Dielectric and Raman studies of Ba_0.06(Na_1/2Bi_1/2)_0.94TiO₃–NaNbO₃ ceramics

Fig. 1a shows the XRD patterns of BNBT-NN samples sintered under air atmosphere. All samples have a perovskite-type structure with different crystal symmetry, and no other peaks were detected within the uncertainty limits of XRD, which suggests the absence of impurity phases. The crystal data of NaNbO₃ (x = 1) and BNBT (x = 0), obtained from the XRD analyses, depicted in Table 1, are consistent with the earlier reports [12, 39–41]. Further, a pure perovskite phase with rhombohedral-tetragonal symmetry is found up to the x = 0.25, while the orthorhombic phase starts appearing and becomes noticeable at x = 0.50. The composition with x = 0.50 is found to have a mixed phase of rhombohedral-tetragonal-orthorhombic symmetry (Table 1). Fig. 1b illustrates the enlarged XRD patterns (46° ⩽ 2θ ⩽ 48°) of all the solid solutions. It can clearly be seen that the crystal structure of the samples at room temperature gradually changes from rhombohedral-tetragonal to orthorhombic symmetry with increasing x, which is apparent by the splitting of 200 reflections into 002 and 200 doublet of orthorhombic phase. The difference in intensity of the splitted peaks becomes prominent from x = 0.75. At very high doping percentages (90 % and 95 %) of NaNbO₃, the ceramics shows pure perovskite phase with orthorhombic symmetry. This indicates that NaNbO₃ has completely integrated into the lattice of Ba_0.06(Na_1/2Bi_1/2)_0.94TiO₃ and formed the solid solution. Thus, BNBT-NN ceramics shows a coexistence of rhombhohedral-tetragonal-orthorhombic phases at x = 0.50. Furthermore, it is observed that the increment of Nb-content in the solid solution, in general, leads to the increase in unit cell volume which may be attributed to the fact that ionic radius of Nb⁺⁵ (0.69 Å) ions is slightly larger than that of Ti⁺⁴ (0.605 Å) ions.

Fig. 1

Fig. 2 shows the SEM micrographs of fractured surface of sintered BNBT-NN ceramics. The nature of the micrographs exhibits the polycrystalline texture of the materials, and grains are distributed throughout the samples. The photographs contain a very few voids suggesting the high density of the materials. The grains of unequal sizes (0.8 µm to 3 µm) were found for the chosen compositions. It is also observed that a few grains are agglomerated and appear larger in size compared to the average size, which is termed as an abnormal grain growth or secondary crystallization. The average grain size for BNBT sample is found to be ∼3 µm and with increasing NN concentration (x), the grain size as well as grain morphology of BNBT-NN ceramics changes. For x = 0.05 the average grain size significantly decreases to nearly 1.25 µm and some pores begin to appear. Further doping of NN inhibits the grain growth and leads to a decrease in grain size. As the substitution level of NN increases from x = 0.50 to x = 0.75 the grains become further smaller (1 µm to 0.8 µm).

Fig. 2

The average grain size of the ceramics becomes minimum when x = 0.75 and increases with further doping. With further increase in NN concentration the average grain size increases slightly to 1 µm. The partial substitution of Ti-ion by Nb-ion results from the differences in their ionic radii, valency and electronegativity which worsen the diffusion coefficient of B-site ion in perovskite lattice [42] and consequently, the grain growth is inhibited with the increase in Nb concentration that results in a decrease in average grain size.

The first-order Raman spectra of the end members Ba_0.06(Na_1/2Bi_1/2)_0.94TiO₃ and NaNbO₃ of BNBT-NN ceramics are shown in Fig. 3a and Fig. 3b, respectively. The peaks of BNBT were found to be Gaussian in line-shape contrary to the expected Lorentzian line-shape fitting over the exponential background from Rayleigh tail. The peaks (FWHM in parenthesis) were observed at 133.3 (19.2) cm⁻¹, 281.3 (53.4) cm⁻¹, 536.2 (49.7) cm⁻¹, 615.3 (28.11) cm⁻¹ and 799.4 (79.2) cm⁻¹. The Gaussian peak profile observed in the Raman spectra may arise due to the distribution of particle sizes in the sample. Contrary to the BNBT pellets, NN shows intense sharp and multiple Lorentzian peaks (Fig. 3b). It agrees well with the results presented in the literature [29]. A peak at 434.2 cm⁻¹ starts appearing from x = 0.5 onwards (Fig. 3c), indicating the change in crystal structure. However, with increasing NN concentration (x), no new peaks are observed, indicating the absence of formation of any new phase and consequently the formation of solid solutions. It can also be seen from Fig. 3c that the bands with lower intensities appear at frequencies that do not differ much from those of the pure NN. Since the Raman spectra of BNBT and NN differ appreciably, the evolution of the structural changes of BNBTNN solid solutions, which depend on composition, can be followed using XRD and dielectric measurement data. Also, the Raman bands are quite broad, which in fact is associated with the disorder of cations at the coordinated sites, and to some overlapping Raman modes [29].

Fig. 3

Fig. 4 shows the variation of ∊ with frequency at room temperature. The value of ∊ is found to decrease with an increase in frequency and beyond 10 kHz it seems to be almost independent of frequency. Also, the value of ∊, in general, decreases with the increasing NN-concentration (x).

Fig. 4

It is known that the phase transition in ferroelectric ceramics depends mainly on chemical composition, microstructure and sintering processes (preparation condition). The transition region extends over some tens of degrees around the temperature of maximum ∊ (∊_max). The electrical polarization, P_r, continuously decreases with increasing temperature rendering it difficult to determine the exact temperature when P_r = 0. The anomalies which take place at ferro-paraelectric phase transition in classical perovskite type ferroelectrics are generally described by the susceptibility (χ) and the order parameter (P) by the expression:

The coupling constant g_ijkl describes the breaking of symmetry by the phase transition. However, it is seen that there exist a set of anomalies in the behavior of some perovskite ferroelectrics with a diffuse phase transition (DPT) which are difficult to explain on the basis of classical theories of ferroelectrics. The maxima of the dielectric constant in DPTs are not well defined. It is thus experimentally difficult to accurately estimate the temperature of the ferro-paraelectric phase transition, T_m (∊_max). In the paraelectric region the dielectric constant exhibits temperature dependence according to the modified Curie-Weiss law:

where ∊_max is the maximum value of the dielectric constant at T_m, C′ and γ (diffusivity parameter) are assumed to be constant, with γ value between 1 and 2. The limiting values γ = 1 and γ = 2 are characteristic of a normal ferroelectric and an ideal relaxor ferroelectric, respectively. Fig. 5 shows the variation of dielectric constant (∊) and loss tangent (tanδ) with the increment in temperature at different frequencies for different compositions of BNBT-NN ceramics. As typical of normal ferroelectrics, ∊ increases gradually with increment in temperature up to the transition temperature (T_m) and then decreases. Also, it is seen that with the increment of NN concentration, maximum value of ∊ (∊_max) decreases while dielectric peak (T_m) shifts towards lower temperature side up to x = 0.25 and then it starts shifting towards higher temperature side and ∊(T) curve becomes less diffuse. This result is consistent with the XRD and Raman data as the orthorhombic phase (Table 1) is coming into force. The decrease in ∊_max implies that the substitution of NN reduces the dipole moment of the lattice and lowers the peak dielectric constant. In all the materials, the room temperature value of tanδ was found to be of the order of 10⁻² at 1 kHz. The low tanδ of this kind can be advantageous when improved detectivity is required. Besides, linear fitting of ∊(T) data, in paraelectric phase, in the expression ∊ = C(T – T_o)⁻¹ allows us to obtain the Curie-Weiss temperature (T_o) for different ceramic compositions: here C is Curie-Weiss constant. It was observed that the value of T_o first shifts towards lower temperature side up to x = 0.25 and then it starts shifting towards higher temperature side with the increase in modifier (NN) percentages and T_o < T_m for all materials, which implies that the phase transitions are of the first order.

Fig. 5

The regions around the dielectric peaks are broadened (Fig. 5), which is one of the most important characteristics of a disordered perovskite type structure with diffuse phase transition (DPT). Fig. 6 shows the variation of ln(1/∊ – 1/∊_max) with ln(T – T_m) for three samples (x = 0, 0.50 and 1.0) at 1 kHz. The graphs show almost linear behavior as temperature changes. The value of exponent, γ, in expression 2 was estimated, respectively to be 1.92, 1.20 and 1.14 for x = 0, 0.50 and 1.0 from the slope of the curves in Fig. 6. We have found γ > 1 for all the cases, the value of which decreases with an increase in NN content. In other words diffusivity decreases with an increase in NN content. This may be due to compositional fluctuations which might produce some kind of heterogeneities in the arrangement of Ba²⁺ and (Na0.51+Bi0.53+)2+${({\text{Na}}_{0.5}^{1 + }{\text{Bi}}_{0.5}^{3 + })^{2 + }}$ ions at A-site Ti⁴⁺ and Nb⁵⁺ ions at B-site that results in decreasing disorder with increasing NN content. This may be explained on the basis of increasing tolerance factor and average ionic radius of A-and B-site cations (Table 2) which results in decreasing disorder as well as dielectric constant as x increases.

Fig. 6