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The Schottky point defect formation in MgSiO3-based ceramics is studied by the density functional theory method. It is shown that the formation of a Mg vacancy ...
Journal of Structural Chemistry. Vol. 56, No. 3, pp. 454-457, 2015. Original Russian Text © 2015 A. N. Chibisov.

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COMPUTER SIMULATION OF THE POINT DEFECT FORMATION IN MgSiO3 -BASED CERAMIC MATERIALS UDC 544.22.022.342

A. N. Chibisov

The Schottky point defect formation in MgSiO3-based ceramics is studied by the density functional theory method. It is shown that the formation of a Mg vacancy at the Mg2 position is more energy-efficient than at the Mg1 position by nearly 1 eV. The silicon vacancy has the highest energy of formation. The most energy-efficient defect is the oxygen vacancy at the O3 position in the enstatite lattice. The results of the effect of atom vacancies on the structural characteristics of MgSiO3 are shown. DOI: 10.1134/S0022476615030075 Keywords: ab initio calculations, defect formation, structural characteristics.

Steatite ceramics (MgSiO3, enstatite) is a wide-gap dielectric material, and due to its high dielectric and mechanical strength and moisture resistance, it is widely used in electronic, electrical and power engineering as a component in the production of high-voltage insulators and high-frequency ceramics [1]. MgSiO3 is also used in medicine to produce dental and orthopaedic prostheses [2]. Enstatite is a low-temperature modification of MgSiO3, and it transforms into proto-enstatite on heating and into clino-enstatite on cooling [3]. The so-called “low-P phase” of proto-enstatite has a orthorhombic structure with the space group Pbcn having a number of formula units Z = 8 and with the following unit cell parameters: a = 9.2554(4) Å, b = 8.7650(5) Å, c = 5.3333(2) Å at the pressure of 0 GPa [4]. Point defects in the enstatite lattice can significantly affect its structural, mechanical, electronic, and, consequently, optical properties [5-7]. Thus, the authors of [7] show that γ-irradiation of MgSiO3 (from a 60Co radiation source) with a dose of ≈12 Gy leads to the formation of O– and F+ defect centers. Under certain conditions the point defects in MgSiO3 are able to develop into dislocations with a certain direction [8]. The authors of [9] show the anisotropy of MgSiO3 electrical conductivity due to structural features of the lattice depending on the pressure and the temperature. Thus, the correct information on the arrangement of defects in the lattice and the types of defects is very important for the prediction of electric and optical characteristics of MgSiO3. Therefore, the objective of this work was to carry out theoretical (quantum mechanical) calculations of point defects in the enstatite structure. Calculation methods and details. All the calculations of the total energy were carried out by means of the density functional theory [10] implemented in the Abinit software package [11] using the generalized gradient approximation (GGA). The pseudopotentials for Mg, Si, and O atoms, produced by the fhi98PP program, were taken from the Abinit software

Computing Center, Far Eastern Branch, Russian Academy of Sciences, Khabarovsk, Russia; [email protected]. Translated from Zhurnal Strukturnoi Khimii, Vol. 56, No. 3, pp. 484-486, May-June, 2015. Original article submitted March 6, 2014. 454

0022-4766/15/5603-0454 © 2015 by Pleiades Publishing, Ltd.

TABLE 1. Effect of Vacancies on a, b, c Parameters and the Volume V of the MgSiO3 Cell Vacancy

a, Å

b, Å

c, Å

V, Å3

Without defects Mg1 Mg2 Si O1 O2 O3

9.2947 9.3214 9.2989 9.3126 9.2842 9.2816 9.2758

8.8752 8.9007 8.8792 8.8923 8.8652 8.8627 8.8572

5.3535 5.3688 5.3559 5.3638 5.3474 5.3459 5.3426

441.626 445.433 442.219 444.179 440.125 439.754 438.935

package [12]. According to the Monkhorst–Pack scheme, a special set of k points 2×2×2 (8 k points) was used for modeling a MgSiO3 unit cell [13]. A super cell with dimensions of 1×1×2 (with the doubled cell parameter c) containing 80 atoms was created for modeling point defects. In this case, the number of k points was four. The energy-cut-off is 816.34 eV. During the calculation process, the self-consistent optimization of the structure with the minimization of interatomic forces up to about 5⋅10–3 eV/Å was carried out; that was enough to obtain correct (close to experimental) values of the cell parameters and the bulk modulus. Results and discussion. The optimization procedure of the MgSiO3 unit cell is described in detail in [14]. Here we give the calculated cell parameters. Thus, a = 9.2947 Å, b = 8.8752 Å, and c = 5.3535 Å, and the unit cell volume is 441.626 Å3. These results are in good agreement with the experimental values: a = 9.2554 Å, b = 8.7650 Å, c = 5.3333 Å and V = 432.650 Å3 (Table 1) [4]. The orthorhombic structure of enstatite with the space group Pbcn is presented in Fig. 1. The MgSiO3 unit cell consists of 40 atoms. Three nonequivalent positions of the oxygen atoms (O1, O2, O3) and two nonequivalent positions of the magnesium atoms (Mg1 и Mg2), and one Si atom are shown in the figure. The formation energy of point defects for the Mg and Si atoms was defined by the equation

E f = E (vac) − E (perf ) + E free (atom),

(1)

where E(perf) is the total energy of the perfect (defect-free) crystal; E(vac) is the energy of the crystal with a point defect; O Efree(atom) is the total energy of the free Mg or Si atom. By calculating the formation energy E f of the oxygen vacancy VO, O we took into account that oxygen atoms leaving the cell formed O2 molecules. The problem of determining the energy E f in

quantum mechanical (ab initio) calculations is still a matter of dispute, because the process is complicated and controversial [15]. In our previous works devoted to the determination of O vacancies in oxide materials [16, 17], we have calculated the O formation energy of vacancies E f by the equation

E Of = E (vac) − E (perf ) +

1

(2) E (O 2 ), 2 where E(O2) is the total energy of the free oxygen molecule. Equation (2) was also used by other authors [15]. Table 2 summarizes the formation energies of Schottky vacancies for Si, three oxygen atoms in nonequivalent O1, O2, and O3 positions, and two magnesium atoms in the nonequivalent Mg1 and Mg2 positions (Fig. 1). Table 2 shows that about 11.22 eV is required for the formation of the Mg atom vacancy in the Mg1 position, and about 10.27 eV is required for this process in the Mg2 position, i.e. less by nearly 1 eV. Out of all the atoms, the silicon vacancy has the highest formation energy; it requires about 19.91 eV. For the formation of the oxygen vacancy in the O1, O2, and O3 positions, it is required 5.80 eV, 5.51 eV, and 5.35 eV respectively. Thus, the most energy-efficient defect is the oxygen vacancy in the O3 position in the MgSiO3 enstatite lattice. When the vacancy is formed in the Mg1 position, the unit cell volume increases due to an increase in the a, b, and c parameters (Table 1). When the vacancy is formed in the Mg2 position, the unit cell volume increases insignificantly. The formation of the Si vacancy also leads to an increase in the cell volume, and the vacancy in the 455

Fig. 1. Atomic structure of the MgSiO3 unit cell. TABLE 2. Energy of Formation of Vacancies in MgSiO3 Vacancy

Ef , eV

Mg1 Mg2 Si O1 O2 O3

11.22 10.27 19.91 5.80 5.51 5.35

oxygen position reduces its volume. The obtained results are in good agreement with the experimental data of [7, 18], where it is demonstrated that γ-irradiation results in the formation of the oxygen vacancy. Our calculations prove this fact. Due to the structural features of the O3 atom positions in the MgSiO3 lattice, during the formation of vacancies they can form clusters, aggregates in the form of linear chains, parallel to the (100) plane, which can develop into dislocations [8]. Our theoretical data on the energy of defect formation in MgSiO3 ceramics and the structural arrangement of defects may be useful for technologists engaged in the production of ceramic materials based on enstatite, and for the analysis of defect diffusion and the electrical conductivity of such materials. In this work, the theoretical investigation of the formation of Schottky point defects in MgSiO3 ceramics was carried out by the density functional theory method. We have calculated the effect of defects on the atomic structure of enstatite. It is demonstrated that the most energy-efficient defect is the oxygen vacancy at the O3 position in the MgSiO 3 lattice. The research was supported by the grant of the Presidium of the Far Eastern Branch of the Russian Academy of Sciences (No. 12-III-А-02-021). The work was carried out on the supercomputer of the Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, Khabarovsk, Russia and partially on the computer cluster of the Moscow State University, Moscow, Russia.

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