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.     

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.     

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.     

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.     

Atomic displacements in the V<Subscript>52</Subscript>O<Subscript>64</Subscript> superstructure and the short-range order in superstoichiometric cubic VO<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> vanadium monoxide with metal vacancies

Atomic displacements in the lattice of the tetragonal V₅₂O₆₄ superstructure have been experimentally determined. It has been found that atomic displacement waves, which are attributed to the formation of the short-range displacement order, appear in the vanadium and oxygen sublattices of this superstructure. It has been shown that the V₅₂O₆₄ superstructure is formed on the basis of disordered superstoichiometric cubic vanadium monoxide with the short-range order in the metallic sublattice. The character of the short-range order is such that vanadium atoms occupying tetrahedral positions are in the environment of four vacant sites of the vanadium sublattice. This means that the superstoichiometric VO_>1.0 vanadium monoxide has a cubic structure differing from the B1-type structure characteristic of most of the strongly nonstoichiometric cubic compounds MX _y (X = C, N, O) of transition metals.     

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.     

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.     

Twinning and short-range order in ordered titanium monoxide

Electron diffraction was used to study the annealed titanium monoxide TiO_1.087 containing the monoclinic ordered phase Ti₅O₅. The diffraction pattern of titanium monoxide in the (112)* _B1 plane of the reciprocal lattice of the parent B1 cubic structure contains not only structural, superstructural, and additional reflections but also a system of planar diffuse strips. It has been established that part of the additional reflections are twins of the superstructure reflections of the monoclinic ordered phase; the twinning plane is the ( $\overline 1 \overline 1 1$ ) plane of the reciprocal lattice of the parent cubic phase. The diffuse scattering contours cover finite plane areas in the reciprocal space characterized by the wave vectors K ₁₀₀ ～ ± (h + 0.07)k ₁₀₀, K ₀₁₀ ～ ±(k + 0.07)k ₀₁₀, and K ₀₀₁ ～ ±(l + 0.07)k ₀₀₁ in the B1 structure. The diffuse scattering is caused by short-range displacement order. Short-range substitution order and the corresponding diffuse scattering are absent.     

Short-range order and twins in ordered titanium monoxide

The structure of annealed titanium monoxide TiO_1.087 containing monoclinic ordered phase Ti₅O₅ was studied by electron diffraction. Along with the set of structural, superstructural, and extra reflections, the diffraction pattern of titanium monoxide shows a set of plane diffuse fringes in the (112)_B1* section of the reciprocal lattice of the basis cubic structure B1. It is shown that some of the extra reflections are due to the twinning of the monoclinic superstructure along the (?1?11) plane of the reciprocal lattice of the basis cubic structure. The diffuse contours enclose plane areas of the reciprocal space with the fixed values of wave vectors K₁₀₀ ～ ±(h+0.07)k₁₀₀, K₀₁₀ ～ ±(k+0.07)k₀₁₀, and K₀₀₁ ～± (l+0.07)k₀₀₁ of the B1 structure. Their appearance is associated with the short-range displacement order.     

Cluster probabilities in ordered titanium monoxide TiO y as functions of the long-range order parameters

The thermodynamic method is being developed for calculating the titanium-oxygen phase diagram in the domain of existence of the nonstoichiometric titanium monoxide TiO _y with vacancies in the metallic and nonmetallic sublattices. To develop the adequate thermodynamic model, the ordering in TiO _y was studied in detail by the x-ray diffraction method. The study showed that the low-temperature state of titanium monoxide is characterized by a nearly ideal atomic ordering in both metallic and oxygen sublattices. The structural analysis of the ordered Ti₅O₅ phase (space group C2/m) in titanium monoxide showed that one should use the multicluster approximation in modeling the free energy of the nonstoichiometric monoxide.     

钛铝合金高温氧化机理电子理论研究

为了从电子层面揭示钛铝合金高温氧化的物理本质,采用递归法与Castep相结合的方式, 计算了原子埋置能、亲和能、结合能等电子结构参数,探索合金氧化机理.研究表明: 氧在钛中有较大固溶度,氧原子可以在钛表面的基体内聚集,逐步向深层扩散. 氧与钛具备较强的亲和力,能形成钛的氧化膜.钛基体中铝原子间具有相互吸引力, 能形成铝的原子团簇.铝原子团簇中的钛原子间相互排斥与铝形成化合物. 铝、钛与氧的亲和能相近,不易发生铝的优先氧化,而是同时生成钛的氧化物和铝的氧化物. Al₂O₃比TiO₂的结合能略低,因而更加稳定,铝在TiO₂中有较大的固溶度, 能替换其中的钛形成更稳定的Al₂O₃氧化物.     

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.     

Comparative study of the heat capacity of icosahedral quasicrystals in solid and liquid states

The heat capacity of icosahedral quasicrystals Al₆₃Cu₂₅Fe₁₂ and Al₆₂Cu_25.5Fe_12.5 has been studied at high temperatures up to 1700 K, which is by almost 400 K higher than the melting point of the material. It has been shown that the melt exhibits an excess heat capacity with respect to that determined by the Dulong-Petit law and that is a direct extension of the excess heat capacity of the solid state. It has been concluded that the excess heat capacity is related, as a whole, to the short-range order in the quasicrystal structure. This circumstance allows the identification of the orbital hybridization as the most probable mechanism of formation of the pseudogap in the electronic structure of the quasicrystals.     

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.     

Role of magnetism in the formation of a short-range order in iron-silicon alloys

The formation of a short-range order in soft magnetic Fe-Si alloys depending on the annealing temperature has been investigated theoretically and experimentally. The B2-type short-range order has been observed in samples quenched from temperatures T > T _C (where T _C is the Curie temperature) with the content c _Si close to the boundary of the two-phase region. Annealing at temperatures T < T _C for the content c _Si ≥ 0.08 leads to an increase in the fraction of regions with the D0₃-type short-range order. The mechanism of the formation of the short-range order in Fe-Si solid solutions has been analyzed by the Monte Carlo simulation with the ab initio calculated interatomic interaction parameters. It has been shown that the energy of the effective Si-Si interaction in bcc iron strongly depends on the magnetic state of the matrix. As a result, the B2-type short-range order is formed at T > T _C and is fixed at quenching, whereas the D0₃-type shortrange order is equilibrium in the ferromagnetic state. The results reveal the decisive role of magnetism in the formation of the short-range order in Fe-Si alloys and allow the explanation of the observed structural features of the alloys depending on the composition and temperature.     

Ordering behaviors of the F.C.C. and B.C.C. phase alloys in the InMg,LiMg and AlZn systems

Expressions of the band-structure energy and the electrostatic energy characterized by the usual long-range and short-range order parameters are given to a binary alloy of simple metals with the f.c.c.-type or b.c.c.-type structure.The ordering energy and the local ordering energy are calculated for the InMg, LiMg and AlZn systems. The numerical results explain successfully the facts that the InMg system has the Ll₀-type and Ll₂-type ordered phases, each of which exists over a wide range of concentration and that the LiMg system has a local order with a negative short-range order parameter, while the AlZn system has that with the positive one. A lattice distortion in the Ll₀-type ordered structure of InMg is also discussed.     

Influence of particle size,stoichiometry, and degree of long-range order on magnetic susceptibility of titanium monoxide

In situ measurements of the magnetic susceptibility of ordered and disordered titanium monoxides TiO_y in the temperature range from 300 to 1200 K have revealed that it depends on the size of crystals, their stoichiometry, and long-range order parameters. Analysis of the data for both the ordered and disordered TiO_y has demonstrated that the dependence of the Van Vleck paramagnetism on the nanocrystal size is inversely proportional due to the breaking of symmetry of the local environment of titanium and oxygen atoms near the surface of nanocrystals. It has been found that the Van Vleck contribution from the atomic vacancy disorder in monoxide nanocrystals of superstoichiometric composition, as well as in the crystalline stoichiometric monoxide, is proportional to the deviation of the degree of long-range order from the maximum value.     

Role of magnetism in the formation of a short-range order in an Fe-Ga alloy

The formation of a short-range order in an Fe-Ga bcc alloy has been studied by Monte Carlo simulation with the use of effective interaction potentials calculated within the density functional theory for the ferromagnetic and paramagnetic states. It has been found that the pronounced short-range order of the D0₃ type is formed at Ga concentrations close to the boundary of the two-phase region at T < T _c, whereas no short-range order is observed at T < T _c. The results obtained are in agreement with the experimental X-ray diffraction analysis. The relation of the features of the short-range order in the Fe-Ga alloy to the magnetostriction value has been discussed.     

New boron barrelenes and tubulenes

The structure of a new class of boron nanostructures—barrelenes and tubulenes—based on a boron atomic lattice constructed by the alternating B-atomic polygons with central atoms and without them has been proposed and their properties have been described. Ab initio density functional calculations have been performed for the energy and electronic structure of the fullerene-barrelene-nanotube series based on the lowest energy fullerene B₈₀. It has been shown that the energy and band gap of a barrelene are lower than the respective quantities of the corresponding fullerene and tend to the respective values for nanotubes in the infinite limit. It has been shown that there are isomers of nanotubes of the same type that are significantly different in symmetry and electronic properties: a semiconductor (C _5v symmetry) and a metal (D _5h symmetry).