping substantially reduces the vacancy formation energy, thereby facilitating the formation of vacancies. Furthermore, the doping of B and Hf exerts a considerable impact on the formation of Zr vacancies (Zr_Vac) and Mo vacancies (Mo_Vac). In addition, Al vacancies (Al_Vac) are most readily formed in the AlCrMoNbZr HEA, while Mo vacancies (Mo_Vac) are most easily formed following the introduction of B and Hf dopants. The VFE in AlCrMoNbZr HEA with and without Hf dopant increases with the increase of the number of Cr and Mo atoms in the local chemical environment, and decreases with the increase of the number of Zr atoms. In conclusion, B doping promotes the formation of vacancy, which is not conducive to the improvement of initial irradiation resistance performance. Fortunately, one can infer from the results of the effect of local chemical environment on VFE that it is rewarding in improving the initial irradiation resistance by increasing the occurrence of Mo–Mo and Zr–Zr arrangement in AlCrMoNbZr HEA.

The influence of aluminum content on thermal properties of copper-aluminum alloys: a first-principles calculation

Abstract Copper-aluminum alloy, also called aluminum bronze, is a type of host material for abradable sealing coatings. The amount of aluminum content obviously affects the properties of the coating. This research uses the density functional theory to calculate the properties of an aluminum bronze with different aluminum content. The copper-aluminum alloy model uses the model of special quasirandom structures (SQS). The elastic constant, melting point, constant pressure specific heat capacity, and thermal expansion coefficient of the copper-aluminum alloys were calculated using the quasi-harmonic approximation (QHA) method. The copper-aluminum alloys with three different nominal components were prepared using vacuum induction melting. The melting point, thermal expansion coefficient, and specific heat capacity of the copper-aluminum alloys were characterized through experiments. The results showed that the melting point of the copper-aluminum alloys decreased with an increase in aluminum content. Additionally, the coefficient of thermal expansion of the copper-aluminum alloy increased with the increase in aluminum content. Furthermore, the specific heat capacity of the copper-aluminum alloy initially increased and then reached a turning point when the β’ phase was generated. The experimental values conform well to the calculated values.

Atomic arrangement and mechanical properties of high-entropy nonoxide ceramics simulated via location preference-based disordered random structure

The cell structures and mechanical properties (i.e., hardness, Young's modulus, shear modulus, and Poisson's ratio) of (Hf0.2Zr0.2Ti0.2Nb0.2Ta0.2)C (HEC) and (Hf0.2Zr0.2Ti0.2Nb0.2Ta0.2)N (HEN) high-entropy ceramics were simulated by special quasi-random structure (SQS) and general random structure (GRS) with atomic occupation preference based on the first-principles density functional theory. The results show that compared to SQS, the cell structure constructed by GRS is more realistic, which is verified via scanning electron microscopy, high resolution transmission electron microscopy and energy dispersive spectroscopy. The mechanical properties simulated by GRS were also determined by microhardness and dynamic elastic modulus testers. The hardness, Young's modulus，shear modulus and Poisson's ratio predicted by GRS are 23.07 GPa, 449.71 GPa, 183.28 and 0.227 for HEC and 22.96 GPa, 413.71 GPa, 162.47 and 0.241 for HEN, which are in a reasonable agreement with the measured results (i.e., 22.05 ± 0.32 GPa, 433 ± 12 GPa, 172 ± 18 GPa, 0.21 for HEC and 22.12 ± 0.13 GPa, 372 ± 23 GPa, 158 ± 11 GPa, 0.23 for HEN). This work can provide a promising reference for preparing high-entropy non-oxide ceramics via the prediction.

Disorder induced band gap lowering in kesterite type Cu2ZnSnSe4 and Ag2ZnSnSe4: a first-principles and special quasirandom structures investigation

Quaternary chalcogenides, i.e. Cu2ZnSnS4, crystallising in the kesterite crystal structure have already been demonstrated as potential building blocks of thin film solar cells, containing only abundant elements and exhibiting power conversion efficiencies of about 14.9% so far. However, due to the potential presence of several structurally similar polymorphs, the unequivocal identification of their ground state crystal structures required the application of more elaborate neutron diffraction experiments. One particular complication arose from the later identified Cu–Zn disorder, present in virtually all thin film samples. Subsequently, it has been shown experimentally that this unavoidable Cu–Zn disorder leads to a band gap lowering in the respective samples. Additional theoretical investigations, mostly based on Monte-Carlo methods, tried to understand the atomistic origin of this disorder induced band gap lowering. Here, we present theoretical results from first-principles calculations based on density functional theory for the disorder induced band gap lowering in kesterite Cu2ZnSnSe4 and Ag2ZnSnSe4, where the Cu–Zn and Ag–Zn disorder is modelled via a supercell approach and special quasirandom structures. Results of subsequent analyses of structural, electronic, and optical properties are discussed with respect to available experimental results, and will provide additional insight and knowledge towards the atomistic origin of the observed disorder induced band gap lowering in kesterite type materials.

High-throughput assessment of stability and mechanical properties of medium- and high-entropy carbides: Bridging empirical criteria and ab-initio calculations

This study assesses the effectiveness of empirical stability descriptors — the normalized geometric packing parameter, lattice size difference, electronegativities mismatch, and the convex hull analysis based on information on mutually dissolving components, and ab-initio calculated entropy forming ability (EFA) for high-throughput materials discovery in high-entropy ceramics. A sample containing 53,130 medium and high-entropy carbide combinations from the Materials Project database has been analyzed, comparing solid solutions selected based on empirical descriptors and EFA calculations. The suitability of various electronegativity scales is evaluated, while Automatic FLOW (AFLOW) partial occupation (AFLOW-POCC) and special quasirandom structures (SQS) calculations provide insights into enthalpies, bulk moduli, and lattice parameters. It is shown that local distortions play a role in determining the stability of high-entropy ceramics and estimated lattice parameters, Young’s modulus, fracture toughness, and Vickers hardness by computational and experimental approaches. Our analysis demonstrates the efficacy of density functional theory (DFT) approaches for high-throughput screening and highlights the need for the further exploration of the cocktail effect on high-entropy ceramics’ mechanical properties.

Towards accurate thermodynamics from random energy sampling

Special Quasi-random Structures (SQSs) are often used to model disordered alloys in small simulation cells. Yet, SQS-based sampling yields chemical potentials (and other thermodynamic properties) that do not match the equilibrium values at some finite temperature, which can for instance be measured in atomic Monte Carlo simulations. This is due to the lack of chemical short-range order in random samples. In this paper, we present a probabilistic analysis of chemical potential calculations based on the distribution of substitution energies and the Widom technique. Performing the analysis by sampling either equilibrium configurations or SQSs, we show that they both yield different results, but that it is possible to correct the results from the random sampling in order to get a result which is much closer to the equilibrium values. The correction is very simple to apply and does not require additional total energy calculations.

Prediction of NbTaTiZr-based high-entropy alloys with high strength or ductility: First-principles calculations

Refractory high-entropy alloys (RHEAs) have a great potential in high-temperature electronics, extensive aerospace and biomedical applications due to their unique strength and ductility. Herein, the effects of alloying elements on the mechanical and electronic properties of NbTaTiZrX (X = V, Mo, Hf, W and Re) RHEAs are investigated by using the density functional theory (DFT) in combination with the special quasi-random structure (SQS) and virtual crystal approximation (VCA) methods. The calculated results show that alloying of Mo, W and Re with high elastic modulus can enhance the strength and the hardness of RHEAs. Among them, NbTaTiZrRe RHEA with the best strengthening effect has a yield strength of exceeds 2 GPa, which is notably higher than other considered high-entropy alloys. For alloying of V and Hf, the ductility of RHEAs is improved, and among which, NbTaTiZrHf RHEA has a relatively best ductility. Compared with other NbTaTiZrX RHEAs, spiral dislocations in NbTaTiZrHf RHEA are more prone to nucleate, and which confirms its excellent ductility. Moreover, the reduction of pseudo energy gaps and the formation of Hf–Hf strong metallic bonds further confirm its metallic ductility from the electronic density of states and charge density. The theoretical predictions in this study are congruent with the existing experimental data, and have certain theoretical guidance relevance for enhancing the mechanical characteristics of NbTaTiZrX (X = V, Mo, Hf, W and Re) RHEAs.

Effects of B2 ordered structure on the mechanical properties of TiZrHfCoNiCu high-entropy alloy

High-entropy alloys (HEAs) were once considered to be typical disordered solid solutions with various atoms randomly distributed in a lattice. Recent studies have found that owing to the chemical complexity of multiple primary elements, HEAs may also form ordered structures that directly influence their mechanical properties. In this study, B2-ordered and body-centered-cubic-disordered structures of TiZrHfCoNiCu HEAs were established using the special quasi-random structure method. The results of first principles calculations and ultrasonic wave velocity measurements indicated that the B2-ordered TiZrHfCoNiCu HEA exhibited superior phase stability, structural stability, and mechanical properties such as strength and hardness. Significantly, the results of this study revealed the physical mechanisms underlying the excellent mechanical properties of ordered HEAs and can guide their design and development accordingly.

High-entropy carbide (Ti0.2Zr0.2Hf0.2Nb0.2Ta0.2)C mechanical properties prediction with the use of machine learning potential

The six-component high-entropy carbide (HEC) (Ti0.2Zr0.2Hf0.2Nb0.2Ta0.2)C has been studied. The electronic structure was calculated by using the ab initio package VASP for a supercell with 512 atoms constructed by using special quasi-random structures. The artificial neural networks potential (ANN-potential) was obtained by deep machine learning. The quality of the ANN-potential was estimated by the value of the energies, forces, and virials standard deviations. The generated ANN-potential was used to analyze both a defect-free model of the specified alloy, with 4096 atoms, and for the first time a polycrystalline HEC model, with 4603 atoms, by using the LAMMPS classical molecular dynamics package. The simulation of uniaxial cell tension was carried out, the elasticity coefficients, the all-round compression modulus, the elasticity modulus, and Poisson’s ratio were determined. The obtained values are in good agreement with the experimental and calculated data, which indicates a good predictive ability of the generated ANN-potential.

Generation of thermal neutron scattering data for GH3535 alloy

Recent studies related to the thermal neutron scattering (TNS) data in reactors were generally focused on fuels and moderators, while the TNS data for structural materials has received little attention. The TNS effect of the GH3535 alloy, a nickel-based alloy widely used in molten salt reactor (MSR), is studied in this work. The partial phonon densities of states (PDOS) for the main metals (Ni, Mo, Cr and Fe) in the alloy, which are required for the TNS data generation, are calculated using the density functional perturbation theory (DFPT) based on a special quasi-random structure (SQS) of the alloy. The TNS cross sections for the main metals in the alloy are generated using the modified NJOY code. To preliminarily validate the TNS data, the calculated scattering cross section, combined with the evaluated absorption cross section of the alloy, is compared with the experimental total cross section, which shows a good agreement. Moreover, an integral neutronics experiment of neutron leakage spectrum is designed to further validate the TNS data. The neutron leakage spectrum is simulated by the Monte Carlo method, which can be compared with the future experimental result. Based on the experiment geometry modeling, the TNS effects of the GH3535 alloy are analyzed at multiple incident neutron energies, sample thicknesses and temperatures, respectively. It is found that the TNS effect of the GH3535 alloy on the neutron leakage spectrum cannot be ignored, and the scattering cross section of the alloy with high precision should be included in designs of MSR.

Tailoring thermodynamic stability, mechanical properties, and anisotropies in TiX (X=Nb, Zr) disordered alloys: A first-principles study

This paper employs first principles to calculate the elastic modulus and anisotropies of β-TiX (X=Nb/Zr) disordered models. Based on the special quasi-random structures (SQS) theory and utilizing the open-source software ICET, disordered structures of β-TiX (X=Nb/Zr) are established, and their formation energies and the stability of the β phase are determined. Subsequently, the elastic constants of these structures are computed, followed by calculations of the elastic anisotropies of Young's modulus and an analysis of alloys prone to fatigue cracking. The insights provided contribute to a deeper understanding of the mechanical properties of β-TiX alloys, facilitating their design and optimization for various applications.

First principles calculation of elastic properties of Fe–C alloys: Effect of interstitial and substitutional carbon element

The effect of different incorporation mechanisms on the elastic properties of hcp Fe–C alloys at high pressures is investigated using density functional theory combined with Monte Carlo special quasi-random structure method. It is found that the different incorporation mechanism has little effect on the bulk modulus B and the compressional wave velocity Vp of hcp Fe–C alloys. However, the values of the shear modulus G and the shear wave velocity Vs in substitutional doping form are generally larger than those in interstitial doping form, which are 17% and 8% higher than G and Vs in interstitial doping form at 250 GPa and 2.5 wt% carbon content. Interestingly, the elastic properties of Fe–C alloy are almost unaffected by interstitial doping sites (octahedral central site and tetrahedral central site) below 250 GPa.

The mechanical properties of (NbMoTaW)Si2 from a first-principles calculations

The realm of ceramic materials has seen a surge in interest directed towards high entropy disilicides due to their exceptional properties. Using the methodologies of density functional theory (DFT) and the special quasi-random structure (SQS), we have delved into the examination of structural stability and the inherent elastic properties of (NbMoTaW)Si2. The available experimental data and the optimized lattice parameters coincide very well. The thermodynamic stability observed in all high entropy ceramics, specifically (NbMoTaW)Si2 disilicides, can be attributed to their negative formation enthalpies. The present results of elastic parameters show that the strength/hardness of (NbMoTaW)Si2 are larger due to the higher bulk and shear moduli. The Vickers hardness of (NbMoTaW)Si2 is higher than the average value of component binary metal silicide, indicating solid solution strengthening effect. The mechanical anisotropy of the (NbMoTaW)Si2 reveals the significant difference in various directions on different crystalline planes. Conducting theoretical research holds significance in facilitating the synthesis of enhanced high entropy disilicides ceramics. Furthermore, such studies are crucial in advancing the evolution and practical utilization of high entropy materials.

Electronic structure and thermodynamic approaches to the prospect of super abundant vacancies in δ-Pu.

Super abundant vacancies (SAVs) have been suggested to form in the fcc phase of plutonium, δ-Pu, under a low-pressure hydrogen environment. Under these conditions, the vacancy concentration is proposed to reach 10-3 at% due to H trapping in vacancies lowering the effective vacancy formation energy. Previous density functional theory (DFT) results suggest that seven H atoms can be trapped in a single vacancy when a collinear special quasirandom magnetic structure is used to stabilize the δ phase, suggesting SAVs are a possible source of H stored in plutonium. In this report, we present DFT results for δ-Pu in the noncollinear 3Q magnetic state to study the formation of SAVs in mechanically stable δ-Pu. Together with these new simulations, we use publicly available computational and experimental data to provide further constraints on the physical conditions needed to thermodynamically stabilize SAVs in δ-Pu. Using several thermodynamic models, we estimate the vacancy concentrations in δ-Pu and discuss the limits of hydrogen driven formation of vacancies in δ-Pu. We find that, when hydrogen in the lattice is equilibrated with gaseous H2, the formation of SAVs in δ-Pu is unlikely and any excess vacancy concentration beyond thermal vacancies would need to occur by a different mechanism.

Why alloying with noble metals does not decrease the oxidation of platinum: a DFT-based ab initio thermo-dynamics study.

Despite its well-known nobility, even platinum is subject to corrosion under the harsh conditions that many technical applications require. Based on the assumption that the platinum loss is mainly caused by the formation of volatile PtO2, alloying is a promising strategy to reduce it. This investigation explores the bulk stability of Pt-Au, Pt-Ir, Pt-Re, Pt-W, Pt-Ag, Pt-Rh, Pt-Cu, Pt-Ni and Pt-Co, as well as their oxides, utilizing density functional theory, as well as ab initio and literature thermodynamic data. The alloy model combines special-quasi random structures with thermodynamic properties interpolated from the constituting metals, which are complemented by the configuration entropy. The results suggest that reducing platinum oxidation by alloying decreases the overall nobility of the alloy, since platinum- and oxygen affinity of the alloying metal are related to each other. Despite this limitation, copper was identified as a promising candidate for stabilizing the platinum catalyst in the Ostwald process.