Special Quasirandom Structures Research Articles

The effect of chemical disorder on magnetic properties of FeNi and Fe2Ni2N alloys

The dependency of magnetic anisotropy constant Ku on the degree of order for L10-ordered FeNi alloys and tetragonally ordered Fe2Ni2N alloys has been investigated using first-principles calculations with special quasi-random structure. The Ku increases with increasing ordering parameter S for both alloys and the Ku of Fe2Ni2N exceeds that of FeNi in the region above S = 0.5, and more than 1 MJ/m3 of Ku can be expected when the S is 0.67 or higher, reaching more than 2 MJ/m3 for fully ordered Fe2Ni2N. We also investigated the Ku of tetragonally ordered Fe2Ni2N for the tetragonal distortion, and found that the Ku is increased with in-plane compressive stain and reaches 2.2 MJ/m3 with a 1 % compression of in-plane lattice parameter.

Identifying the crystal structure of T1 precipitates in Al-Li-Cu alloys by ab initio calculations and HAADF-STEM imaging

• A new ground-state T1 structure was proposed using the cluster expansion combined with convex hull analysis. • Atomic-resolution HAADF-STEM images verify the reliability of the new T1 structure. • The Al-Li corrugated layers at the phase boundary were revealed by atomic force and bonding calculations. Controversial experimental reports on the crystal structure of T 1 precipitates in Al-Li-Cu alloys have existed for a long time, and all of them can be classified into five models. To clarify its ground-state atomic structure, herein, we have combined high-throughput first-principles calculations and CALPHAD, as well as aberration-corrected HAADF-STEM experiments. Employing the special quasi-random structure (SQS) and supercell approximation (SPA) methods to simulate the local disorder on Al-Cu sub-lattices, we find that none of the present models can satisfy the phase stability in Al-Li-Cu ternary system based on temperature-dependent convex hull analysis. Using the cluster expansion (CE) formulas, structural predictions derived from the five-frame models were performed. Subsequently, by introducing the vibrational contribution to the free energy at aging temperatures, we proposed a novel ground-state T 1 structure that maintains a coherent relationship with Al-matrix at the 〈 112 〉 Al orientation. The underlying phase transition between the variants of T 1 precipitates was further discussed. By means of ab initio molecular dynamics (AIMD) simulations, we resolved the controversy regarding the number of atomic layers constituting the T 1 phase and acknowledged the existence of Al-Li corrugated layers. The root cause of this structural distortion is triggered by atomic forces and bondings. Our work can have an positive impact on the novel fourth generation of Al-Cu-Li alloy designs by engineering the T 1 strengthening phase.

Effective electronic band structure of monoclinic β−(AlxGa1−x)2O3 alloy semiconductor

In this article, the electronic band structure of a β−(AlxGa1−x)2O3 alloy system is calculated, with β−Ga2O3 as the bulk crystal. The technique of band unfolding is implemented to obtain an effective band structure for aluminum fractions varying between 12.5% and 62.5% with respect to gallium atoms. A 160-atom supercell is used to model the disordered system that is generated using the technique of special quasi-random structures, which mimics the site correlation of a truly random alloy by reducing the number of candidate structures that arise due to the large number of permutations possible for alloy occupation sites. The impact of the disorder is then evaluated on the electron effective mass and bandgap, which is calculated under the generalized gradient approximation.

Investigation of PbSnTeSe High-Entropy Thermoelectric Alloy: A DFT Approach

Thermoelectric materials have attracted extensive attention because they can directly convert waste heat into electric energy. As a brand-new method of alloying, high-entropy alloys (HEAs) have attracted much attention in the fields of materials science and engineering. Recent researches have found that HEAs could be potentially good thermoelectric (TE) materials. In this study, special quasi-random structures (SQS) of PbSnTeSe high-entropy alloys consisting of 64 atoms have been generated. The thermoelectric transport properties of the highest-entropy PbSnTeSe-optimized structure were investigated by combining calculations from first-principles density-functional theory and on-the-fly machine learning with the semiclassical Boltzmann transport theory and Green-Kubo theory. The results demonstrate that PbSnTeSe HEA has a very low lattice thermal conductivity. The electrical conductivity, thermal electronic conductivity and Seebeck coefficient have been evaluated for both n-type and p-type doping. N-type PbSnTeSe exhibits better power factor (PF = S2σ) than p-type PbSnTeSe because of larger electrical conductivity for n-type doping. Despite high electrical thermal conductivities, the calculated ZT are satisfactory. The maximum ZT (about 1.1) is found at 500 K for n-type doping. These results confirm that PbSnTeSe HEA is a promising thermoelectric material.

Special quasirandom structures description of the local structure of disordered Bi0.5K0.5TiO3

Polar nanoregions (PNRs) are believed to play a decisive role in the local and macroscopic polarization in relaxor ferroelectrics. The limited microscopic understanding of the structure and dynamics of PNRs hampers the rational design of new lead-free materials. Here, the local structure of A-site disordered Bi0.5K0.5TiO3 (BKT) is investigated using synchrotron x-ray and neutron pair distribution function (PDF) analysis and density functional theory (DFT) optimized special quasirandom structures (SQSs). DFT-relaxed SQS with a 4 × 4 × 4 supercell size can reproduce the experimental PDFs of disordered BKT, as well as the partial PDFs and total polarization, with comparable results to those reported from a combined analysis of x-ray and neutron PDF data with large-box reverse Monte Carlo methods. We find that small Bi3+-rich polar clusters are likely to be the microscopic origin of relaxor behavior in disordered BKT, and that the existence of large polar nanoregions (PNRs) is not necessary to explain the relaxor properties. Our results also highlight the great potential of the SQS approach to gain a nanoscale-to-microscopic understanding of other relaxor solid solutions.

Trade-Off for Better Balanced Nonlinear Optical Performance with Disordered Si in ZnGeP2

ZnGeP2 (ZGP) possesses prominent mid-far infrared nonlinear optical (NLO) performance but suffers from a narrow bandgap. A comparative analysis revealed that the bandgap could be enhanced by substituting Si for Ge in ZGP, successfully synthesizing a series of ZnSixGe1–xP2 crystals with enlarged bandgaps compared with that of ZGP. Interestingly, when the x varies from 0 to 0.5, in addition to obtaining improved bandgaps, the second-harmonic generation (SHG) responses are enhanced simultaneously, which is abnormal because they are usually inversely proportional. Theoretical calculations with special quasirandom structures show that the NLO coefficient decreases gradually with increasing Si content, but the decrease is tiny in the 0–50% range and acute in the 50–100% range of Si. The transmission experiment of the ZnSi0.25Ge0.75P2 wafer indicates that the introduction of silicon effectively improves the transmittance in the 1–2 μm range. The enhanced transmittance and maintained NLO coefficients result in a better macroscopic SHG response. Combined with an increased laser-induced damage threshold, the introduction of Si becomes a practical approach to improve performance and extend the application of ZGP crystals.

Strengthening mechanisms of AlCoCrFeNi-WC-Ti coating from first-principles calculations

The AlCoCrFeNi-WC-Ti composite coating exhibits excellent hardness and wear resistance, which mainly comes from the various strengthening mechanisms. An accurate prediction model is crucial for analyzing the hardness contribution of various strengthening mechanisms. In this study, AlCoCrFeNi and AlCoCrFeNiW 0.5 supercells were constructed by the special quasi random structure (SQS), and then the elastic moduli were obtained by first-principles calculations. Using the elastic moduli, a predicted model was established for the hardness contribution. The results showed that the shear modulus of AlCoCrFeNi and AlCoCrFeNiW 0.5 alloys is 80.43 GPa and 68.64 GPa, respectively. Solid solution strengthening with a hardness contribution of 248.5 HV is the dominant strengthening mechanism for the AlCoCrFeNi-WC-Ti composite coating. The sum of hardness contribution is 271.4 HV from various strengthening mechanisms. And compared with the Vickers hardness, the relative error is only 7.4%. For the AlCoCrFeNiW 0.5 alloy, namely the coating matrix (CM) of the AlCoCrFeNi-WC-Ti, its sum of hardness contributions is 251.2 HV. Compared with the nanoindentation hardness, the relative error is 4.8%, which indicates that the predicted model is accurate for the hardness contribution. The mechanical constants of AlCoCrFeNi and AlCoCrFeNiW 0.5 SQS supercells were calculated by first-principles calculations. Using the mechanical constants, an accurate prediction model was established for the hardness contribution. • The mechanical constants of AlCoCrFeNi and AlCoCrFeNiW 0.5 were calculated by first-principles calculations. • The shear modulus is 80.43 GPa, and 68.64 GPa, for AlCoCrFeNi, and AlCoCrFeNiW 0.5 , respectively. • The sum of hardness contributions is 275.5 HV from various strengthening mechanisms. • The relative error is only 5.8% between the predicted hardness and the Vickers hardness.

Effects of short-range order on phase equilibria and opto-electronic properties of ternary alloy ZnxCd1-xTe

We employ first principles methods based on density functional theory and beyond to study ZnxCd1-xTe, 0≤x≤1, alloys in the zinc blende (B3) crystal structure. Cluster Expansion and Monte Carlo formalisms were deployed to provide a phase diagram determining consolute temperature of 387 K at 40% Zn concentration. Opto-electronic properties are computed with the hybrid HSE06 functional for disordered ZnxCd1-xTe alloys, which were simulated using special quasi-random structures. Bowing effects in the bandgap and effective carrier masses were observed in alloying which can be attributed to local geometrical distortions as portrayed by bond length distributions. Downward bowing in the electronic bandgap will be beneficial in photovoltaic applications through increased net photocurrent. Absorption coefficients show robust absorption in ZnxCd1-xTe as indicated by substantial optical absorption throughout all Zn concentrations, aided by low reflectivity that ensures a high absorption. Presence of short-range order in Zn0.25Cd0.75Te was observed through clustering and anti-clustering among different cationic species of Zn and Cd. It has a value of 0.11 at 1000 K compared to −0.79 at 400 K. The bandgap of Zn0.25Cd0.75Te at 1000 K was found to be slightly higher, 0.05 eV, than at 400 K, consistent with the value of short-range order. Thus, short-range order and possibly composition can be used in the design and synthesis of the appropriate solar cell, thereby improving the performance in this system.

Machine learning prediction of the mechanical properties of refractory multicomponent alloys based on a dataset of phase and first principles simulation

In this work, a dataset including structural and mechanical properties of refractory multicomponent alloys was developed by fusing computations of phase diagram (CALPHAD) and density functional theory (DFT). The refractory multicomponent alloys, also named refractory complex concentrated alloys (CCAs) which contain 2–5 types of refractory elements were constructed based on Special Quasi-random Structure (SQS). The phase of alloys was predicted using CALPHAD and the mechanical property of alloys with stable and single body-centered cubic (BCC) at high temperature (over 1,500°C) was investigated using DFT-based simulation. As a result, a dataset with 393 refractory alloys and 12 features, including volume, melting temperature, density, energy, elastic constants, mechanical moduli, and hardness, were produced. To test the capability of the dataset on supporting machine learning (ML) study to investigate the property of CCAs, CALPHAD, and DFT calculations were compared with principal components analysis (PCA) technique and rule of mixture (ROM), respectively. It is demonstrated that the CALPHAD and DFT results are more in line with experimental observations for the alloy phase, structural and mechanical properties. Furthermore, the data were utilized to train a verity of ML models to predict the performance of certain CCAs with advanced mechanical properties, highlighting the usefulness of the dataset for ML technique on CCA property prediction.

Accurate and Efficient Prediction of Highly Disordered Bi2O3 with Optimum Structure Pool: Combined Approach of the Special Quasirandom Structure Method and Structure Sampling

Accurate and Efficient Prediction of Highly Disordered Bi₂O₃ with Optimum Structure Pool: Combined Approach of the Special Quasirandom Structure Method and Structure Sampling

AI-accelerated materials informatics method for the discovery of ductile alloys

In computational materials science, a common means for predicting macroscopic (e.g., mechanical) properties of an alloy is to define a model using combinations of descriptors that depend on some material properties (elastic constants, misfit volumes, etc.), representative for the macroscopic behavior. The material properties are usually computed using special quasi-random structures (SQSs), in tandem with density functional theory (DFT). However, DFT scales cubically with the number of atoms and is thus impractical for a screening over many alloy compositions. Here, we present a novel methodology which combines modeling approaches and machine-learning interatomic potentials. Machine-learning interatomic potentials are orders of magnitude faster than DFT, while achieving similar accuracy, allowing for a predictive and tractable high-throughput screening over the whole alloy space. The proposed methodology is illustrated by predicting the room temperature ductility of the medium-entropy alloy Mo-Nb-Ta.

Theoretical studies of optoelectronic properties of AlP1-xBix ternaries: Promising light sources for fiber optic communications

The aim of this paper is to investigate the optoelectronic properties of the new ternary alloys AlP1-xBix at different concentrations of Bismuth x (0 ≤ x ≤ 1), using super cell 16 atoms special quasi-random structures within the full-potential linearized augmented plane wave method (FP-LAPW) employing Wien2k based on the density functional theory. The generalized gradient approach of Perdew et al. (GGA-PBEsol) was used to study the structural properties. The electronic and optical properties were predicted using the local density (LDA) and Tran–Blaha-modified Becke–Johnson (TB-mBJ) approaches. The lattice parameters (a), bulk modulus (B) and band gap energy (Eg) are calculated and analyzed for ternary alloys and their binaries. It is found that the variation of the lattice constant a(x) exhibits a small bowing parameter equal to (−0.1366Å) according to Vigard's law. Band structure analysis shows that AlP1-xBix ternaries have direct band gaps for concentrations x (0 ≤x ≤ 1). The (TB-mBJ) results show that the band gap values of AlP1-xBix vary from 2.322 eV to 0.426 eV which corresponds to wavelengths from 0.534μm to 2.910μm. Furthermore, we investigated in detail the optical properties of AlP1-xBix ternaries. We can point out that this work represents the first theoretical study on these ternaries. The calculation confirms that the AlP1-xBix ternary alloys are promising candidate for optoelectronics, and in particular for light sources for fiber-optic communications.

Modelling the Defect Processes of Materials for Energy Applications

The technological requirement for ever more efficient materials for the energy and electronics sectors has led to the consideration of numerous compositionally and structurally complicated systems. These systems include solid solutions that are difficult to model using electronic structure calculations because of the numerous possibilities in the arrangement of atoms in supercells. The plethora of such possible arrangements leads to extensive and large numbers of potential supercells, and this renders the investigation of defect properties practically intractable. We consider recent advances in oxide interfaces where studies have demonstrated that it is feasible to tune their defect processes effectively. In this review, we aim to contribute to the ongoing discussion in the community on simple, efficient and tractable ways to realise research in solid solutions and oxide interfaces. The review considers the foundations of relevant thermodynamic models to extract point defect parameters and the special quasirandom structures method to model the supercell of solid solutions. Examples of previous work are given to highlight these methodologies. The review concludes with future directions, systems to be considered and a brief assessment of the relevant methodologies.

Revisit the VEC criterion in high entropy alloys (HEAs) with high-throughput ab initio calculations: A case study with Al-Co-Cr-Fe-Ni system

Valence electron concentration (VEC) was treated as a useful parameter to predict the stability of solid solution phases. However, the available experimental data to support this criterion is far from enough. In the current study, the high-throughput ab initio modeling is applied to investigate the relative stability of FCC and BCC single crystals of the Al-Co-Cr-Fe-Ni high entropy alloys (HEAs) by using the special quasi-random structure (SQS) approach. The predictions start with pure elements of the Al-Co-Cr-Fe-Ni system and are continued with binaries, ternaries, and quaternary compositions, which come up with 180 compositions (360 structures). After that, the reliability of the VEC criterion is testified. The results show that the VEC criterion not only works for the stable structure but also works effectively for metastable structure when both FCC and BCC are not thermodynamic stable. However, it is found that the old VEC criterion proposed by Guo et al. fails to work effectively for compositions containing high concentrations of light-weight metals such as Al at VEC< 5. To solve this problem, the present work proposed a new VEC rule to define the stability of FCC and BCC structures at the ground state. With the implementation of the new VEC rule, the effectiveness of the VEC rule (EVEC) of both FCC and BCC structures is enhanced, especially for pure elements and binary compositions, indicating that this rule does not only work effectively for multicomponent systems but also works for low-order systems. • The Effectiveness of empirical VEC rule in the Al-Co-Cr-Fe-Ni system was systematically discussed. • The HT-ab initio calculations were performed to investigate the relative stability of FCC and BCC structure in the Al-Co-Cr-Fe-Ni system. • 180 compositions (360 structures) were investigated based on the Special Quasi-random Structures (SQS) method. • A new VEC criterion was proposed based on the results of the HT-calculations.

First-principles study of 3sp impurity (S, P, Si, Al) effects on vacancy-mediated diffusion in Ni and Ni-33Cr alloys

The effect of minor impurities on vacancy-mediated processes is a critical factor causing unanticipated degradation rates in structural alloys. We investigate the 3sp impurity effect by first-principles calculations to derive impurity-modified diffusion in dilute Ni. Calculations are also performed for special quasi-random structures (SQSs) of Ni-33Cr to investigate the similarity of representative hops that affect vacancy-mediated kinetics. The results show considerable enhancement of vacancy mobility by P and S for Ni and Ni-Cr alloys due to vacancy binding and reduced migration barriers of the re-orientation hops at the vicinity of the impurity atom. The enhanced diffusion can cause variability of microstructure changes and degradation rates in industrial Ni-based alloys, particularly for structural components where local segregation of impurities can occur due to non-equilibrium conditions.

Lattice distortion and the influence on mechanical and thermodynamic properties of high entropy (HfZrTaNbTi)X (X=C, N, NC) by Ab initio investigation

Novel high-entropy ceramics have been rapidly developing and exhibiting excellent properties. In this paper, the structural distortion and the influence on mechanical and thermodynamic properties of (HfZrTaNbTi)C, (HfZrTaNbTi)N and (HfZrTaNbTi)(NC) are systematically studied by employing density functional theory in conjunction with special quasi-random structure (SQS). Our results show that lattice distortion enhances the structural stability of these high-entropy ceramics by lowering the formation and mixing enthalpy. The local lattice distortion in considered ceramics is further quantified in terms of constituent atoms displacement and bond length distribution, suggesting that (HfZrTaNbTi)C and (HfZrTaNbTi)N possess the smallest and largest distortion, respectively. While the distortion in anion and cation mixed (HfZrTaNbTi)(NC) is intermediate. The elastic properties illustrate that the distortion improved the ductility of high-entropy ceramics at the slight expense of strength and stiffness. The electronic structures show that (HfZrTaNbTi)C has the strongest covalent bonds and (HfNbTaTiZr)N possesses a stronger ionic character. After distortion, the DOS at the Fermi level for the three ceramics is reduced and the charge density is significantly enhanced, revealing the underlying mechanism for stability improvement. Combining the Debye-Grüneisen model, the thermodynamic properties and the influence of lattice distortion are further studied. It is found that lattice distortion improves thermal expansion and heat storage capacity. Simultaneously, the distortion also increases the entropy of ceramics, thereby enhancing the stability in high-temperature environments. This paper provides a valuable reference for understanding crucial properties and designing promising multi-cation and anion mixed high-entropy ceramics by revealing the vital role of lattice distortion.

The intrinsic mechanical properties of NbTaTiZr and the influence of alloying elements Mo and W: A first-principles study

The intrinsic mechanical properties of NbTaTiZr and NbTaTiZrX (X Mo, W) are studied by using a first-principles calculation in combination with special quasi-random structure. For NbTaTiZr RHEA, the ideal tensile strength (ITS) and compressive strength (ICS) along [001] direction is respectively calculated to be 5.64 GPa and −18.4Gpa at the strain 11% and −20%. For shear loading along (211)[111] slip system, the ideal shear strength (ISS) is 3.03 GPa as the strain is about 20%. With addition of Mo into NbTaTiZr, the ITS, ICS and ISS respectively increase up to 9.7, −19.3 and 4.73 GPa, and the addition of W enhances the ITS, ICS and ISS up to 10.5, −21.1 and 5.12 GPa, respectively. Hence addition of Mo or W can significantly improve the ideal strength, especially stronger impact of W element. The calculated elastic moduli E [001] and G [111] are in reasonable agreement with the initial slope of the stress-strain relationship. The derived dimensionless ITS and ISS from first-principle calculations is underestimated the ideal strength in comparison with the prediction by the universal empirical model. Then the microcosmic mechanism is further studied by examination of the detailed bond length variation of three HEAs during the corresponding deformation. Near the critical strain under of tension and shear, the slower descend of stress originates from the gradual breakage of atomic bonds, while the compressive stress decreases rapidly owing to all bond fracturing almost simultaneously. Finally, the ideal strength of three HEAs is further analyzed from electronic structure. • The ideal strength is studied using ab initio calculations based on special quasi-random model. • The ideal strength and critical strain show NbTaTiZr has good strength and ductility. • The dimensionless ideal strength is overestimated in the empirical model. • The slow descend of tensile/shear stress results from the gradual breakage of atomic bonds. • The rapid decrease of compressive stress is due to the almost simultaneous fracture of all bonds.

Energy and mechanical properties predictions in Fe-Ni binary system by ab initio calculations

The fcc random solid solutions in Fe-Ni binary system were investigated using ab initio calculations. Density functional theory (DFT) was applied along with supercells generated by the Special Quasi-Random Structure (SQS) method to predict the enthalpy of mixing and magnetic and elastic properties. The results were compared with relevant experimental and computational data produced by other groups. The effect of SQS supercell size and relaxation procedure on the predicted properties of the alloys were also studied. Our calculations show that 16-atoms SQS model provides adequate approach to the mixing energy of the alloy. However, calculation of mechanical properties requires larger supercell. Excellent agreement between experimental and calculated elastic properties was found in fcc region of Fe-Ni system.

A first-principles-based high fidelity, high throughput approach for the design of high entropy alloys

Here, we present a preselected small set of ordered structures (PSSOS) method, a first principles-based high fidelity (HF), high throughput (HT) approach, for fast screening of the large composition space of high entropy alloys (HEAs) to select the most energetically stable, single-phase HEAs. Taking quinary AlCoCrFeNi HEA as an example system, we performed PSSOS calculations on the formation energies and mass densities of 8801 compositions in both FCC and BCC lattices and selected five most stable FCC and BCC HEAs for detailed analysis. The calculation results from the PSSOS approach were compared with existing experimental and first-principles data, and the good agreement was achieved. We also compared the PSSOS with the special quasi-random structures (SQS) method, and found that with a comparable accuracy, the PSSOS significantly outperforms the SQS in efficiency, making it ideal for HF, HT calculations of HEAs.

First-principles study of hydrogen-vacancy interactions in CoCrFeMnNi high-entropy alloy

Vacancies can easily capture H atoms in metals, forming hydrogen-vacancy complexes/clusters. In this work, the hydrogen-vacancy interactions in CoCrFeMnNi high-entropy alloy (HEA) were studied with first-principles calculations based on the density functional theory (DFT). The special quasi-random structure (SQS) method was used to construct a chemically disordered HEA, and the effects of solute H atoms on the formation energy of monovacancy, the formation energy and binding energy of multi-vacancy cluster were calculated. It is found that an H atom prefers to occupy an octahedral interstitial site neighboring a vacancy and attracts the charge from the surrounding first-nearest neighbor atoms (e.g. Co, Ni, Fe or Mn atom, excluding Cr atom), weakening the stability of the atoms around the vacancy and reducing the vacancy formation energy in CoCrFeMnNi HEA. After introducing H atoms, the formation energies of both vacancy and vacancy cluster decrease in CoCrFeMnNi HEA, but they are still higher than those in pure Fe and Ni. In addition, the reduction of the binding energy of vacancies in CoCrFeMnNi HEA is much lower than that in pure Fe and Ni, and the binding energy of vacancies even increases in some cases. The results of the first-principles calculations indicate that the solute hydrogen atoms, although promoting vacancies, unfavorably combining vacancies into clusters to form micro-voids. This provides a good explanation for the good resistance to hydrogen embrittlement of CoCrFeMnNi HEA observed in experiments.