Synthesis, X-ray diffraction and dielectric studies of the ceramic samples ($1-x$)BaTiO₃$\cdot x$PbFe${}_{2/3}$W${}_{1/3}$O₃ ($0\le x\le 1$) system

1. Introduction

Solid solutions with a perovskite crystal structure based on ferroelectric barium titanate BaTiO₃ possess interesting properties from a scientific and applied point of view. Therefore, they have been intensively studied over the past few decades.^1,2,3,4,5 As a result, a variety of these kinds of solid solutions have been obtained and studied, and many of them have found applications, e.g., as condenser, posistor, piezoelectric materials, etc. Nevertheless, it should be noted that the solid solutions of a potentially promising system ($1-x$)BaTiO₃⋅xPbFe${}_{2/3}$W${}_{1/3}$O₃ (BT–PFW) remain very poorly studied. Only one work has been found by us on this system,⁶ which presents the results of preliminary studies of the dielectric and magnetic properties, as well as of their Mössbauer spectra on the ceramic samples with $0.70\le x\le 1$. In this work, the temperature dependences of the real part of the permittivity ${\epsilon }_{\mathrm{\text{1}}}(T)$ were studied at a fixed frequency $f=100$ kHz. We show that the conclusion made in Ref. 6 about the relationship of the maxima observed in the dependences ${\epsilon }_{\mathrm{\text{1}}}(T)$ with ferroelectric phase transitions needs to be clarified, since the reason appearance of this maxima can be connected with the dielectric relaxation occurring in the samples.

Barium titanate with a perovskite structure exhibits bright ferroelectric properties with a Curie point equal to $T_C=403$K, where the symmetry of crystals changes from cubic (C) to tetragonal (T). In barium titanate, below $T_C$, two-phase transitions of the first order were observed, from tetragonal to orthorhombic (O), and from orthorhombic to rhombohedral (R) phase, at $T_{\mathrm{\text{T/O}}}\approx 273$K and $T_{\mathrm{\text{O/R}}}\approx 183$K, respectively.^1,2,3,4,5

Unlike the tetragonal ferroelectric phase BaTiO₃, lead ferro tungstate PFW has cubic symmetry at all temperatures and does not exhibit ferroelectric properties, showing typical response for relaxor ferroelectrics (RFEs).^{2,7,8,9,10,11,12} In the temperature dependence of permittivity, ${\epsilon }_1(T)$, a blurred relaxation maximum is observed at $T_m\approx 190$K with a high value of dielectric permittivity, ${\epsilon }_{1m}\approx 5000$, the behavior typical for RFEs. The position $T_m$ of this maximum shifts with frequency growth toward high temperatures, obeying the Vogel–Fulcher law

where $k_B$ is the Boltzmann constant, ${\tau }_{\text{o}}$, $E_a$ and $T_{\mathrm{\text{VF}}}$ are the fitting parameters.¹¹ For classical relaxor ferroelectric of the PbMg${}_{1/3}$Nb${}_{2/3}$O₃ type they are considered as relaxation time at high temperature ($T\to \infty$), the activation energy for polarization fluctuations of a separate polar nanoregion (PNR), the Vogel–Fulcher freezing temperature. It is believed that at temperatures below $T_{\mathrm{\text{VF}}}$, the dynamics of PNRs freeze (they become static) and the system passes into a nonergodic relaxor glassy state with the directions of the dipole moments of individual PNRs randomly fixed in different directions.¹¹

The noted differences between BT and PFW indicate that changes in the composition of the ($1-x$)BT⋅xPFW solid solutions will cause changes in the symmetry of their crystal lattice and the realization of various dielectric states. Additional interest in the study of the PFW is caused by the coexistence of the relaxor ferroelectric and antiferromagnetic properties.^{2,7,8,9,10,11,12} Due to the relatively high temperature of the magnetic phase transition ($T_N=363$K), PFW is considered a promising component that can be used to create new magnetoelectric compositions.

In the family of perovskite-like phases A[B1]${}_{1-m}$[B2]_mO₃, $m=1/2$, 1/3, the PFW phase has the lowest sintering temperature ($<900^{\circ }$C). Therefore, PFW is used as an additive to other relaxor compositions to reduce their sintering temperature below 1000°C.^2,12,13,14 Such a reduction is important for dielectric materials used in the development of multilayered ceramic capacitors since the high sintering temperature of BaTiO₃ ($>1300^{\circ }$C) makes it necessary to use expensive metal, Pd, as internal electrodes. Lowering the sintering temperature makes it possible to sinter multilayer ceramic capacitors together with relatively inexpensive interlayer electrodes with a low melting point, such as Ag/Pd alloys.

In connection with the above, the purpose of this work was to obtain ceramic samples of the ($1-x$)BT⋅xPFW, $0\le x\le 1$ system and to study its structural and dielectric properties.

2. Experimental Procedure

2.1. Synthesis of ceramics

The samples were synthesized in an air atmosphere by solid phase reactions method using conventional ceramic technology. The oxides of the PbO (brand “G-2” with at least 98.7% of the base substance), TiO₂ (extra pure grade, $\ge 99.9$%), Fe₂O₃ (analytical grade, $\ge 99$%), WO₃ (high-purity grade, $>99.9$%) and barium carbonate BaCO₃ (analytical grade, $>99$%) were used as starting materials. The compositions of the synthesized and studied samples corresponded to the formula ($1-x$)BaTiO₃⋅xPbFe${}_{2/3}$W${}_{1/3}$O₃ (BT–PFW) with $x=0$–1. The charge for ceramic synthesis was prepared by homogenizing mixtures of the above components by mixing them in a porcelain mortar in an air environment.

The annealing of the homogenized mixtures was carried out in a furnace SNOL 12/16 (Technoterm, Russia) at a temperature of 800–1230°C for 4h with several intermediate cooldowns and grindings of the annealed products. The annealing temperature with the growth of x was gradually reduced from 1230°C for $x=0$ to 800°C for $x=1$.

The annealing products were crushed and formed into cylindrical disks with a diameter of $D\approx 10$mm and a thickness of 1–3mm at a pressure of $p\approx 60$MPa. The obtained disks were sintered for 2–4h at temperatures about 100°C above the annealing temperatures. As a result, the ceramic samples were obtained with densities equal to 80–95% of the theoretical density. To study the electrophysical properties of the obtained samples, electrodes were deposited on their base planes by burning an Ag-containing paste at $T\approx 850^{\circ }$C.

2.2. X-ray diffraction studies

The phase composition of the synthesized ceramic samples was determined by X-ray diffraction (XRD) using an upgraded X-ray diffractometer DRON-4 (Bourevestnik, Russia) with filtered cobalt radiation. Ge powdered crystals were used as an internal standard. The ICDD database was used for phase identification.¹⁵

2.3. Dielectric studies

Measurements of the real part (${\epsilon }_1$) of the complex dielectric permittivity (${\epsilon }^{\ast }={\epsilon }_1$ − $i{\epsilon }_2$) and the loss tangent tan$\delta$ of the synthesized samples were carried out by using the immittance meter E7-30 (MNIPI, Belarus) in the temperature range $T=80$–700K and in the frequency interval $f=25$Hz–1MHz, with the amplitude of the probing electric signal equal to 1V. The imaginary part ${\epsilon }_2$ of the complex permittivity was calculated using the expression ${\epsilon }_2={\epsilon }_1\cdot \mathrm{\text{tan}}\delta$.

2.4. Measurements of thermally stimulated depolarization currents

Measurements of thermally stimulated depolarization currents (TSDC) of the samples were performed in the short-circuit mode with a universal voltmeter-electrometer V7-30 when samples were heated at a rate of 0.2–0.4K/s in the temperature range of 80–420K (10–300K in some cases). The polarization of the samples was carried out by applying a permanent electric field with a strength of 1.5–2.5kV/cm to them during their cooling from temperatures exceeding the temperature of ferroelectric or relaxor maximum observed on the dependences ${\epsilon }_1(T)$.

3. Results and Discussion

3.1. Results of the X-ray diffraction studies

XRD shows that the predominant phase in the samples is the (Ba${}_{1-x}$Pb_x)(Ti${}_{1-x}$Fe${}_{2x/3}$W${}_{x/3}$)O₃ solid solutions with a perovskite structure (Fig. 1(a)). The samples with $0\le x<0.25$ were practically single-phase, and the samples with $0.25\le x<1$ contained an impurity of the tetragonal phase with the parameters $a=5.620$ Å, $c=12.73$ Å corresponding to BaWO₄.¹⁵ The maximum content of this impurity phase reached 15wt.% at $x=0.60$–0.90. On the XRD patterns of the samples with $0\le x<0.05$, the splitting of reflexes characteristic of tetragonal phases was observed. At $x\ge 0.05$, there is no splitting of reflections (Fig. 1(b)).

Concentration dependences of the unit cell parameters of the solid solutions and their crystal lattice symmetry at 296K are shown in Fig. 2. The addition of PFW to barium titanate gradually reduces the degree of its tetragonality c/a; for $x=0.05$ it becomes equal to 1, and the crystal lattice of the solid solutions in the region $x=0.05$–1 acquires cubic symmetry.

An increase in the PFW content in the solid solutions leads to a decrease of the reduced unit cell parameter $a_p={(a^{2}c)}^{1/3}$ in the concentration range $x=0$–0.80. This decrease in $a_p$ is replaced by an increase in the region $x=0$.80–1. Such feature of the $a_p(x)$ dependence is explained by the fact that the predominant effect on the $a_p$ of the solid solutions (Ba${}_{1-x}$Pb_x)(Ti${}_{1-x}$Fe${}_{2x/3}$W${}_{x/3}$)O₃ in these concentration ranges is a decrease in the average cationic size at the A position of the perovskite structure (r(Ba${}^{2+})=1.61$ Å, r(Pb${}^{2+})=1.49$ Å)),¹⁶ and an increase in the average cation size at the B position of the perovskite structure (r(Ti${}^{4+})=0.605$ Å, r(Fe${}_{2/3}^{3+}$W${}_{1/3}^{6+})=0.630$ Å), respectively.¹⁶

3.2. Results of the dielectric measurements

The results of the dielectric measurements are presented in Figs. 3, 4, A.1 and A.2 in the form of the temperature-frequency dependencies of ${\epsilon }_1(T,f$), ${\epsilon }_2(T,f$) and tan$\delta (T,f$). Figure 2 presents the concentration dependencies of the temperature at which the maximum is observed in the dependence ${\epsilon }_1(T)$, of the magnitude ${\epsilon }_1$ at the maximum (${\epsilon }_{1m}$) and at room temperature (${\epsilon }_{1\mathrm{\text{RT}}})$, of the peak width ($\mathrm{\Delta }{T}_m$) at half height of the maximum. The dependences ${\epsilon }_1(T,f$) and tan$\delta (T,f)$ of the BT samples display three pronounced maxima corresponding to the phase transitions occurring in the BT and leading to successive changes of its symmetry from cubic to tetragonal (at the Curie point $T_C=408$K), from tetragonal to orthorhombic (at $T_{\mathrm{\text{T/O}}}=288$K) and from orthorhombic to rhombohedral (at $T_{\mathrm{\text{O/R}}}=195$K) (Fig. A.1), by the literature data for BT.^1,2,3,4,5

Samples with $x=0$–0.04 exhibit ferroelectric properties similar to those of BT with three phase transitions at $T_C$, $T_{\mathrm{\text{T/O}}}$ and $T_{\mathrm{\text{O/R}}}$ (Figs. 3 and A.1). Addition of the PFW component to BT causes a decrease in $T_C$ and $T_{\mathrm{\text{T/O}}}$ and an increase in $T_{\mathrm{\text{O/R}}}$, (Figs. 2, 3 and A.1). As a result, the temperatures of these phase transitions converge. At $x\approx 0.08$, the three-phase transition temperatures merge, and at $x>0.08$, the solid solutions exhibit only one phase transition, whose temperature decreases to 245K as the PFW content grows up to $x=0.09$. In the concentration range $0.05\le x<0.10$, there is a significant broadening of the maximum in ${\epsilon }_1(T)$ around $T_C$, which is characteristic of ferroelectrics with a diffuse phase transition (FE DPT).

Shift toward high temperatures of the maxima positions seen in the temperature dependences of the real (at $T_m$) and imaginary (at $T_{\mathrm{\text{mi}}}$) parts of the dielectric permittivity with increasing frequency for samples with $x\ge 0.10$ (Figs. 3, 4 and A.1) indicates relaxor character of these maxima.

In the concentration region $0.10\le x\le 0.25$, the solid solutions exhibit dielectric properties that are characteristic of the RFEs of the PMN type. There is a broad maximum in dependences ${\epsilon }_1(T,f)$ and ${\epsilon }_2(T,f)$ which shows a pronounced frequency dispersion (Figs. 3, 4 and A.1); as in other relaxors, the temperatures of these maxima $T_m$ and $T_{\mathrm{\text{mi}}}$ shift to high temperatures during frequency f growth, following the Vogel–Fulcher law $f=f_{o}exp[E_a$/$k_B(T_{m(i)}-T_{\mathrm{\text{VF}}})]$ (Fig. 4).¹¹ The values of the fitting parameters $f_o$, $E_a$, $T_{\mathrm{\text{VF}}}$ were determined by processing the $T_{\mathrm{\text{mi}}}(f)$ dependencies with the Vogel–Fulcher formula; found parameters’ values (see, Fig. 4) correspond well to those known for RFEs. We thus conclude that the studied solid solutions in the range $0.10\le x\le 0.25$ belong to the class of RFEs.

A further increase in the PFW content in the samples in the range $0.25<x\lesssim 0.90$ leads to a significant decrease and blurring of the maximum observed on the ${\epsilon }_1(T)$ dependence in the temperature range 100–200K, herewith its dependence ${\epsilon }_1(T,f)$ ceases to exhibit the frequency dispersion characteristic of RFEs. At $x=0.75$ and 0.80, these maxima practically do not manifest itself (Fig. A.1).

The addition of the BT component to the PFW phase in the region $x=0.9$–1 leads to a rather sharp degradation of its ferroelectric relaxation properties which manifests itself in the disappearance of the dependence of $T_m$ on f and a significant decrease in the value of ${\epsilon }_{1m}$ (Fig. A.1, $x=0.90$).

Thus, an increase in the PFW content in ($1-x$)BT⋅xPFW solid solutions causes a change in their dielectric properties from FE in the region $0\le x<0.10$, to RFE in the region $0.10\le x\le 0.25$, then to nonferroelectric and nonrelaxor ferroelectric in the region $0.25<x\lesssim 0.90$ and then again to RFE in the region $0.90\lesssim x\le 1$. Such behavior can be explained, apparently, by a change in the ferroelectrically active sublattice of ($1-x$)BT⋅xPFW solid solutions from Ti to Pb with an increase in them PFW content.^2,10,11 An increase in the PFW content leads to a decrease in the content of ferroelectrically active Ti cations and, accordingly, to a weakening of correlations between the dipole moments of TiO₆ octahedra, it prevents the formation of PNRs. Similarly, an increase in the BT content in the region of $0.90\lesssim x\le 1$ causes a decrease in the content of ferroelectrically active Pb cations, followed by a loss of RFE properties. Due to the presence in the structure of solid solutions with $0.25<x\lesssim 0.90$ dipole structural units arising from displacements of Ti${}^{4+}$ and/or Pb${}^{2+}$ cations from their central positions,^4,10,11 it can be assumed that solid solutions of these compositions can be classified as dipole glasses with weak or no correlations between dipoles even at low temperatures.

The high ${\epsilon }_{1m}$ value measured at the maximum in the dielectric constant of BT is preserved in the solid solutions with $x=0$–0.10 (${\epsilon }_{1m}\approx 5000$–8000). Further increase of the PFW content in the samples caused a rather sharp decrease in maximum magnitude to 1500 at $x=0.13$ (Figs. 2, 3 and A.1). Transition from the concentration region of FE compositions ($x<0.10$) to the region of RFE compositions ($0.10\le x\le 0.25$) is accompanied by a significant broadening of the ${\epsilon }_1$ peak on the dependence ${\epsilon }_1(T)$ at $T_C$ or $T_m$ (Figs. 3, A.1 and A.2). The presence of a sharp local maximum $\mathrm{\Delta }{T}_m$ on the $\mathrm{\Delta }{T}_m(x)$ dependence at $x=0.05$ (Fig. 2) is obviously caused by the fact that for $x=0.05$, the three peaks ${\epsilon }_1$ at $T_C$, $T_{\mathrm{\text{T/O}}}$, $T_{\mathrm{\text{O/R}}}$ approached each other so closely that it is impossible to distinguish from the general broad peak ${\epsilon }_1$ the contribution from the peak at $T_C$.

Note that the presence, at high temperatures ($T>250$K) on the ${\epsilon }_1(T)$ and tan$\delta (T)$ dependences in some compositions, of the relaxation maxima that show temperature-activated behavior with an activation energy $E_a\approx 0.40$eV (Figs. 3 and A.1), is probably caused by the mobile oxygen vacancies, the presence of which is inherent in samples of lead-containing oxides.^12,17

3.3. Results of the thermally stimulated depolarization currents measurements

Three pronounced maxima are observed in the dependences of the TSDC(T) of ferroelectric samples with $x=0$–0.04 (Figs. 3 and A.1), the position of which corresponds to the temperatures of phase transitions taking place at $T_C$, $T_{\mathrm{\text{T/O}}}$ and $T_{\mathrm{\text{O/R}}}$. These maxima are obviously caused by C/T, T/O, O/R phase transitions, while the currents in the samples are pyroelectric in nature.

Contrary to the FE compositions, for the RFE compositions ($0.10\le x\le 0.25$, $0.90\lesssim x\le 1$) the temperature of the current maximum is much lower than the temperature of the dielectric maximum (Figs. 5 and A.1), the difference between the two can reach 50–150K. The proximity of the low-temperature maximum position of TSDC to the Vogel–Fulcher temperature found in the RFE compositions suggests that the occurrence of this maximum can be caused by the depolarization of the polar state of the sample, which arises due to some ordering of the electric dipoles when the sample was cooled in the polarizing electric field below the freezing temperature $T_{\mathrm{\text{VF}}}$. Similar maxima of the TSDC(T) dependences were observed for the other RFEs, e.g., ($1-x$)PbMg${}_{1/3}$Nb${}_{2/3}$O₃–xPbSc${}_{1/2}$Nb${}_{1/2}$O₃, $x=0.05$, 0.10, BaZr_xTi${}_{1-x}$O₃, $x=0.35$, Pb(Fe${}_{1-x}$Co_x)${}_{2/3}$W${}_{1/3}$O₃, $0\le x<0.20$.^12,18,19

4. Conclusions

(1)	Using the solid phase reaction method, the ceramic samples of the ($1-x$)BaTiO3⋅xPbFe${}_{2/3}$W${}_{1/3}$O3, $x=0$–1 system were synthesized. The performed XRD phase analysis showed that the predominant phase in the samples is (Ba${}_{1-x}$Pbx)(Ti${}_{1-x}$Fe${}_{2x/3}$W${}_{x/3}$)O3 solid solutions with a perovskite structure, herewith samples with $x=0$–0.25 are practically single-phase, and samples with $x\ge 0.25$ contain up to 15 mass.% of the impurity BaWO4 phase.
(2)	The increase of the PFW content in the samples causes an increase of the solid solutions crystal lattice symmetry at room temperature from tetragonal at $x\le 0.04$ to cubic at $x\ge 0.05$.
(3)	In the temperature range 100–570K and in the frequency interval 25Hz–1MHz, the temperature-frequency dependences of the permittivity ${\epsilon }_1(T,f)$ and the loss tangent tan$\delta (T,f)$ of the obtained samples were studied. The TSDC in the samples was studied in the range of 100–420K. It is established that the growth of the PFW content in the ($1-x$)BT⋅xPFW solid solutions causes a gradual change in their dielectric properties from ferroelectric (at $0\le x<0.10$) to relaxor ferroelectric (at $0.10\le x\le 0.25$), then to the properties, resembling those of dipolar glass with a weak or zero correlation between dipoles, even at low temperatures (at $0.25<x\lesssim 0.90$), and then again to the relaxor ferroelectric properties (at $0.90\lesssim x\le 1$).

Acknowledgments

This work was supported by the Ministry of Science and Higher Education of Russia (project FSFZ-2022-0007), the equipment of the MIREA RTU Collective Use Center was used, which received the support of the Ministry of Education of the Russian Federation under the Agreement No. 075-15-2021-689 dated 01.09.2021.1.

ORCID

D. Yu. Fedulov  https://orcid.org/0000-0003-4864-9784

K. E. Kamentsev  https://orcid.org/0000-0002-1763-0012

A. A. Bush  https://orcid.org/0000-0003-3990-9847

V. I. Kozlov  https://orcid.org/0000-0003-2117-5056