Research data for the diffusion mechanisms of Na+ ions in Na1 – xMg1 – xAl1 + x(XO4)3 (X = Mo, W) compounds with the NASICON-type structure (space group R $$\bar {3}$$ c, Z = 6) are reported. Solid solutions in the homogeneity range 0.1 ≤ x ≤ 0.5 for X = Mo and 0.4 ≤ x ≤ 0.6 for X = W have been prepared by solid-state synthesis. Conductivity measurements and NMR spectroscopy data indicate fast sodium diffusion in the studied samples: the ionic conductivity reaches the values of about 10–3 S/cm at T > 800 K. The frequency of elementary ionic jumps is on the order of 104 s–1 at T ≈ 500 K, and the activation energy is equal to 0.8–0.9 eV. The results have shown that the ionic conductivity in molybdates is higher than in tungstates. The growth of magnesium concentration increases the concentration of local coordinations Mg2+–Na+–Mg2+, acting as traps for moving sodium ions. The above conclusions are supported by ab initio calculations according to which the barrier for sodium diffusion from the Mg2+–Na+–Mg2+ position is expected to be higher than those for the Mg2+–Na+–Al3+ and Al3+–Na+–Al3+ ones.

The electronic structure of NaMFe(MoO4)3 (M = Mn, Fe, Co, Ni, Zn) molybdates isostructural α-NaFe2(MoO4)3 or β-NaFe2(MoO4)3 has been studied for the first time. Taking into account the electronic correlation in the Hubbard model, it is shown that these compounds are semiconductors with a band gap from 1.2 to 2.6 eV. Sodium diffusion pathways in α-NaFe2(MoO4)3 and β-NaFe2(MoO4)3 structures have been established, it is shown that in compounds with the structure of β-NaFe2(MoO4)3 the energy barrier is almost twice lower. Modeling of sodium extraction showed that these molybdates should have a high potential from 3 to 5 V and small changes in the volume and enthalpy of formation depending on the sodium content. According to our results, low-symmetric molybdates NaMFe(MoO4)3 (M = Mn, Fe, Co, Ni, Zn) have diffusion properties and cathode voltage similar to NASICON-structure type compounds, and can also be promising materials for sodium-ion batteries.

Sodium polyanionic compounds with transition metals are of considerable research interest for the search of new cathode materials for sodium-ion batteries. In this work, we employed ab initio calculations to evaluate three key battery properties: phase stability, diffusion barriers and redox voltage of low-symmetry molybdates NaMFe(MoO4)(3) (M = Mg, Ni) with alpha- and beta-NaFe2(MoO4)(3) structures. First, we showed that the Hubbard Ucorrection within the GGA + Uapproach is necessary to correctly refer these molybdates to semiconductors. The sodium diffusion along various pathways was thoroughly examined, which allowed us to establish the most probable pathways with the lowest migration barriers. These compounds have different directions of sodium diffusion with twice different barriers that was associated to the peculiarities of their crystal structure. The high potentials and structural stability during sodium extraction, along with low-diffusion barriers predicted for NaMFe(MoO4)(3) (M = Mg, Ni) indicate that these molybdates may be promising high-voltage cathode materials for sodium-ion batteries.

The electronic structures of NaMFe(MoO4)3 (M = Mn, Fe, Co, Ni, Zn) molybdates isostructural to α-NaFe2(MoO4)3 or β-NaFe2(MoO4)3 is studied. Taking into account the electronic correlation in the Hubbard model, it is shown that these compounds are semiconductors with the band gap of 1.2–2.6 eV. The sodium diffusion pathways in the α-NaFe2(MoO4)3 and β-NaFe2(MoO4)3 structures are determined, and it is shown that the energy barrier in the compounds with the β-NaFe2(MoO4)3 structure is almost twice lower. The simulation of sodium extraction shows that these molybdates must have a high potential from 3 to 5 V and insignificant changes in the volume and the formation enthalpy depend on the sodium content. According to the obtained data, low-symmetry NaMFe(MoO4)3 (M = Mn, Fe, Co, Ni, Zn) molybdates exhibit diffusion properties and cathode voltage similar to those in the compounds of the NASICON structural type and also can be promising materials for sodium-ion batteries.

Alluaudite-type compounds are currently considered as a promising class of materials for sodium-ion batteries, and understanding of the diffusion processes in them is very important. Using the Na-23 MAS NMR and ab initio calculations, we established the mechanism of sodium diffusion in Na4-2xM1-x(MoO4)(3) (M = Mg, Zn, Cd) depending on the type of M-element and x. A comparison of the results obtained for various alluaudite-type compounds shows the crucial effect of the M-cation on the Na-ion dynamics in this class of materials. Higher concentration and charge of M-element increase the concentration of vacancies in the Na-sublattice and enhance the sodium mobility. Moreover, the Na dynamics increases with the M-ion size. The occupancy of the M site and the type of T atom in the TO4 group also determine the mechanism of sodium diffusion in alluaudites, whether it is one-dimensional or two-dimensional. These findings may help a deeper understanding of sodium diffusion processes in alluaudite-type compounds and their development as materials for sodium-ion batteries.

The electronic structure and the diffusion of sodium in Na4 – xKxMg(MoO4)3 with an alluaudite structure are studied with ab initio methods. This molybdate is a dielectric with a band gap of 3.5 eV for x = 0, 0.25. The most probable positions of potassium in the sodium sublattice and the preferred pathways for sodium migration are found. The barriers for sodium diffusion in Na4 – xKxMg(MoO4)3 depend significantly on the composition, the position of potassium, and the migration path. The introduction of potassium decreases significantly the barriers to both one-dimensional (1D) and two-dimensional (2D) sodium diffusion. Potassium in 1D channels, however, can hinder the rapid migration of sodium, and the conductivity increases sharply only at high temperatures due to the order–disorder transition.

The electronic structure and sodium diffusion in Na4-xKxMg(MoO4)3 with an alluadite structure have been investigated by ab initio methods. It was found that this molybdate is an insulator with a band gap of 3.5 eV for x = 0.25. The most probable positions of potassium in the sodium sublattice have been determined, and the preferred pathways for sodium migration have been established. It has been shown that the barriers to sodium diffusion in Na4-xKxMg(MoO4)3 significantly depend on the composition, position of potassium, and migration path. The introduction of potassium leads to a significant decrease in the barriers to both one-dimensional (1D) and two-dimensional (2D) sodium diffusion. However, the presence of potassium in 1D channels can hinder the rapid migration of sodium, and a sharp increase in conductivity occurs only at high temperatures due to the order-disorder transition.

In this work, the electronic structure, sodium diffusion, and sodium (de)intercalation in NASICON-type molybdates NaMR(MoO4)3 (M = Mg, Ni; R = Cr, Fe) were studied using the density functional theory (DFT) within the GGA and GGA + U approaches. We found that an inclusion of intraatomic electronic correlations has a strong effect on the band gap of these compounds, which exhibit a semiconducting behavior with a band gap of 2.0–2.7 eV according to the GGA + U calculations. The barriers for sodium hops (0.5–0.9 eV) depend on the formation energy of vacancy in the initial and final positions of the path due to the different local surrounding of Na sites. Our study revealed that the operating range of reversible cycling of NaqMR(MoO4)3 should be 0.33 ≤ q ≤ 3. The predicted extraction and intercalation voltages demonstrate that these NASICON-type molybdates may be promising electrode materials for sodium-ion batteries.

Here we present an ab initio insight into the electronic structure and sodium diffusion in A(3-x)Na(1+x)(MoO4)(2) with trigonal (A = Cs) and monoclinic (A = K) glaserite-type structures. Our DFT calculations predict the stability of K3-xNa1+x(MoO4)(2) to high sodium content and a significantly smaller homogeneity region for Cs3-xNa1+x(MoO4)(2) in accordance with experimental findings. These molybdates are wide-gap insulators with a band gap of 4.2 eV, which is very weakly dependent on the sodium content. The calculated electric field gradients at the Na and A sites were related to the anisotropy of electronic charge distribution and used to predict the quadrupole frequencies of the Cs-133, K-39 and Na-23 NMR lines in Cs3-xNa1+x(MoO4)(2) and K3-xNa1+x(MoO4)(2). We examined the possible diffusion paths of M.+ ions and showed that the direct Na-Na migration is unlikely due to a large energy barrier in both molybdates. Instead, the Na+ ions can migrate through the A positions with much lower barriers in A(3-x)Na(1+x)(MoO4)(2). Therefore, designing stable non-stoichiometric compositions may be a way to reach good sodium-ion diffusion in double molybdates with the glaserite-type structure.

The electronic structure and the magnetic properties of molybdates NaxMy(MoO4)3 (M = Mn, Fe, Co, and Ni) which are promising materials for sodium batteries have been studied in the framework of the density functional theory with the GGA and GGA+U approximations for the first time. The calculations show that all the compounds are insulators. An important role of the correlation effects, provided by the on-site Coulomb interactions, was established in the formation of the band gap in these compounds. The quadrupole constants of  23Na nuclei are calculated in the nonmagnetic and ferromagnetic states within the GGA and GGA+U approaches. It is shown that the quadrupole frequencies for nonequivalent crystallographic positions of sodium are in different frequency ranges, which allows to study the diffusion of sodium in these compounds by the Nuclear Magnetic Resonance method.

Alluaudite-type compounds have been recently proposed as new promising cathode materials for sodium batteries due to their high operating voltage, high capacity and good cyclability. In this work, we present the GGA and GGA + U studies of sodium diffusion and (de)intercalation mechanism in alluaudite NaxMn2(MoO4)(3), as well as its electronic structure and magnetic properties. We predict that, unlike the known alluaudite sulphates, the Na-ion migration in this molybdate should occur not only through one-dimensional channels along the c axis, but also due to their cross-linking, which is responsible for two-dimensional diffusion. These cross-channel sodium hops with the low-energy barriers may reduce the negative influence of defects and improve rate. They can also provide additional mobile ions to the main channels and play an important role in (de) intercalation. The charging process involves the Na+ extraction in a specific sequence from different Na sites, which is accompanied by a Mn3+/Mn2+ redox reaction and has an average redox potential of 3.89 V. A large volume shrinkage during the last desodiation stages narrows the Na migration channels that impedes the diffusion and removal of all Na from NaxMn2(MoO4)(3). (C) 2019 Elsevier B.V. All rights reserved.

AbstractThe electronic structure and the magnetic properties of molybdates Na_ x M_ y (MoO_4)_3 (M = Mn, Fe, Co, and Ni) which are promising materials for sodium batteries have been studied in the framework of the density functional theory with the GGA and GGA+ U approximations for the first time. The calculations show that all the compounds are insulators. An important role of the correlation effects, provided by the on-site Coulomb interactions, was established in the formation of the band gap in these compounds. The quadrupole constants of ^23Na nuclei are calculated in the nonmagnetic and ferromagnetic states within the GGA and GGA+ U approaches. It is shown that the quadrupole frequencies for nonequivalent crystallographic positions of sodium are in different frequency ranges, which allows to study the diffusion of sodium in these compounds by the Nuclear Magnetic Resonance method.

The alluaudite-type oxides have recently been proposed as perspective cathode materials for rechargeable sodium-ion batteries. Here we present ab initio insights into the sodium diffusion in alluaudite molybdates Na2+2xM2-x(MoO4)(3) (M = Fe, Co, Ni), as well as their structural, electronic, and redox properties. Among the various compositions of Na2+2xM2-x(MoO4)(3), the most stable configuration turned out to be Na3M1.5(MoO4)(3). The sequence of sodium extraction from nonequivalent sites, vacancy formation energy and cell volume shrinkage were studied in Na3M1.5(MoO4)(3). Our calculations predict the high redox voltages of 3.9, 4.6, and 4.9 V for M = Fe, Co, and Ni, respectively. Desodiation reduces the band gap in these molybdates that suggests an enhancement of electronic conductivity, which along with fast sodium diffusion and high voltage, is important for good electrochemical performance. Our results demonstrate that alluaudite molybdates have diffusion and redox properties as sulphates, and can also be promising high-voltage cathode materials for sodium-ion batteries.

В рамках подхода МО ЛКАО исследованы редкоземельные гранаты RE 3 Al5O 12 (RE = La-Lu, Y).Рассчитан фононный спектр Y 3 Al5O 12 в -точке.Анализ векторов смещений, полученных из расчета ab initio, позволил провести отнесение фундаментальных колебаний в структуре Y 3 Al5O 12 .Рассчитаны упругие постоянные для кристаллов RE 3 Al5O 12 .Расчеты выполнены в рамках теории функционала плотности.Показана необходимость использовать гибридные функционалы

Rare-earth garnets with the general formula RE 3 Al 5 O 12 (RE = La–Lu, Y) are investigated in the MO LCAO approximation. The phonon spectrum of Y 3 Al 5 O 12 at the Γ point is calculated. Fundamental vibrations in the structure of Y 3 Al 5 O 12 are assigned based on an analysis of ab initio calculated displacement vectors. The elastic constants of the RE 3 Al 5 O 12 crystals are determined. Calculations are performed in terms of the density functional theory. The need to use hybrid functionals, which take into account the contribution of the nonlocal exchange into the Hartree–Fock formalism, is shown. The description of inner shells of the rare-earth ion down to 4 f inclusive by a pseudopotential (4 f -in-core) is shown to ensure significant reducing the computer cost, with the description accuracy of the structure and the lattice dynamics being preserved. The CRYSTAL program, intended for ab initio calculations of periodic structures, is used.

The second-rank spin Hamiltonian parameters of Gd 3+ and Eu 2+ orthorhombic centers in crystals of the yttrium aluminum garnet Y 3 Al 5 O 12 have been analyzed within the framework of the superposition model for the zero-field splitting of the ground state. It has been shown that the description of the experimental data in this model is possible only under the assumption of relaxation of the ligand environment of the paramagnetic impurity.

В рамках суперпозиционной модели для начального расщепления основного состояния проведен анализ параметров спинового гамильтониана второго ранга ромбических центров Gd3+ и Eu2+ в иттрий-алюминиевом гранате. Показано, что описание экспериментальных данных в этой модели возможно только при допущении релаксации лигандного окружения парамагнитной примеси. Работа выполнена в рамках государственного задания Минобрнауки РФ для Уральского федерального университета. Измерения проведены на спектрометре Центра коллективного пользования "Современные нанотехнологии" Уральского федерального университета. DOI: 10.21883/FTT.2017.05.44384.286

The ab initio calculation of the crystal structure and the phonon spectrum of crystals RFe3(BO3)4 (R = Pr, Nd, Sm) has been performed in the framework of the density functional theory. The ion coordinates in the unit cell, the lattice parameters, the frequencies and the types of fundamental vibrations, and also the intensities of lines in the Raman spectrum and infrared reflection spectra have been found. The elastic constants of the crystals have been calculated. For low-frequency A 2 mode in PrFe3(BO3)4, a “seed” vibration frequency that strongly interacts with the electronic excitation on a praseodymium ion was found. The calculation results satisfactory agree with the experimental data.