Two-sublattice ordering in titanium monoxide

The disordered and ordered structures of nonstoichiometric titanium monoxide Ti_xO_z≡TiO_y(y=z/x) containing structural vacancies simultaneously in the nonmetallic and metallic sublattices were studied. In the stoichiometry range from TiO_0.9 to TiO_1.1, an ordered monoclinic phase [space group C2/m (A12m/1)] of the Ti₅O₅ type is formed in the TiO_y monoxide at temperatures below 1300 K. The disorder-order TiO_y?Ti₅O₅ phase-transition channel involves Lifshitz {k₁₀} and non-Lifshitz {k₄} and {k₁₁} star rays. The ordering proceeds as a first-order phase transition with a decrease in the volume of the basal cubic lattice. The titanium and oxygen distribution functions in the metallic and nonmetallic sublattices of titanium monoxide are calculated. The domain of allowed values is determined for the long-range order parameter.     

A thermodynamic model of ordering of nonstoichiometric titanium monoxide TiO y with structural vacancies in the oxygen and titanium sublattices

A thermodynamic model of ordering of nonstoichiometric titanium monoxide TiO _y with structural vacancies in the oxygen and titanium sublattices has been developed taking into account the long-range Coulomb interactions. Methods for calculating the internal energy and entropy of this compound have been proposed. The free energy is represented in the form of a function of long-range order parameters, stoichiometry, and temperature. It has been found that the order-disorder phase transition in the titanium monoxide should occur according to the mechanism of a first-order phase transition. The calculated dependences of the critical values of the long-range order parameters and temperatures on the composition y have demonstrated that, when the composition deviates from stoichiometry, the disordering of structural vacancies in different sublattices should proceed at different temperatures.     

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 .     

Electronic structure and stability of nonstoichiometric titanium monoxide TiO y with structural vacancies in one of the sublattices

The electronic structure of nonstoichiometric titanium monoxide TiO _y with different compositions y, which contains structural vacancies either in the metallic sublattice or in the nonmetallic sublattice, has been investigated using the supercell method within the DFT-GGA approximation with pseudopotentials. The cases of ordered and disordered arrangements of vacancies have been considered. It has been found that the complete removal of vacancies from the sublattice is energetically unfavorable, and the ordering of oxygen vacancies according to the type of the Ti₆O₅□₁ superstructure, as well as titanium vacancies according to the Ti₅?₁O₆ type, does not lead to the stabilization of the B1 basic structure of titanium monoxide.     

Probabilities of octahedral clusters depending on long-range order parameters and composition in nonstoichiometric titanium monoxide TiO y

A method for calculating the probabilities of cluster configurations in ordered superstructures of strongly nonstoichiometric compounds depending on the composition and the order parameter is described using the Ti₅O₅ superstructure of nonstoichiometric titanium monoxide TiO _y . Analytic expressions are derived for the dependences of the probabilities of the main cluster configurations in the Ti₅O₅ superstructure on the fraction of atomic positions in the titanium and oxygen sublattices and on the long-range order parameter. The probabilities of configurations are calculated for various long-range order parameters taking into account experimental data on the concentration of structural vacancies in the titanium and oxygen sublattices. The dependences of the probabilities of cluster configurations on the short-range order parameter are established from the relations between the superstructure long-range and short-range order parameters.     

Investigation of structural vacancies in titanium monoxide by electron-positron annihilation

Local atomic environment of vacancies in nonstoichiometric titanium monoxide ranging in composition from TiO_0.74 to TiO_1.26 was studied by electron-positron annihilation. Analysis of the Doppler broadening spectra of the annihilation gamma line for titanium and liquid oxygen showed that positrons in titanium monoxide are trapped by titanium vacancies. Experiments revealed that the lifetime of positrons in ordered and disordered titanium monoxide TiO _y increases with increasing oxygen content y and varies from 184 to 210 ps. Data on the valence electron density permitted the prediction that the lifetime of free positrons in stoichiometric titanium monoxide is about 140 ps and the lifetime of positrons localized in an oxygen vacancy is about 170 ps. The method used to analyze the gamma-line Doppler broadening spectra makes it possible to determine the type and number of atoms around a vacancy and to investigate order-disorder phase transformations in nonstoichiometric compounds.     

Ordered orthorhombic phases of titanium monoxide

Symmetry analysis is carried out for the ordered phases of cubic monoxide TiO_y with relative oxygen contents y<1 and y>1. It is established that a partially ordered orthorhombic phase (space group Immm)—a derivative of the orthorhombic M₃X₂□ superstructure (at y<1.0) or the inverse superstructure M₂■X₃ (at y>1)—may arise in TiO_y. The distribution of Ti and O atoms, oxygen vacancies □, and titanium vacancies ■ in unit cells of the orthorhombic ordered phases is determined. The phases are formed through the order-disorder transition channel along two rays of a non-Lifshitz star {k ₄}, and the ordering proceeds as a first-order phase transition. The distribution functions of Ti atoms over the sites of metallic and O atoms over the sites of nonmetallic sublattices are calculated for the orthorhombic superstructures of cubic titanium monoxide TiO_y.     

Internal energy and parameters of the order-disorder phase transition in titanium monoxide TiO y

Quantum-mechanical ab initio calculations are used to simulate the free energy functions for titanium monoxide TiO _y . The effect of the long-range order of the Ti₅O₅ type superstructure on the internal energy of the compound is studied by the supercell method. The dependences of the configuration entropy and free energy on the long-range order parameter are determined. It is found that the order-disorder phase transition in titanium monoxide must occur in accordance with the mechanism of the first-order phase transition with a critical value of the long-range order parameter of 0.971. The calculated parameters of the phase transition are compared with the experimental data and the results obtained using the model of point charges and by calculating the Madelung energy. It is concluded that the short-range order and the phonon entropy must be taken into account in calculating the equilibrium phase diagrams for strongly nonstoichiometric compounds.     

Electronic structure of disordered titanium monoxide TiO<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> depending on stoichiometry

The electronic structure of disordered nonstoichiometric titanium monoxide TiO _y depending on the oxygen content has been studied by the supercell method in the DFT-GGA approximation with the use of pseudo-potentials. An increase in the oxygen content in TiO _y leads to a decrease in the electron density of states near the Fermi level. The calculation of the enthalpy of formation of the ordered and disordered phases has shown that the disordered phase TiO _y is more energetically favorable than the phase without the TiO structural vacancies but is less favorable than the ordered Ti₅O₅ phase. The stability of the disordered phase increases with the oxygen content.     

Electronic structure of titanium monoxide with randomly distributed vacancies

The electronic structure of titanium monoxide TiO _y (0.810 ≤ y ≤ 1.262) in the high-temperature cubic phase with vacancies randomly distributed over the titanium and oxygen sublattices is calculated in the coherent potential approximation. The changes in the electronic spectra with the concentration of vacancies are retraced. The calculated spectra are compared to the available experimental data.     

The influence of imperfection of the crystal lattice on the electrokinetic and magnetic properties of disordered titanium monoxide

The conductivity and magnetic susceptibility of disordered titanium monoxide TiO_y (0.920≤y≤1.262) containing vacancies in titanium and oxygen sublattices are investigated. For TiO_y monoxides with an oxygen content y≤1.069, the temperature dependences of the conductivity are described by the Bloch-Grüneisen function at a Debye temperature ranging from 400 to 480 K and the temperature dependences of the magnetic susceptibility are characterized by the contribution from the Pauli paramagnetism due to conduction electrons. The behavior of the conductivity and magnetic susceptibility of TiO_y monoxides with an oxygen content y≥1.087 is characteristic of narrow-gap semiconductors with nondegenerate charge carriers governed by the Boltzmann statistics. The band gap ΔE between the valence and conduction bands of TiO_y monoxides with y≥1.087 falls in the range 0.06–0.17 eV.     

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.     

Effect of the long-range order in the vacancy distribution on the electronic structure of titanium monoxide TiO1.0

The effect of the long-range order in the vacancy distribution according to the type of monoclinic Ti₅O₅ superstructure on the electronic structure of titanium monoxide TiO _y with the stoichiometric composition has been studied by the supercell method within the DFT-GGA approximation with the use of pseudopotentials. It has been established that, in spite of an increase in the Fermi energy, the stability of the compound increases with increasing degree of the long-range order η. The ordering of the structural vacancies leads to the considerable increase in the depth of the pseudogap at the Fermi level. It has been shown that the effect of the long-range order on the electronic structure in the range of η from 0 to 1.0 is much weaker than the effect of the nonstoichiometry of TiO _y in the range of y from 0.75 to 1.33.     

Identification of structural vacancies in carbides,oxides, and sulfides by Doppler broadening of the gamma-ray line

A method has been developed to identify the sublattices of a crystal structure in which there are atomic vacancies. This method is based on determining the chemical environment of vacancies and is implemented using the method of the positron annihilation by measuring the momentum distribution of core electrons. To determine the characteristic momentum distribution of electrons, a special two-detector spectroscopy is used, which ensures measurements of Doppler broadening of the annihilation gamma-ray line with a high (up to 10⁶) signal-to-noise ratio. To test the method, vacancies in irradiated silicon carbide (6H-SiC), sintered nonstoichiometric titanium carbides (TiC _y ) and titanium monoxides (TiO _y ), and chemically deposited lead and cadmium sulfides (PbS and CdS) have been identified. Vacancies in the carbon and silicon sublattices have been identified in silicon carbide after irradiation by low- and high-energy electrons, respectively. Vacancies in the nonmetal sublattice have been identified in TiC _y . Vacancies in the metal sublattice have been identified in TiC _y , as well as in PbS and CdS.     

Observation of structural vacancies in titanium monoxide using transmission electron microscopy

Structural vacancies were directly observed in nonstoichiometric ordered titanium monoxide using high-resolution transmission electron microscopy under a magnification of 4×10⁶. The observation of structural vacancies became possible due to their ordering and the formation of continuous vacancy channels in certain crystallographic directions. Microdiffraction was employed to orient the sample in the direction permitting the observation of vacancy channels. Transmission electron microscopy providing a magnification of tens of thousands of times revealed that titanium monoxide grains do not contain cracks and macropores and confirmed that the free volume detected picnometrically in the titanium monoxide is concentrated in structural vacancies on the titanium and oxygen sublattices.     

Dependence of Van-Vleck paramagnetism on the size of nanocrystals in superstoichiometric TiO<Subscript> <Emphasis Type="Italic">y</Emphasis> </Subscript>

In situ measurements of the magnetic susceptibility of titanium monoxide nanocrystals with superstoichiometric composition TiO_y (y > 1) in the 300–1200 K temperature range showed that this value depends not only on the structural state of a sample, but also on the size of crystals. Analysis of data obtained for both ordered and disordered TiO_y showed that the Van-Vleck paramagnetism is inversely proportional to the nanocrystal size because of breakage of the symmetry of local environment of the near-surface atoms of titanium and oxygen. The Van-Vleck paramagnetism contribution due to atomic-vacancy disorder in superstoichiometric titanium monoxide nanocrystals, as well as in the stoichiometric composition, is proportional to a deviation of the degree of long-range order from its maximum value.     

Two-dimensional quantum ferromagnet,magnetic chains,and oxygen ordering in La<Subscript>2</Subscript>NiO<Subscript>4.125</Subscript> single crystals

A method using the atom-vacancy ordering phenomenon for the visualization of structural vacancies in crystals was suggested and implemented. The ordered nonstoichiometric titanium monoxide Ti₅O₅ was taken as the object of investigation, because the structural vacancies in this compound can be observed due to the formation of continuous vacancy channels in certain crystallographic directions. The structural vacancies in the specially oriented sample of ordered titanium monoxide were directly observed by high-resolution transmission electron microscopy with a magnification of 4×10⁶.     

Investigation of the influence of nonstoichiometry and doping with carbon and nitrogen on the electronic spectrum of rutile by the coherent potential method

The electronic spectra and magnetic properties of rutile (TiO₂), nonstoichiometric rutile (TiO_{2 ? δ}), and stoichiometric and nonstoichiometric rutiles doped with carbon or nitrogen (TiO_{2 ? y ? δ}C _y and TiO_{2 ? y ? δ}N _y , y(δ) = 0, 0.03, 0.06) have been calculated using the coherent potential method. The used method of investigation has made it possible for the first time to calculate the disordered arrangement of impurity atoms and vacancies in the oxygen sublattice with their arbitrary concentration. The changes in the electronic spectrum and magnetic properties with variations in the concentration of dopants have been investigated. The possible photocatalytic activity of considered compositions has been analyzed.     

Electrical conductivity and magnetic susceptibility of titanium monoxide

Conductivity and magnetic susceptibility of disordered cubic titanium monoxide TiO_y(0.920≤y≤1.262) are studied. Temperature dependences of the conductivity of TiO_y monoxides with y≤1.069 are described by the Bloch-Grüneisen function with Debye temperature 400–480 K, and temperature dependences of the susceptibility include Pauli paramagnetism of conduction electrons. The behavior of conductivity and susceptibility of TiO_y with y≥1.087 is typical of semiconductors with nondegenerate charge carriers obeying Boltzmann statistics. The band gap ΔE between the valence and conduction bands of TiO_y(y≥1.087) is 0.06–0.17 eV, and effective mass of charge carriers is equal to 7–14 electron masses.     

Disorder-order phase transformations and electrical resistivity of nonstoichiometric titanium carbide

Phase transformations of the disorder-order type in the homogeneity region of nonstoichiometric titanium carbide TiC_y (0.5<y<1.0) have been studied. It has been established that, depending on the actual composition of TiC_y, there may form in it for T<980–1000 K a cubic or a trigonal ordered Ti₂C phase (space groups Fd3m and , respectively) and a rhombic ordered Ti₃C₂ phase (space group C222₁). The effect of ordering on the electrical resistivity of the nonstoichiometric carbide TiC_y was studied, and the temperatures of the reversible disorder-order equilibrium transitions determined. The ordering in titanium carbide is shown to be a first-order phase transition. Fiz. Tverd. Tela (St. Petersburg) 40, 1332–1340 (July 1998)