Sub-switching domain effect for analysis the non-linear dielectric behavior of (K0.49 Na0.49Li0.02) (Nb0.98Sb0.02)O3 ceramic based on Rayleigh model

The solid-state sintering technique has been implemented to synthesize (K0.5Na0.5NbO3)-0.02(LiSbO3) (KNN-LS) Pb-free ceramic. The crystal structure, dielectric and ferroelectric properties of the prepared material were investigated. Pure orthorhombic perovskite phase [I(220)/I(002) = 1.68] with Amm2 space group has been detected at room temperature for sintered ceramic. Two anomalous permittivity peaks corresponding to orthorhombic–tetragonal (O–T) phase transition at T = 175 °C and tetragonal–cubic (T–C) phase transition at T = 355 °C have been observed. At polymorphic phase transition, the Rayleigh model shown the extrinsic contributions caused by domain wall motion is about 80%, while the intrinsic contribution attributed to the lattice distortion is about 20%. Ferroelectric properties were investigated in a wide range of temperatures (RT-225)°C. The results shown a conductive material at high temperature due to the higher cation disorder and leakage current above PPT. The present results are interested for understanding the mechanism of t permittivity–temperature behavior of KNN-doped LS ions based on Rayleigh model. The large remnant polarization and low coercive field below PPT make the material a suitable candidate for energy storage application.


Introduction
Ferroelectric ceramic materials are widely used in several electronic applications, such as sensors, actuators, and transducers [1][2][3][4][5][6][7]. Owing to the environmental restrictions on lead-based materials and their high toxicity, (K 1-x ,Na x ) NbO 3 has drawn much attention as promising lead-free candidates materials instead of lead-based such as PZT due to its excellent performance [8][9][10][11][12]. When x = 0.5, the system shown an outstanding piezoelectric property due to form morphotropic phase boundary (MPB) as a contributed to orthorhombic-tetragonal phase coexistence or a combination KNbO 3 ferroelectric with NaNbO 3 anti-ferroelectric at room temperature. Furthermore, it has a high Curie temperature > 400 °C which makes the material as a suitable candidate for a piezoelectric applications in a wide range of temperature [13]. However, the volatilization of alkali components at high sintering temperature is the most drawback of this system [14]. Therefore, several numbers of researches have been paid attention to improve the functional properties and sinterability of KNN to be more applicable as piezoelectric materials. The enhancement procedures are doping the material with ferroelectric materials, such as BaTiO 3 , (Bi,Na)TiO 3 [15], SrTiO 3 [16], etc., non-ferroelectric materials, such as LiNbO 3 , LiTaO 3 , LiSbO3 [16]. Moreover, the shift of the polymorphic phase transition (PPT) to near room temperature has resulted in a significant improvement in dielectric and piezoelectric characteristics [17]. In general, the dielectric and piezoelectric responses are almost always non-linear and hysteretic behavior. It is well understood, dielectric activity can be generally conducted by 1 3 intrinsic and extrinsic contributions; the intrinsic contribution demonstrates the dielectric response due to lattice distortion and domain wall propagation, which always reversible when applying external electric fields. On the other hand, the extrinsic contribution, might be attributed to the reversible or irreversible movement of the domain walls or phase boundaries motion [18,[18][19][20][21]. However, near T O-T dielectric properties have several limitations, such as excessive temperature influence of piezoelectric characteristics, which is a major drawback for commercial applications. Understanding the dielectric response at polymorphic phase transitions is critical for improving the thermal stability of KNN-based ceramics. Furthermore, few studies that have a considerable impact on their practical applications have been conducted. As a result, additional investigation is required. To solve the previous issues, the Rayleigh model is being used in the domain's sub-switching region. Furthermore, Rayleigh law has been applied in textured KNN ceramics with high level of parallels to the external electric field and the results reported increased the dielectric response due to lattice deformation effect [22]. Recently, Bin Peng et al. evaluate domain wall motion in (K 0.5 Na 0.5 ) NbO 3 during polymorphic phase transition [23]. On the other hand, whereas ferroelectric materials offer a wide variety of uses in energy inter-conversion based on the ease with which the polarization and coercive field may be changed with temperature. The present work introduces an overview for understanding the dielectric nonlinearity mechanism of KNN-LS ceramic using the Rayleigh model at sub-coercive electric fields and extract the dominant contribution of intrinsic and extrinsic value to dielectric characteristics near polymorphic phase transitions (PPT). Furthermore, mechanisms on ferroelectric properties in the over wide range of temperatures were investigated.

Preparation and characterization
The 0.98 K 0.5 Na 0.5 NbO 3 -0.02LiSbO 3 (abbreviated as KNLNS) ceramics were fabricated via the conventional solid-state reaction method. For 12 h, the raw materials K 2 CO 3 (99%), Na 2 CO 3 (99.8%), Nb 2 O 5 (99.5%), Li 2 CO 3 Sb 2 O 5 (99.99%) were ball-milled. The mixture was dried and calcined at 850 °C for 2 h. The calcined powders were then uniformly crushed into pellets with a diameter of 10 mm and a thickness of 1-1.5 mm. The powders were then thoroughly mixed with polyvinyl alcohol (binder) and granulated to obtain a harmonious mixture to proceed with the sintering. At 1090.0C for 3 h with a heating rate of 5 • C/min, the pressed pellets were sintered to air and then cooled to room temperature at 5 • C/min. In the air, all calcination and sintering steps were carried out. The compositional crystal structure was examined at an angle of two thetas from 20° to 70°, using an X-ray diffractometer(XRD) (Philips diffractometer PW 3020) with monochromatic CuKα (Ţ = 1.54178 Å). The microstructure was observed using a scanning electron microscope (SEM, JEOL JSM-5500LV, scanning microscope JEOL). Electrical characterizations were performed using silver electrodes that fired at 850 °C for 30 min. The dielectric sample measurements were performed using the LCR meter as a function of frequency and temperature. The ferroelectric properties estimated by the P-E loop of sintered ceramic were measured at a wide range of temperatures (RADIANT Precision Premium II Multiferroic Ferroelectric Test System 10 kV HVI-SC Model 609B) Ferroelectric measurement system.

Phase structure and microstructure properties
The room temperature patterns of X-ray diffraction (XRD) for (0.98) [(K 0.5 Na 0. 5)NbO 3 ]-0.02 LiSbO 3 calcined powder and sintered ceramic were performed and the patterns were displayed into Fig. 1. As observed, a pure perovskite structure with no obvious any track for secondary phase or additional peaks into calcined powder pattern within the detectable limit of the XRD, indicates that 0.02 LS has diffused successfully entirely the KNN lattice to form KNN-LS solid solution. The diffraction peaks were cited from KNN with orthorhombic symmetry (PDF# 71-0946) and (Amm2) space group. As it is well known, the ionic radius of Li + (1.23 Å) is very close to the ionic radius of Na + (1.39 Å) and, K + (1.6 Å), so it is suitable to occupy the A site of KNN lattice, while the ionic radius of Sb 5+ is (0.6 Å) is very close to the ionic radius of Nb 5+ (0.69 Å), so it is suitable to occupy the B site of KNN lattice [2]. The Bragg reflections of the sintered ceramic at 1080 °C/2 h shown the same pattern of calcined powder indicate the thermal stability of compound at high sintering temperature. A complete solid solution with pure perovskite phase and orthorhombic structure was attributed to the low melting points of Li 2 CO 3 (723 °C), and Sb 2 O 5 (380 °C) make the KNN-LS ceramics form a complete solid solution with pure perovskite phase and orthorhombic structure. To investigate the effect of Li + , Sb +5 ions and thermal processing calcination/sintering conditions have any influence on the orthorhombic/tetragonal structure of KNN, we can use the following formula (Eqs. 1, 2).
(1) Orthorhombic = where I hkl represents the intensity of the corresponding peaks (hkl), and the ratio is estimated to be 1.7 for pure orthorhombic phase and 0.53 for tetragonal phase [24]. The equation shown the value is 1.85 for KNN-LS powder and 1.7 for sintered ceramics which reveal that the KNN-LS modulate its orthorhombicity by sintering processing.  boundary size of pure KNN [25] could be owing to the lower ionic radius of Li and Sb ions comparable to the ionic radius of Na, K and Nb ions which prohibit materials for grain growth process. The lower grain boundary is contributed in decreasing the sintering temperature from 1100 °C for pure KNN [26] to 1080 °C for the present sample. Furthermore, lower melting point of Li 2 O 3 720 °C and melting point of Sb 2 O 5 is 380 °C can also responsible for reducing the sintering temperature of KNN. Therefore, when the sintering temperature decreased, it could not provide the enough energy for the grain growth process.The obvious liquid phase and porosity exist into grain boundary are due to Na 2 O volatilization during the sintering process lead to a deviation from stoichiometry phase and porosity exist into grain boundary are due to Na 2 O volatilization during the sintering process lead to a deviation from stoichiometry. The analysis on the grain size distributions of KNN-LS ceramics is shown in Fig. 5. The average grain size of pure KNN ceramics is approximately 2.26 μ m [27], which were calculated using the grain size distribution. On the other hand, the average grain size of KNN-LS ceramics is 2.2 μ m and grain growth is typically dependent on grain boundary mobility; however, the pores are the most important factor influencing grain boundary mobility.

Dielectric properties
The temperature dependence of permittivity for KNN-LS sintered ceramic at 1080 °C/2 h measured at different frequencies (1, 100, and 1000 kHz) is shown in Fig. 3. In agreement with the previously reported works, the permittivity vs. temperature curve is revealed two anomalies permittivity peaks corresponding to orthorhombic where the permittivity increased with increasing the applied electric field. Figure 5 depicts the dielectric permittivity ′ E 0 dependancey on electric field at different temperatures. The figure revealed an essentially linear relationship of permittivity as a function of electric field and both of intrinsic and extrinsic coefficients can be obtained from these relation, Furthermore, to clarify the largest dielectric response of the present ceramic at polymorphic phase transition point, the changes of reversible and irreversible coefficients corresponding to temperature have been displayed into Fig. 6.
The results indicate that the temperature strongly influences the intrinsic and extrinsic values during both the orthorhombic phase and the polymorphic phase transition (PPT). The irreversible coefficient α caused by domain wall motion is increased with temperature and possess the maximum value at 175 °C. When the sample heated above T O-T , the α value declines significantly and possesses the minimum value around 200 • C, this behavior is attributed to the clamping effect which grow in the tetragonal phase [23], In addition, there are two factors related to domain walls that influence the irreversible response: domain wall mobility and domain wall density. Moreover, a large number of the domain walls may reduce the domain wall mobility, which may counteract the effect of the domain wall density [28,30], Furthermore, lattice distortion and internal stress may increase during the polymorphic phase transition, and the number of domain walls may increase to minimize the internal stress, as a result, the α magnitude reduces dramatically. In contrast, the initial permittivity reaches the maximum at 200 • C. Figure 6(a) also demonstrates that above 200 °C, the initial permittivity decreases dramatically as the temperature rises, which is ascribed to the increase in domain wall density [30], which reduces spontaneous distortion. In contrast, we can see that as the temperature rises, the Rayleigh coefficient rises again; this is because the temperature is adequate to enhance the mobility of the domains (as we know that the domain walls are thermally activated). However, the increase is not significant because of the large number of domain walls, which clamp the mobility of domains. Figure 6(b) refers to the terms .E 0 ∕ � E 0 and init E 0 ∕ ′ E 0 which are calculated to determine the ratio of the intrinsic contribution from the reversible lattice distortion and extrinsic contributions from the irreversible domain wall movement to the total dielectric response. As shown in Fig. 6(b), the ratio .E 0 ∕ � E 0 represents about 80% of the total permittivity at PPT. Once the temperature rises above 175 • C, the domain wall mobility may decrease due to the increasing domain wall density during polymorphic phase transition, which also results in a decrease in the value and the Fig. 3 Dependence of dielectric constant (ɛ) on temperature (measured at 10,100 and 1000 kHz) for KNLNS ceramics to tetragonal phase transition at lower temperature (T O-T = 175 °C) and tetragonal-cubic phase transition at higher temperature (T T-C = 355 °C). The relative decreasing of phase transition temperatures values compared to pure KNN are attributed to that as previously reported [26], Nb 5+ with Sb 5+ reduces Tc.

Rayleigh analysis
The dielectric response in ferroelectric materials usually nonlinear under external electric field can be adequately described using Rayleigh relations Eqs. (3,4) [28,29] at sub-switching of domain at low amplitude of electric. The Rayleigh model assumed that dielectric activity can be divided into intrinsic and extrinsic contributions, where the intrinsic contribution reflects the lattice distortion or domain wall propagation, while the extrinsic contribution can be ascribed to the domain wall displacement and as consequently the domain grows.
where E is the applied electric field corresponding to maximum amplitude E 0 , P refers to the polarization under the applied electric field. The coefficient ′ init represents the intrinsic contribution of dielectric response and the Rayleigh coefficient. Irreversible domain wall mobility or extrinsic coefficient is denoted by E 0 [28,29]. Figure 4 shows the '(P-E) hysteresis loops' in a series amplitude of electric field (2-6 kV/cm) in the wide range of temperature (RT-225 °C). All hysteresis loops can be well fitted by Rayleigh Eq. (4), The typical measured and calculated P-E hysteresis loops for KNLNS ceramics during a wide range of temperatures ratio .E 0 ∕ � E 0 . On the other hand, the ratio init E 0 ∕ ′ E 0 represents about 20% from the total permittivity. As a result, the irreversible domain wall motion is the major contributor at the coexistence point between orthorhombic and tetragonal phases (PPT).

In-situ Ferroelectric characterization at switching region
One of the most essential components in current applications, such as sensors, electronic devices, and energy storage, is to investigate the ferroelectric characteristics at a wide range of temperatures to enhance the thermal stability. Figure 7 shows the polarization and current-dependent electric field of KNN-LS sintered ceramic at various temperatures (RT-225 °C). The polarization and current hysteresis loops show normal ferroelectric loop from RT up to PPT temperature (175 °C), then a conductive P-E loop combined with high conductivity current has been conducted at high temperature > 175 °C. The maximum current value into (I-E) loop corresponding to coercive field (E c ) is attributed to the domain switching contribution [31]. Decreasing the remnant polarization with temperature might be owing to disturbance of the atoms from their equilibrium positions and as consequently increasing the degree of cations disorder. Furthermore, increasing the thermal activation leads to pinshed the ferroelectricity and as consequently decrease the P r value at high temperature. The decreasing into E c value at high temperature is attribute to retraction of the domain size caused by the domain motion effect. While decreasing the domain switching current by increasing temperature could be related to dilution of the degree of orthorhombic phase and as consequently increase of the crystal lattice symmetry. As shown in Fig. 8, above 150 • C, we can observe that the remnant polarization and the coercive field increases attributed to the great value of domain switchability at higher temperature [32]. In contrast, the conductivity current at high applied field was observed to be increased by the temperature increase of above 225 • C. This could be attributed to the high leakage current and dielectric loss values at high temperature ( Fig. 9), due to the dependence of spontaneous polarization, Ps, dielectric permittivity loss and conductivity of ferroelectric materials on temperature [33].

Conclusion
In conclusion, (K 0.5 Na 0.5 NbO 3 )-0.02(LiSbO 3 ) (KNN-LS) lead-free ceramic was synthesized by solid-state sintering technique. The maximum values of permittivity peaks are attributed to (O-T) at PPT and (T-C) at Curie temperature. Rayleigh analysis shows the largest permittivity value at polymorphic phase transition and is attributed to the largest value of extrinsic contributions caused by the domain growth effect. Ferroelectric properties dependent on various temperatures show increase in the coercive field, dielectric loss and leakage current at high temperature. Based on the present results, material is a suitable candidate for energy storage application due to the large remnant polarization and low coercive field below PPT.   6 a The initial dielectric permittivity ( init ), the dielectric Rayleigh coefficient ( ) and total permittivity ′ E 0 . b The ratio .E 0 ∕ � E 0 (irreversible contribution) and the ratio init E 0 ∕ ′ E 0 (reversible contribution)for KNN-0.02LS ceramics Fig. 7 The temperature dependence of P(E) hysteresis loops and I(E) loops for KNN-LS ceramic