The Structural and Dielectric Properties of Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75, 1.0)

Abstract

A new series of layered perovskite-like oxides Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75, 1.0) was synthesized by the method of high-temperature solid-state reaction, in which partial substitution of bismuth (Bi) atoms in the dodecahedra of the perovskite layer (A-positions) by Nd atoms takes place. X-ray structural studies have shown that all compounds are single-phase and have the structure of Aurivillius phases (APs), with close parameters of orthorhombic unit cells corresponding to space group A2₁am. The dependences of the relative permittivity ε/ε₀ and the tangent of loss tgσ at different frequencies on temperature were measured. The piezoelectric constant d₃₃ was measured for Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75) compounds of the synthesized series.

1. Introduction

In 1949, while studying the Bi₂O₃-TiO₂ system, V. Aurivillius established the formation of an oxide: Bi₄Ti₃O₁₂ with a perovskite-type structure [1]. Then, within two years, he obtained several more oxides with a similar structure [2,3]. However, at the first stage, V. Aurivillius limited himself to studying only the structure of the compounds obtained. Only ten years later G. Smolenskiy, V. Isupov and A. Agranovskaya [4] discovered the ferroelectric properties of Bi₂PbNbO₉, which belongs to this class of compounds. Subsequently, several tens of Aurivillius phases were obtained, and almost all of them turned out to be ferroelectrics [5,6,7,8,9,10]. Aurivillius phases (APs) form a large family of bismuth-containing layered perovskite type compounds, with the chemical composition described by the general formula A_m–1Bi₂B_mO_3m+3. The crystal structure of the APs consists of alternating [Bi₂O₂]²⁺ layers separated by m perovskite-like layers [A_m-1B_mO_3m+1]^2–, where A are ions with large radii (Bi³⁺, Ca²⁺, Gd³⁺, Sr²⁺, Ba²⁺, Pb²⁺, Na⁺, K⁺, Y³⁺, Ln³⁺ (lanthanides)) and have dodecahedral coordination, while the B-positions inside oxygen octahedra are occupied by strongly charged (≥3⁺) cations with a small radius (Ti⁴⁺, Nb⁵⁺, Ta⁵⁺, W⁶⁺, Mo⁶⁺, Fe³⁺, Mn⁴⁺, Cr³⁺, Ga³⁺, etc.).The value of m is determined by the number of perovskite layers [A_m-1B_mO_3m+1]²⁻ located between the fluorite-like layers [Bi₂O₂]²⁺ and can take integer or half-integer values in the range 1–5 (Figure 1).

If m is a half-integer number, then in the lattice, there are alternative perovskite layers with m differing by 1. For example, at m = 1.5, the lattice has an equal number of layers with m = 1 and m = 2. The value m = 1 corresponds, for example, to the compound Bi₂WO₆, m = 2 corresponds to Bi₂PbNbO₉, m = 3 corresponds to Bi₄Ti₃O₁₂, m = 4 corresponds to Bi₄CaTi₄O₁₅, m = 5 corresponds to Bi₄Sr₂Ti₅O₁₈.

Positions A and B can be occupied by the same or by several different atoms. Atomic substitutions in positions A and B have a significant effect on the electrophysical characteristics of the APs. In particular, there are large changes in the values of dielectric constants, conductivity. Moreover, Curie temperature T_C can also vary within wide limits. Thus, the study of cation-substituted APs plays an important role in the creation of materials for various technological applications.

The structure of Bi₂A_m−1B_mO_3m+3 compounds above the Curie point T_C is tetragonal and belongs to the space group I4/mmm. The type of space group below the Curie point T_C depends on the value of the number m. For odd m, the space group of the ferroelectric phase is B2cb or Pca2₁, for even m, it isA2₁am, and for half-integer m, it isCmm2 or I2cm.

This work considers the conditions for the existence of these compounds [11]:

$$t_1<t=\left[\right(1.12R_A+R_{\mathrm{O}})/\sqrt{2}(R_B+R_{\mathrm{O}}\left)\right]<t_2,$$

(1)

where R_A, R_B are the cation radii, R_O is the oxygen anion radius, t is the Goldschmidt tolerance factor. The boundary values of the tolerance factor, which determines the possibility of the existence of a compound belonging to the APs, are defined as t₁ = 0.870 and t₂ = 0.985. A detailed study of the regularities of changes in the Curie temperature of the Aurivillius phases on such parameters as the radii and electronegativity of the A- and B-cations, as well as on the cell parameters, was carried out in [12]. Some anomalies in the properties of layered ferroelectrics A_m−1Bi₂B_mO_3m+3 were also considered [13]. In particular, it was shown that Bi₂O₂ layers have a constricting effect on the layered structure of these compounds, but the strength of such an effect decreases with an increase in the number of perovskite layers. Moreover, it was shown that the Curie temperatures pass through a maximum with increasing distortions of the pseudoperovskite cell in the perovskite-like layer, and the position of the maximum changes with a change in the number of perovskite layers m. Despite the fact that the crystal structure of the APs has been fairly well studied by various methods (X-ray powder diffraction, neutron diffraction, etc.), some aspects related to the distortion of the APs’ unit cell from the “ideal” tetragonal system with the space group I4/mmm(139), and the reasons for such distortions, are of scientific interest. The structural features of APs, which determine the appearance of ferroelectric properties in these compounds, have also not been sufficiently clarified. Basically, this is attributed to the displacement of the B-ion (Ti⁴⁺, Nb⁵⁺, Ta⁵⁺) from the center of the oxygen octahedron in the perovskite layers. Scientific interest in the synthesis and study of new APs is stimulated by numerous examples of their use in various electronic devices, due to their unique physical properties (piezoelectric, ferroelectric, etc.). They demonstrate low temperature coefficients of dielectric and piezoelectric losses, and low aging temperatures in addition to high Curie temperatures (T_C ≤ 965 °C) [14,15].

In recent years, more attention has been placed on the design and studies of new APs [16,17,18,19,20]. The APs, such as SrBi₂Nb₂O₉ (SBN), SrBi₄Ti₄O₁₅ (SBTi),SrBi₂Ta₂O₉ (SBTa), La_0.75Bi_3.25Ti₃O₁₂ (BLT) and so on, were accepted as excellent materials for the energy independent ferroelectric memory with small access time (FeRAM) [21,22,23,24,25]. Bi₃TiNbO₉ (BTNO) with m = 2 that consists of (Bi₂O₂)²⁺ layers between which there are (BiTiNbO₇)^2– layers [26] is a promising material for fabricating high temperature piezoelectric sensors because of their very high Curie temperature T_C (914–921 °C) [14,15], despite the fact that the piezoelectric modulus of BTNO ceramic is fairly low (d₃₃ < 7 pC/N) [27]. Numerous examples [28,29,30,31,32,33,34,35,36,37,38,39,40,41,42] showed that replacements of atoms in A- and also in B-positions of an AP’s crystal lattice led to a change in the structure, the dielectric properties and significantly influenced the polarization processes in these compounds.

The purpose of this study was to investigate the dielectric characteristics when bismuth cation (A-position) is replaced by neodymium ions of the basic composition Bi₃Ti_1.5W_0.5O₉. It was previously observed that the partial replacement of bismuth ions by neodymium cations in the series of perovskite-like Bi-containing oxides Bi₃TiNbO₉, Bi₃TiTaO₉ led to a significant decrease in the phase transition temperature (Curie temperature T_C) and a change in dielectric properties [43].

2. Experimental Section

Polycrystalline samples of APs were synthesized by the solid-phase reaction of the corresponding Bi₂O₃,TiO₂, Nd₂O₃, WO₃. After weighting in accordance with the stoichiometric composition and a thorough grinding of the initial compounds with the addition of ethyl alcohol, the pressed samples were calcined at a temperature of 770 °C for 2 h. The samples were fired in a laboratory muffle furnace in air. Then, the samples were repeatedly ground and pressed into pellets with a diameter of 10 mm and a thickness of 1.0–1.5 mm, followed by the final synthesis of APs at a temperature of 1100 °C (for 2 h).

The X-ray diffraction patterns were recorded on a DRON-3M diffractometer with attachment for powder diffractionand an X-ray tube BSV21-Cu with a Cu X-ray tube. The Cu K_α1,α2 radiation was separated from the total spectrum with the use of a Ni-filter. The X-ray diffraction patterns were measured in the range of 2θ angles from 10° to 65° with a scan step of 0.02° and an exposure (intensity registration time) of 4 s per point. The analysis of the profiles of the diffraction patterns, the determination of the positions of the lines, their indexing (hkl), and the refinement of the unit cell parameters were performed by using the PCW 2.4 program [44]. For dielectric permittivity and electrical conductivity measurements, on flat surfaces of samples of APs, in the form of disks with a diameter of 10 mm and a thickness of approximately 1 mm, electrodes were deposited, using an Ag-paste annealed at a temperature of 700 °C (for 1 h). The temperature and frequency dependences of the dielectric characteristics were measured using an E7-20 immittance meter in the frequency range from 100 kHz to 1 MHz and at temperatures in the range from room temperature to 900 °C. All the samples were poled in an oil bath at 125 °C under 35 kV/cm for 30 min.

3. Results and Discussion

Powder X-ray diffraction patterns of all investigated solid solutions Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75, 1.0) correspond to single-phase APs with m = 2, and do not contain additional reflections isostructural to the known perovskite-like oxide Bi₃Ti_1.5W_0.5O₉. It was found that all synthesized APs crystallize in an orthorhombic system with a unit cell space group A2₁am(36). The diffraction patterns of all the compounds correspond to the APs with m = 2. Figure 2 shows the experimental powder X-ray diffraction patterns of the studied compounds.

According to the data of X-ray diffraction, the parameters of the unit cell and the volume of the unit cell were determined; they are given in

Table 1. Unit cell parameters a₀, b₀, c₀, V, a_t is the parameter of the tetragonal period, c′ is the octahedron height along axis c, δc′ is the deviation of the unit from the cubic shape, δb is the rhombic distortion.

Compounds	a0, Å	b0, Å	c0, Å	V, Å3	c′, Å	at, %	δc′, %	δb0, %
Bi2.75Nd0.25Ti1.5W0.5O9	5.3861	5.3742	24.8572	719.51	3.7586	3.8043	−1.2	−0.2
Bi2.5Nd0.5 Ti1.5W0.5O9	5.3916	5.3742	24.8421	719.81	3.7263	3.8063	−2.1	−0.3
Bi2.25Nd0.75 Ti1.5W0.5O9	5.3977	5.3875	24.8388	722.31	3.7258	3.8131	−2.28	−0.18
Bi2 NdTi1.5W0.5O9	5.4013	5.3903	24.8388	723.17	3.7248	3.8154	−2.28	−0.2

.

Table 1 also shows the parameters of the orthorhombic δb₀ and tetragonal δc′ deformation; average tetragonal period a_t, coefficient of tolerance t and the average thickness of one perovskite layer c′; c′ = 3c₀/(8 + 6m) is the thickness of a single perovskite-like layer, m is the number of layers, a_t = (a₀ − b₀)/2$\sqrt{2}$ is the average value of the tetragonal period, a₀, b₀, c₀ are the lattice periods, δc′ = (c′− a_t)/a_t is the deviation of a cell from a cubic shape, that is a lengthening or shortening from a cubic shape, δb₀ = (b₀− a₀)/a₀ is the rhombic deformation. The obtained unit cell parameters of the studied APs Bi_3−xNd_xTi_1.5W_0.5O₉ samples (x = 0.25, 0.5, 0.75, 1.0) are close to those determined earlier: a = 5.4018 (2) Å, b = 5.3727 (4) Å, c = 24.9388 (1) Å [23]. In order to obtain the degree of distortion of the ideal structure of perovskite in Nd³⁺, we determined the tolerance factor t, which is presented in

Table 2. Dielectric characteristics of Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75, 1.0): Curie temperature T_C, piezomodule d₃₃, tolerance factor t, relative permittivity ε/ε₀, activation energy E_n.

Compounds	TC, °C	d33, pC/N	t	ε/ε0(T) (at 100 kHz)	E1/E2/E3, eV
Bi2.75Nd0.25Ti1.5W0.5O9	681	10	0.9778	1000	0.67/0.29/0.06
Bi2.5Nd0.5 Ti1.5W0.5O9	637	5	0.9745	500	0.77/0.31/0.1
Bi2.25Nd0.75 Ti1.5W0.5O9	617	3.5	0.9713	550	0.65/0.21
Bi2 NdTi1.5W0.5O9	165	0	0.9681	160	-

.

The tolerance factor t was introduced by Goldschmidt [45] as a geometric criterion that determines the degree of stability and distortion of the crystal structure:

$$t=(R_A+R_{\mathrm{O}})/\left[\sqrt{2}\right(R_B+R_{\mathrm{O}}\left)\right],$$

(2)

where R_A and R_B are the radii of cations in positions A and B, respectively; R_O is the ionic radius of oxygen. Values of tolerance factors t for the samples under study are shown in Table 2. In this work, the tolerance coefficient t was calculated taking into account the Shannon ionic radii for the corresponding coordination numbers (CN) (O²⁻ (CN = 6) R_O = 1.40 Å, Nd³⁺ (CN = 6) R_Nd3+ = 1.27 Å, W⁶⁺ (CN = 6) R_W6+ = 0.6 Å, Ti⁴⁺ (CN = 6) R_Ti = 0.605 Å). Shannon [46] did not provide the ionic radius of Bi³⁺ for coordination with CN = 12. Therefore, its value was determined from the ionic radius with CN = 8 (R_Bi = 1.17 Å) multiplied by an approximation factor of 1.179, then for Bi³⁺(CN = 12) we got R_Bi = 1.38Å.

In addition to the results of structural studies, temperature dependences of the relative permittivity ε and the loss tangent tgσ were obtained at various frequencies. Figure 3 shows the temperature dependences of the relative permittivity ε(T) and the dielectric loss tangent for Nd³⁺ Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75, 1.0) at a frequency from 100kHz to 1 MHz.

For Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75), the ε(T) dependences are clearly pronounced. The intensity ε(T) in the range of 0.25–0.75 drops almost two times, while the dielectric loss decreases almost ten times. The temperature dependence of the relative permittivity ε/ε₀ for the AP Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 1.0) at a frequency from 100 kHz to 1 MHz has a strongly diffuse transition, which is usually typical of ferroelectric relaxors. The obtained values of the activation energy E_a of charge carriers in Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75) at frequency of 100 kHz are presented in Table 2.

The activation energy E_a was determined from the Arrhenius equation:

σ = (A/T)exp[−E_a/(kT)],

(3)

where σ is the electrical conductivity, k is a Boltzmann’s constant, and A is a constant, E_a is the activation energy. A typical dependence of lnσ on 1/(kT) (at a frequency of 100 kHz), which was used to determine the activation energies E_a, is shown in Figure 4 for the APsBi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75). All three of these compounds Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75) have different temperature ranges in Figure 4, in which the activation energies E_a have significantly different behavior. If for the first two compounds x = 0.25, 0.5, three regions of the activation energy E_a of charge carriers are observed, then we observe only two regions for the compound x = 0.75. In the low-temperature range, the electrical conductivity is predominantly determined by impurity defects with very low activation energies of the order of a few hundredths of an electron-volt. For the Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.5, 0.75) compounds, we do not observe a region with a clearly pronounced impurity conductivity.

At the same time, we observe for these compounds a decrease in the dielectric loss tangent and, as a consequence, a decrease in the conductivity. The decrease in the conductivity can be attributed to a decrease in oxygen vacancies.

Figure 5 shows the dependence of the unit cell parameters a, b, c on the parameter x. As seen from Figure 5, parameter a and b increase, while parameter c decreases for the entire series of compounds. It should also be noted that, despite the decrease in the thickness c′ of the perovskite layer, the volume of the unit cell V increases. The change in the unit cell parameters a, b, c, V and APs Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75, 1.0) is associated, among other things, with the difference in radii in the ions in position A, which have a dodecahedral layer, where position A is occupied by Bi³⁺ ions (R_Bi3+ = 1.38 Å [46]) and replaced by Nd³⁺ ions with a much smaller radius (R_Nd3+ = 1.27 Å [46]).

It should be noted that the observed increase in the unit cell volume at x = 0.25–1.0 is associated only with a change in the unit cell parameters b and a, while the parameter c decreases. At the same time, if the parameter b changes almost linearly, then the parameter a has a non-linear dependence. It can be assumed that such a situation is possible if the neodymium ion has an ellipsoidal shape with a constant semi-major axis.

In Table 2, we can see the piezoelectric constant d₃₃ for the Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75). For the Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 1.0), the piezoelectric constant d₃₃ could not be measured.

4. Conclusions

Series of layered bismuth perovskite oxides Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75, 1.0) were synthesized by the solid-state method. The X-ray structural studies performed in our work showed that all the compounds obtained have single-phase with an orthorhombic crystal lattice (space group A2₁am, Z = 36). An analysis of the details of the AP-structure showed that an increase in the neodymium concentration x from 0.25 to 1.0 and a partial replacement of bismuth ions with neodymium ions lead to a decrease in the dielectric loss tangent and a decrease in ε/ε₀. For the entire series of synthesized compounds, the parameter c (thickness of the perovskite layer) decreases with an increase in neodymium cations. At the same time, the volume of the unit cell increases with decreasing c due to an increase in parameters a and b. Isovalent substitutions of Bi³⁺ ions by Nd³⁺ ions lead to a decrease in oxygen vacancies and leakage current and, accordingly, to a decrease in the dielectric loss tangent. Replacement of Bi³⁺ ions with Nd³⁺ ions, which have an ionic radius less than the ionic radius of bismuth, leads to a decrease in the Curie temperature T_C. This effect is observed only upon doping with neodymium ions. The temperature dependences ε/ε₀(T) in Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75) exhibit a high-temperature anomaly associated with the Curie temperature T_C, which corresponds to the transition from the paraelectric phase to ferroelectric. For Bi_2.75Nd_0.25Ti_1.5W_0.5O₉ the piezoelectric constant is 10 pC/N and tgσ < 1 at 1 MHz. Elements Bi_3−xNd_xTi_1.5W_0.5O₉ (x = 0.25, 0.5, 0.75, 1.0) of the synthesized series can become the basis for creating new lead-free piezo-ferroelectric materials.