Special Quasirandom Structures Research Articles

Defect energetics for diffusion in CrMnFeCoNi high-entropy alloy from first-principles calculations

We investigated the bulk properties and formation, in addition to the migration energies of vacancies in CrMnFeCoNi using first-principles calculations based on the special quasi-random structure (SQS) approach. The ferromagnetic state of this material was more stable than the paramagnetic state, which mainly originates from the increase in the magnetic moment of Cr atoms. Moreover, the average of the vacancy formation energy of each element was almost the same at approximately 2.0 eV while the average of the vacancy migration energy of each element increased with increasing atomic number. As a result, the activation energy increased from Cr to Ni. The lattice distortion around each element, which exhibited a decreasing trend with increasing atomic number, contributed to a reduction of both the formation and migration energy of the vacancies. The downward shift of 3d orbitals during the migration process also contributed to a reduction of the energy barrier.

Impact of local composition on the energetics of E-centres in Si1\u2212xGex alloys

The energetics of the defect chemistry and processes in semiconducting alloys is both technologically and theoretically significant. This is because defects in semiconductors are critical to tune their electronic properties. These processes are less well understood in random semiconductor alloys such as silicon germanium as compared to elementary semiconductors (for example silicon). To model the random silicon germanium alloy we have employed density functional theory calculations in conjunction with the special quasirandom structures model for different compositions. Here we show that, the energetics of substitutional phosphorous-vacancy pairs (E-centres) in Si1−xGex alloys vary greatly with respect to the local Ge concentration and the composition of the alloy. The most energetically favourable E-centres have a Ge atom as a nearest neighbour, whereas the dependence of the binding energy of the E-centres with respect to alloy composition is non-linear.

Thermodynamic description of the K, Be//F, Cl salt system with first-principles calculations

Reciprocal molten halides are a distinctive class of high-temperature ionic liquids used as thermal and electrolytic media in the respective fields of MSR (molten salt nuclear reactor) and metallurgy. Strong Short-Range Ordering (SRO) from both the first-nearest (cation-anion) and second-nearest (cation-cation and anion-anion) neighbors defy accurate theoretical simulations of their physical and chemical properties and hence impede quantitative designs of optimum media applicable to industrial sectors. Based upon the Modified Quasichemical Model in the Quadruplet Approximation (MQMQA) coupled with the Multi-State Model (MSM), we developed a model (K+, BeIV2+, Be24+//F−, Cl−) to describe the thermodynamic behavior of the complex reciprocal K, Be//F, Cl liquid, where various types of SRO were evidenced by theoretical and experimental observations. This combinatorial method can quantitatively generate various sorts of quadruplets, thus providing structural entities to build other thermo-physical models. The thermodynamic properties of solid salts were also investigated to be able to calculate the entire reciprocal phase diagram. A vast amount of DFT (Density Functional Theory)-based first-principles predictions was performed based on various combinations of Pseudopotentials and Exchange-Correlation Functionals, SQS (special quasi-random structure) models of solid solutions and data-mining screened crystal structures of double salts. The calculations are in satisfactory agreement with the available experimental data, thus showing that the simulation capability could promote industrial advancements through a quantitative design of innovative materials.

Electronic band structure, thermodynamics and optical characteristics of BeO1−xAx(A = S, Se, Te) alloys: Insights from ab initio study

Special quasi-random structure (SQS) was used to investigate the structural, electronic, and optical characteristics of the binary and ternary beryllium chalcogenide alloys. The computations were performed using the pseudopotential technique. The GGA-WC scheme was applied to study the structural and optical features of these present alloys, while the HSE06 hybrid functional was used to correct the underestimation of the electronic band structure. The optimized lattice constants and bulk modulus demonstrate a non-linear tendency with increasing x concentration. The phase transition may occur for all ternary alloys at x = 0.5 with the orthorhombic assumed crystal system. The ternary alloys of BeO1−xAx (A = S, Se) at 0.5 ⩽ x ⩽1 have an indirect band gap, while BeO1−xTex0.5 ⩽ x ⩽ 1 manifest a metallic demeanor using HSE06 formalism. The optical spectra were computed and discussed in detail. Furthermore, the thermodynamic stability of the studied compounds was examined using the miscibility critical temperature.

Thermodynamic Properties of Wx(TaTiVCr)1−x High‐Entropy(‐Like) Alloy and Influence of Tungsten Content

Based on quasi‐harmonic Debye–Grüneisen model and thermal equation of state, thermodynamic properties of high‐entropy(‐like) alloy Wx(TaTiVCr)1−x (x = 0.30–0.67) phases have been studied by first principles density functional theory calculations combined with special quasi‐random structure (SQS) model, and the influence of W content is predominantly emphasized. Present investigations show that bulk modulus B of Wx(TaTiVCr)1−x declines with increasing temperature, and the softening tendency is similar for various W content, although the strength of Wx(TaTiVCr)1−x demonstrates overall lowering with simultaneous alloying of Ta, Ti, V, and Cr. The thermal expansion coefficient of Wx(TaTiVCr)1−x rises nonlinearly with increasing temperature, and the increase rate is lowered with more W content. The temperature dependence of heat capacity at constant volume CV and constant pressure CP of Wx(TaTiVCr)1−x also exhibits analog behavior at various W content. Thermodynamic entropy of Wx(TaTiVCr)1−x increases dramatically with temperature, and the contribution from electronic entropy, configuration, and vibrational entropy is discussed in detail. In addition, the Debye‐temperature and Grüneisen parameter are also analyzed. The present results are very valuable for optimizing the composition and comprehensive properties of W‐containing high‐entropy(‐like) alloys.

First principles investigation into the phase stability and enhanced hardness of TiN-ScN and TiN-YN alloys

We study the phase stability, mechanical properties, and electronic structure of two quasi-binary ceramic systems, Ti1-xScxN and Ti1-xYxN (0 ≤ x ≤ 1), using first principles methods based on density functional theory, cluster expansion formalism, and Monte Carlo techniques. Owing to the similarity in ionic radii and electronegativities of their respective transition metals, strong exothermic mixing of TiN and ScN is predicted, with four ordered intermetallic phases lying on the convex hull: TiScN2, TiSc8N9, TiSc9N10, and Ti3Sc2N5. These structures form layered rocksalt-type configurations to minimize strain energy while maximizing occupation of bonding states. The fully-detailed phase diagram including these predicted ground states and known end members is constructed, revealing an upper consolute temperature of 660 K. In contrast to Ti1-xScxN, the mismatched properties of TiN and YN lead to large structural distortions and positive strain energies. As a result, endothermic mixing with significant upward bowing in the formation energy is observed at intermediate concentrations, with the consolute temperature of 7225 K being predicted from the phase diagram of Ti1-xYxN. TiN, ScN, and YN are found to display hardness values of 23.4, 25.1, and 20.6 GPa respectively, in good agreement with experimental data. The intermetallic phase Ti3Sc2N5 is predicted to exhibit an exceptionally high hardness of 27.3 GPa. From analysis of projected electronic density of states and Crystal Orbital Hamiltonian Populations, we attribute enhanced hardness to strong nitrogen p and metal d hybridization, being related to 3d eg occupation, and decreased tendency towards shearing, being related to minimal 3d t2g occupation. These features extend to the case of random solutions, which we model using special quasirandom structures, showing a maximum hardness at a valence electron concentration of 8.4. Based on these findings, we suggest Ti1-xScxN alloys for implementation in hard coating applications.

Phase field parameters for battery compounds from first-principles calculations

In this work, we present and apply schemes to determine from first-principles calculations the relevant effective parameters used in phase field theory simulations of battery compounds. In particular, we derive that a consistent free energy density can be obtained by mean-field sampling, which is especially suited for materials with different configurations on a lattice, such as alloys or Li intercalation batteries. In addition, it is demonstrated that mean-field sampling can be performed very effectively with the use of special quasi random structures and that experimentally determined free energy density parameters for ${\mathrm{LiFePO}}_{4}$ are reproduced by density functional theory calculations. The additional computation of interfacial and strain energy parameters allows us to present a consistent phase field parametrization of ${\mathrm{Li}}_{2}{\mathrm{FeSiO}}_{4}$ without relying on experimental data.

An Ab Initio Study of Vacancies in Disordered Magnetic Systems: A Case Study of Fe-Rich Fe-Al Phases.

We have performed quantum-mechanical calculations to examine the impact of disorder on thermodynamic, structural and electronic (magnetic) properties of Fe-Al systems with vacancies. A series of supercells was used and their properties were computed employing density-functional theory (DFT) as implemented in the VASP package. Our case study is primarily aimed at a disordered solid solution FeAl but we have compared our results also with those obtained for the ordered FeAl intermetallic compound for which experimental data exist in literature. Both phases are found in Fe-Al-based superalloys. The Fe-18.75at.%Al solid solution was simulated using special quasirandom structures (SQS) in three different disordered states with a different distribution of Al atoms. In particular, we have considered a general disordered case (an A2-like variant), the case without the first nearest neighbor Al-Al pairs (a B2-like distribution of atoms) and also the case without both the first and second nearest neighbor Al-Al pairs (the D0-like variant, in fact, an Fe-rich FeAl phase). The vacancy formation energies as well as the volumes of (fully relaxed) supercells with vacancies showed a large scatter for the disordered systems. The vacancy formation energies decrease with increasing concentration of Al atoms in the first coordination shell around the vacancy (an anti-correlation) for all disordered cases studied. The computed volumes of vacancies were found significantly lower (by 25–60%) when compared with the equilibrium volume of the missing atoms in their elemental states. Lastly, we have analyzed interactions between the vacancies and the Fe atoms and evaluated vacancy-induced changes in local magnetic moments of Fe atoms.

First-principles investigations of the magnetic phase diagram of Gd1−xCaxMnO3

We studied for the first time the magnetic phase diagram of the rare-earth manganites series Gd$_{1-x}$Ca$_{x}$MnO$_{3}$ (GCMO) over the full concentration range based on density functional theory. GCMO has been shown to form solid solutions. We take into account this disordered character by adapting special quasi random structures at different concentration steps. The magnetic phase diagram is mainly described by means of the magnetic exchange interactions between the Mn sites and Monte Carlo simulations were performed to estimate the corresponding transition temperatures. They agree very well with recent experiments. The hole doped region $x<0.5$ shows a strong ferromagnetic ground state, which competes with A-type antiferromagnetism at higher Ca concentrations $x>0.6$.

Investigation of thermodynamic properties of high entropy (TaNbHfTiZr)C and (TaNbHfTiZr)N

Based on density functional theory calculation in conjunction with quasi-harmonic Debye-Grüneisen model, thermodynamic properties of (TaNbHfTiZr)C and (TaNbHfTiZr)N are studied, in which the chemical disorder is modeled with the special quasi-random structure. Thermodynamic entropies for both materials rise significantly due predominantly to vibrational contribution, and (TaNbHfTiZr)N is more stable at high temperatures because its entropy increment is more dramatic with increasing temperature. Although the high temperature softening effect is very similar, (TaNbHfTiZr)N is more beneficial for higher temperature applications because of the much larger bulk modulus. Thermal expansion coefficients for both materials increase first rapidly then slowly, and (TaNbHfTiZr)N is more slightly susceptible to temperature. For (TaNbHfTiZr)C and (TaNbHfTiZr)N, the heat capacities at constant volume and pressure demonstrate similar behaviors, being larger than metal high entropy HfNbTaTiZr. The present investigations provide helpful insights into the thermodynamic behaviors for both materials.

Theory of the energy fluctuation of multicomponent alloys

Structural models are usually employed to calculate the physical properties of random alloys. The “Special Quasirandom Structures” (SQS) method was proposed to maximize the randomness of systems with given sizes in 1990. However, hitherto there is no theory to guide the finding of such system sizes with appropriately small energy fluctuations as input for the SQS method. To this end, we propose an effective theory to treat the fluctuations of energies for random multicomponent alloys. The theory is validated by accurate Wang-Landau Monte Carlo sampling in the cases of body-centered cubic FeCo and face-centered cubic NiCoCr alloys.

Impact of Nano-Scale Distribution of Atoms on Electronic and Magnetic Properties of Phases in Fe-Al Nanocomposites: An Ab Initio Study.

Quantum-mechanical calculations are applied to examine magnetic and electronic properties of phases appearing in binary Fe-Al-based nanocomposites. The calculations are carried out using the Vienna Ab-initio Simulation Package which implements density functional theory and generalized gradient approximation. The focus is on a disordered solid solution with 18.75 at. % Al in body-centered-cubic ferromagnetic iron, so-called -phase, and an ordered intermetallic compound FeAl with the D0 structure. In order to reveal the impact of the actual atomic distribution in the disordered Fe-Al -phase three different special quasi-random structures with or without the 1st and/or 2nd nearest-neighbor Al-Al pairs are used. According to our calculations, energy decreases when eliminating the 1st and 2nd nearest neighbor Al-Al pairs. On the other hand, the local magnetic moments of the Fe atoms decrease with Al concentration in the 1st coordination sphere and increase if the concentration of Al atoms increases in the 2nd one. Furthermore, when simulating Fe-Al/FeAl nanocomposites (superlattices), changes of local magnetic moments of the Fe atoms up to 0.5 are predicted. These changes very sensitively depend on both the distribution of atoms and the crystallographic orientation of the interfaces.

Experimental investigations and thermodynamic modelling of the Cr–Nb–Sn–Zr system

This work reports the Calphad modelling of the Cr–Nb–Sn–Zr quaternary system. In a previous paper, the thermodynamic modelling of the Cr–Nb–Sn system was presented. Since no experimental data were available for the Cr–Sn–Zr ternary system, new experimental data are provided, within this study, on the isothermal section at 900 °C. A ternary C14 phase has been identified on the Sn-poor side of the phase diagram. In addition to these experimental data, Density Functional Theory (DFT) calculations are carried out in order to determine formation enthalpies of the stable and metastable compounds. At last, the Special Quasirandom Structures (SQS) method is jointly used with DFT calculations in order to estimate the mixing enthalpies of the A2 and A3 binary solid solutions. Finally, these experimental and calculated data in addition to those from the literature, are used as input data for the Calphad modelling of the Cr–Zr, Nb–Zr and Sn–Zr binary systems and the Cr–Nb–Zr, Cr–Sn–Zr and Nb–Sn–Zr ternary systems. A complete database for the Cr–Nb–Sn–Zr quaternary system is provided.

Atomic interactions in C15 Laves phases

The C15 phase ( $$Fd\bar{3}m$$ ) has been extensively studied by several methodologies to evaluate its atomic interactions. Ideally ordered at the $$AB_2$$ composition, this Laves phase is known to present a non-stoichiometry domain accommodated by substitutional atomic disorder at high temperature. With the Cu–Mg system as an example, a cluster expansion method study revealed that first neighbors pair interaction is positive yielding a favorable mixing of Cu and Mg atoms in 16d site and a homogeneity extended in the Mg-richer side. To guide the thermodynamic modeling of the C15 phase, special quasi-random structure cells have been generated at several compositions to simulate atom mixing with and without the merging of 8a and 16d sites. Combined with electronic density functional theory, calculation on several systems (Ta–V, Cr–Nb, Mo–Zr and Cr–Ti) was done to estimate the mixing energies on the two different sublattices. The results are compared to published assessments and open a discussion on the acceptability of the traditional thermodynamic model.

Optimizing special quasirandom structure (SQS) models for accurate functional property prediction in disordered 2D alloys

2D materials such as MXenes have garnered attention in a wide field of applications ranging from energy to environment to medical. Properties of 2D materials can be tailored via alloying and in some cases, solid-solutions (disordered alloys) are formed. To predict the disordered alloy properties via first-principles, the model structure needs to imitate the random arrangements of alloyants and yet remains computationally tractable. Using density functional theory and the cluster expansion method, we investigate the accuracy of using of special quasirandom structures (SQSs) for predicting disordered 2D alloy properties, evaluating the effect of SQS supercell size on the prediction quality of formation energies, elastic properties, and structural parameters. We illustrate the findings with 5 different disordered binary MXene alloy systems (where M = Ti and M′ = Zr, Hf, V, Nb, or Ta), demonstrating that SQSs around 6–8 times the primitive cell (N = 6–8) are sufficient to attain convergence in the property predictions versus supercell size. For formation energies, SQSs with N > 4 are found to reproduce the formation energies of the fully disordered phase within ~2.5 meV. For the simulation of the experimentally-synthesized TiNbCO2, we find convergence in structural parameters and elastic tensors at N ~ 6. We traced the convergence of the predictions to the convergence in the band structure-related properties via analysis of the electronic densities-of-states and the projected crystal overlap Hamilton population. Our findings suggest that modest sized SQSs would reproduce the properties of disordered MXene alloys. The results should help guide the investigations of structure-property relationships in other disordered 2D materials as well.

Enhancing the Photocatalytic Performance of MXenes via Stoichiometry Engineering of Their Electronic and Optical Properties.

Combining both density functional theory and the cluster expansion method, we investigate 3 binary MXene alloy systems of semiconducting Ti2CO2, Zr2CO2, and Hf2CO2, where the transition metals substitute one another (i.e., Ti2(1- x)Zr2 xCO2, Ti2(1- x)Hf2 xCO2, and Zr2(1- x)Hf2 xCO2). We show that this group of MXene alloys forms the solid-solution phase across all compositions. Special quasirandom structures are generated to model the solid-solution phase of these alloys, using which we demonstrate how their structural, mechanical, electronic, and optical properties are tuned via stoichiometry engineering. These alloys exhibit outstanding mechanical strength and stability. They possess indirect band gaps of 1.25-1.80 eV. For Ti2(1- x)Zr2 xCO2 and Ti2(1- x)Hf2 xCO2, they display higher absorbance in the solar spectrum than their constituent Zr2CO2 and Hf2CO2, respectively. Most of the MXene alloys also show appropriately aligned band edges for water splitting. We predict the Ti2(1- x)Zr2 xCO2 alloy with x = 0.2778 to be the most promising water-splitting photocatalyst among the MXenes studied here, outperforming its constituents, Ti2CO2 and Zr2CO2, when solar absorbance performance and band-edge alignments are simultaneously considered. This work demonstrates that alloying can be used to effectively tune photocatalytic performance.

Structural and electronic properties of wurtzite, zincblende and rocksalt Al1 − xInxN ternary alloys at ambient and high pressure

ABSTRACTAlthough AlInN is originally a wurtzite structure, zincblende and rocksalt are other potential phases. It will be interesting to have a comparative study of the physical properties of this compound in various phases. A DFT-based study of wurtzite, zincblende and rocksalt phases of AlInN alloys is carried out. Structural (lattice parameter, bulk modulus) and electronic properties (energy band gap, and electron effective mass) of the Al1 − xInxN alloys are investigated, at ambient pressure, throughout the whole range of indium contents for all considered phases. High pressure effects on the studied parameters are also examined, with the phase transition pressures computed for different values of In concentrations, and compared with available data. Structural density functional calculations are performed with Perdew–Burke–Ernzerhof gradient-corrected functional for solids (PBEsol), while electronic structure is computed with the modified Becke–Johnson (TB-mBJ) potential exchange to ensure a better accuracy of calculated the band gaps. Alloy randomness is taken into account using a special quasi-random structure.

First-principles quantitative prediction of the lattice thermal conductivity in random semiconductor alloys: The role of force-constant disorder

The standard theoretical understanding of the lattice thermal conductivity, $\kappa_{\ell}$, of semiconductor alloys assumes that mass disorder is the most important source of phonon scattering. In contrast, we show that the hitherto neglected contribution of force-constant (IFC) disorder is essential to accurately predict the $\kappa_{\ell}$ of those polar compounds characterized by a complex atomic-scale structure. We have developed an \emph{ab initio} method based on special quasirandom structures and Green's functions, and including the role of IFC disorder, and applied it in order to calculate the $\kappa_{\ell}$ of $\mathrm{In_{1-x}Ga_xAs}$ and $\mathrm{Si_{1-x}Ge_x}$ alloys. We show that, while for $\mathrm{Si_{1-x}Ge_x}$, phonon-alloy scattering is dominated by mass disorder, for $\mathrm{In_{1-x}Ga_xAs}$, the inclusion of IFC disorder is fundamental to accurately reproduce the experimentally observed $\kappa_{\ell}$. As the presence of a complex atomic-scale structure is common to most III-V and II-VI random semiconductor alloys, we expect our method to be suitable for a wide class of materials.

Computation of stability, elasticity and thermodynamics in equiatomic AlCrFeNi medium-entropy alloys

We investigated the phase stability, elastic and thermodynamic properties of equimolar medium-entropy alloys (MEAs) AlCrFeNi by performing first-principles calculations in combination with quasi-harmonic Debye–Gruneisen model. Both body-centered cubic (BCC) and face-centered cubic structures in ferromagnetic (FM) and non-magnetic states are described using the special quasirandom structures technique. All the considered MEAs can form single-phase solid solutions and are dynamically stable, and FM BCC AlCrFeNi is the most stable. The elastic moduli including bulk modulus B, shear modulus G and Young’s modulus E of AlCrFeNi are calculated by first-principles and estimated by using the rule of mixtures (ROM) from their pure components. The lattice constants a of first-principles calculations are well reproduced by ROM. The obtained B and G of the two methods are close to equality lines with a minor scatter. The relevant free energies’ contributions including structural, configurational, vibrational and electronic excitations are taken into account to calculate the equilibrium lattice constants a, volumetric thermal expansion coefficient α, Debye temperature ΘD, constant volume heat capacity Cv, vibrational entropy Svib, electronic entropy Selec, vibrational Helmholtz free energies Fvib and electronic Helmholtz free energies Felec of AlCrFeNi MEAs at finite temperature. The thermodynamic properties strongly depend on crystal structures and magnetic states, and FM BCC AlCrFeNi shows the largest Svib and α, and the lowest Fvib among the considered MEAs. Finally, electronic density of states is analyzed to clarify the physical origin of AlCrFeNi MEAs with different crystal structures and magnetic states.

Alloy broadening of the transition to the nontrivial topological phase of Pb1−xSnxTe

Transition between the topologically trivial and non-trivial phase of Pb_{1-x}Sn_{x}Te alloy is driven by the increasing content $x$ of Sn, or by the hydrostatic pressure for $x<0.3$. We show that a sharp border between these two topologies exists in the Virtual Crystal Approximation only. In more realistic models, the Special Quasirandom Structure method and the supercell method (with averaging over various atomic configurations), the transitions are broadened. We find a surprisingly large interval of alloy composition, $0.3<x<0.6$, in which the energy gap is practically vanishing. A similar strong broadening is also obtained for transitions driven by hydrostatic pressure. Analysis of the band structure shows that the alloy broadening originates in splittings of the energy bands caused by the different chemical nature of Pb and Sn, and by the decreased crystal symmetry due to spatial disorder. Based on our results of ab initio and tight binding calculations for Pb_{1-x}Sn_{x}Te we discuss different criteria of discrimination between trivial and nontrivial topology of the band structure of alloys.