Special Quasirandom Structures Research Articles

Electronic and thermoelectric properties of Mg2GexSn1−x (x = 0.25, 0.50, 0.75) solid solutions by first-principles calculations∗Project supported by the National Natural Science Foundation of China (Grant No. 11647010) and the Foundation from the Higher Education and High-quality and World-class Universities (Grant No. PY201611).

The electronic structure and thermoelectric (TE) properties of Mg2GexSn1−x (x = 0.25, 0.50, 0.75) solid solutions are investigated by first-principles calculations and semi-classical Boltzmann theory. The special quasi-random structure (SQS) is used to model the solid solutions, which can produce reasonable band gaps with respect to experimental results. The n-type solid solutions have an excellent thermoelectric performance with maximum zT values exceeding 2.0, where the combination of low lattice thermal conductivity and high power factor (PF) plays an important role. These values are higher than those of pure Mg2Sn and Mg2Ge. The p-type solid solutions are inferior to the n-type ones, mainly due to the much lower PF. The maximum zT value of 0.62 is predicted for p-type Mg2Ge0.25Sn0.75 at 800 K. The results suggest that the n-type Mg2GexSn1−x solid solutions are promising mid-temperature TE materials.

First-Principles Calculations of Defect Structures in B2 AlCo and GaCo

First-principles electronic structure calculations have been performed for defect structures in nonstoichiometric B2 AlCo and GaCo. To determine the type of constitutional defects, the compositional dependence of the energy of formation and lattice parameter was obtained by calculations employing supercells of various sizes (16 and 32 atoms) as well as special quasirandom structures (SQSs) developed for random pseudobinary A1−xBxC with compositions x = 0.25 and 0.5. According to the results, Co vacancies are the constitutional point defects in the Al-rich side of both B2 AlCo and B2 GaCo, while Co vacancies present the minimum energy for the Ga-rich side. For the Co-rich side of both B2 AlCo and B2 GaCo, the Co antisite is the most stable defect. To investigate the thermal defect concentrations at finite temperature, we adopted the Wagner–Schottky model using enthalpies of formation of point defects obtained from the SQS approach. The present results suggest that the predominant thermal defects in AlCo are of complex type whereas for GaCo they are of interbranche Co type. The results of these calculations show agreement with available theoretical and experimental data.

Stacking fault energies of nondilute binary alloys using special quasirandom structures

Generalized stacking fault energies of nondilute binary alloys in the Ag-Au-Pd system are calculated using density functional theory and special quasirandom structures. Supercells containing 90 and 135 atoms are compared for direct calculations of the generalized stacking fault energy, and the axial interaction model is used to estimate the intrinsic stacking fault energy. The axial interaction model approximates the directly calculated energy to within 10% in most cases, but is sensitive to the particular structures used. Increasing the number of atoms used for direct calculations decreases the uncertainty of the calculated stacking fault energies in most cases, and we show that this uncertainty is related to certain correlations between pairs of adjacent layers within the supercell.

First-principles calculations and thermodynamic modeling of the Sn-Ta system

A thermodynamic description of the Sn-Ta system was developed using the CALPHAD (CALculation of PHAse Diagram) approach in combination with first-principles calculations. A positive enthalpy of mixing of the body centered cubic phase was predicted, using special quasirandom structures (SQS), indicating the tendency to form a miscibility gap. The finite temperature thermodynamic properties of Ta3Sn and TaSn2 were calculated by the Debye-Grüneisen model as well as phonon calculations using the supercell approach. The results from first-principles calculations along with the previously reported decomposition temperature of TaSn2, 868°K, were used to evaluate the Gibbs energy parameters of the TaSn2, Ta3Sn intermetallics and the liquid phase. No decomposition temperature of Ta3Sn has previously been reported in the literature but was predicted in this work to be 2884°K. The calculated phase diagram agrees well with available experimental information of the Sn-Ta system and also compares well with similar systems such as Nb-Sn and V-Sn.

Thermodynamic modelling of the Cr-Nb-Sn system

The Cr-Nb-Sn system has been studied experimentally, by first principles calculation and finally modeled with the Calphad method. The experimental study has been carried out on the Cr-Sn binary system to determine the solubility of Sn in the A2 (Cr) solid solution, but also in the Cr-Nb-Sn ternary system in order to determine phase equilibria of the isothermal section at 800°C and 1100°C. Besides, the formation enthalpies of all the ordered configurations of the C15 and A15 phases and the stoichiometric Nb6Sn5 and NbSn2 phases have been calculated using the Density Functional Theory (DFT). The mixing enthalpies of the A2 binary solid solutions have been estimated using the Special Quasirandom Structures (SQS). All these new experimental and calculated data have been taken into account for a new thermodynamic assessment of the three binary and the ternary systems.

Sc and Nb dopants in SrCoO3 modulate electronic and vacancy structures for improved water splitting and SOFC cathodes

SrCoO3 is a promising material in the field of electrocatalysis. Difficulties in synthesising the material in its cubic phase have been overcome by doping it with Sc and Nb ions [Mater. Horiz.2015, 2, 495–501]. Using ab initio calculations and special quasi random structures we undertake a systematic study of these dopants in order to elucidate the effect of doping on electronic structure of the SrCoO3 host and the formation of oxygen vacancies. We find that while the overall electronic structure of SrCoO3 is preserved, increasing the Sc fraction leads to a decrease of electrical conductivity, in agreement with earlier experimental work. For low Sc and Nb doping fractions we find that the oxygen vacancy formation increases relative to undoped SrCoO3. However, as the dopants concentration is increased the vacancy formation energy drops significantly, indicating a strong tendency to accommodate high concentration of oxygen vacancies and hence non-stoichiometry. This is explained based on the electronic instabilities caused by the presence of Sc ions which weakens the B-O interactions as well as the increased degree of electron delocalization on the oxygen sublattice. Sc dopants also shift the p-band centre closer to the Fermi level, which can be associated with experimentally reported improvements in oxygen evolution reactions. These findings provide crucial baseline information for the design of better electrocatalysts for oxygen evolution reactions as well as fuel-cell cathode materials.

Systematic ab initio investigation of the elastic modulus in quaternary transition metal nitride alloys and their coherent multilayers

We give a comprehensive overview of the elastic properties of cubic quaternary transition metal nitride alloys and coherent nitride multilayers for design of wear resistant hard coatings. The elastic stiffness constants of the alloys are calculated using the special quasirandom structure method. For multilayers with sharp interfaces we prove the applicability of a linear-elasticity approximation and show that it can be used with success instead of performing direct computationally demanding ab initio calculations. We explore the trends and the potential of multicomponent alloying in engineering the strength and ductility of both, quaternary alloys and their multilayers. We investigate X(1−x−y)TixAlyN alloys where X is Zr, Hf, V, Nb or Ta, and present an analysis based on increasing x. We show that with increasing Ti content ductility can increase in each alloy. Elastic isotropy is observed only in (Zr,Hf,V)(1−x−y)TixAlyN alloys in the middle of the compositional triangle, otherwise a high Young's modulus is observed along [001]. We predict that coherent TiN/X(1−x−y)TixAlyN and ZrN/X(1−x−y)TixAlyN alloy multilayers with the [111] interfacial direction show increasing ductility with increasing x, while the multilayers with the [001] orientation become more brittle. We show that the Young's moduli variation in the parent bulk quaternary nitride alloy provide a reliable descriptor to screen the Young's modulus of coherent multilayers in high-throughput calculations.

CPA descriptions of random Cu-Au alloys in comparison with SQS approach

The lattice constant, formation enthalpy, and elastic parameters of Cu1-xAux (0⩽x⩽1) alloys in the face centered cubic crystallographic phase are investigated by using the first-principles exact muffin-tin orbitals and plane-wave pseudopotential methods in order to explore the effect of alloying with special focus on the impact of local lattice distortion (LLD) on the above properties. The compositional disorder is treated within the framework of the coherent potential approximation (CPA) and the special quasi-random structure (SQS) scheme. Calculations based on SQS and CPA show that, while LLD lowers significantly the formation enthalpy of Cu1-xAux due to the large size mismatch between Cu and Au atoms, it has negligible influence on the lattice constants and elastic parameters. These findings confirm the reliability of CPA for computing the enthalpy changes upon isotropic and unisotropic lattice distortions in disordered alloys with sizable atomic size differences.

Composition dependent order-disorder transition in NdxZr1−xO2−0.5x pyrochlores: A combined structural, calorimetric and ab initio modeling study

The order-disorder phase transition in the NdxZr1−xO2−0.5x system is studied by complementary techniques which include wet chemical synthesis of a series of compositions with various Nd/Zr ratios with the final annealing at 1873 K, X-ray diffraction, oxide melt solution calorimetry and ab initio thermodynamic modeling. Our structural data indicate the transition from ordered to disordered pyrochlore at x ∼0.31 at a temperature of 1873 K. Our calorimetric data show a transition enthalpy of ∼30 kJ/mol, which corresponds to an entropy of disordering of ∼16 J/K/mol. The latter value is significantly smaller than the configurational entropy of transition computed under the assumption of complete disorder in a fluorite phase, indicating a substantial degree of order remaining in the fluorite phase at the temperature of synthesis. The considered phases are computed ab initio using a series of special quasi-random structures that emulate the complete or partial disorder. The results of our calculations and thermodynamic modeling are in good agreement with the measured lattice parameters, the Nd content at the order-disorder transition, and the measured formation and transformation enthalpies. Thus our combined experimental and modeling results provide valuable insight into the disordering of this pyrochlore phase and of other pyrochlore materials.

Alloying effect on the elastic properties of refractory high-entropy alloys

Ab initio total energy calculations are used to determine the elastic properties of TiZrVNb, TiZrNbMo and TiZrVNbMo high-entropy alloys in the body centered cubic (bcc) crystallographic phase. Calculations are performed using the Vienna Ab initio Simulation Package and the Exact Muffin-Tin Orbitals methods, and the compositional disorder is treated within the frameworks of the special quasi-random structures technique and the coherent potential approximation, respectively. Special emphasis is given to the effect of local lattice distortion and trends against composition. Significant distortion can be observed in the relaxed cells, which result in an overlap of the first and second nearest neighbor (NN) shells represented in the histograms. When going from the four-component alloys TiZrVNb and TiZrNbMo to the five-component TiZrVNbMo, the changes in the elastic parameters follow the expected trends, except that of C44 which decreases upon adding equiatomic Mo to TiZrVNb despite of the large shear elastic constant of elemental Mo. Although the rule of mixtures turns out to be a useful tool to estimate the elastic properties of the present HEAs, to capture the more delicate alloying effects one needs to resort to ab initio results.

Mechanical properties of zirconium-based random alloys: Alloying elements and composition dependencies

We present a detailed investigation on mechanical properties of Zr-X (X=Ti, Hf and Sc) alloy systems using the first-principles calculations in conjunction with special quasi-random structures (SQSs). It is found that the strength of mechanical coefficients such as elastic constants and elastic modulus depend linearly on the composition in Zr-Hf and Zr-Sc systems, whereas they depend parabolically on the composition in Zr-Ti system. Such a phenomenon is mainly induced by the presence of Zr-X metallic bond in the alloy systems. In addition, the strength of mechanical coefficients can be well described as a function of alloying composition by a special quadratic function that only has one coefficient F: y=MZr(1-x)+MXx+x(1-x)F. With this function, mechanical coefficients of Zr-X alloy systems in whole composition range can be quickly estimated. Moreover Ti can considerably enhance the ductility of Zr when Ti concentration is 0.43.

Temperature dependent phase stability of Ti(C1−xNx) solid solutions using first-principles calculations

We investigated lattice dynamic and temperature-dependent thermodynamic phase stabilities of Ti(C1−xNx) solid solutions using first-principles calculations within the quasi-harmonic approximation. Phonon dispersion and density of states were obtained by the finite-element method. Special quasi-random structures were used to mimic the random distribution of carbon and nitrogen atoms in the sublattice of Ti(C1−xNx). The reliability of the models and calculations were obtained by comparing the structural and elastic properties of Ti(C1−xNx) with previous results. The random mixing of carbon and nitrogen atoms had a minor effect on the elastic properties, but greatly influenced the dynamic stability. Thermodynamic phase stability was investigated using the formation energy of the solid solutions. The phonon density of states with the quasi-harmonic approximation yielded accurate formation energies at various temperatures. Nitrogen-rich phases showed noticeable changes in thermodynamic stability with increasing temperature, and their phase stability decreased quickly in comparison with the carbon-rich phases. Our results provide fundamental insights into Ti(CN) solid solutions that will help underpin the use and production of Ti(CN) materials.

Structural, energetic and dynamical properties of ordered and disordered bcc Fe25at.%Ni alloys: A first-principles study

Using first-principles phonon calculations and the Quasi-Harmonic approach, the structural, energetic and dynamical properties of ordered (D03) and disordered Fe25at.%Ni bcc alloys have been investigated. All calculations are based on the Projector Augmented Wave (PAW) method of the Density Functional Theory (DFT). The Special Quasirandom Structure (SQS) method has been used to model the disordered structure. It is found that 25at.% Nickel substitution increases the lattice parameter and consequently decreases the C11 and C12 elastic constants and bulk modulus of bcc-iron. Simultaneously, the C44 elastic constant increases with Ni substitution. The calculated formation energies of the disordered structures at 0K are lower than those of the ordered one. The predicted phonon spectra reveal the dynamical stability of both SQS and D03 structures. Finally, the Gibbs free energy functions indicate that the relative stability of the disordered structure vs the ordered one increases with increasing temperature.

Special quasirandom structures for perovskite solid solutions

Special quasirandom structures (SQS) are presently generated for disordered (A′1−xx)BX3 and A(B′1−xx)X3 perovskite solid solutions, with x = 1/2 as well as 1/3 and 2/3. These SQS configurations are obtained by imposing that the so-called Cowley parameters are as close to zero as possible for the three nearest neighboring shells. Moreover, these SQS configurations are slightly larger in size than those available in the literature for x = 1/2, mostly because of the current capabilities of atomistic techniques. They are used here within effective Hamiltonian schemes to predict various properties, which are then compared to those associated with large random supercells, in a variety of compounds, namely (Ba1−xSrx)TiO3, Pb(Zr1−xTix)O3, Pb(Sc0.5Nb0.5)O3, Ba(Zr1−xTix)O3, Pb(Mg1/3Nb2/3)O3 and (Bi1−xNdx)FeO3. It is found that these SQS configurations can reproduce many properties of large random supercells of most of these disordered perovskite alloys, below some finite material-dependent temperature. Examples of these properties are electrical polarization, anti-phase and in-phase octahedral tiltings, antipolar motions, antiferromagnetism, strain, piezoelectric coefficients, dielectric response, specific heat and even the formation of polar nanoregions (PNRs) in some relaxors. Some limitations of these SQS configurations are also pointed out and explained.

Order-disorder transitions in the Fe2VAl Heusler alloy

A Rietveld analysis of neutron powder diffraction patterns obtained in situ during temperature scans shows that Fe2VAl crystallizes at room temperature in the fully ordered L21 structure and transforms at 1080 °C and at 1190 °C into partially disordered B2 and fully disordered A2 variants respectively. The low temperature stability of the L21 structure as well as the two high temperature L21 → B2 → A2 transitions are theoretically predicted by a combination of ab-initio (electronic structure and phonons) and thermodynamic calculations performed on special quasi-random structures. Pronounced cold work effects and the pre-transitional antisite defects which are observed respectively at 25 °C under mechanical stress and at high temperature (above 800 °C), appear to be generic effects in the family of Heusler alloys.

Temperature-dependent stable phase domains of Zr–C–N (Zr–ZrC–ZrC0.96–Zr(C1−xNx)−ZrN, x = 0.1–0.9) systems from ab initio calculations and experimental results

Despite the importance of ZrC, ZrN, and their intermediate solid solutions, the temperature-dependent phase stability of the Zr–C–N system has not previously been determined precisely. This work reports these phase stabilities determined experimentally and using ab initio calculations within the quasi-harmonic approximation. Special quasi-random structure models and supercell models with random substitution were used to mimic the random atomic distribution of C and N in the sublattice of Zr(C1−xNx) solid solutions. The results indicated that volume and high-temperature entropy changes are important to determine the free energy of the solid solutions and that moderate temperatures (∼1500–2000 K) were needed to synthesize Zr(C1−xNx) solid solutions. The calculated stable phase domains were then successfully produced. Our results clarify the synthesis and stable phase prediction of the Zr–C–N system under certain external conditions, and they will help broaden the applicability of ZrC, ZrN, and their solid solution phases.

Evaluation of the tantalum-titanium phase diagram from ab-initio calculations

The thermodynamic properties of the Ta-Ti binary system below 900 °C are not well known. In particular, the location and shape of the solvus between the phase separation region at low temperatures and the solid solution at high temperatures are not well defined. In this study, we present a thermodynamic description for this system based on ab-initio calculations. The formation enthalpies of bcc and hcp solid solutions are estimated using the special quasi-random structures methodology and their vibrational free energy calculated by the quasi-harmonic Debye model. The excess energies of the solid solutions are fitted to a sub-subregular model and used to define the phase diagram of the binary system. It is shown that the current empirical assessment of the energies of the pure elements leads to a phase diagram that strongly departs from the known experimental features at low temperatures. An ab-initio guided correction of these energies is necessary to obtain correctly the low temperature phase separation and the high temperature solid solution. The predicted solvus of the phase diagram is qualitatively different from those previously reported for the Ta-Ti system. It exhibits a miscibility gap between two distinct bcc phases, similar to those that exist in the closely related binary systems Ta-Zr, Ta-Hf, Cr-Ti, Mo-Ti, V-Ti, and Ti-W.

Computational Design and Preparation of Cation‐Disordered Oxides for High‐Energy‐Density Li‐Ion Batteries

Cation‐disordered lithium‐excess metal oxides have recently emerged as a promising new class of high‐energy‐density cathode materials for Li‐ion batteries, but the exploration of disordered materials has been hampered by their vast and unexplored composition space. This study proposes a practical methodology for the identification of stable cation‐disordered rocksalts. Here, it is established that the efficient method, which makes use of special quasirandom structures, correctly predicts cation‐ordering strengths in agreement with accurate Monte‐Carlo simulations and experimental observations. By applying the approach to the composition space of ternary oxides with formula unit LiA0.5B0.5O2 (A, B: transition metals), this study discovers a previously unknown cation‐disordered structure, LiCo0.5Zr0.5O2, that may function as the basis for a new class of cation‐disordered cathode materials. This computational prediction is confirmed experimentally by solid‐state synthesis and subsequent characterization by powder X‐ray diffraction demonstrating the potential of the computational screening of large composition spaces for accelerating materials discovery.

Investigations of the mechanical properties of the Zr8Ti8 random alloy

The mechanical property of alloys plays a vital role in applications. In order to probe the mechanical property of the Zr–Ti alloy, we have successfully generated a 16-atom special quasi-random structure (SQS) at concentration 0.5 for the Zr–Ti alloy ([Formula: see text]) with supercell ([Formula: see text]) based on the hcp Bravais cell, which has the same shape with the hcp Bravais cell. Such an SQS can be used as a good template at the 0.5 concentration of all binary hcp random alloys as the initial step for the further description of their alloy properties. Our calculated bulk modulus of [Formula: see text] is 101.7[Formula: see text]GPa, falling within the region for the extreme two constituents [Formula: see text] B[Formula: see text] B[Formula: see text]). Obtained [Formula: see text] of [Formula: see text] (3.60) is significantly larger than those of Zr (2.75) and Ti (2.64), which means that the ductility of [Formula: see text] alloy is better than those of its constituents. The maximum Cauchy stress of [Formula: see text] is 20.53[Formula: see text]GPa at strain ([Formula: see text] in [0001] direction. In addition, this SQS template for [Formula: see text] has been proved to be mechanically stable.

Thermodynamic assessment of the Pd[sbnd]Rh[sbnd]Ru system using calphad and first-principles methods

Palladium, rhodium and ruthenium are abundant fission products that form in oxide fuels in nuclear reactors. Under operating conditions, these Platinum-Group Metal (PGM) fission products accumulate in high concentration at the rim of the oxide fuel and mainly precipitate into metallic solid solutions. Their thermochemistry is of significant interest to predict the high temperature chemical interactions between the fuel and the cladding or the possible precipitation of PGM phases in high level nuclear waste glasses.To predict the thermodynamic properties of these PGM fission products, a thermodynamic modeling is being developed on the ternary PdRhRu system using the Calphad method. Because experimental thermodynamic data are scarce, Special Quasirandom Structures coupled with Density Functional Theory methods were used to calculate mixing enthalpy data in the solid solutions. The resulting thermodynamic description based on only binary interaction parameters is in good agreement with the few data on the ternary system.