Compositional induced structural phase transitions in (1 − x)(K_0.5Na_0.5)NbO₃–x(Ba_0.5Sr_0.5)TiO₃ ferroelectric solid solutions

Abstract

Ferroelectric materials exhibiting switchable and spontaneous polarization have strong potential to be utilized in various novel electronic devices. Solid solutions of different perovskite structures induce the coexistence of various phases and enhance the physical functionalities around the phase coexistence region. The construction of phase diagrams is important as they describe the material properties, which are linked to the underpinning physics determining the system. Here we present the phase diagram of (K_0.5Na_0.5NbO₃)–(Ba_0.5Sr_0.5TiO₃) (KNN-BST) system as a function of composition and their associated physical properties. Lead-free (1 − x)KNN–xBST (0 ≤ x ≤ 0.3) solid solution ceramics were synthesized by conventional solid-state reaction technique. The X-ray diffraction and Raman spectroscopic studies indicate composition-dependent structural phase transitions from an orthorhombic phase for x = 0 to orthorhombic + tetragonal dual-phase (for 0.025 ≤ x ≤ 0.15), then a tetragonal + cubic dual-phase (x = 0.2) and finally a cubic single phase for x ≥ 0.25 at room temperature (RT). Among these, the orthorhombic + tetragonal dual-phase system shows an enhanced value of the dielectric constant at room temperature. The phase transition temperatures, orthorhombic to tetragonal (T_O-T) and tetragonal to cubic (T_C), decrease with the increase in BST concentrations. The ferroelectric studies show a decrease of both 2P_r and E_C values with a rise in BST concentration and x = 0.025 showed a maximum piezoelectric coefficient.

Introduction

The piezoelectric effect realized in some dielectric materials is characterized by the conversion of mechanical energy into electrical energy and vice-versa. Ferroelectric materials are non-linear dielectrics and are also a sub-group of piezoelectric materials, which have spontaneous and electrically switchable polarization (P)^1,2. Thus, at present, multifunctional ferroelectric materials are widely used in numerous electrical/electronic devices such as sensors, electrostrictive actuators, electro-mechanical transducers, multilayer ceramic capacitors, integrated non-volatile memory and high-density energy storage devices^1,2. The widely used ferroelectric materials for device applications are lead-based material systems, viz., PbTiO₃, Pb(Zr_xTi_1−x)O₃ (PZT), (1 − x)Pb(Mg_1/3Nb_2/3O₃)–xPbTiO₃ (PMN–xPT), Pb_1−xLa_x(Zr_yT_1−y)_1−x/4O₃ (PLZT) due to their excellent di-, ferro-, and piezo-, electric properties^1,2,3,4,5,6. Most of the Pb-based ferroelectric materials used in the industry contain more than 60 wt% of lead. Therefore, the high volatility lead-based ferroelectrics pose an environmental concern and are also detrimental to human health^4,5,6. To create awareness of environmental safety, restrictions were imposed by Waste of Electrical and Electronic Equipment⁵ and Restriction of certain Hazardous Substances directives^4,5,

Figure 2

Rietveld refined X-ray powder diffraction patterns of (1 − x)KNN-xBST for (a) x = 0 using Amm2 model (b) x = 0.025 and (c) x = 0.10 using Amm2 + P4mm model (d) x = 0.20 using P4mm+$Pm\overline{3 }m$ model and (e) x = 0.30 using $Pm\overline{3 }m$ model. The inset shows a magnified view of the fitted {200}_pc and {222}_pc reflections.

For x = 0, the XRD data was fitted using Rietveld refinement technique with single-phase Amm2 crystal structure, and the result shows a good agreement between the experimental and the selected structural model (Fig. 2a). A magnified view of the fitted data of the higher order reflections {200}_pc and {222}_pc are shown in the insets of Fig. 2. Although from visual analysis of the doublet nature of the pseudocubic {200}_pc and {400}_pc reflections suggest an Amm2 structure for x = 0.025 (Fig. 1), Rietveld analysis revealed a poor fit with the single phase Amm2 structure. A dramatic improvement in the peak fit occurs by including the P4mm phase along with the Amm2 phase (Fig. 2b). However, we have also fitted the XRD data for x = 0.025 by considering single phase Amm2, single phase P4mm, and combination of both Amm2 and P4mm (Amm2 + P4mm) phases. The best fit was observed for the (Amm2 + P4mm) co-existence model. The Rietveld refined XRD patterns for single-phase Amm2 and dual-phase (Amm2 + P4mm) are shown in Supplementary Fig. S2. For x = 0.05, Rietveld refinement of the XRD patterns continued with Amm2 + P4mm space groups, and a good fit was also observed for this dual phase. Although x = 0.10 and 0.15 look to be tetragonal, the Rietveld refinement using the single phase P4mm space group resulted in a poor fit. The best quality of fit was achieved using a combination of both tetragonal P4mm and orthorhombic Amm2 phases. Figure 2c shows the representative Rietveld refinement pattern for x = 0.10. The magnified fitted plot of {200}_pc and {222}_pc reflections is also presented in the inset of Fig. 2c for better clarity. It was observed that the phase fraction of the tetragonal phase increases with increasing BST concentration in the phase co-existence region. The pseudo-cubic reflections for x = 0.20 appear to be cubic, so we have fitted that data using $Pm\overline{3 }m,$ which resulted in a very poor fit. Thus, the Rietveld refinement for x = 0.20 was carried out using different models such as (i) single phase $Pm\overline{3 }m$, (ii) single phase P4mm, and (iii) both $Pm\overline{3 }m$ and P4mm phases (P4mm + $Pm\overline{3 }m$). The Rietveld refinement fit was improved when the tetragonal phase is included along with the cubic phase in the structural model. Thus the Rietveld refinement for x = 0.20 was carried out using dual phase $Pm\overline{3 }m$ and P4mm phases (P4mm + $Pm\overline{3 }m$), and the result shows a good agreement between the experimental and chosen theoretical model (Fig. 2d). For comparison we have also shown the fitted data using both $Pm\overline{3 }m$ and P4mm+$Pm\overline{3 }m$ phases in the Supplementary Fig. S3. Finally, Rietveld refinements of the XRD pattern for x = 0.30 with single phase cubic $Pm\overline{3 }m$ space group has been carried out, and a good fit has been observed (Fig. 2e). The refined structural parameters obtained for all the Rietveld refinements are given in Table S2 in the Supplementary Material.

Summarily, the Rietveld refinement on the XRD analysis reveals that (1-x)KNN-xBST ceramic exhibits the single phase Amm2 crystal structure for x = 0, the coexistence of Amm2 + P4mm structure for the composition range 0.025 ≤ x ≤ 0.15, the coexistence of P4mm+$Pm\overline{3 }m$ structure for x = 0.20 and single phase $Pm\overline{3 }m$ crystal structure for x = 0.30. We have also checked the presence of all elements and their respective valence states of x = 0.1 sample as representative of the KNN-BST system via high-resolution X-ray photoelectron spectroscopy (XPS). All the elements are found to be present, and their original valence states have not been changed significantly (Supplementary Material Fig. S4).

Raman spectroscopic study

Raman spectroscopy is a nondestructive, effective probe to investigate the structural phase transition of ferroelectric materials because of its sensitivity to structural symmetry³⁹. Raman scattering is also responsive to local heterogeneities associated with compositional and structural disorder. Thus, the composition-dependent Raman scattering spectra of the KNN-BST system have been investigated to realize the effects of BST concentration on local heterogeneities of KNN-BST ceramics. The reduced intensity, ${{I}}^{\text{r}}\left(\omega \right)$, corrected for the Bose–Einstein phonon population and observed Raman scattering intensity, I(ω) are related by the following equation^40,41.

$${\text{I}}^{\text{r}}\left(\omega \right)\text{ } = \frac{{\text{I}}\text{(}\omega \text{)}}{\omega \text{[}{\text{n}}\left(\omega \right)\text{+1]}},$$

(1)

where, ${\text{n}}\left(\omega \right)\text{ = }\frac{1}{{\text{exp}}\left(\frac{\hbar \omega }{{\text{k}}_{\text{B}}{\text{T}}}\right)-1}$ stand for the Bose–Einstein population factor in which k_B and ħ denote Boltzmann and Dirac constants, respectively. All reduced Raman spectra in the frequency range of 25–100 cm⁻¹ were fitted by admixture of a Lorentzian central peak (CP) and damped harmonic oscillators (DHOs) model to comprehend the effects of BST do** on KNN-BST ceramics^40,41:

$$I^{r} \left( \omega \right){ = }\frac{{{2}A_{{{\text{CP}}}} }}{\pi }\frac{{\Gamma_{{{\text{CP}}}} }}{{{4}\omega^{{2}} { + } \Gamma_{{{\text{CP}}}}^{{2}} }} + \mathop \sum \limits_{{\text{i}}} \frac{{A_{{\text{i}}} \Gamma_{{\text{i}}} \omega_{{\text{i}}}^{{2}} }}{{\left( {\omega^{{2}} - \omega_{{\text{i}}}^{{2}} } \right)^{{2}} { + }\omega^{{2}} \Gamma_{{\text{i}}}^{{2}} }},$$

(2)

where Γ_CP and A_CP represent the full width at half maximum (FWHM) and intensity of the CP, respectively, which is associated with the relaxation process of precursor dynamics. $\omega$_i, Γ_i, and A_i represent frequency, dam** constant, and intensity of the ith optical Raman active mode, respectively.

The observed Raman scattering spectra measured at room temperature of the KNN-xBST ceramics as a function composition is shown in Fig. 3a. The Rietveld refinements of the XRD spectrum reveal that KNN belongs to the orthorhombic phase with Amm2 symmetry. The temperature dependence of the dielectric properties also suggests that KNN belongs to the orthorhombic phase at room temperature. According to group theory analysis, the Amm2 symmetry has 12 optical modes at the zone center, and the irreducible representations are 4A₁ + A₂ + 4B₁ + 3B₂^42,43. In polycrystalline ceramic samples, it is difficult to assign the vibrational mode symmetries directly from the Raman scattering experiment; therefore, we follow the assignments of mode symmetry in [(K_0.56Na_0.44)(Nb_0.65Ta_0.35)O₃, KNNT] single crystals⁴².

Figure 3

(a) Raman spectra of KNN-xBST ceramics as a function of composition. (b, c) The fitted Raman spectra using Eq. (2) at some selected composition. (d) The frequency shift (upper part) of Raman active modes, and the FWHM and intensity of the CP (lower part) of KNN-xBST ceramics as a function of composition.

The composition-dependent Raman spectra of the KNN-xBST ceramics measured at room temperature are shown in Fig. 3a. The Raman spectrum in the frequency range of 25–1000 cm⁻¹ of the KNN consist of mainly B₂(TO₁) (~ 58 cm⁻¹), B₁(TO₁) (~ 79 cm⁻¹), A₁(TO₁) (~ 106 cm⁻¹), A₁(TO₂) (~ 141 cm⁻¹), A₁(LO₁) (~ 198 cm⁻¹), B₁(TO₂) (~ 236 cm⁻¹), A₁(TO₃) (~ 260 cm⁻¹), A₁(LO₂) (~ 438 cm⁻¹), B₂(TO₂) (~ 550 cm⁻¹), A₁(TO₄) (~ 619 cm⁻¹), and A₁(LO₃) (~ 856 cm⁻¹) as shown in Fig. 3a–c. The broad weak mode at about 705 cm⁻¹ (Fig. 3a–c) may be due to the mismatch of ionic radii at crystallographically equivalent sites induced lattice disorder⁴⁴. Note that A₁(TO₃), B₂(TO₂), A₁(TO₄), and A₁(LO₃) each modes splits into two modes denote as A₁(TO₃)₁ (~ 257 cm⁻¹) and A₁(TO₃)₂ (~ 272 cm⁻¹), B₂(TO₂)₁ (~ 550 cm⁻¹) and B₂(TO₂)₂ (~ 569 cm⁻¹), A₁(TO₄)₁ (~ 599 cm⁻¹) and A₁(TO₄)₂ (~ 619 cm⁻¹), A₁(LO₃)₁ (~ 856 cm⁻¹) and A₁(LO₃)₂ (~ 884 cm⁻¹), respectively. The Raman mode splitting may be due to the different local order regions in KNN ceramics⁴⁵. The observed Raman modes of the KNN ceramics correspond to the orthorhombic phase^42,43, which is supported by XRD and dielectric results. It is found that the B₂(TO₁) mode completely disappears, and B₂(TO₂)₁ and B₂(TO₂)₂ modes merge at x = 0.025 as shown in Fig. 3a,d. The complete disappearance of the B₂(TO₁) mode and merging of the B₂(TO₂) mode denote the structural change of the KNN-BST ceramics. It is important to note that an over-damped phonon mode appears near 99 cm⁻¹ at x = 0.025 (Fig. 3b). The over-damped phonon may correspond to the E(TO₁) mode of the tetragonal phase of the KNN-BST ceramics⁶. Thus, the disappearance of the B₂(TO₁) mode and the appearance of an over-damped E(TO₁) mode indicates the structural change of the KNN-BST from an orthorhombic to a tetragonal phase. This is consistent with the Rietveld refinement of the XRD spectra of KNN-BST (0.025 ≤ x ≤ 0.15), which revealed the coexistence of the orthorhombic (Amm2) and tetragonal (P4mm) phases. The existence of the B₂(TO₂) may indicate the phase coexistence of orthorhombic (Amm2) and tetragonal (P4mm) phases in KNN-BST (0.025 ≤ x ≤ 0.15) ceramics. Further increasing the BST composition, both A₁(TO₂) cm⁻¹ and A₁(LO₁) modes become closer to each other and eventually vanish at x ≥ 0.20 (Fig. 3b,d). The vanishing of these Raman modes above x = 0.20 is a clear indication of structural transformation from tetragonal to cubic phase. The phase transition and the coexistence of tetragonal and cubic $(Pm\overline{3 }m$) phases i.e., P4mm + $Pm\overline{3 }m$ phase at x = 0.20 are confirmed by Rietveld refinement of the XRD spectra of KNN-xBST (x = 0.20) ceramics. It is worth noting that the overdamped E(TO₁) mode corresponds to the tetragonal phase and still exists at x = 0.20. The presence of E(TO₁) mode may imply the coexistence of tetragonal and cubic phases at x = 0.20 by Raman scattering as well. Note that the overdamped E(TO₁) mode completely disappeared at x = 0.30, indicating the structural transformation from mixed P4mm+$Pm\overline{3 }m$ phases to a pure cubic $(Pm\overline{3 }m)$ phase. The first-order Raman mode is not allowed in cubic $Pm\overline{3 }m$ symmetry according to Raman selection rules. However, the intense first-order Raman modes persist in the cubic phase at x ≥ 0.30. The presence of first-order Raman modes in the cubic phase KNN–xBST (x = 0.30) denotes the breaking of symmetry caused by the local polar clusters i.e., polar nano regions PNRs^40,41.

The Raman spectra of the KNN–xBST can also be explained using the vibrational modes of isolated cations and coordination polyhedrons. In this case, the vibrations stem from the internal modes of NbO₆/TiO₆ octahedrons and the translational modes of K⁺/Na⁺/Ba²⁺/Sr²⁺ cations. The vibrations of NbO₆/TiO₆ octahedrons consist of A_1g(ν₁) + E_g(ν₂) + 2F_1u(ν_3, ν₄) + F_2g (ν₅) + F_2u(ν₆), in which A_1g(ν₁), E_g(ν₂), and F_1u(ν₃) modes are stretching and the rest are bending modes^42,43. The Raman modes in the low-frequency range lower than 200 cm⁻¹ can be assigned to the translational modes of the K⁺/Na⁺/Ba²⁺/Sr²⁺ cations and rotation of the octahedron, while other internal vibrational modes of the octahedron appear in the high-frequency range of 200–900 cm⁻¹. In the low-frequency region, the ν₆ mode associated with NbO₆/TiO₆ octahedron may also appear, and the Raman ν₆ mode corresponds to peaks near 141 cm⁻¹⁴³. The modes at about 58 cm⁻¹ and 79 cm⁻¹ are associated with the translational modes of K⁺/Na⁺/Ba²⁺/Sr²⁺ cations, whereas the mode near 198 cm⁻¹ is related to K⁺/Na⁺/Ba²⁺/Sr²⁺ cations versus NbO₆/TiO₆ octahedron⁴³. The mode at around 106 cm⁻¹ is related to the rotational mode of the NbO₆/TiO₆ octahedron⁴². The modes near 236 cm⁻¹ and 260 cm⁻¹ were attributed to the ν₅ mode. The modes at about 438 cm⁻¹, 550 cm⁻¹, 619 cm⁻¹, and 705 cm⁻¹ are identified as ν₄, ν₂, ν₁, and ν₃ modes of the NbO₆/TiO₆ octahedron, respectively⁴³. The coupled ν₁ + ν₅ mode is commonly treated as the peak at 856 cm⁻¹⁴³. It is found that the intense ν₁ (619 cm⁻¹) and ν₅ (260 cm⁻¹) modes become weak upon increasing the BST composition (Fig. 3a). The intense ν₁ and ν₅ modes indicate the near-perfect NbO₆/TiO₆ octahedron of pure KNN (x = 0) belongs to Amm2 symmetry⁴³. It is important to note that ν₁ and ν₅ (260 cm⁻¹) modes of the KNN split into two with the addition of BST. The splitting of the modes is likely due to the substitution of Nb ions with Ti ions, which leads to a distortion of the crystal structure of the KNN and breaks the symmetry of NbO₆/TiO₆ octahedron⁴². Also, note that the frequency of these modes shifts to lower frequency in a slightly scattered way with increasing the BST compositions (Supplementary Fig. S5). The slightly scattered values may be due to the existence of mixed phases. This result suggests that the substitution of Nb ions with Ti ions may weaken the binding strength of the octahedron, which is caused by increasing the distance between Nb/Ti cations and its coordinated oxygen due to their lattice mismatch.

The composition dependence of the CP, which is related to the relaxation process of dynamics PNRs, has been investigated to comprehend the nature of phase transition and the effects of BST composition on local heterogeneities in KNN–xBST ceramics. The presence of the CP is a common feature of either a crystal or a ceramic undergoing the order–disorder phase transition, while the soft mode phenomena denotes a displacive phase transition of ferroelectric materials. The low-frequency B₂(TO₁) mode near 58 cm⁻¹ is found in the orthorhombic phase of pure KNN ceramics, while the overdamped E(TO₁) mode near 91 cm⁻¹ is observed in the mixed (orthorhombic + tetragonal) phases of the KNN–xBST (0.025 ≤ x ≤ 0.15) in this study. It is difficult to comment on the soft-mode nature of the low-frequency B₂(TO₁) and E(TO₁) modes without temperature-dependent Raman scattering results. Thus, the presence of noticeable CP may indicate the order–disorder nature of the ferroelectric phase transition of KNN–xBST ceramics^40,41,46. In the paraelectric cubic phase of ferroelectric materials, the dynamic PNRs start to appear at the so-called Burns temperature (T_B)⁴⁷. However, dynamic PNRs turn into static PNRs at an intermediate temperature (T^*)^40,41. In ferroelectric phases, these static PNRs develop into randomly oriented nano-domain states and transform into macro-domain states due to the freezing of local polarization^48,49. As can be seen in the lower part of Fig. 3d, the Γ_CP, which is related to the relaxation process of precursor dynamics^40,41,46 increases at x = 0.025, is almost constant in the region; 0.025 ≤ x ≤ 0.15, and then increases when x increases to 0.30. It is expected that the correlation among nano-domain states may be strengthened in the same phase with increasing the BST concentration, owing to the increase of the number density and/or size of randomly oriented nano-domain states resulting in a decrease in the value of the Γ_CP^6,50. Note that the value of Γ_CP increases with the BST composition except in the range of 0.025 ≤ x ≤ 0.15 composition. The increase of the Γ_CP denotes the structural phase transition of KNN–xBST. It is significant that the value of Γ_CP is almost constant in the range of 0.025 ≤ x ≤ 0.15, where KNN–xBST belongs to (orthorhombic + tetragonal) phases. These results suggest that the correlation among nano-domain states may be broken and/or weaken resulting in the almost constant fluctuations of domain wall motion due to the coexistence of phases⁶.

Microstructural studies

The surface morphology of the ceramics was studied with FESEM. Figure 4 shows the selected FESEM micrographs of the (1 − x)KNN–xBST ceramics for x = 0, 0.025, 0.10, and 0.20 respectively (other compositions are shown in the Supplementary Material, Fig. S6). The FESEM image for KNN (x = 0) shows that due to abnormal grain growth, the microstructure consists of grains of different sizes because grain growth is different for different grains²⁵. The well-defined grains for x = 0 suggest that the grain growth process is almost complete during the sintering process. However, the presence of few scattered pores cannot be avoided. The grain size decreases with an increase in BST concentration indicating that abnormal grain growth is reduced with BST²⁵. The addition of BST results in a compact microstructure and uniform distribution of grains. The uniform fine-grained microstructure is suitable for higher mechanical strength and high electro-mechanical coefficient⁵¹. The average grain size is calculated using ImageJ software and it is found to be 2.52 μm (for x = 0). With increasing BST concentration the grain size reduces and for the higher BST compositions, the average grain size is calculated to be in the range 0.38–0.17 μm. See the summary of grain sizes in Table S3 in the Supplementary Section. We have measured the density of the ceramics by Archimedes’ principle. The density of the ceramics varies from 94 to 96% of the theoretical density.

Figure 4

FESEM micrographs of the (1 − x)KNN–xBST ceramics for (a) x = 0, (b) x = 0.025, (c) x = 0.10, (d) x = 0.20.

Dielectric studies

The variation of dielectric constant (ε_r) and loss tangent (tanδ) as a function of temperature (T) at different frequencies were investigated to study the ferroelectric phase transition behavior in (1 − x)KNN–xBST solid-solutions (Fig. 5). The temperature dependence of the dielectric constant and loss tangent for x = 0, 0.025, 0.05, 0.15 and 0.20 at selected frequencies of 1 kHz, 5 kHz, 10 kHz, 50 kHz, and 100 kHz are shown in Fig. 5a–e (other compositions are shown in the Supplementary section, Fig. S7). The dielectric constant decreases with increasing frequency regardless of composition and temperature, which is a characteristic feature of polar dielectric materials⁵.

Figure 5

Variation of ε_r and tanδ as a function of temperature at selected frequencies of (1 − x)KNN–xBST ceramics for (a) x = 0, (b) x = 0.025, (c) x = 0.05, (d) x = 0.15, (e) x = 0.20 and (f) comparision of dielectric constant with temperature for all compositions at 10 kHz.

For pure KNN (x = 0), the ε_r versus temperature plot shows an increased value of ε_r with an increase in temperature, along with the appearance of two distinct anomalies in the measured temperature range. The first small anomaly around 210 °C corresponds to an orthorhombic to tetragonal (T_O-T) phase transition, while the sharp peak around 405 °C relates to the ferroelectric tetragonal to paraelectric cubic phase transition (T_C)^13,14. The temperature-dependent dielectric loss also shows anomalies around the same temperatures, which is shown in the inset of Fig. 5a. The appearance of a peak in the temperature-dependent dielectric constant (ε_r) and loss tangent (tanδ) confirms the ferroelectric phase transitions. For the ceramics with x = 0.025 and 0.05, the two anomalies corresponding to T_O-T and T_C are observed similar to x = 0 (Fig. 5b,c). However, both the T_O-T and T_C shift to the lower temperature and the tetragonal-cubic transition peaks broaden. Compared to 210 °C for pure KNN, the T_O-T is reduced to 170 °C for x = 0.025 and 85 °C for x = 0.05. Furthermore, the T_C values shift to 375 °C and 325 °C for x = 0.025 and x = 0.05, respectively; suggesting the possibility to lower the T_O-T to room temperature at higher BST concentration.

As the BST content increases further, the ε_r versus T plot for x = 0.10 and 0.15 do not show any phase transition corresponding to T_O-T and the only peak corresponding to tetragonal-cubic transition is observed (Fig. S7a, Fig. 5d). This suggests that, T_O-T shifts below the room temperature and the T_C value is found to be 220 °C and 130 °C for x = 0.10 and 0.15 respectively. However, the ε_r versus T plot for x = 0.20 does not show a clear transition corresponding to T_C, which suggests that the material is in the paraelectric phase at RT. For x = 0.20, though Rietveld refinement of the XRD data shows the existence of both tetragonal and cubic phases (P4mm + $Pm\overline{3 }m$), however, the tetragonal phase fraction is quite low. Therefore, the dominant contribution from the cubic symmetry is responsible for the paraelectric phase at RT. For higher concentrations of BST i.e. for x = 0.3, the phase transition corresponding to T_C is also not visible (Fig. S7b), which may suggest that T_C decreases and shifts below the room temperature, which is beyond the investigated temperature range in the present study. The disappearance of the paraelectric-ferroelectric phase transition peak in the ε_r versus T plot suggests the cubic structure of x = 0.3 at room temperature which agrees with the XRD data.

For a clear observation of the effect of BST substitution on KNN ceramic, the temperature dependence of ε_r for the ceramics with 0 ≤ x ≤ 0.3 is plotted at a constant frequency of 10 kHz, which is shown in Fig. 5f where the inset is a plot of ε_r versus T for x = 0. Therefore, it can be concluded that, both T_O-T and T_C decrease systematically with the increase in BST concentration in KNN.

To confirm the nature of phase transition (normal/relaxor type), we have fitted the temperature-dependent dielectric permittivity data in the paraelectric region using modified Curie Wiess law. The modified Curie–Weiss equation^2,6 can be expressed as

$$\frac{1}{{{\upvarepsilon }_{r} }} - \frac{1}{{{\upvarepsilon }_{m} }} = \frac{{\left( {T - T_{C} } \right)^{{\upgamma }} }}{C},$$

(3)

where ε_m = maximum value of ε_r at T_C, C = modified Curie Weiss constant, and γ = degree of diffuseness. The value of γ can be found from the slope of the ln(1/ε_r − 1/ε_m) versus ln(T − T_m) plot and it varies from 1 to 2. The degree of diffuseness for normal ferroelectric materials is found to be 1, while it is 2 for very diffuse/relaxor type ferroelectric^2,6.

The degree of diffuseness upon BST substitution in the present case has been extracted from the graphs of ln(1/ε_r − 1/ε_m) versus ln(T − T_m) at 10 kHz for the (1 − x)KNN–xBST ceramics (0 ≤ x ≤ 0.15) and are plotted in the paraelectric region as shown in Supplementary Fig. S8. From Fig. S8, the linear fit suggests that the modified Curie–Weiss law is satisfied. For x = 0, the value of γ is found to be 1.14, and the γ value increases with an increase in BST concentration (for example, γ = 1.77 for x = 0.15). The increase in γ value with ‘x’ represents the escalation in the diffuse phase transition, which suggests the relaxor-like behavior of the (1 − x)KNN–xBST solid solution⁵².

Ferroelectric and piezoelectric properties

Ferroelectric properties of the (1 − x)KNN–xBST ceramic solid solutions were studied through the polarization versus electric field hysteresis loop (P–E loop) measurements at room temperature. The electrical poling close to the coercive field has been done prior to the P–E hysteresis measurements. The reason behind this pre-poling process is to orient the dipoles to obtain a net polarization in the material. It has been already reported that due to such electrical poling, the octahedra become more stable as it reduces the local structural heterogeneity and promotes long-range ferroelectric ordering. This, in fact, results in well-saturated ferroelectric hysteresis loops as can be seen elsewhere^2,8.

Figure 6 shows the RT P–E hysteresis loop of poled KNN-BST ceramics (0 ≤ x ≤ 0.15) at a frequency of 5 Hz. The P–E loop of pure KNN (x = 0) shows well-defined and non-linear behavior which suggests the ferroelectric nature. The partial unsaturated shape of the upper portion of pure KNN is due to the leakage through the large capacitive area with lossy-like behavior. However, with an increase in BST concentration, the area of the hysteresis loop decreases systematically. The PE loop for KNN (pure) showed higher 2P_r and E_C values compared to BST modified samples. By comparing the P–E hysteresis loops in different crystallographic phases for the KNN system, it has been reported that the remnant polarization (2P_r) and coercive field (E_C) are higher in the orthorhombic phase compared to the other crystallographic phases similar to the report of Shirane et al.⁵³. For higher BST concentration i.e. for x = 0.2 and 0.3, we did not observe any saturated loops because of the paraelectric nature of the ceramics at room temperature. The ferroelectric parameters such as remnant polarization (2P_r) and coercive field (E_C) were calculated using the formula ${2P}_{r}^{0}= {P}_{r}^{+0}-{P}_{r}^{-0}$ and ${2E}_{C}^{0}= {E}_{C}^{+0}-{E}_{C}^{-0}$ and their variation with compositions along with the correlation with other physical properties will be discussed below.

Figure 6

Ferroelectric hysteresis loop of poled samples of (1 − x)KNN–xBST ceramics at RT.

In order to study the effect of BST addition on the physical properties of (1 − x)KNN–xBST solid solutions, piezoelectric coefficient (d₃₃), ferroelectric parameters (2P_r and E_C) and dielectric constant (ε_r) at room temperature were compared for different BST concentrations. Figure 7 shows the variation of dielectric constant, coercive field, remnant polarization and piezoelectric coefficient with x for the (1 − x)KNN–xBST ceramics with 0 ≤ x ≤ 0.3. For pure KNN (x = 0), the dielectric constant at RT is found to be 268. With increasing BST concentration, the dielectric constant, ε_r increases initially and reaches a maximum (ε_r = 672) for x = 0.1. After that, the ε_r versus x graph shows a gradual decrease in ε_r value up to x = 0.20 and then saturates. On the other hand, the ferroelectric properties (2P_r and E_C) decrease with an increase in BST content. For pure KNN, relatively high 2P_r (28.15 μC/cm²) and high E_C (11.18 kV/cm) values are observed which may be due to the orthorhombic phase of KNN. With increasing BST concentration the E_C value decreases, is a minimum for x = 0.1 (E_C = 8.06 kV/cm) and subsequently it slightly increases. Similarly, the remnant polarization decreases with increasing x, and for x ≥ 0.05 it becomes nearly constant. Thus, with the addition of BST, the ferroelectric parameters decrease. However, the piezoelectric coefficient (d₃₃) increases; for pure KNN, the d₃₃ is found to be 61 pC/N. As the BST content increases, d₃₃ increases sharply to 96 pC/N for x = 0.025, becomes maximum and after that, it decreases slowly with further increase in x.

Figure 7

Variation of (a) dielectric constant, (b) coercieve field, (c) remnant polarization, and (d) piezoelectric coefficient with x for (1 − x)KNN–xBST ceramics at room temperature.

The piezoelectric coefficient d₃₃ for perovskite-based ferroelectric materials can be represented by the formula^54,55

$$d_{33} = 2Q_{11} {\upvarepsilon }_{0} {\upvarepsilon }_{33} P_{3} ,$$

(4)

where P₃ = polarization along the polar axis and approximately equals to P_r in this case, ε₀ = dielectric permittivity in free space, ε₃₃ = ε_r is the dielectric permittivity, and Q₁₁ = electrostrictive coefficient which varies between 0.05 and 0.1 m⁴ C⁻²⁵⁵. In the present case, with increasing BST concentration the ε_r increases and at the same time, 2P_r decreases (for the low value of x) due to the decrease in phase transition temperature. Since d₃₃ is directly proportional to ε_r, the increased value of ε_r leads to enhancement of d₃₃. At the same time due to the direct dependence of d₃₃ on P_r, because P_r decreases linearly with x, d₃₃ turns over and decreases for x > 0.025. Thus, the observed enhancement of d₃₃ for x = 0.025 as expected is due to the simultaneous contribution from both increased ε_r and decreased value of 2P_r. So the d₃₃ value is a competition between these two parameters. A similar type of variations has also been observed in BT-modified KNN System¹³.

The detailed study correlating the structural phase transition behavior is presented in the phase diagram of (1 − x)KNN–xBST solid solutions as shown in Fig. 8. This phase diagram has been drawn based on the room temperature X-ray diffraction, Raman spectroscopy studies and the temperature-dependent dielectric properties discussed before. Pure KNN crystallizes in the orthorhombic structure (SG: Amm2) at RT. The phase diagram consists of a paraelectric cubic phase for the high temperature at a lower concentration of BST and at RT for a higher concentration of BST in (1 − x)KNN–xBST solid solutions.

Figure 8

Phase diagram of (1 − x)KNN–xBST ceramics for 0 ≤ x ≤ 0.3. The labels O, T, and C denote orthorhombic, tetragonal and cubic phases respectively.

With increasing BST concentration, KNN transforms from orthorhombic to phase coexistence region (i.e., orthorhombic + tetragonal), then to (tetragonal + cubic) phases and finally to cubic phase for x ≥ 0.25 (based on the XRD and Raman data). The phase coexistence region of the orthorhombic + tetragonal phase (0.025 ≤ x ≤ 0.15) forms a pentagon region above the pure orthorhombic phase. On the other hand, the coexistence region tetragonal + cubic forms a triangle below the cubic phase. In the coexistence region of the orthorhombic + tetragonal phase, the phase formation of the tetragonal phase increases with increasing BST composition and transforms to the tetragonal + cubic coexistence phase at x = 0.15. Finally, it transforms to a cubic phase at x ≥ 0.25. With increasing temperature, the orthorhombic phase of KNN transforms to the tetragonal phase and finally to the cubic paraelectric phase. However, the orthorhombic + tetragonal phase coexistence region transforms to the tetragonal phase and finally to the cubic phase. Similarly, the phase coexistence region of the tetragonal + cubic phase transforms to a cubic phase with increasing temperature.

Conclusions

In summary, the effect of BST concentration on the structural, morphological, dielectric, ferroelectric and piezoelectric properties of (1 − x)KNN–xBST ceramics has been investigated over a wide range of compositions (0 ≤ x ≤ 0.3). The XRD and Raman spectroscopic studies suggest a compositional-driven structural phase transition from the orthorhombic (Amm2) phase to the orthorhombic + tetragonal (Amm2 + P4mm) phase, then to the tetragonal + cubic (P4mm + $Pm\overline{3 }m$) phase and finally to cubic ($Pm\overline{3 }m$) phase with increase in BST concentration at room temperature. For pure KNN, the temperature-dependent dielectric properties show two phase transitions i.e., orthorhombic to tetragonal (T_O-T) phase transition and tetragonal to cubic phase transition (T_C). Both the phase transition temperatures decrease with increasing BST concentration and for x ≥ 0.1, T_O-T is expected to be below the RT. The dielectric constant at RT increases with BST concentration up to x = 0.1 and after that, it decreases. The ferroelectric hysteresis loop shows ferroelectric behavior up to x = 0.15 and paraelectric behavior for x = 0.25 and 0.30. The observed decrease in 2P_r and E_C values with an increase in BST concentration can be attributed to the centrosymmetric paraelectric phase of BST. A maximum piezoelectric coefficient (d₃₃ = 96 pC/N) was observed for x = 0.025. A phase diagram has been presented based on the temperature-dependent dielectric, RT XRD, and Raman data.