Coherent potential approximation simulation of the evolution of the electronic structure of titanium monoxide with the d
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Coherent Potential Approximation Simulation of the Evolution of the Electronic Structure of Titanium Monoxide with the Degree of Vacancy Ordering M. A. Korotina*, N. A. Skorikova, A. V. Lukoyanova,b, V. I. Anisimova,b, M. G. Kostenkoc, and A. A. Rempel’c,b a
Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 18, Yekaterinburg, 620990 Russia *email: [email protected] b Ural Federal University, Yekaterinburg, 620002 Russia c Institute of SolidState Chemistry, Ural Branch, Russian Academy of Sciences, ul. Pervomaiskaya 91, Yekaterinburg, 620990 Russia Received June 11, 2014
Abstract—An idea is formulated and implemented to take into account the change in the electrostatic inter action 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 mon oxide Ti5O5 ordered according to a monoclinic superstructure is studied as a function of the degree of vacancy ordering in the titanium and oxygen sublattices. DOI: 10.1134/S1063776114100057
The theoretical simulation of vacancy systems is performed using various approaches. The most widely used approach is the electronic density functional the ory with various approximations for an exchangecor relation potential using a supercell model. A supercell is formed when the unit cell of a system to be studied is enlarged by several times in certain or all translation vector directions. A vacancy is simulated via the removal of one atom from a certain crystallographic site in a supercell. In this approach, vacancies are ordered both spatially, which is determined by super cell translation vectors, and structurally, which is determined by the crystallographic site in a supercell. Supercell model calculations inevitably encounter the problem of considering a large number of configura tions of possible relative vacancy positions inside a supercell and the absence of grounded considerations regarding the partial contribution of each configura tion to an average solution. An additional disadvan tage is the discreteness of vacancy concentrations con sidered in such a model: it is determined by the super cell sizes and, correspondingly, requires a high computational power. In the absence of the possibility of simulating large supercells (e.g., in the case of critically low vacancy concentrations), an electronic structure can be calcu lated using an alternative approach, such as the Monte Carlo method and the cluster variation method (where the interatomic interaction parameters for clusters are theoretically found) [1]. Nevertheless, the coherent potential approximation (CPA) [2], which can be
applied to describe both spatially and structurally dis ordered systems [3], has received wider acceptance. Titanium monoxide TiOy is characterized by not only a high content of structural vacancies in the anion and cation sublattices but also possible ordering of vaca
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