Synthesis, Crystal Structure, and Thermal Properties of Substituted Titanates Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂

Abstract

Titanates Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂ have been obtained by the solid-phase synthesis using sequential annealing of the Bi₂O₃, Nd₂O₃, Pr₆O₁₁, and TiO₂ stoichiometric mixtures in air at temperatures of 1003–1323 K. Their crystal structure has been established by X-ray diffractometry and the high-temperature heat capacity has been determined by differential scanning calorimetry. Based on the experimental C_p = f(T) data, the main thermodynamic functions have been calculated.

1 INTRODUCTION

The Bi_4 – xR_xTi₃O₁₂ (R is the rare-earth element, REE) solid solutions are obtained by substituting REEs for a part of bismuth in titanate Bi₄Ti₃O₁₂. Recently, there has been a sustainable interest in such materials. The solid solutions containing La [1–3], Ce [2], Nd [4–6], Sm [7–9], Eu [10], Er [11], Pr, Nd, Cd, and Dy [12, 13] were synthesized. The layered bismuth titanate-based solid solutions attract attention because the substitution of REEs for bismuth changes the properties (permittivity, conductivity, Curie temperature, etc.) of titanate. According to [3, 14, 15], the substitution of La for Bi reduces the fatigue and polarization of Bi₄Ti₃O₁₂. It is believed that such materials surpass the well-known ferroelectric lead zirconate [3] in some functional characteristics. Most studies on the substituted bismuth titanate deal with its electrical properties. This is due to the prospects of their application in acousto- and optoelectronics, piezoelectric transducers, ferroelectric memory, etc. Nevertheless, despite such attention to these materials, many of their properties have been understudied. This concern, first of all, the thermal characteristics. Some of the available data on the crystal structure of the solid solutions are contradictory. For example, it was reported in [13, 14] that the substitution of REEs for Bi preserves the orthorhombic symmetry, while in [3, 16] it was stated that it changes for tetragonal one. The phase diagrams of the Bi₄Ti₃O₁₂–R₄Ti₃O₁₂ systems have not been built. Note that, in the phase diagrams of Nd₂O₃–TiO₂ [17], Er₂O₃–TiO₂ [18], Lu₂O₃–TiO₂ [19], Bi₂O₃–TiO₂–Y₂O₃ [20], La₂O₃–TiO₂ [21], Gd₂O₃ (Dy₂O₃)–TiO₂ [22], and R₂O₃–TiO₂ (R = La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Yb, Y) [23], no R₄Ti₃O₁₂ compounds were observed. Nevertheless, the data on their formation were reported: Eu₄Ti₃O₁₂ [23], La₄Ti₃O₁₂ [24, 25], and Nd₄Ti₃O₁₂ [17]. Computer modeling of these systems requires data on the thermodynamic properties of the resulting compounds. Such data are lacking in the literature, except for the simple oxides and B-i₄Ti₃O₁₂.

This study presents the results of the synthesis of titanates Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂ and investigations of their crystal structure and thermophysical properties.

2 EXPERIMENTAL

The substituted titanates Bi₂Pr₂Ti₃O₁₂ and Bi-₂Nd₂Ti₃O₁₂ were obtained by the solid-phase synthesis from the initial oxides Bi₂O₃, Nd₂O₃, and TiO₂ (of special purity grade) and Alfa Aesor Pr₆O₁₁ (99.999%). To do that, the stoichiometric mixtures of the pre-calcined oxides were homogenized in a Retsch PM 100 planetary ball mill (Germany) with zirconium dioxide glasses and balls at a working vessel rotation rate of 180 rpm and a processing time of 30 min. Since the obtained powders subjected to such processing can interact with the environment [26], they were immediately placed in polyethylene containers, evacuated, and sealed. After that, they were pressed using a Y-LJ‑CIP-20B isostatic press (P = 150 MPa and τ = 5 min). The obtained samples were burnt in air for 10 h at temperatures of 1073, 1103, 1153, 1273, and 1323 K (1203 K, 20 h). After each temperature, they were ground in a planetary mill and pressed again under the same conditions. The X-ray diffraction powder patterns of the titanates Bi₂Nd₂Ti₃O₁₂ and Bi₂Pr₂Ti₃O₁₂ were recorded on a Bruker D8 ADVANCE diffractometer (CuK_α radiation) at room temperature using a VANTEC linear detector.

The heat capacity of the titanates Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂ was measured by differential scanning calorimetry using a NETZSCH STA 449 C Jupiter thermal analyzer (Germany). The experimental technique was similar to that described previously in [27, 28]. The experimental error was no more than 2%.

3 EXPERIMENTAL RESULTS

All the reflections in the X-ray diffraction patterns were indexed in a P4₂/nmc tetragonal cell. Therefore, this structure was taken as an initial model for the Rietveld refinement in the TOPAS 4.2 program [29]. The two Bi sites exist in the independent part of the cell and both of them were occupied with Bi/Pr and Bi/Nd ions for each phase, respectively. The occupancies of the sites were refined and, to increase the stability of the refinement, the sum of the number of Bi and Pr(Nd) ions in the cell was restricted by linear equations. As a result, the refinement of all the structures was stable and yielded low infidelity factors (Table 1). The atomic coordinates and thermal parameters are given in Table 2 and the main bond lengths, in Table 3; the difference X-ray diffraction patterns are shown in Fig. 1.

Table 1. Main experimental parameters and results of refinement for Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂

Table 2. Atomic coordinates and isotropic thermal parameters of the Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂ solid solutions

Table 3. Main bond lengths (Å)

Fig. 1.

(1) Experimental, (2) calculated, and (3) difference profiles of the X-ray diffraction patterns for (a) Bi₂Pr₂Ti₃O₁₂ and (b) Bi₂Nd₂Ti₃O₁₂ after the refinement using the derivative difference minimization method. Bars show the calculated reflection positions.

The structure of unsubstituted bismuth titanate has been studied repeatedly. The results obtained appeared contradictory. In particular, according to [11, 30], Bi₄Ti₃O₁₂ has a rhombic unit cell (sp. gr. Fmmm) at room temperature. Most authors believe that this titanate is characterized by sp. gr. B2cb [13, 14, 16] or Aba2 [31, 32] (obtained by the transformation from B2cb (Aba2 : abc = B2cb : b'c'a' [31])). According to our data, Bi₄Ti₃O₁₂ has sp. gr. Aba2. These data and Table 1 show that, upon substitution of    Pr or Nd for Bi, the structure changes (sp. gr. P4₂/nmc). According to the data from [33], the Bi₂R₂Ti₃O₁₂ (R = La, Pr, Nd, Sm) compounds have sp. gr. I4/mmm with unit cell parameters of a ~ 3.8 Å and c ~ 33 Å. A similar situation was noted for B-i₂Nd₂Ti₃O₁₂ [16] and Bi₂La₂Ti₃O₁₂ [34]. At the same time, there are different data. According to [35], the -Bi₂La₂Ti₃O₁₂ compound forming in the course of the reaction between K₂La₂Ti₃O₁₀ and BiOCl has an orthorhombic unit cell (a = 5.441(1) Å, b = 5.399(1) Å, and c = 32.944(4) Å).

The search for a suitable phase related to the low-symmetry Aba2 phase by the group properties, which was carried out by us in the PSEUDO program [36], showed that the most suitable structures (the atomic displacement is smaller than 1 Å) can be two structures with sp. gr. P4₂/nmc and I4/mmm. The test refinement for both models yielded Bragg factors R of 2.50% and 1.69% (P4₂/nmc) and 3.91% and 3.49% (I4/mmm) for Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂, respectively. Taking into account that these values for the P4₂/nmc model turned out to be noticeably smaller, as well as the fact that the numbers of the refined structural parameters for the two models are similar (8 refined coordinates for I4/mmm and 9 coordinates for P4₂/nmc) and that the I4/mmm structure had the high thermal parameters for all oxygen atoms, the P4₂/nmc model was preferred.

The effect of temperature on the heat capacity of Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂ is illustrated in Fig. 2. With an increase in temperature from 320 to 1000 K, the C_p values naturally increase and the dependences C_p = f(T) do not contain any kinds of extrema. According to the data from [37], the dependence C_p = f(T) for unsubstituted bismuth titanate has an extremum in the region of the ferroelectric phase transition at 943 K, which is not observed for Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂. A similar phenomenon was previously observed in studying the heat capacity of cuprates La_2 – xSr_xCuO₄ (0 ≤ x ≤ 0.2) [38]. As the Sr concentration increases, the extremum in the curve C_p = f(T) shifts toward lower temperatures.

Fig. 2.

Temperature dependences of the molar heat capacity for (1) Bi₂Pr₂Ti₃O₁₂ and (2) Bi₂Nd₂Ti₃O₁₂.

The experimental results on the heat capacity of Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂ can be described by the Maier–Kelley equation [39]

$${{C}_{p}} = a + bT - c{{T}^{{ - 2}}},$$

(1)

which have the form

$$\begin{gathered} {{C}_{p}} = (419.9 \pm 1.1) + (96.90 \pm 1.2) \times {{10}^{{ - 3}}}T \\ - \;(29.99 \pm 1.05) \times {{10}^{5}}{{T}^{{ - 2}}}, \\ \end{gathered} $$

(2)

$$\begin{gathered} {{C}_{p}} = (417.1 \pm 1.1) + (54.55 \pm 1.2) \times {{10}^{{ - 3}}}T \\ - \;(46.90 \pm 1.11) \times {{10}^{5}}{{T}^{{ - 2}}} \\ \end{gathered} $$

(3)

for the investigated bismuth titanates (J K^–1 mol^–1).

The correlation coefficients for Eqs. (2) and (3) are 0.9979 and 0.9982 and the maximum deviations of the experimental points from the smoothing curves are 1.17% and 1.23%, respectively.

It was impossible to compare the obtained results on the heat capacity of Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂ with the data of other authors, since the latter are lacking. Therefore, we studied the effect of the composition of the solid solutions on their heat capacity (Fig. 3). To ignore the difference in molar masses, specific heats c_p are presented. It can be seen that, with an increase in the REE concentration, the c_p values at 298 K naturally increase. This is apparently indicative of the reliability of the obtained heat capacities for Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂.

Fig. 3.

Effect of the composition of the Bi₂Pr_2 – xTi₃O₁₂ (1) and Bi₂Nd_2 – xTi₃O₁₂ (2) solid solutions on their heat capacity.

Using Eqs. (2) and (3), the thermodynamic functions of the substituted bismuth titanates were calculated using the available thermodynamic relations. The results are given in Table 4.

Table 4. Thermodynamic properties of Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂

4 CONCLUSIONS

Substituted titanates Bi₂Pr₂Ti₃O₁₂ and Bi₂Nd₂Ti₃O₁₂ were obtained by the solid-phase synthesis. The crystal structure was determined and the effect of temperature (320–1000 K) on the heat capacity was investigated. The thermodynamic functions were calculated using the experimental C_p = f(T) data.