ISSN 1063-7834, Physics of the Solid State, 2009, Vol. 51, No. 3, pp. 507–513. © Pleiades Publishing, Ltd., 2009. Original Russian Text © V.G. Zavodinsky, A.N. Chibisov, 2009, published in Fizika Tverdogo Tela, 2009, Vol. 51, No. 3, pp. 477–482. 507 1. INTRODUCTION Among three crystalline forms of the titanium diox- ide (rutile, anatase, brookite), the anatase has attracted considerable attention of researchers owing to the extensive applications as a catalyst, a component of solar cells, and a coloring pigment. The TiO 2 dioxide possessing a large reflection coefficient has been widely used for protecting space vehicles against solar radiation. However, in this case, the important factor is the resistance of the coating with respect to the forma- tion of color centers, which in the titanium dioxide are predominantly represented by oxygen vacancies. In recent years, investigations have been aimed at devel- oping technologies that make it possible to increase the radiation resistance of coatings based on the TiO 2 ana- tase. For this purpose, the introduction of metal impuri- ties into the titanium dioxide is one of the promising directions. In particular, Mikhaœlov et al. [1] showed that the introduction of silicon at small doses increases the reflection coefficient, the addition of magnesium decreases the reflection coefficient, and the simulta- neous doping with magnesium and zinc increases the radiation resistance. It should be noted that an increase in the concentration of all these elements (from 0.5 to 1.0%) leads to a decrease in the reflection coefficient and a deterioration of the radiation resistance. The mechanism of the influence of these impurities on the properties of the titanium dioxide remains unclear and requires detailed investigations, including with the use of theoretical approaches. The present study was devoted to the solution of this problem. 2. CALCULATION METHOD The introduction of impurities and the formation of vacancies in the TiO 2 dioxide are frequently accompa- nied by the spin polarization. Therefore, the total energy and the electronic structure were calculated with the FH196spin program package, which is a modifica- tion of the FH196md program package [2] previously used with advantage for many systems, including tran- sition metal oxides [3–5]. This program package is based on the spin-unrestricted version of the electron- density functional theory, the pseudopotential method, and the use of a plane-wave basis set. In this work, we used the pseudopotentials of titanium and oxygen that were constructed with the FHI98PP program package [6]. The pseudopotentials were checked for the absence of the so-called ghost states and used for determining the equilibrium lattice parameters and the bulk elastic modulus of the anatase. These pseudopotentials are separable, transferable, and norm-conserving pseudo- potentials [6]. The calculated values of the lattice parameters and the elastic modulus differed from the experimental values by no more than 2 and 10%, respectively. A similar procedure was used for choosing the pseudopotentials of impurity atoms. In all cases (except for titanium), the pseudopotentials were calcu- lated using the Troullier–Martins scheme [7]. For tita- nium, the s and p components were determined accord- ing to the Hamann technique [8] and the d component was calculated within the Troullier–Martins scheme. The parameters of the pseudopotentials used are listed in Table 1. Influence of Impurities on the Stability and Electronic States of Titanium Dioxide in the Form of Anatase V. G. Zavodinsky a, * and A. N. Chibisov b, ** a Institute of Materials Science, Far East Division, Russian Academy of Sciences, ul. Tikhookeanskaya 153, Khabarovsk, 680042 Russia * e-mail: vzavod@mail.ru b Institute of Geology and Nature Management, Far East Division, Russian Academy of Sciences, Relochnyi per. 1, Blagoveshchensk, 675000 Russia ** e-mail: andreichibisov@yandex.ru Received July 16, 2008 Abstract—The behavior of impurities (Si, Zr, Mg, Zn) in the titanium dioxide with an anatase structure is investigated using the electron-density functional method (with due regard for the spin polarization). The influ- ence of these impurities on the formation of oxygen vacancies and the specific features of the electronic struc- ture is studied. It is demonstrated that the impurities can both improve and deteriorate the optical characteristics of the titanium dioxide. PACS numbers: 71.15.Mb, 71.20.-b DOI: 10.1134/S1063783409030123 1 DEFECTS AND IMPURITY CENTERS, DISLOCATIONS, AND PHYSICS OF STRENGTH