M. G. Kostenko

Inclusion of the correlation short-range order in Ab initio calculations of the energy of the ground state by example of titanium monoxide TiO1.0

A variant of the distribution of structural vacancies at which the crystal structure of ordered compounds simultaneously has a long-range order and correlation short-range order has been proposed and analyzed. The long-range order determines the fraction of vacancies in the atomic and vacancy sublattices of the superstructure formed because of ordering. The correlation short-range order takes into account energy favorable correlations in the arrangement of vacancies, which exist in disordered phases and are not determined by the long-range order. The possibility of the correlation short-range order has been examined by ab initio methods by example of ordering of vacancies in titanium monoxide TiO1.0 according to the type of monoclinic superstructure M5X5mon. It has been shown that partially ordered modifications with the correlation short-range order are energetically favorable as compared to the modifications without the correlation short-range order.

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 TiO1.0 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.

Electronic Structure of Disordered Titanium Monoxide TiO y Depending on Stoichiometry

The electronic structure of disordered nonstoichiometric titanium monoxide TiOy 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 TiOy 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 TiOy 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.

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 TiOy 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 TiOy in the range of y from 0.75 to 1.33.

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 TiOy. 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.

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 TiOy. 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.

Relationship between short- and long-range orders in nonstoichiometric titanium monoxide (TiOy)

The relationship between the short- and long-range orders in various phases of nonstoichiometric titanium monoxide (TiOy) 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 TiOy.

Short-range order in disordered transition metal oxides, carbides, and nitrides with the B1 structure

A method has been proposed for the simulation of the atomic structure of disordered phases of nonstoichiometric transition metal oxides, carbides, and nitrides with the B1 structure taking into account the short-range order in the arrangement of structural vacancies. The simplest structural models constructed with allowance for pair correlations between vacancies within the first four coordination spheres have been considered. A computer simulation of the atomic structure of disordered phases with the inclusion of the short-range order has been performed. For each structural model, the maximum possible concentration of vacancies and the short-range order parameters at different concentrations have been calculated. For a further experimental verification, the influence of the short-range order on the shape of the X-ray scattering spectrum has been investigated by calculating the theoretical X-ray diffraction patterns according to the Debye formula. The influence of the short-range order on the total energy of the disordered phases has been analyzed by ab initio methods. It has been shown that, in some cases, the proposed structural models of the short-range order are energetically favorable as compared to the model of statistical arrangement of vacancies.

Coherent Potential Approximation Simulation of the Evolution of the Electronic Structure of Titanium Monoxide with the Degree of Vacancy Ordering

An idea is formulated and implemented to take into account the change in the electrostatic interaction between lattice sites when vacancies substitute for atoms using the coherent potential approximation in the calculation method proposed by us earlier [3]. The change in the electronic structure of titanium monoxide Ti5O5 ordered according to a monoclinic superstructure is studied as a function of the degree of vacancy ordering in the titanium and oxygen sublattices.

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 TiOy 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.