Projector Augmented Wave Method Research Articles

Energy structure of mixed halide CeF2Cl and CeFCl2 crystals

The band energy structures of CeF2Cl and CeFCl2 crystals have been calculated using the projector augmented-wave (PAW) method and the hybrid exchange-correlation functional PBE0. The valence band top consists of 2p states of F and 3p states of Cl. An energy gap is observed between the 5d states of Ce in the bottom part of the conduction band of both crystals, forming two subbands, 5d1 and 5d2, with very different effective electron masses (2.49 m0 and 0.19 m0 for CeF2Cl and 5.95 m0 and 0.84 m0 for CeFCl2, respectively). The 4f states of Ce are placed within the forbidden band. The obtained values for the band gap of CeF2Cl and CeFCl2 crystals are 6 eV and 4.6 eV, respectively.

GPAW: An open Python package for electronic structure calculations.

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Formic acid stability in different solvents by DFT calculations.

New technologies have been developed toward the use of green energies. The production of formic acid (FA) from carbon dioxide (CO[Formula: see text]) hydrogenation with H[Formula: see text] is a sustainable process for H[Formula: see text] storage. However, the FA adduct stabilization is thermodynamically dependent on the type of solvent and thermodynamic conditions. The results suggest a wide range of dielectric permittivity values between the dimethyl sulfoxide (DMSO) and water solvents to stabilize the FA in the absence of base. The thermodynamics analysis and the infrared and charge density difference results show that the formation of the FA complex with H[Formula: see text]O is temperature dependent and has a major influence on aqueous solvents compared to the FA adduct with amine, in good agreement with the experiment. In these conditions, the stability thermodynamic of the FA molecule may be favorable at non-organic solvents and dielectric permittivity values closer to water. Therefore, a mixture of aqueous solvents with possible ionic composition could be used to increase the thermodynamic stability of H[Formula: see text] storage in CO[Formula: see text] conversion processes. Using the Quantum ESPRESSO package, density functional theory (DFT) calculations were performed with periodic boundary conditions, and the electronic wave functions were expanded in plane waves. For the exchange-correlation functional, we use the vdW-DF functional with the inclusion of van der Waals (vdW) forces. Electron-ion interactions are treated by the projector augmented wave (PAW) method with pseudopotentials available in the PSlibrary repository. The wave functions and the electronic densities were expanded employing accurate cut-off energies of 6.80[Formula: see text]10[Formula: see text] and 5.44[Formula: see text]10[Formula: see text] eV, respectively. The electronic density was computed from the wave functions calculated at the [Formula: see text]-point in the first Brillouin-zone. Each structural optimization was minimized according to the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, with force and energy convergence criteria of 25 meV[Formula: see text]Å[Formula: see text] and 1.36 meV, respectively. The electrostatic solvation effects were performed by the [Formula: see text] package with the Self-Consistent Continuum Solvation (SCCS) approach.

The effect of f-electrons on the structural phase transition, mechanical and electronic properties in light rare-earth bismuthides

ABSTRACT The electronic structure, phase transition pressure and mechanical properties of light rare-earth bismuthides (PrBi, NdBi, PmBi and SmBi) have been investigated by full geometry optimization using Vienna Ab-Initio Simulation Package (VASP) which has been used in combination with the projector augmented wave (PAW) method and the generalized gradient approximation (GGA) over the local density approximation (LDA) for exchange-correlation functional. We focus our attention on the lattice constants and elastic constants of these compounds. These compounds undergo a phase transition from the NaCl (B1) structure to the body-centered tetragonal (BCT) structure. We also report the density of states (DOS) of these rare earth bismuthides. In the case of PrBi and NdBi, the 4f states are treated as valence states. The effects of on-site Coulomb repulsion and the spin-orbit coupling (SOC) on the electronic structure are also studied.

Adhesion properties of the B- and N-doped graphene/Fe(110) interface

Influence of B and N substitutional impurities on the adhesion properties, electronic and magnetic characteristics of the external and internal graphene/Fe(110) semi-coherent interface was investigated by the projector augmented-wave method within the density functional theory. The analysis of interatomic distances, charge densities, charge transfer and magnetic states of atoms was performed. It was shown that B-doped graphene has a higher adhesion energy on the Fe(110) surface and in the iron bulk in comparison with the undoped systems; whereas, N-doped graphene in the Fe bulk demonstrates the opposite trend and on the surface it has no effect. Boron acts as electron donor that increases charges of the nearest C atoms by 0.5–0.6e. Nitrogen due to its high electronegativity is an acceptor and as a result the nearest C atoms lose 0.2–0.3e. Both impurities, depending on the position, influence differently on the magnetic moment of the nearest iron atoms.

The Mott transition in the 5d[formula omitted] compound Ba[formula omitted]NaOsO[formula omitted]: A DFT+DMFT study with PAW spinor projectors

Spin–orbit coupling has been reported to be responsible for the insulating nature of the 5d1 osmate double perovskite Ba2NaOsO6 (BNOO). However, whether spin–orbit coupling indeed drives the metal-to-insulator transition (MIT) in this compound is an open question. In this work we investigate the impact of relativistic effects on the electronic properties of BNOO via density functional theory plus dynamical mean-field theory calculations in the paramagnetic regime, where the insulating phase is experimentally observed. The correlated subspace is modeled with spinor projectors of the projector augmented wave method (PAW) employed in the Vienna Ab Initio Simulation Package (VASP), suitably interfaced with the TRIQS package. The inclusion of PAW spinor projectors in TRIQS enables the treatment of spin–orbit coupling effects fully ab-initio within the dynamical mean-field theory framework. In the present work, we show that spin–orbit coupling, although assisting the MIT in BNOO, is not the main driving force for its gapped spectra, placing this material in the Mott insulator regime. Relativistic effects primarily impact the correlated states’ character, excitations, and magnetic ground-state properties.

Hydride-Ion Conduction in AELiH3 (AE = Sr, Ba)

Hydride ions (H–) are expected to conduct fast in solids owing to their monovalent state, appropriate ionic radius for conduction, and large polarizability. Thus, H– is a promising class of the charge carrier with high mobility, and may be applicable to the electrochemical reaction in batteries and fuel cells. The K2NiF4–type structure, wherein the perovskite KNiF3 and the rock-salt KF layers are stacked along the c-axis, has been the most researched material as a hydride-ion conductor, e.g., K2NiF4–type oxyhydrides of La2–x–y Sr x +y LiH1–x+y O3–y [1]. In this study, we focused on perovskite-type hydrides, AELiH3 (AE = Ca, Sr, Ba). A simple perovskite structure is expected to have high ionic conductivity, because it ensures a three-dimensional diffusion pathway for the anion species [2-6].First, the migration energy of H– ions in the AELiH3 materials were evaluated using nudged elastic band (NEB) calculations. The migration pathway between adjacent H– sites via vacancies was considered. First-principles calculations were performed using the projector-augmented wave method and PBEsol functional as implemented in the VASP code. The H– diffusivity of sodium-doped SrLiH3 was investigated using density functional theory molecular dynamics. AELiH3 were experimentally synthesized using a mechanochemical method, and their ionic conductivities were evaluated using electrochemical impedance spectroscopy. To further improve the ionic conductivity of these materials, hydride-ion vacancies were introduced by replacing the A-site cation with the monovalent cation of Na+. Neutron powder diffraction (NPD) data were collected at room temperature using a time-of-flight diffractometer (BL09 SPICA) at the J-PARC facility. The distribution of the nuclear scattering length density was analyzed by the maximum entropy method (MEM) using the Z-MEM code. The effect of the alkali-earth element at A-site on the migration energy of H– was evaluated using NEB. The migration energy are estimated to be 24, 35, and 39 kJ mol–1 for CaLiH3, SrLiH3, and BaLiH3, respectively. These low migration energy (< 40 kJ mol–1) suggest that the perovskite-type AELiH3 are suitable substances for hydride-ion conduction. AELiH3 (AE = Sr, Ba) were synthesized via mechanical milling process. The X-ray diffraction patterns of SrLiH3 and BaLiH3 were attributed to a cubic perovskite structure with the space group Pm–3m. For CaLiH3, the starting materials of CaH2 and LiH remained in the product, and the perovskite-type CaLiH3 could not be synthesized. The ionic conductivities of SrLiH3 and BaLiH3 at 100 °C were 4.6 × 10–7 and 6.7 × 10–9 S cm–1, respectively. This clearly denotes the characteristic of hydride ion; a smaller ionic radius of the A-site cation results in a lower migration energy and a higher ionic conductivity. Solid solutions of Sr1–x Na x LiH3–x were obtained in the range of 0 ≤ x ≤ 0.075. The ionic conductivity was enhanced upon Na-doping. The highest conductivity was observed for Sr0.925Na0.075LiH2.925 (x = 0.075) with a bulk conductivity of 5.0 × 10–6 S cm–1 at 25.6 °C. The figure shows the refined crystal structure of Sr0.925Na0.075LiH2.925 obtained by a Rietveld analysis of the NPD data, in addition to the isosurface plot of the nuclear density obtained by MEM. Rietveld analysis confirmed the presence of H defects and a remarkable anisotropy of the thermal oscillations of H. The negative nuclear density at the H sites showed broadening along the {100} direction. These structural features suggest that hydride ions conduct via vacancies between their adjacent sites. The choice of small cations at the A sites and the presence of hydrogen vacancies in perovskite-type hydrides resulted in high hydride-ion conductivity. [1] Kobayashi et.al., Science, 351, 1314–1317(2016). [2] Bai, Q. et.al., ACS Appl. Energy Mater., 1, 1626–1634(2018). [3] Ishihara, T. et.al., J. Am. Chem. Soc., 116, 3801–3803(1994). [4] Li, M. et.al., Nat. Mater., 13, 31–35(2014). [5] Hull, S. et.al., J. Phys.: Condens. Matter, 11, 5257–5272(1999). [6] Yamane, Y. et.al., Solid State Ionics, 179, 605–610(2008). Figure 1

First-Principle Studies on Local Lattice Distortions and Thermodynamic Properties in Non-Stoichiometric Thorium Monocarbide

Thorium monocarbide (ThC) is interesting as an alternative fertile material to be used in nuclear breeder systems and thorium molten salt reactors because of its high thermal conductivity, good irradiation performance, and wide homogeneous composition range. Here, the influence of carbon vacancy site and concentration on lattice distortions in non-stoichiometric ThC1−x (x = 0, 0.03125, 0.0625, 0.125, 0.1875, 0.25, or 0.3125) is systematically investigated using first-principle calculations by the projector augmented wave (PAW) method. The energy, mechanical parameters, and thermodynamic properties of the ThC1-x system are calculated. The results show that vacancy disordering has little influence on the total energy of the system at a constant carbon vacancy concentration using the random substitution method. As the concentration of carbon vacancies increases, significant lattice distortion occurs, leading to poor structural stability in ThC1−x systems. The changes in lattice constant and volume indicate that ThC0.75 and ThC0.96875 represent the boundaries between two-phase and single-phase regions, which is consistent with our experiments. Furthermore, the structural phase of ThC1−x (x = 0.25–0.3125) transforms from a cubic to a tetragonal structure due to its ‘over-deficient’ composition. In addition, the elastic moduli, Poisson’s ratio, Zener anisotropic factor, and Debye temperature of ThC1-x approximately exhibit a linear downward trend as x increases. The thermal expansion coefficient of ThC1−x (x = 0–0.3125) exhibits an obvious ‘size effect’ and follows the same trend at high temperatures, except for x = 0.03125. Heat capacity and Helmholtz free energy were also calculated using the Debye model; the results showed the C vacancy defect has the greatest influence on non-stoichiometric ThC1−x. Our results can serve as a theoretical basis for studying the radiation damage behavior of ThC and other thorium-based nuclear fuels in reactors.

VASP2KP: k⋅p Models and Landé g-Factors from ab initio Calculations

The k⋅p method is significant in condensed matter physics for the compact and analytical Hamiltonian. In the presence of magnetic field, it is described by the effective Zeeman’s coupling Hamiltonian with Landé g-factors. Here, we develop an open-source package VASP2KP (including two parts: vasp2mat and mat2kp) to compute k⋅p parameters and Landé g-factors directly from the wavefunctions provided by the density functional theory (DFT) as implemented in Vienna ab initio Simulation Package (VASP). First, we develop a VASP patch vasp2mat to compute matrix representations of the generalized momentum operator , spin operator , time reversal operator , and crystalline symmetry operators on the DFT wavefunctions. Second, we develop a python code mat2kp to obtain the unitary transformation U that rotates the degenerate DFT basis towards the standard basis, and then automatically compute the k⋅p parameters and g-factors. The theory and the methodology behind VASP2KP are described in detail. The matrix elements of the operators are derived comprehensively and computed correctly within the projector augmented wave method. We apply this package to some materials, e.g., Bi2Se3, Na3Bi, Te, InAs and 1H-TMD monolayers. The obtained effective model’s dispersions are in good agreement with the DFT data around the specific wave vector, and the g-factors are consistent with experimental data. The VASP2KP package is available at https://github.com/zjwang11/VASP2KP.

Using Noncovalent Interactions to Test the Precision of Projector-Augmented Wave Data Sets.

The projector-augmented wave (PAW) method is one of the approaches that are widely used to approximately treat core electrons and thus to speed up plane-wave basis set electronic structure calculations. However, PAW involves approximations, and it is thus important to understand how they affect the results. Tests of the precision of PAW data sets often use the properties of isolated atoms or atomic solids. While this is sufficient to identify problematic PAW data sets, little information has been gained to understand the origins of the errors and suggest ways to correct them. Here, we show that the interaction energies of molecular dimers are very useful not only to identify problematic PAW data sets but also to uncover the origin of the errors. Using dimers from the S22 and S66 test sets and other dimers, we find that the error in the interaction energy is composed of a short-range component with an exponential decay and a long-range electrostatic part caused by an error in the total charge density. We propose and evaluate a simple improvable scheme to correct the long-range error and find that even in its simple and readily usable form, it is able to reduce the interaction energy errors to less than half on average for hydrogen-bonded dimers.

Unveiling the mechanism of surface corrugation formation on a quasi free-standing bi-layer graphene via experimental and modeling investigations

Extensive studies have been conducted to accomplish the controls over the formation of surface corrugations on chemical vapor deposited (CVD) graphene. However, the underlying mechanism of the surface corrugation formation on graphene remains elusive, due to the difficulty delineating the growth-induced surface corrugations from wrinkles formed during graphene transfer with the use of a supporting layer casted on top of the sample. In this study, “quasi free-standing” graphene was realized using the weakly-interacting h-BN layer during a wet transfer process to study the surface corrugation formation on graphene. The weak interaction of graphene with the supporting h-BN layer allows for the growth-induced surface corrugations to be released, enabling the investigation of the primary mechanism for the graphene corrugation behavior during the transfer process. The experimental measurements of surface corrugations were conducted using atomic force microscopy (AFM) to reveal that surface corrugations are formed following the graphene’s crystallographic directions. Density functional theory calculations using the projector augmented-wave (PAW) method and Perdew-Burke-Ernzerhof (PBE) exchange correlation functional were also conducted for two models of “atomic-scale ripples” and “nanoscale wrinkles” and showed that all of them are formed along the crystallographic axis of graphene, which is in good agreement with the experimental observations.

Mean inner potential of elemental crystals from density-functional theory calculations: Efficient computation and trends

The mean inner potential (V0) of crystals plays an important role in electron microscopy. In a few cases, it has been measured experimentally, using mostly electron holography; however, it is not uncommon to find reports that disagree by a few volts regarding the mean inner potential of the same material. Different levels of theory have also been used to estimate its value, often by building the crystal as a superposition of isolated atoms or ions—an independent-atom approximation that does not take bonding into account. In a few cases, density-functional theory (DFT) calculations were done to capture such bonding, frequently using computer-intensive all-electron approaches. In this article, we describe in detail a faster implementation based on postprocessing files produced by a DFT code that relies on the projector-augmented wave method. We deployed this approach to compute values of V0 for 44 elemental solids, and we provide the first quantum-mechanical calculation of the mean inner potential beyond the independent-atom approximation for many of them. We also report instances in which different surface terminations for the same material led to differences in V0 of more than 3 V, highlighting the dependence of the mean inner potential on the boundary conditions of the sample. Finally, by comparing our values of V0 with other material properties, we show that it correlates mostly linearly with the mass density, that it can be used to compute a good approximation to the orbital diamagnetic contribution to the magnetic susceptibility, and that it provides a simple route to compute atomic scattering amplitudes for forward scattering of electrons.

Ab initio study of structural, mechanical and electronic properties of 3d transitional metal carbide in cubic rocksalt (rs), zincblende (zb), and cesium chloride (cc) structures by using LDA and GGA Approximation.

This study rigorously investigates three 3d transition metal carbide (TMC) structures via LDA and GGA approximations. It examines cohesive energy (Ecoh), Vickers hardness (Hv), mechanical stability, and electronic properties. Notably, most 3d TMCs exhibit higher cohesive energy than nitrides, and rs-TiC demonstrates a Vickers hardness of 25.66 GPa, outperforming its nitride counterpart. The study employs theoretical calculations to expedite research, revealing mechanical stability in CrC and MnC (GGA) and CrC (LDA in cc structure), while all 3d TMCs in rs and seven in zb structures show stability. Charge transfer and bonding analysis reveal enhanced covalency along the series, influenced by the interplay between p orbitals of carbon and d orbitals of the metal. Most 3d TMCs exhibit metallic properties, excluding zb-TiC and zb-FeC in all phases. An inverse correlation between elastic constant C44 and electronic states near the Fermi level (EF) emerges, guiding applications and design. This study efficiently uncovers 3d TMC properties, offering insights for applications and design. We employed the Vienna ab initio Simulation software (VASP) to perform computations based on density functional theory (DFT). Our approach incorporated both the projector augmented wave (PAW) and PW91 general gradient approximation (GGA) methods within the local density approximation (LDA).

Systematic Characterization of Electronic Metal-Support Interactions in Ceria-Supported Pt Particles.

Electronic metal-support interactions affect the chemical and catalytic properties of metal particles supported on reducible metal oxides, but their characterization is challenging due to the complexity of the electronic structure of these systems. These interactions often involve different states with varying numbers and positions of strongly correlated d or f electrons and the corresponding polarons. In this work, we present an approach to characterize electronic metal-support interactions by means of computationally efficient density functional calculations within the projector augmented wave method. We describe Ce3+ cations with potentials that include a Ce4f electron in the frozen core, overcoming prevalent convergence and 4f electron localization issues. We systematically explore the stability and chemical properties of different electronic states for a Pt8/CeO2(111) model system, revealing the predominant effect of electronic metal-support interactions on Pt atoms located directly at the metal-oxide interface. Adsorption energies and the reactivity of these interface Pt atoms vary significantly upon donation of electrons to the oxide support, pointing to a strategy to selectively activate interfacial sites of metal particles supported on reducible metal oxides.

Bonding mechanism and magnetic ordering in Laves phase λ1−MgCo2 intermetallic compound from theoretical and experimental studies

In the present work we have studied the bonding mechanism and magnetism in a hexagonal λ1−MgCo2 Laves phase intermetallic formed at rA/rB= 1.280. Ab initio theoretical calculations for MgCo2 using the projector-augmented wave method implemented in the VASP code showed that Mg carries a formal charge +1.7 |e| while Co atoms are also positively charged with around +0.7 |e| being donated to establish the interatomic covalent Co-Co bonding in a three-dimensional network of Co tetrahedra. MgCo2 is a metallic conductor with ferromagnetic properties and TC=303 K. Neutron Powder Diffraction study showed a collinear ordering of the Co moments, their alignment along the c-axis of the hexagonal unit cell with an average moment of 1.51(2) μB/atom Co. Ab initio computational studies indicate that the Co moments reach the experimentally observed value approx.1.5 μB when the unit cell volume exceeds 160 Å3 (average Co-Co distances 2.43 Å).

13C NMR Chemical Shifts of Saccharides in the Solid State: A Density Functional Theory Study

In this work we present a systematic, theoretical investigation of the 13C NMR chemical shifts for several mono-, di- and trisaccharides in the solid state. The chemical shifts have been calculated using density functional theory (DFT) together with the gauge including the projector augmented wave (GIPAW) method as implemented in the CASTEP program. We studied the changes in the 13C NMR chemical shifts in particular due to the formation of one or two glycosidic linkages and due to crystal water. The largest changes, up to 14 ppm, are observed between the mono- and disaccharides and typically for the glycosidic linkage atoms, but not in all cases. An analysis of the bond angles at the glycosidic linkage and the observed changes in chemical shifts displays no direct correlation between them. Somewhat smaller changes in the range of 2 to 5 ppm are observed when single crystal water molecules are close to some of the atoms. Relating the changes in the chemical shifts of the carbon atoms closest to the crystal water to the distance between them does, however, not lead to a simple relation between them.

Phaseless auxiliary field quantum Monte Carlo with projector-augmented wave method for solids.

We implement the phaseless auxiliary field quantum Monte Carlo method using the plane-wave based projector augmented wave method and explore the accuracy and the feasibility of applying our implementation to solids. We use a singular value decomposition to compress the two-body Hamiltonian and, thus, reduce the computational cost. Consistent correlation energies from the primitive-cell sampling and the corresponding supercell calculations numerically verify our implementation. We calculate the equation of state for diamond and the correlation energies for a range of prototypical solid materials. A down-sampling technique along with natural orbitals accelerates the convergence with respect to the number of orbitals and crystal momentum points. We illustrate the competitiveness of our implementation in accuracy and computational cost for dense crystal momentum point meshes compared to a well-established quantum-chemistry approach, the coupled-cluster ansatz including singles, doubles, and perturbative triple particle-hole excitation operators.

The Influence of Halide Ion Substitution on Energy Structure and Luminescence Efficiency in CeBr2I and CeBrI2 Crystals.

This study aims to determine the optimum composition of the CeBr1-xIx compound to achieve the maximum light output. It is based on calculations of the band energy structure of crystals, specifically taking into account the characteristics of the mutual location of local and band 5d states of the Ce3+ ions. The band energy structures for CeBr2I and CeBrI2 crystals were calculated using the projector augmented wave method. The valence band was found to be formed by the hybridized states of 4p Br and 5p I. The 4f states of Ce3+ are located in the energy forbidden band gap. The conduction band is formed by the localized 5d1 states, which are created by the interaction between the 5d states of Ce3+ and the 4f0 hole of the cerium ion. The higher-lying delocalized 5d2 states of Ce3+ correspond to the energy levels of the 5d states of Ce3+ in the field of the halide Cl0 (Br0) hole. The relative location of 5d1 and 5d2 bands determines the intensity of 5d-4f luminescence. The bottom of the conduction band is formed by localized 5d1 states in the CeBr2I crystal. The local character of the bottom of the conduction band in the CeBr2I crystal favors the formation of self-trapped Frenkel excitons. Transitions between the 5d1 and 4f states are responsible for 5d-4f exciton luminescence. In the CeBrI2 crystal, the conduction band is formed by mixing the localized 5d1 and delocalized 5d2 states, which leads to quenching the 5d-4f luminescence and a decrease in the light output despite the decrease in the forbidden band gap. CsBr2I is the optimum composition of the system to achieve the maximum light output.

Ground state structural, lattice dynamic, thermodynamic and optical properties of the Ba2CaMoO6 ordered perovskite

Ab-initio calculations based on density functional theory have been performed to establish the ground state properties for the double perovskite type material Ba2CaMoO6. The calculations were carried out through the Projector Augmented Wave Method and the exchange and correlation was described using the Perdew-Burke-Ernzerhof parameterization of the Generalized Gradient Approximation. The study included structural analysis of the material, as well as thermodynamic, cell dynamics and optical properties at its transition between the tetragonal I4/m and cubic Fm 3‾ m phases. The results on the structural stability reveal that the phase with space group of I4/m is more stable. Likewise, the structural phase transition was obtained for a pressure of 0.067 GPa. On the other hand, the analysis of the electronic properties shows that the material presents a semiconducting behaviour, with a direct band gap of 2.40 eV and 2.26 eV for the tetragonal and cubic structures, respectively. In addition to agreeing with the experimental values reported in the literature, the results suggest possibilities for the application of this material in photodetectors, light emitters and devices for power electronics. © 2023 Elsevier Science. All rights reserved.

Оценка энергии формирования вакансий в ОЦК-, ГЦК- и ГПУ-металлах с использованием теории функционала плотности

Introduction. Vacancies are among the crystal lattice defects that have a significant effect on the structural transformations processes during thermal, chemical-thermal, thermomechanical, and other types of alloys treatment. The vacancy formation energy is one of the most important parameters used to describe diffusion processes. An effective approach to its definition is based on the use of the density functional theory (DFT). The main advantage of this method is to carry out computations without any parameters defined empirically. The purpose of the work is to estimate vacancy formation energy of BCC-, FCC- and HCP-metals widely used in mechanical engineering and to compare these findings obtained using various exchange-correlation functionals (GGA and meta-GGA). Computation procedure. The computations were carried out using the projector-augmented wave method using the GPAW code and the atomic simulation environment (ASE). The Perdew-Burke-Ernzerhof, MGGAC and rMGGAC functionals were used. The wave functions were described by plane waves within simulations. Vacancies formation energy was evaluated using supercells approach with a size 3 × 3 × 3. Computations were carried out for BCC-metals (Li, Na, K, V, Cr, Fe, Rb, Nb, Mo, Cs, Ta, W), FCC-metals (Al, Ni, Cu, Rh, Pd, Ag, Ir, Pt, Au, Pb, Co) and HCP-metals (Be, Ti, Zr, Mg, Sc, Zn, Y, Ru, Cd, Hf, Os, Co, Re). Results and discussion. A comparison of the defined vacancy formation energies indicates the validity of the following ratio of values: . The values obtained using the open source GPAW code are characterized by the same patterns as for widely spread commercially distributed program VASP. It was revealed that the use of the PBE and MGGAC functionals leads to a slight deviation relative to the experimentally determined vacancies formation energy in contrast to the computations using rMGGAC.