V<Subscript>52</Subscript>O<Subscript>64</Subscript> tetragonal superstructure of cubic vanadium monoxide with vacancies in the metal sublattice

The atom-vacancy ordering of cubic vanadium monoxide VO_1.29, which has basis cubic structure B1 and structural vacancies in the metal sublattice, has been studied using the x-ray diffraction method. It has been shown that the formation of the tetragonal (space group I4₁/amd) ordered phase V₅₂O₆₄ of cubic vanadium monoxide VO_y proceeds as a first-order phase transition through the disorder-order channel including 22 nonequivalent superstructure vectors of four stars {k ₁₀}, {k ₄}, {k ₃}, and {k ₂}. The distribution function of the vanadium atoms in the V₅₂O₆₄ tetragonal superstructure has been calculated.     

Monoclinic superstructure V<Subscript>14</Subscript>O<Subscript>6</Subscript> of the tetragonal solid solution of oxygen in vanadium

The monoclinic (space group C2/m) superstructure of V₁₄O₆, which is formed in the atom-vacancy ordering of the tetragonal solid solution of oxygen in vanadium, is studied by the methods of x-ray diffraction and symmetry analysis. It has been found that the channel of the order-disorder phase transition attributed to the formation of the monoclinic suboxide V₁₄O₆ includes six superstructure vectors belonging to three non-Lifshitz stars {k ₁₋₁}, {k ₁₋₂}, and {k _1–3} of one type {k ₁}. The distribution function of the O atoms in the V₁₄O₆ monoclinic superstructure has been calculated. It has been shown that the displacements of V atoms distort the body-centered tetragonal metal sublattice, thus preparing the formation of the fcc sublattice and the transition from the suboxide V₁₄O₆ to the cubic vanadium monoxide with the B1 structure.     

Ordered monoclinic vanadium suboxide V<Subscript>14</Subscript>O<Subscript>6</Subscript>

The monoclinic (space group C2/m) superstructure of the suboxide V₁₄O₆, which is formed as a result of the atomic and vacancy ordering of the tetragonal solid solution of oxygen in vanadium, is investigated using X-ray diffraction and symmetry analysis. The monoclinic suboxide V₁₄O₆ is observed in the vanadium oxide samples VO_0.57, VO_0.81, and VO_0.86 synthesized at 1770 K and the samples VO _y (0.87 ≤ y ≤ 0.98) additionally annealed at 1470 K after the synthesis. It is established that the channel of the disorder-order phase transition associated with the formation of the monoclinic suboxide V₁₄O₆ includes six superstructure vectors belonging to three non-Lifshitz stars of one type {k ₁}. The distribution function of the oxygen atoms in the monoclinic superstructure of the suboxide V₁₄O₆ is calculated. It is demonstrated that the displacements of vanadium atoms distort the body-centered tetragonal metal sublattice, thus preparing the formation of the facecentered cubic sublattice and the transition from the suboxide V₁₄O₆ to the cubic vanadium monoxide with the B1 structure.     

DO<Subscript>3</Subscript>-type cubic structure of nonstoichiometric vanadium monoxide

An X-ray diffraction study indicates that nonstoichiometric vanadium monoxide VO _y ≡ V _x O _z (y = z/x) has a cubic structure of the DO₃ type (space group Fm $ \bar 3 $ \bar 3 m), where vanadium atoms are not only at the 4(a) sites of the metal fcc sublattice, but also at the tetrahedral 8(c) sites. This circumstance fundamentally distinguishes monoxide VO _y from strongly nonstoichiometric MX _y compounds with the B1 structure and the same space group, where atoms M and X and structural vacancies ▪ and ▭ of the metal and nonmetal sublattices, respectively, are distributed over the 4(a) and 4(b) sites. The dependence of the filling factor q of the tetrahedral interstices by vanadium atoms on the relative content y of oxygen in VO _y has been obtained. It has been shown that the composition of cubic vanadium monoxide should be represented as VO _y ≡ V _x O _z ≡ V _{x − 2q} V_2q ^(t)▪_{1 − x + 2q} O _z ▭_{1 − z} , taking into account the structure.     

The disorder-order transition in cubic vanadium monoxide with vacancies in the metal sublattice

The disorder-order transition in cubic vanadium monoxide VO_y (y = 1.29, 1.30) possessing a B1 type structure and containing vacancies only in the metal sublattice has been studied by X-ray diffraction and symmetry analyses. It is established that the formation of a tetragonal (space group I4₁/amd) ordered V₅₂O₆₄ phase in cubic vanadium monoxide VO_y proceeds in the form of the first-order phase transition via a channel involving 22 nonequivalent superstructural vectors of four stars ({k ₁₀}, {k ₄}, {k ₃}, and {k ₂}). The distribution function of V atoms in the tetragonal V₅₂O₆₄ superstructure is calculated, and it is found that the real ordered V_51.6O₆₄ phase exhibits significant atomic displacements. The boundaries of the domain of existence of the V₅₂O₆₄ phase at 54–60% O are determined in the phase diagram of the V-O system.     

Cluster formation in LiNi<Subscript>0.4</Subscript>Fe<Subscript>0.6</Subscript>O<Subscript>2</Subscript>

The structure of an LiNi_0.4Fe_0.6O₂ cubic solid solution is determined using magnetic measurements and electron diffraction. It is found that this solid solution has a microinhomogeneous structure due to the formation of superparamagnetic clusters. The electron diffraction analysis of LiNi_0.4Fe_0.6O₂ samples has revealed diffuse scattering characteristic of the substitutional short-range order in ordered solid solutions with a B1-type structure. It is shown that the short-range order is associated with the LiNiO₂-type rhombohedral superstructure (space group \(R\bar 3m\)), i.e., with the redistribution of lithium and nickel atoms in the (111)_B1 alternating planes. The short-range order is observed in regions with a nickel content higher than the mean nickel content corresponding to the macroscopic composition.     

Short-range order and nonstoichiometry in titanium monoxide TiO<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> from DFT calculations

Structural models of short-range order in the arrangement of structural vacancies have been proposed for stoichiometric and nonstoichiometric compositions of titanium monoxide TiO _y . A combined effect of the short-range order and nonstoichiometry on the ground-state energy and the electronic structure of the compound has been investigated using the first-principles methods. The energetically favorable models of short-range order reproduce the local distribution of atoms and vacancies, which is characteristic of the Ti₅O_5(mon) and Ti₅O_5(cub) superstructures. In these models, the correlations between the vacancies of the metal sublattice and the vacancies of the nonmetal sublattice make a more significant contribution to the decrease in the energy of the compound as compared with the correlations between the vacancies in only one of the sublattices.     

Relationship between short- and long-range orders in nonstoichiometric titanium monoxide (TiO<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript>)

The relationship between the short- and long-range orders in various phases of nonstoichiometric titanium monoxide (TiO _y ) has been analyzed for the first time. The types of the local environment of lattice sites in the metal and nonmetal (oxygen) sublattices of Ti₅O₅, Ti₃O₂, Ti₂O₃, and Ti₄O₅ superstructures are described. It is established that, in phases where ordering takes place simultaneously in both sublattices, all parameters of the superstructural short-range order determining the positions of atoms and vacancies in the first three coordination spheres can be uniquely expressed via the long-range order parameters. If the ordering takes place only in one sublattice, then five of the six short-range order parameters vanish. It is shown that, using data on the maximum absolute values of six short-range order parameters and on the fractions of occupied atomic positions in titanium and oxygen sublattices, it is possible to predict the type of ordered phase expected to form in the nonstoichiometric titanium monoxide TiO _y .     

Concentration phase transition near the stoichiometric composition of vanadium monoxide VO<Subscript>1.00</Subscript>

The concentration dependences of the magnetic susceptibility and lattice parameter of cubic vanadium monoxide have been measured in the composition range from VO_0.81 to VO_1.07. Near the stoichiometric composition VO_1.00, the concentration dependences exhibit a stepwise increase in the specific magnetic susceptibility (by approximately 0.7 × 10^?6 cm³/g) and lattice constant (by about 0.002 nm). These effects can be related to the concentration phase transition, which occurs in vanadium monoxide with a change from a substoichiometric composition to superstoichiometric. At such a transition, along with a decrease in the concentration of oxygen vacancies, tetrahedrally coordinated vanadium interstitials are formed, as a result of which the B1 structure changes to a more complex cubic phase structure with the same space group Fm-3m.     

Disintegration of a coarse-grained vanadium monoxide VO<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> powder

A coarse-grained powder of nonstoichiometric cubic vanadium monoxide VO _y is disintegrated in a Retch PM 200 planetary ball mill. Milling of the coarse-grained vanadium monoxide powder VO _y at a rate of rotation of 500 rpm for 2 h significantly broadens diffraction lines, and the crystal structure of vanadium monoxide VO_1.00 after milling remains the same. High-resolution scanning electron microscopy and X-ray diffraction studies of the microstructure of vanadium monoxide demonstrate that high-energy milling can produce vanadium monoxide powders with an average crystallite size of 23 ± 10 nm. The vanadium monoxide produced by milling has a crystallite size that is half the crystallite size in the titanium monoxide produced by severe plastic deformation.     

Monoclinic superstructure V14O6 of the tetragonal solid solution of oxygen in vanadium

The monoclinic (space group C2/m) superstructure of V₁₄O₆, which is formed in the atom-vacancy ordering of the tetragonal solid solution of oxygen in vanadium, is studied by the methods of x-ray diffraction and symmetry analysis. It has been found that the channel of the order-disorder phase transition attributed to the formation of the monoclinic suboxide V₁₄O₆ includes six superstructure vectors belonging to three non-Lifshitz stars {k ₁₋₁}, {k ₁₋₂}, and {k _1–3} of one type {k ₁}. The distribution function of the O atoms in the V₁₄O₆ monoclinic superstructure has been calculated. It has been shown that the displacements of V atoms distort the body-centered tetragonal metal sublattice, thus preparing the formation of the fcc sublattice and the transition from the suboxide V₁₄O₆ to the cubic vanadium monoxide with the B1 structure. Original Russian Text ? A.I. Gusev, D.A. Davydov, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 10, pp. 746–751.     

Effect of ordering on the structure and heat capacity of cubic vanadium carbonitrides VC<Subscript>x</Subscript>N<Subscript>y</Subscript>

Experimental results are presented on measurements of the crystal structure and heat capacity of nonstoichiometric cubic vanadium carbonitrides VC_xN_y (x + y = 0.85) in the region of disorder-order phase transitions. It is found that ordered phases V₆(C,N)₅□ and V₈(C,N)₇□ with the structures of the V₆C₅ and V₈C₇ types form in vanadium carbonitrides at a temperature of ～1100 K through the first-order phase transition mechanism. The channels of disorder-order transitions are determined. It is found that, in the nonmetal sublattice of the detected ordered phases, C and N atoms form one sublattice and structural vacancies □ form another sublattice. C and N atoms are randomly distributed in their sublattice.     

Superposition of M<Subscript>5</Subscript>X<Subscript>5</Subscript> superstructures and X-ray diffraction in TiO<Subscript>1.0</Subscript> titanium monoxide

The interpretation of diffraction spectra of ordered high-temperature phases of solid solutions and strongly nonstoichiometric compounds is discussed. It has been shown that variations of the intensities of superstructure reflections, which cannot be explained within simple ordering models, can be due to the superposition of superstructures with different symmetries in the matrix of the basis crystal structure. Using an example of atom–vacancy ordering in TiO_1.0 titanium monoxide, a model of the order–order transition state formed by the superposition of low-temperature monoclinic (space group A2/m (C2/m)) and high-temperature cubic (space group Pm3?m) M₅X₅ superstructures has been proposed. It has been shown that the transition state is thermodynamically equilibrium and should be implemented instead of the M₅X₅ cubic superstructure. The transition state model can be considered as an M_(5–i)X_(5–i) superstructure (i = 1, 14/18, 11/18) with the monoclinic symmetry (space group P1m1).     

Effect of carbon vacancies on the electric resistivity of nonstoichiometric VC<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> vanadium carbide

The influence of the temperature, concentration, and distribution of structure vacancies of the carbon sublattice on the electric resistivity ρ of nonstoichiometric VC _y vanadium carbide (0.66 ≤ y ≤ 0.875) has been studied in the temperature range of 300–1200 K. The symmetry and structure characteristics of the ordered V₆C₅ and V₈C₇ phases formed owing to low-temperature annealing on various sections of the homogeneity region of the VC _y carbide. The dependence of the residual electric resistivity on the content of the disordered vanadium carbide is explained by the atom-vacancy interaction and the change in the carrier concentration in the homogeneity region of VC _y .     

Neutron diffraction analysis of a defect vanadium monoxide close to the equiatomic vanadium monoxide

Neutron and X-ray diffraction analyses are applied to studying the defect structure of synthesis-temperature quenched and low-temperature annealed vanadium monoxides VO _y (0.90 ≤ y ≤ 0.97) close to the equiatomic monoxide VO_1.0. It is found that the monoxides VO_0.90 and VO_0.97 contain structural vacancies not only in the oxygen sublattice, but also in the metal sublattice. In addition to the cubic disordered phase VO _y with the structure B1, the monoclinic superstructure V₁₄O₆ with space group C2/m is present in the synthesized VO_0.90 sample and in the annealed VO_0.90 and VO_0.97 samples. The formation of the V₁₄O₆ superstructure is attributed to the ordering of oxygen atoms and nonmetal vacancies in the lattice of the tetragonal solid solution of oxygen in vanadium. No simultaneous ordering of metal and oxygen vacancies in two sublattices of the cubic vanadium is observed.     

Long- and short-range order in the Pd<Subscript>6</Subscript>B monoclinic superstructure and M<Subscript>6</Subscript>X<Subscript>5</Subscript> and M<Subscript>6</Subscript>X allied superstructures

Symmetry analysis of the Pd₆B monoclinic superstructure (space group C2/c) formed in the cubic (with the B1 structure) solid solution of boron in palladium (PdB _y ) has been carried out. The formation of this superstructure proceeds as a first-order phase transition via the disorder-order channel including nine nonequivalent superstructure vectors of four stars {k ₁₀}, {k ₄}, {k ₃}, and {k ₀}. For the Pd₆B monoclinic super-structure (space group C2/c), the distribution function for boron atoms is calculated and the interval of admissible values of the long-range order parameters is defined. It is shown that the transition channel determined in this way coincides with the channel in which the M₆X monoclinic superstructure (space group C2) is formed; therefore, the Pd₆B superstructure can also be described in space group C2 to the same degree of accuracy. The higher symmetry of the monoclinic model (space group C2/c) suggests that it describes the structure of the Pd₆B phase (Pd₆B□₅), as well as of mutually inverse phases M₆X□₅ and M₆X₅□, more adequately than the model with space group C2. It is shown that superstructures of the M₆X□₅ type (space groups C2/c, C2, C2/m, and P3₁) and inverse superstructures of the M₆X₅□ type with the same space groups have the positions of the nearest surrounding of metal atoms by two types of nonmetallic sublattice sites located in the first and second coordination spheres.     

Magnetism of LiMn<Subscript>2</Subscript>O<Subscript>4</Subscript> manganite in structurally ordered and disordered states

The specific features of the crystal structure and the magnetic state of stoichiometric lithium manganite in the structurally ordered Li[Mn₂]O₄ and disordered Li_{1 − δ}Mn_δ[Mn_{2 − δ}Li_δ]O₄ (δ = 1/6) states have been investigated using neutron diffraction, X-ray diffraction, and magnetic methods. The structurally disordered state of the manganite was achieved under irradiation by fast neutrons (E _eff ≥ 1 MeV) with a fluence of 2 × 10²⁰ cm⁻² at a temperature of 340 K. It has been demonstrated that, in the initial sample, the charge ordering of manganese ions of different valences arises at room temperature, which is accompanied by orthorhombic distortions of the cubic spinel structure, and the long-range antiferromagnetic order with the wave vector k = 2π/c(0, 0, 0.44) is observed at low temperatures. It has been established that the structural disordering leads to radical changes in the structural and magnetic states of the LiMn₂O₄ manganite. The charge ordering is destroyed, and the structure retains the cubic symmetry even at a temperature of 5 K. The antiferromagnetic type of ordering transforms into ferrimagnetic ordering with local spin deviations in the octahedral sublattice due to the appearance of intersublattice exchange interactions.     

Simulation of the short-range order in disordered cubic titanium monoxide TiO1.0

A model of the atomic structure with the short-range order in the vacancy distribution for the disordered cubic phase of titanium monoxide TiO_1.0 has been proposed. The effect of the short-range order on the electronic structure and the stability of the compound has been studied by the supercell method within the DFT-GGA approximation with the use of pseudopotentials. It has been established that the appearance of the short-range order considerably decreases the total energy. The decrease in the energy is comparable with the energy gain during the ordering of the vacancies according to the type of monoclinic superstructure Ti₅O₅ to the long-range order parameter η = 0.7. It has been shown that the discrepancies between the theoretical and experimental electronic spectra of titanium monoxide can be explained by allowance for the short range order.     

Conductivity and spectroscopic studies of Li<Subscript>2</Subscript>O-V<Subscript>2</Subscript>O<Subscript>5</Subscript>-B<Subscript>2</Subscript>O<Subscript>3</Subscript> glasses

Lithium vanadium-borate glasses with the composition of 0.3Li₂O–(0.7-x)B₂O₃–xV₂O₅ (x?=?0.3, 0.325, 0.35, 0.375, 0.4, 0.425, 0.45, and 0.475) were prepared by melt-quenching method. According to differential scanning calorimetry data, vanadium oxide acts as both glass former and glass modifier, since the thermal stability of glasses decreases with an increase in V₂O₅ concentration. Fourier transform infrared spectroscopy data show that the vibrations of [VO₄] structural units occur at V₂O₅ concentration of 45 mol%. It is established that the concentration of V⁴⁺ ions increases exponentially with the growth of vanadium oxide concentration. Direct and alternative current measurements are carried out to estimate the contribution both electronic and ionic conductivities to the value of total conductivity. It is shown that the electronic conductivity is predominant in the total one. The glass having the composition of 0.3Li₂O-0.275B₂O₃-0.475V₂O₅ shows the highest electrical conductivity that has the value of 7.4?×?10^?5 S cm^?1 at room temperature.     

Antisite defects and valence state of vanadium in Na<Subscript>3</Subscript>V<Subscript>2</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript>

Electron paramagnetic resonance (EPR) studies have been performed with the aim of determining the valence state and local crystal structure of the nearest environment of vanadium ions in the initial, charged, and discharged samples of the cathode material Na_xV₂(PO₄)₃ (1 ≤ x ≤ 3). It has been found that the charged sample (x = 1) is characterized by an intense signal corresponding to V⁴⁺ ions located in a highly distorted octahedral crystal field. An EPR signal with the g-factor close to the g-factor of the V⁴⁺ ion has also been observed in the initial sample (x = 3), where the intensity of the resonance signal is one order of magnitude lower than that in the charged sample. It has been revealed that the resonance signal under consideration is associated with the formation of antisite defects when a part of vanadium ions are located in sites of sodium ions. It has also been found that the intensity of this signal increases after a complete charge–discharge cycle (x = 3).