Site occupancy effects of Mg impurities in BaTiO3

Journal of Alloys and Compounds 809 (2019) 151847

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Site occupancy effects of Mg impurities in BaTiO3 R. Machado a, A. Di Loreto a, b, A. Frattini a, b, M. Sepliarsky a, M.G. Stachiotti a, * a b

Instituto de Física Rosario, Universidad Nacional de Rosario, 27 de Febrero 210 Bis, 2000, Rosario, Argentina
Area Física, Dpto. de Química Física, FCByF, Universidad Nacional de Rosario, 2000, Rosario, Argentina

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 April 2019 Received in revised form 6 August 2019 Accepted 12 August 2019 Available online 13 August 2019

A first-principles based atomistic model is developed to investigate intrinsic effects of Mg incorporation into A- and B-sites of BaTiO3. We find that the replacement of Ba by Mg at A-site positions generates local electric dipoles due to Mg off-centering along [001] directions, which increase the Curie temperature and decrease the cell volume. The inverse dependence is observed for B-site doped compositions, where the defect dipoles decrease the Curie temperature and expand the volume. Temperature-composition phase diagrams are constructed for both site locations and the effect of the two types of defects on the switching process is investigated. The theoretical predictions are used to shed light on experimental results of Mg-doped ceramics manufactured to induce a given occupation site. The comparison indicates that the incorporation of Mg into the B-site is thermodynamically favorable whereas the properties observed for the A-site ceramics cannot be explained from the intrinsic effects described by the model. © 2019 Elsevier B.V. All rights reserved.

Keywords: Atomistic modeling First-principles calculations Ferroelectricity BaTiO3

1. Introduction Barium titanate (BaTiO3, BT) is one of the most extensively studied functional materials due to its excellent piezoelectric and dielectric properties, and it is currently used for a number of electro-optic, dielectric and electromechanical applications [1e3]. This compound has the perovskite (ABO3) structure, with Ba2þ and Ti4þ cations on the A and B site, respectively. In principle, other metal ions can substitute both cations to obtain required characteristics for different applications. For example, dopants have been used to modify the Curie temperature, to alter the nature and sequence of the phase transitions and/or to tune electric and piezoelectric properties [4,5]. Doping strategies are generally separated into iso- and aliovalent (donors and acceptors) and into A- and B-site species within the perovskite structure. This structure can accept ions of different size, so that a large number of different dopants can be placed in the BT lattice. Typical examples of isovalent A-site dopants include Sr2þ, Ca2þ, Pb2þ and Cu2þ. B-site modifications include Zr4þ, Hf4þ, Sn4þ and aliovalent species such as Fe3þ and Nb5þ. Despite the large number of studies that were conducted on this topic, the site occupancy and defect chemistry of some dopants is still a controversial subject. For instance, it was reported that Ca2þ can substitute on both A- and B-sites depending

* Corresponding author. E-mail address: stachiotti@ifir-conicet.gov.ar (M.G. Stachiotti). https://doi.org/10.1016/j.jallcom.2019.151847 0925-8388/© 2019 Elsevier B.V. All rights reserved.

on the batched stoichiometry [6]. Similarly, Y3þ and other rareearth cations were also found to be amphoteric but with a higher solid solubility on the A-site [7]. Mg2þ is another controversial case. Several studies have been reported for the Mg doping of BaTiO3 and BaZrxTi1-xO3 ceramics using batched stoichiometries to induce Asite [8e12] or B-site [13e17] occupancy. Therefore, it is generally assumed that this ion can occupy with high solubility either A or B sites as iso- or alio-valent dopant, respectively. A theoretical study combining first-principles calculations and thermodynamics theory [18] showed that Mg predominantly occupies the Ti site in BaTiO3, but the Mg solution site changes from the Ti to the Ba or vice versa, depending on the phase composition. The ionic radius of Mg2þ in 6-fold coordination is small (0.065 nm), and those ions can occupy Ti4þ (0.061 nm) sites in titanates, generating a charged defect. When the 4 þ ions are replaced by Mg2þ, negatively charged defects will be formed and a corresponding number of positively charged oxygen vacancies will be required to satisfy the site balance and charge neutrality conditions. On the other hand, the ionic radius of Mg2þ in 12-fold coordination is about 0.120 nm, so this ion can also substitute Ba2þ (0.161 nm) at the A site, generating a neutral defect. This situation resembles the case of Liþ impurities in KTaO3 or KNbO3, where lithium ions occupy the A site of the perovskite structure. In this case, Li impurities take off-center positions along [001] orientations with a displacement as large as a quarter of the lattice constant [19e23]. Even more, it has been reported recently that Liþ ions can occupy both A and B sites in BaTiO3, modifying its

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structural and electrical properties [24]. Therefore, it is important to elucidate the site occupancy effects of Mg impurities in the BT perovskite lattice since, even in very low concentrations, they can considerably alter the functional properties of the material. In this work, we used an atomistic approach to investigate the effects of Mg incorporation into A- and B-sites of BaTiO3 and gain insight into the behavior observed in experiments. The simulation scheme involved a combination of first-principles calculations with interatomic potential techniques as a multiscale approach to investigate finite-temperature properties. Temperature-composition phase diagrams were constructed for both occupation sites and the effect of the defect dipoles on the switching behavior was investigated. Ceramic samples with different Mg contents at A and B sites were fabricated under identical synthesis conditions to perform a systematic comparison with the theoretical predictions. The paper is organized as follows. Sec. II describes the computational aspects of the study (Sec. II.A) and the experimental methods (Sec. II.B). The results are presented in Sec. III. The fitting of the interatomic potential parameters is presented in Sec. III.A, while the molecular dynamics results are showed in Sec. III.B. The properties of the ceramic samples, the comparison with theoretical results, and conclusions are discussed in Sec. III.C.

2. Methods 2.1. Computer simulation approach We consider a core-shell force field, which includes all degrees of freedom [25,26]. In this ab initio based interatomic potential, an atom is modeled as a charged core connected to a massless charged shell and the equilibrium distance between them is a representation of its electronic polarization. The interactions between different atoms are controlled by interatomic potentials whose parameters are fitted to first-principles calculations. This multiscale approach combined with molecular dynamics simulations was revealed to be powerful to predict the behavior of ferroelectric compounds at finite temperature [27]. In this work we develop a shell model for Mg-doped BaTiO3 adjusting the potential parameters to energy wells and forces obtained from first-principles calculations as implemented in the VASP package [28]. That is, no explicit experimental data had been used as input for the fitting. The model contains fourth-order coreshell couplings (k2 k4), long-range Coulombic interactions and short-range interactions described by two different types of potentials. A Born-Mayer potential V ¼ A e r/r is used for the BaeO, MgeO and TieO pairs, and a Buckingham potential V(r) ¼ A e r/ r þ C/r6 is used for OeO interactions. Two different sets of potentials were fitted for the MgeO interaction: one for Mg in the A-site position (MgA-O) and another for the B-site position (MgBeO). These two interatomic potentials were also obtained by adjusting their parameters to reproduce ab initio total energy calculations for Mg displacements along different directions in a 2  2  2 supercell. Molecular-dynamics (MD) simulations, using the DL-POLY package [29], were used to investigate the composition- and temperature-driven phase transitions. The Mg2þ cations were randomly distributed over the A and B sites. The runs were performed employing a Hoover constant-(s,T) algorithm with external stress set to zero; all cell lengths and cell angles were allowed to fluctuate. Periodic boundary conditions over 5000 atoms were considered. The time step was 0.4 fs, which provided enough accuracy for the integration of the shell coordinates. The total time of each simulation, after 5 ps of thermalization, was 45 ps.

2.2. Preparation of ceramic samples Mg-doped BaTiO3 ceramics were fabricated by the conventional solid-state reaction method. The powders were synthesized from a mixture of BaCO3, MgO and TiO2 by a milling process using a planetary ball mill equipment (Torrey Hills Technologies ND 0.4 L). The precursors were initially dried at 230  C for 4 h to take out the absorbed moisture and milled for 12 h. Milled powders with target compositions Ba1-xMgxTiO3 and BaMgxTi1-xO3-d with x ¼ 0, 0.01, 0.03 and 0.05 were calcined at 1100  C for 4 h. After that, they were wet milled again and mixed with a polyvinyl butyral (PVB) binder solution. The green pellets (die-pressed disks with dimensions of Ø10 mm  2 mm) were sintered at 1450  C for 4 h. The microstructure of the samples was analyzed using XRD and SEM techniques, with a Philips X'Pert Pro diffractometer and a Leitz AMR 1000 microscope, respectively. An LCR meter (QuadTech 7600 plus) attached to a programmable cryostat was used to record the temperature dependence of the dielectric properties of silver electrode ceramics. The ferroelectric properties were measured using a conventional Sawyer-Tower circuit. 3. Results 3.1. Development of interatomic potentials for pure and Mg-doped BaTiO3 We first developed an atomistic model for BT by fitting its parameters to density functional theory calculations. The input data to adjust the shell model parameters were obtained from the general gradient approximation for solids (PBEsol) [30]. The input information for the parameter least-squares fit procedure corresponded to GGA results of the optimized crystal structures, energy as a function of volume and strain, underlying potential energy surfaces for structural distortions and forces between atoms. To illustrate the quality of the fitting, we show in Fig. 1 the energy as a function of volume for the four relevant phases of BaTiO3. In that figure the cubic, tetragonal, orthorhombic and rhombohedral structures were optimized at each volume. It is clear that the resulting interatomic potentials reproduce the energetics of each phase in good agreement with the ab initio results.

Fig. 1. Energy as a function of volume for the four relevant phases of BaTiO3. The cubic (C), tetragonal (T), orthorhombic (O) and rhombohedral (R) structures were optimized at each volume. Dashed lines: first-principles calculations. Solid lines: shell model.

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We then used MD simulations to test the temperature-driven phase transition sequence. We observed that the phase transition sequence of BaTiO3 is correctly reproduced. The model exhibits three successive structural phase transitions with increasing temperature: rhombohedral(R)-orthorhombic(O)-tetragonal(T)cubic(C). The MD results for the different phases and the comparison with experimental data are presented in Table 1. The potential model underestimates the Curie temperature (Tc) with respect to experiment (230 K versus 390 K), which is a reasonable error for this type of force field. However, if Tc is rescaled to match the experimental value, the T-O and O-R transition temperatures are close to the experimental values. The lattice parameters also compare very well with experimental data. Two sets of interatomic potentials were developed to simulate Mg impurities in BT: one for the A-site position and another for the B-site. The potentials must be compatible with the model for pure BaTiO3 in that (i) the defects are neutral and (ii) for simulating the alloys, the difference between the two A-site (B-site) ions lies in the different BaeO (TieO) and MgA-O (MgBeO) interactions, and the different polarizabilities of the ions. The MgeO interatomic potentials were obtained by adjusting their parameters to ab initio total energy surfaces. The fitting procedure was performed for one Mg impurity in a 2  2  2 supercell of the cubic phase. In the case of A-site doping, a MgA-O potential was developed to reproduce the energetics of Mg off-center displacements in BT obtained from ab initio calculations. The energy is evaluated from an ideal A-site position, with all ions’ coordinates frozen in the centrosymmetric positions except for Mg. Fig. 2a shows total energy curves for Mg displacements along the [001], [011] and [111] directions. The ab initio calculations clearly indicate that the impurity has a strong tendency to off centering, with a displacement of 0.75 Å along the [001] direction and an energy gain of 140 meV. We note that this energetics resembles the one reported for Liþ impurities in KNbO3 [22], but with larger energy barriers. We show in Fig. 2a that we were able to adjust a MgA-O interatomic potential, compatible with the model developed for the pure material, which reproduces offcenter displacements and energy gains in good agreement with

Table 1 Transition temperatures, structural parameters, and spontaneous polarization for the different phases of BaTiO3. The experimental results are taken from Ref. [31]. Parameter

MD Simulation

Experimental [31]

Rhombohedral a (Å) a (deg) volumen (Å3) P (mC/cm2)

4.0007 89.811 64.018 23

4.0035 89.843 64.168 22

Tc (oK)

237

190

Orthorhombic a (Å) b (Å) c (Å) volume (Å3) P (mC/cm2)

3.9820 5.6629 5.6847 128.19 19

3.9855 5.6738 5.6903 128.67 18

Tc (oK)

288

280

Tetragonal a (Å) c (Å) volume (Å3) P (mC/cm2)

3.9881 4.0282 64.07 16

3.9938 4.0361 64.378 17

Tc (oK)

390

390

Cubic a (Å) volume (Å3)

4.0002 64.01

4.0090 64.04

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Fig. 2. Energy as a function of Mg displacement along different crystallographic directions, from an ideal A-site (a) and B-site (b) position in 2  2  2 supercell. For B-site defect the oxygen vacancy V∙∙O is situated along the negative direction of the axis. Dashed lines: first-principles calculations. Solid lines: shell model.

ab initio results. A similar procedure was used to determine the MgBeO potential, where the parameters were adjusted to reproduce total energy calculations for the displacements of the Mg ion from the B-site position. In this case, the negative charge of Mg'0 Ti (Ti4þ is replaced by Mg2þ) is compensated by the positive charge of an oxygen vacancy V∙∙O, forming a charge-neutral defect dipole (Mg'0 Ti -V∙∙O). Hence, the fitting procedure was performed for one defect dipole in a 2  2  2 supercell, where the Mg impurity and the oxygen vacancy were located in neighboring sites. Fig. 2b shows that the adjusted potential perfectly reproduces the ab initio results. 3.2. Molecular dynamics simulations of Mg-doped BaTiO3 We characterize the influence of Mg incorporation into A- and B-sites on the temperature-driven phase transitions by comparing the phase diagram of BaTiO3 with the ones corresponding to the solid solutions MgxBa1-xTiO3 and BaMgxTi1-xO3-x. As an illustrative example, we present the results for the composition x ¼ 0.012, where the MD simulations were performed randomly distributing twelve Mg2þ impurities in a 10  10  10 supercell. In the case of Bsite occupancy, the (Mg'0 Ti -V∙∙O) defect-dipoles were oriented along the six possible orientations causing the total dipole moment

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to cancel. The resulting lattice constants and polarization components as a function of temperature are presented in Figs. 3 and 4, for A-site and B-site occupancies respectively. It is clear that Mg impurities appreciably influence the lattice constants. For A-site occupancy, the doping leads to shrinkage of the unit cell volume and increase the tetragonality (c/a ratio) of the room temperature phase (Fig. 3a). The impurities also increase the polarization (Fig. 3b) due to their strong off-center displacement along [001] directions. Regarding the transition temperatures, A-site Mg doping produces a decrease in the temperatures for the rhombohedralorthorhombic and orthorhombic-tetragonal phase transitions, while the temperature of the tetragonal-cubic ferroelectric phase transition increases. This behavior is similar to the one reported for Li impurities in KNbO3, where the temperature shifts (which can be inferred from the reorientation dynamics of the off-center impurities in each phase) produce an increase in the temperature range of stability of the tetragonal phase [22]. The opposite behavior is observed, however, for B-site occupancy (Fig. 4), where the (Mg'0 Ti -V∙∙O) defect dipoles decrease the Curie temperature, expand the volume, and reduce tetragonality and polarization (Fig. 4a and b). Temperature-composition phase diagrams for the two occupation sites obtained from the MD simulations are presented in Fig. 5. Fig. 5a shows the phase behavior of MgxBa1-xTiO3 solid solutions

Fig. 4. Temperature-driven phase transitions for the B-site composition BaMg0.012Ti0.988O2.988 resulting from MD simulations: cell parameters a, b, and c (a) and polarization components px, py and pz (b) as a function of temperature. For comparison, dashed lines represent the MD results for BT.

Fig. 3. Temperature-driven phase transitions for the A-site composition Mg0.012Ba0.988TiO3 resulting from MD simulations: cell parameters a, b, and c (a) and polarization components px, py and pz (b) as a function of temperature. For comparison, dashed lines represent the MD results for BT.

with x < 4%. The diagram shows a decrease in the ReO and O-T transition temperatures with increasing x, while the Curie temperature rises. The scratched area (x > 2%) is a phase coexistence region where the polarization of the system is oriented along a noncrystallographic direction. It might be expected that at high Mg concentrations, off-center displacements show frustration of the Mg impurities in finding the optimal direction of displacement, which would originate relaxor behavior. A similar feature was observed for LixK1-xNbO3 [22]. The phase behavior of BaMgxTi1-xO3-x alloys is shown in Fig. 5b. The diagram indicates that Mg impurities at B-site decrease the Curie temperature, from 390 K (at x ¼ 0%) to ~320 K (at x ¼ 2%) and it remains practically constant for concentrations greater than 2%. The ReO transition temperature increases with Mg content while the O-T remains almost constant. It is important to note that the three transition temperatures tend to merge at a concentration of ~2%. This convergence of the transition temperatures agrees with experimental results reported for BaTiO3 ceramics doped at the Bsite with acceptor impurities [32]. Therefore, a single transition is observed for high Mg content: from a low-temperature ferroelectric phase where the polarization lies along a non-crystallographic direction, to a high-temperature cubic paraelectric phase. All these features are produced by the (Mg'0 Ti -V∙∙O) defect dipoles that

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Fig. 5. Temperature-composition phase diagram of MgxBa1-xTiO3 (a) and BaMgxTi1-xO3-x (b) resulting from the MD simulations. The experimental points are included for comparison. The scratched areas are phase coexistence regions where the polarization is oriented along a non-crystallographic direction.

locally modify the elastic and electrostatic fields. Finally, we performed MD simulations to compare the polarization reversal processes that take place under an applied electric field. The simulations were carried out for the room temperature tetragonal phase (Px ¼ Py ¼ 0, Pz s 0) of the pure and doped systems with a Mg content of 0.6%. An equivalent behavior is observed when the electric field is applied parallel and perpendicular to the polar z-axis, which indicates an isotropic response to electric fields. The calculated P-E hysteresis loops are shown in Fig. 6. For comparison, the loop for the defect-free material is included. It is clear that both defect configurations display hysteresis loops with shapes similar to the pure sample, but with quite different coercive fields (Ec). We note however that the coercive fields obtained in the simulations greatly exceed those measured experimentally because our model excludes grain boundaries, surfaces and domain walls which would all act as nucleation sites. In spite of that, the simulations clearly show that A-site Mg impurities increase Ec, while the coercive field decreases when Mg2þ ions occupy the B sites. The

Fig. 6. Molecular dynamics simulations of polarizationeelectric field (PeE) hysteresis loops in the tetragonal phase of Mg-doped BaTiO3 with A-site and B-site occupancies. For comparison, the loop for the defect-free material is included. The reported hysteresis loops are obtained from an averaged over multiple cycles.

noticeable increase of Ec obtained for the A-site configuration is due to the difficulty of reorienting the off-center Mg dipoles, which are aligned parallel to the polar axis in the tetragonal phase. The decrease of the coercive field for the B-site configuration matches other MD results [33,34] on the switching process of perovskites in the presence of B-site defect dipoles. In that case the defects were simulated through charged dummy atoms interacting with the bulk ions through Coulomb interactions. Interestingly, those simulations predict that a generic B-site dopant under aged conditions can modify the material's hysteretic response producing pinched or double hysteresis loops [33,34]. 3.3. Comparison with experimental results and conclusions Several studies have been reported in the literature on the investigation of BaTiO3-based ceramics doped with Mg at the A-site [8e12] and B-site [13e17]. However, it is not possible to discern from those experiments whether the properties variation upon doping come from intrinsic or extrinsic effects. In this section we use the theoretical predictions to shed light on that issue. To perform a systematic comparison between theoretical and experimental results, a set of samples was fabricated under identical synthesis conditions. So, ceramics with target compositions Ba1xMgxTiO3 and BaMgxTi1-xO3-d with x ¼ 0 (BT), 0.01, 0.03 and 0.05 (hereafter referenced as BMTA-100.x and BMTB-100.x, respectively) were prepared as described in Section II-B. Fig. 7 shows the X-ray diffraction patterns of the resulting samples. The patterns show that almost all compositions present single-phase perovskite structure (JCPDS-00-005-0626). With the exception of the BMTA-3 sample, no secondary peaks above noise are detected in the diffraction patterns. That sample displays additional low-intensity peaks at ~35.7 and 43.6 , which can be assigned to monoclinic Ba2Ti5O12 (JCPDS-01-070-2270). On the other hand, the BMTB-5 sample displays a completely different diffraction pattern, which corresponds to the hexagonal BT phase (JCPDS-01-076-0738). This phase is considered a result of the hexagonal close packing of Ba and O atoms, with Ti partial occupancy of octahedral sites [35]. The extra oxygen vacancy due to the acceptor impurity (Mg'0 Ti) expedites its formation. This is in agreement with previous reports which showed that the hexagonal BT phase can be kinetically stabilized at room temperature by the sintering of acceptor-doped BaTiO3 [14,36]. SEM images of surface morphologies for BT, BMTA-1 and BMTB-1 samples are presented in Fig. 8. It is clear that Mg doping affects the

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Fig. 7. XRD patterns of ceramic samples with different Mg content at A and B sites.

microstructural development. Fig. 8a shows that grains are mostly 100 mm size for the pure BT. BMTA-1 (Fig. 8b) and BMTB-1 (Fig. 8c) present similar microstructures but with smaller grain sizes (20e40 mm). The grain sizes decrease even more when the Mg content is increased (10e20 mm for 3%). Fig. 9a and b shows the variation of the room-temperature dielectric constant (εr) and loss tangent (tand) as a function of frequency for A-site and B-site occupancies, respectively. Almost negligible dispersion is observed in all the ceramics over the range 100 Hze2MHz. A reduction of both εr and tand with the increase of Mg content is observed in the A-site samples (Fig. 9a). On the contrary, Fig. 9b shows an increment in the dielectric constant and the low-frequency dispersion of tand, which indicates that the dipolar complex (Mg'0 Ti -V∙∙O) is able to reorient with the field. Note that the hexagonal BMTB-5 ceramic displays a dielectric constant of ~200, much smaller than that of the perovskite phase. Fig. 10 shows the temperature dependence of the dielectric constant and the corresponding losses. The data were taken on heating at 10 KHz. All ceramics exhibit a sharp C-T phase transition peak at Tc. The ferroelectric T-O peaks can also be detected, while the peaks corresponding to the O-R phase transition cannot be reliably assigned in samples with high Mg content. Clearly Tc decreases with increasing Mg content for both occupation sites. Tc shifts are much more pronounced in B-site than in A-site samples. A similar behavior is observed for the O-T phase transition. To compare with the theoretical predictions, the experimental transition temperatures determined from the dielectric peaks have been included in Fig. 5. The agreement is not good for the A-site configuration (Fig. 5a). The most noticeable difference is the behavior of the Curie temperature upon doping: while the simulations predict that Tc increases, due to a coupling between the offcenter Mg relaxation dynamics and the macroscopic polarization of the host matrix, a decrease is observed in the experiments. Note that a reduction of the Curie temperature was also reported in Asite Mg-doped BaZrxTi1-xO3 ceramics [9,12]. In Ref. [9] the temperature shifts were ascribed to the decrease in grain size. However, it is unlikely that the shifts observed in our samples are associated with size effects, since these effects are not expected in grains with the dimensions showed in Fig. 8. A better agreement between theory and experiments is achieved for the B-site compositions, where TC decreases with x at low concentrations while it remains stable above 1.8 mol% Mg (Fig. 5b). Note that a quite similar behavior for TC (x) was reported for BaMgxTi1-xO3-d ceramics prepared by the Pechini method [14].

Fig. 8. SEM images showing surface morphologies of: (a) BaTiO3, (b) Mg0.01Ba0.99TiO3, and (c) BaMg0.01Ti0.99O3-d ceramics. The white scale bars correspond to 100 mm.

Another feature relevant to compare is the behavior of the unit cell volume (Vc) upon doping, showed in Fig. 11. While an impurityinduced decrease of Vc is obtained from the MD simulations of the MgxBa1-xTiO3 solid solutions, the refinement of the X-ray diffraction patterns (Fig. 7) displays the opposite behavior. The agreement

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Fig. 9. Frequency dependence of the dielectric constants (filled symbols) and dielectric losses (open symbols) of MgxBa1-xTiO3 (a) and BaMgxTi1-xO3-d (b) ceramics.

is again satisfactory only for compositions batched to induce B-site occupancy, where a volume expansion is driven by the presence of (Mg'0 Ti -V∙∙O) defect-dipoles. We note that our theoretical predictions about the behavior of TC and Vc upon Mg doping account for the amphoteric behavior observed in BaTiO3 ceramics doped with Ca2þ [6]. In fact, it was shown that Ca2þ at the A site produces the increment of TC and the reduction of the unit cell volume, while the opposite behavior was observed when Ca2þ ions replace Ti4þ [6]. A similar behavior was also observed for Liþ ions occupying both A and B sites in BaTiO3 [24]. We thus conclude that those experiments provide strong support to the results obtained in the atomistic simulations. We finally address the site occupancy effects on ferroelectric properties. Polarization-electric field (P-E) hysteresis loops are shown in Fig. 12. The measurements were performed at roomtemperature and 50 Hz. All curves showed saturation when an electric field of ~2 kV/mm was applied. BaTiO3 displays a remnant polarization (Pr) ~ 5 mC/cm2 and a coercive field (Ec) of ~400 V/mm. The coercive field is practically independent of the Mg content in MgxBa1-xTiO3 ceramics (Fig. 12a), while it decreases slightly for direct B-site substitution (Fig. 12b). The second behavior agrees with the simulation results, while the strong increase in Ec predicted for the A-site compositions was not observed. We note, however, that a marked increase in Ec with the increase in dopant concentration was reported in the case of MgxBa1-xTi0.98Zr0.02O3 lead-free piezoceramics [10]. The most noticeable feature of the hysteresis measurements is that all doped samples exhibit pinched

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Fig. 10. Temperature dependence of the dielectric constants (lines) and dielectric losses (dots) at 10 KHz of MgxBa1-xTiO3 (a) and BaMgxTi1-xO3-d (b) ceramics. The data were taken during the heating processes of the thermal cycle.

Fig. 11. Variation of the unit cell volume (Vc) as a function of Mg concentration for A and B site occupancies.

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slight increment of the unit cell volume (Fig. 11), (ii) the decrease of the Curie temperature (Fig. 10a), (iii) the pinched ferroelectric hysteresis loops (Fig. 12a), and (iv) the presence of the Ti-rich Ba2Ti5O12 secondary phase (Fig. 7). Interestingly, a decrement of Tc has been also observed when Mg is incorporated as additive (i.e., without inducing a specific site occupancy) [16,17,38], which is another indication of the B-site occupancy preference. In summary, we presented a first-principles based interatomic potential approach to investigate the site occupancy effects of Mg impurities in BaTiO3. The composition- and temperature-driven phase transitions were investigated by using molecular dynamics simulations. Phase diagrams for both A-site and B-site occupancies were constructed. The comparison with experimental results provided important information on the location effects and solubility of the impurities. We concluded that the solubility of Mg in BaTiO3 strongly depends on the lattice site in which the substitution occurs. While the incorporation of Mg2þ ions into the B-site is thermodynamically favorable, these impurities are preferably not incorporated in the A-site of the perovskite lattice. Then, the properties variation upon doping observed in the A-site ceramic samples cannot be explained from the intrinsic effects obtained by the model. We hope that this multiscale scheme, where no explicit experimental data has been used as input, becomes a powerful theoretical tool to elucidate site occupancy effects of other controversial dopants. Acknowledgments This work was sponsored by Consejo Nacional de Inves
cnicas (CONICET) and Agencia Nacional tigaciones Científicas y Te
n Científica y Tecnolo
gica (ANPCyT) de la República de Promocio Argentina. MGS thanks support from Consejo de Investigaciones de la Universidad Nacional de Rosario (CIUNR). References Fig. 12. Room-temperature polarization hysteresis loops of MgxBa1-xTiO3 (a) and BaMgxTi1-xO3-d (b) ceramics. The cycles were measured at 50 Hz.

loops, which could be an indication of the presence of defectdipoles under aged conditions [33,34]. While (Mg'0 Ti -V∙∙O) defect-dipoles are naturally formed to satisfy site balance and charge neutrality conditions in B-site doped ceramics, the A-site off-center Mg impurities cannot explain such hysteresis behavior. These pinched loops may result from the presence of aged defectdipoles, non-reorientable under electric field, such as (Mg'0 Ti -V∙∙O) if undesirable B-site occupancy has occurred, or (V∙∙Ba -V∙∙O) if Mg2þ has failed to replace Ba2þ in the A site. The comparison between theoretical and experimental results indicates that the incorporation of Mg into the B-site of the BaTiO3 structure is thermodynamically favorable, that is practically all Mg2þ ions occupy Ti-sites when the samples are fabricated to induce B-site occupancy. On the contrary, in spite of the several studies performed on titanates doped with Mg at the A site [8e12], the majority of the Mg2þ ions would not be incorporated at the A-site of the perovskite lattice. We note that similar conclusions have been reached for the solubility of Mg in the quantum paraelectric compound SrTiO3 [37], where a very weak solubility (~1%) in the A-site was reported. The authors argued that the Mg ions, which were not incorporated into the A-site, are located at the grain boundaries of SrTiO3 forming a different phase [37]. Although this is a feasible scenario in BaTiO3, even for our lowest doping, we cannot rule out a simultaneous occupation of both A and B sites. A double-site occupation could account for the following: (i) the

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