3.1-Crystal structure analysis
Fig. 1(a) shows the x-ray diffraction patterns of (BKNT –xST– BCT) calcined powder at 850°C for 4h. It is clear to notice that all patterns shows a single perovskite phase and no track for detection second phase under detection limit of XRD confirm diffuse both of BCT and ST into BKNT lattice to form BKNT-ST-BCT solid solution. Moreover the patterns were observed shift to lower angle at high content of ST implying increasing the particle size Fig. 1(b) shows XRD patterns of the sintered ceramics at 1130oC for 4h. It is obvious that all compositions possess a pure perovskite crystal structure in whole range of angles. ST shown greatly effect into the crystal structure of BKNT where by enlarged XRD patterns two peaks corresponding (002)/(200) ferroelectric phase with tetragonal structure were detected at low content of ST (0.0, 0.05, 0.1) while only single peak corresponding (200) re1axor phase was observed at (ST=0.15 and 0.2). This suggests that Sr2+ disrupt the long-range order of ferroelectric phase and as consequently resulting short range order with polar nano-range of re1axor phase. In the present system we substitute Na+1, K+1 and Bi3+ by Sr2+ into A-site of lattice promoting oxygen vacancies in the sample so that the random bond disorder is caused by oxygen vacancies and the domain wall displacement becomes limited due to the domain wall pinning. On the other hand present Sr2+ into the A-sites of lattice lead to compositiona1 fluctuations, structura1 disorder in equiva1ent crysta11ographic fluctuations and as consequently the lattice distortion will be more dominated than wall displacement as intrinsic contribution.
Fig .2. shows the surface morphology of BKNT-x ST-BCT sintered ceramics (x=0.0-0.2) at 1130oC for 4h. It can be observed that a small pores exist to grain boundary has been observed into the morphology of ST=0.0, however the other compositions exhibit more dense of microstructure and uniform grain boundaries indicating enhancement the microstructure of BKNT by ST addition. The pores-free at high concentration of ST is very useful and important for dielectric, piezoelectric and ferroelectric properties. The porous effect can be an easy way for increasing the current conduction and dielectric loss and as consequently increase the coercive field [17]. On the other hand it is worth to noting that the shape of grain boundary is completely changed from normal ferroelectric with cubic shape of grain of BKNT at (x≤0.1) to re1axor grain of BKNT-ST (at x≥0.15) with larger size rather than the other compositions confirmed XRD pattern Fig (1.b).
3.2-Dielectric characterizations
Fig .3 shows the temperature dependence of dielectric constant εr and dielectric loss tan(δ) for (0.95- x)(BKNT)- x(ST)-0.05BCT (x=0.0-0.2) virgin sintered ceramic compositions measured at different frequencies between (RT-450oC). Two distinctive anomalies dielectric peaks corresponding to ferroelectric to re1axor diffused phase transition at low temperature (Tfr) and re1axor to paraelectric phase transition at high temperature (Tc) have been detected for all compositions belong (x≤0.15), while only one permittivity peak is detected in whole range of temperature corresponding to re1axor - paraelectric phase transition at Curie temperature at x=0.2. The two dielectric anomalies are probably associated with the evolution of polar nanoregions (PNRs) with different symmetry [18]. At lower temperature, the permittivity strongly dependent the applied frequency while above the hump peak no obvious change on dielectric constant with frequency confirm present the re1axor behavior. High phase transitions indicate that the present compositions have promising prospects in high temperature sensor applications such as piezoelectric sensors. The second phase transition is clearly decreased by increasing ST-content (Tc=325oC at ST=0.0, Tc=115oC at ST=0.2) however no obvious clear trend for affected Tfr by ST addition which it could be due to the compositional fluctuation at low temperature. Dielectric loss dependence temperature and frequency as well was studied for all compositions where all the present samples shown low value of dielectric loss compare to pure BNT at room temperature [19] which indicates that the BKNT-ST-BCT ceramics are a promising candidate for energy storage applications. Moreover decreasing the value of tan loss is a good indication for decreasing the coercive field and as consequently enhanced the poling conditions for pure BNT ceramic. Fig 4. shows variation dielectric permittivity and dielectric loss tan(δ) with temperature for (0.95-x)(BKNT)- x(ST)-0.05BCT (x=0.0-0.2) poled sintered ceramic at high amplitude of applied electric field (E=60kV/cm) for 30min close to phase transition temperature of each compound as a poling conditions. All compositions belong (x≤0.15) shown the same behavior of virgin samples with a little bit change into the temperature of ferroelectric relaxor diffused phase transition. The hump peak of ferroelectric to relaxor transition was observed shifted to higher temperature for poled samples indicate increase the degree of long-range ordering, increase the domain size and ferroelectricity phase by applied high electric field. The ST=0.2 poled sample shown different behavior compared to virgin sample however it shown a similar behavior compared to (x≤0.15) samples. The first phase transition at depolarization temperature indicate present ferroelectric to re1axor phase transition while the second peak is due to re1axor to paraelectric phase transition. this indicate the domain grow caused by domain wall displacement and the motion of interphase boundaries as an extrinsic contribution at high electric field.
3.3. Rayleigh Analysis
3.3. 1. Extrinsic contributions
Fig. 5(a) shows polarization dependent electric field (P-E) hysteresis loop with low amplitude of sub-switching field (1-10kV/cm) at different temperatures (25-185oC) i.e. in ferroelectric and relaxor phase regions of ST=0.0 virgin sintered ceramic. It is clear to notice that the measured data of P-E loop can be well fitted by Rayleigh equation which can confirm the applied field undergo the Rayleigh region and the domain structure unchanged at these fields. All measured curves belong (T≤100oC) shown normal ferroelectric P-E loop where the area loop clearly increases with increasing amplitude field while all curves measured at (T>100oC) shown present a relaxor phase with slim P-E loop. These results are agreements with dielectric-temperature curves (Fig 3). Fig. 5(b) shows relative dielectric constant dependent electric field at different T which calculated from the relation [εr = Pmax/Emax]. It can observe that a linear relationship between permittivity and applied electric field in whole range of T which indicate the results are agreement with (eq 2.) of Rayleigh relationship. Then, we further obtain both of intrinsic coefficient (εrintri) and extrinsic coefficient α from permittivity-electric field relation at each temperature. according to eq 2. In order to understand the mechanism of permittivity behavior, temperature dependence both of reversible (εrintri) and irreversible (α) coefficients have been displayed into Fig. 5(c). The figure shown that both of intrinsic and extrinsic coefficients increases with T producing a maximum value at Tfr. The red dash curve represent real permittivity values obtained from (ε-T) curve at 100Hz (Fig. 3). We can see the real permittivity shown the same behavior of intrinsic and extrinsic coefficients curve where the anomalous peak of permittivity was observed at Tfr as well. However as the composition shown form ferroelectric phase belong (T≤100oC), so this indicate that the extrinsic contribution is dominated than intrinsic contribution of dielectric activity response at this range of T. By further heating above T=100oC we can see an interesting behavior where the extrinsic coefficient decreased while the intrinsic coefficient increased and according to Fig.3. the real permittivity was observed increased in this range and the material possess a relaxor phase. This implying that the permittivity activity matching with intrinsic coefficient behavior and it’s dominated than extrinsic contribution which consider the reason for strong dielectric response at this range of T. It can thus be concluded that the extrinsic dielectric response caused by domain wall motion is the major contribution for strong dielectric response in ferroelectric phase up to T=100oC, however the intrinsic dielectric response caused by lattice distortion is the major contribution for strong dielectric response in relaxor phase above T>100oC. Fig. 6 (a,b and c) shown the same measurements and calculations of ST=0.05 sintered ceramic. From Fig. 6(c) it can observe that the irreversible contribution caused by motion of interphase boundaries possess the maximum value at Tfr (T~60oC) where the material is ferroelectric phase then decreased with raising temperature. While the maximum peak of reversible contribution caused by lattice deformation was observed at (T~100oC) where the material possess the relaxor phase. Present the permittivity hump peak at T~60oC in Fig.3 implying that the major contributions of dielectric activity response is coming from extrinsic contribution at this range of T. Fig. 7(c) display variation of intrinsic and extrinsic coefficients corresponding temperature of ST=0.1 virgin sintered ceramic. The figure shown the enhancement of extrinsic contribution can be ascribed to dielectric hump peak around diffused phase transition (Tfr~150oC). On the contrary, the suppression and pinched of irreversible contribution above Tfr could be due to diminishing of interface boundaries motion by further heating and as consequently grow the reversible contribution effect caused by domain wall propagation and lattice distortion in relaxor phase[8]. From the above discussion we can concluded that the enhancement of extrinsic contribution caused by domain wall displacement is responsible for form ferroelectric phase with long range order below the diffused phase transition of ST≤0.1.
5.2. Intrinsic contributions
Rayleigh behavior of [BKNT-xST-BCT] (x=0.15 and 0.2) virgin sintered ceramics have been displayed in Fig. (8,9) respectively. Both of Fig. 8(a) and Fig. 9(a) shows polarization dependence low amplitude of sub-switching electric field in different T (25-185oC) where the measured data can be well fitted by Rayleigh relation. Fig. 8(b) and Fig. 9(b) describe the variation of permittivity with applied electric field at diff T and it is clear to observe that a linear relationship between permittivity and electric field which refer to agreement the measured data with (Eq.2). Intrinsic and extrinsic coefficients of dielectric response were extracted and obtained from the linear fitting. Variation of reversible and irreversible coefficients corresponding to temperature of ST=0.15 ceramic has been displayed in Fig. 8(c). As we can see extrinsic coefficients increased with increasing T and producing (αmax) at T~50oC then decreased with further heating while the intrinsic contribution increased and shown the maximum peak at T~100oC. Fig. 3 shown the permittivity enhanced by T and εmax was observed at phase transition temperature T~100oC, this imply that the real permittivity enhanced close to Curie temperature due to largely contribution of intrinsic coefficient for strong dielectric response in the vicinity of phase transition temperature (Tc). Fig. 9(c) shown the same behavior of intrinsic and extrinsic contributions into dielectric activity of ST=0.2 sintered ceramic respected to temperature. A similar behavior and discussion to ST=0.15 can be observed where both of these composition possess relaxor phase at room temperature. In the conclusion we can said that in the relaxor phase, the intrinsic contribution caused by lattice deformation is play an important and dominated role on high and large real permittivity activity in the vicinity of phase transition temperature.
) and applied electric field (E) can be described by Rayleigh equation model as the following
represent the intrinsic contribution of permittivity which induced by lattice distortion and Eo is the maximum value of electric field, α is the is the Rayleigh constant and αEo reflect the extrinsic dielectric permittivity caused by domain wall displacement or domain wall motion.