Enhanced Energy Storage Performance by Relaxor Highly Entropic (Ba_0.2Na_0.2K_0.2La_0.2Bi_0.2)TiO₃ and (Ba_0.2Na_0.2K_0.2Mg_0.2Bi_0.2)TiO₃ Ferroelectric Ceramics

Abstract

Dielectric ceramic capacitors have attained considerable attention due to their energy storage performance in the field of advanced high/pulsed power capacitors. For such a purpose, configurationally disordered composite material engineering, with the substitution of suitable oxide cations at a single lattice site have demonstrated a strong dielectric relaxor phase with the ability to show high performance capacitive properties. Herein, two prominent high-entropy ceramics systems (Ba_0.2Na_0.2K_0.2A_0.2Bi_0.2)TiO₃, (with A = La and Mg) were fabricated to evaluate their structural, ferroelectric and dielectric properties. XRD patterns and Rietveld refinement of the XRD analysis confirmed the cubic structure $Pm\overline{3}m$ space group of the ceramics. The relative dielectric analysis of Ba_0.2Na_0.2K_0.2La_0.2Bi_0.2TiO₃ (BNKLBT) and Ba_0.2Na_0.2K_0.2Mg_0.2Bi_0.2TiO₃ (BNKMBT) ceramics were demonstrated with relaxor ferroelectric behavior having diffusion coefficients of 1.617 and 1.753, respectively. Moreover, BNKLBT and BNLMBT ceramics presented better stored energy density (1.062 J/cm³ and 0.8855 J/cm³, respectively) and high energy conversion efficiency (80.27% and 82.38%, respectively) at an electric field of 100 kV/cm. The results clearly demonstrate that such high-entropy configured ceramics have the potential to be used in efficient energy storage devices.

1. Introduction

Materials possessing the ability to perform multifunctional properties to be utilized in various advanced technological applications simultaneously have always remained of interest to researchers and scientists. The rapid growth in the demand of fossil fuels for energy purposes has compelled societies to shift towards alternative energy sources. Dielectric ceramic capacitors have gained considerable attention and are environmentally friendly. However, it is still challenging to achieve high recoverable energy density (W_rec) and effective energy conversion efficiency (ƞ) simultaneously in dielectric materials, which has restricted the possible high level use of dielectric ceramics in energy storing applications [1,2,3]. Bi_0.5Na_0.5TiO₃ (BNT) is a perovskite ferroelectric material with a remnant polarization (P_r) of ~40 µC/cm² and Curie temperature of ~310 °C [4]. BNT in combination with other materials has shown strong abilities for energy storage applications. W.P. Cao et al. reported the fabrication of a Bi_0.5Na_0.5TiO₃-SrTiO₃ (BNT-ST) ceramic system, which established a ferroelectric/relaxor phase transition and delivered a high W_rec of 0.65 J/cm³ at 65 kV/cm [5]. Moreover, Lu et al. reported the fabrication of an A and B-sites doped ((Bi_0.5Na_0.5)_0.93Ba_0.07)_1−xLa_x Ti_1−yZr_yO₃ ceramic system with an energy storage density (W_ST) of 1.21 J/cm³ [6]. Similarly, Bi_0.5K_0.5TiO₃ (BKT) is another perovskite ferroelectric material with dielectric relaxor behavior [7]. Yu et al., reported the synthesis of a 0.94(0.75Bi_0.5Na_0.5TiO₃–0.25Bi_0.5K_0.5TiO₃)–0.06BiAlO₃ ceramic system with an ƞ of 73.2% [8]. However, discovering materials showing high W_rec and ƞ simultaneously is challenging.

Having explored advanced materials for the best merits, the concept of high-entropy ceramics was introduced by Rost et al., [9]. In their approach, five or more suitable oxide cations (either equimolar or near-equimolar ratios) at single lattice site were accommodated [10]. For this strategy the free energy from the fabricated materials was achieved by entropic contributions from cohesive energy, which also stimulated the thermodynamic stability of the material [11]. Perovskite (ABO₃) structures are considered suitable for adapting these strategies as they possess tolerance factors within the range of 0.77 < t < 1.10, which can be disturbed by the radii of ions; hence, the lattice sites of the structure can easily be occupied by the ions of even variant valance states and ionic radii [12]. After replacing the ions at A or B-sites of ABO₃, lattice distortion or defect production is expected that can disturb the perovskite structure and result in unique properties of the material [13]. Du et al., reported the fabrication of a Ba(Ti_1/6Sn_1/6Zr_1/6Hf_1/6Nb_1/6Ga_1/6)O₃ ceramic system with a relative density of 92.7% [14]. Pu et al. studied a high entropy (Na_0.2Bi_0.2Ba_0.2Sr_0.2Ca_0.2)TiO₃ ceramic with a discharge energy density of 1.02 J/cm³ [15]. Similarly, Liu et al., successfully fabricated (Bi_0.2Na_0.2K_0.2Ba_0.2Ca_0.2)TiO₃ with a tolerance factor t = 1.01, and a W_ST of 0.684 J/cm³ [16].

Our study focused fabrication of new high-entropy configured ceramic materials. (Ba_0.2Na_0.2K_0.2La_0.2Bi_0.2)TiO₃ (BNKLBT) and (Ba_0.2Na_0.2K_0.2Mg_0.2Bi_0.2)TiO₃ (BNKMBT) ceramics were deliberately engineered to optimize their structural and dielectric relaxor phase evolution. Moreover, the BNKLBT and BNKMBT ceramics had high energy conversion efficiencies (ƞ) > 80%, with better values for dielectric capacitors.

2. Fabrication and Characterization

(Ba_0.2Na_0.2K_0.2La_0.2Bi_0.2)TiO₃ (BNKLBT) and (Ba_0.2Na_0.2K_0.2Mg_0.2Bi_0.2)TiO₃ (BNKMBT) ceramic samples were fabricated by conventional solid state reactions followed by a fast increment and decrement of temperature (15 °C/min) to avoid volatilization of the bismuth and sodium content. High purity Bi₂O₃ (Aladin, 99.9%), Na₂CO₃ (Sigma Aldrich, 99.98%), K₂CO₃ (Sigma Aldrich, 99.98%), La₂O₃ (Aladin, 99.9%), BaCO₃ (Sigma Aldrich, 99.98%), MgO (Alfa Aesar, 99.99%) and TiO₂ (Aladin, 99.9%) powders were weighted with the stoichiometric ratios of (Ba_0.2Na_0.2K_0.2La_0.2Bi_0.2)TiO₃ and (Ba_0.2Na_0.2K_0.2Mg_0.2Bi_0.2)TiO₃ and milled at 30 rpm in ethanol for 18 h. The mixed powders were dried in an oven at 100 °C overnight and then calcinated at 800 °C for 3 h. The calcinated BNKLBT and BNKMBT powders were then ground, and ball-milled for 12 h at 30 rpm and dried before cold iso-statically pressing the powders into disk shapes with a diameter of 11 mm under 200 MPa pressure. Afterwards, ceramics were placed in sealed crucibles with extra prepared powder around the disks to avoid Bi and Na volatilization during high temperature sintering. Finally, the compacted ceramic samples at both concentrations were sintered at 1250 °C for 4 h at a fast heating and cooling rate (15 °C/min).

Structural phase transformation and phase impurity of fabricated BNKLBT and BNKMBT ceramic samples were investigated by X−ray diffraction (XRD, PANalytical, Netherlands) analysis with a scan rate of 0.02° s⁻¹ for a 2θ scan range of 20–70°. Structural confirmation of the fabricated ceramic samples was confirmed with Rietveld refinement of the attained XRD patterns of the ceramic using FULLPROF software. Morphological analysis and 2-dimentsional (2D) colored elemental mapping of the synthesized samples were performed by field emission scanning electron microscopy (FE-SEM, FEI Quanta 200, Hillsboro, Oregon) at an acceleration voltage of 10 kV. Later, prepared ceramic samples were polished to a thickness of ~0.7 mm and an Ag electrode was pasted on both surfaces of the ceramics to measure their dielectric and ferroelectric properties. Ferroelectric analysis with electric field-dependent polarization loops (P−E loops) was measured at a frequency 10 Hz using a ferroelectric tester (aixACCT TF Analyser 1000). Relative dielectric constant versus temperature (ɛ_r−T) curves and dielectric loss (tanδ) versus temperature curves at the frequency range of 100 Hz to 1 MHz were recorded using an HP4980A, Agilent LCR analyzer.

3. Results and Discussion

Figure 1a shows XRD analysis of the single phase BNKLBT ceramic. The XRD pattern of BNKLBT ceramic was analyzed using Bi_0.5Na_0.5TiO₃ (BNT, PDF#46-0001), Bi_0.5K_0.5TiO₃ (BKT, PDF#36-0339), LaTiO₃ (LTO, PDF#49-0426) and BaTiO₃ (BTO, PDF#31-0174) as reference comparisons. Similarly, Figure 1c shows XRD analysis of the BNKMBT ceramic with Bi_0.5Na_0.5TiO₃ (BNT, PDF#46-0001), Bi_0.5K_0.5TiO₃ (BKT, PDF#36-0339), MgTiO₃ (MTO, PDF#06-0494), and BaTiO₃ (BTO, PDF#31-0174) as reference comparisons. It is noticeable that the fabricated BNKLBT and BNKMBT ceramics possess crystalline single phase perovskite structures. Figure 1b shows the amplified 39–48° XRD analysis for BNKLBT and Figure 1d shows the amplified 38–48° XRD analysis for the BNKMBT ceramics, where peak splitting (002/200) is not visible, consistent with the coexistence of rhombohedral and tetragonal structures of the morphotropic phase boundary [17]. The sharp (200) peak at 45.8° confirms the cubic structure of both samples, and there are no rhomboheral or tetragonal phases [5]. From the amplified images of BNKLBT and BNKMBT it can be seen that both (111) and (200) diffraction peaks match the PDF card of the BTO material, whereas BTO consists of a cubic structure with the $Pm\overline{3}m$ space group. Hence, both BNKLBT and BNKMBT ceramics appear to possess cubic structures with the space group $Pm\overline{3}m$, but more confirmation is required. For further analysis of the structure of both high-entropy ceramics, the tolerance factor of the ceramics was measured as follows [16];

$$t=\raisebox{1ex}{$(R_A+R_O)$}\!\left/ \!\raisebox{-1ex}{$\sqrt{2}\left(R_B+R_O\right)$}\right.$$

(1)

where R_A is the ionic radius of the A-site, R_B is the ionic radius of the B-site and R_O is the ionic radius of oxygen in the perovskite structure. The ionic radius of each constituent element is shown in

Table 1. Ionic radii of R_A, R_B and R_O.

Ions	Bi3+	Na+	K+	La3+	Mg2+	Ba2+	Ti4+	O2−
Ionic Radii (Å)	1.03	1.39	1.64	1.35	0.89	1.61	0.605	1.4

.

The cubic phase maintains a stable structure in the range of 0.9 ≤ t ≤ 1.0 [18]. Here the calculated tolerance factor for the BNKLBT ceramic is 0.99 and for BNKMBT ceramic is 0.958. Jiang et al., reported that high entropy perovskite materials show tolerance factors in the range 0.97 ≤ t ≤ 1.03 [19]. Liu et al. reported a tolerance factor of 1.01 for a high-entropy ceramic with a cubic structure [16]. The tolerance factors of BNKLBT and BNKMBT ceramics are well within the range of the cubic phase. From XRD analysis of BNKLBT and BNKMBT ceramics at 45.8°, a sharp (200) peak was found, which is the confirmation of the cubic phase of both ceramic samples.

To further analyze the structural phases for BNKLBT and BNKMBT ceramics, Rietveld refinement of the XRD patterns of both samples were performed with FULLPROF software (Figure 2a,b). Here the cubic structure with the space group $Pm\overline{3}m$ was treated as the reference structure. Figure 2a,b shows the refined XRD results, where the excellent R_WP, R_P and χ² refined factors with R_P and R_WP are below 8%. The agreement between observed and calculated XRD patterns for BNKLBT and BNKMBT ceramics shows the existence of the cubic phase with the space group $Pm\overline{3}m$.

Figure 3a,b shows images of the top surface images of BNKLBT and BNKMBT ceramics respectively. No holes or cracks appear on the ceramic surfaces, confirming that the high temperature sintering process did not affect the ceramics. Highly dense samples were produced under the high pressure (200 MPa), with a density of 5.86 g/cm³ for BNKLBT and 5.78 g/cm³ for BNKMBT. The grain sizes for both ceramics were in the range of 1–2.5 µm. To further analyze the proper uniform distribution of each element in the ceramics, elemental distribution mapping was performed. Ti had the highest degree of dispersion for both ceramic samples because of its high stoichiometric ratio. All other constituent elements in both ceramic compositions were the same except La for BNKLBT and Mg for BNKMBT. Both La and Mg had uniform distributions, but with a lesser degree of distribution because of their low stoichiometric ratios in the ceramics. Morphological analysis clearly confirmed the contribution and presence of all constituent elements.

Temperature−dependent relative dielectric constant (ɛ_r) plots for BNKLBT and BNKMBT samples are shown in Figure 4a,e for the temperature range 27–500 °C, and under a frequency range of 100 Hz to 1 MHz. Strong, long-range dielectric maxima (ɛ_m) dispersion appeared at wide transition temperatures (T_m), which indicates that the fabricated ceramics belong to the relaxor ferroelectrics family [20]. In the ɛ_r−T curves, some temperature shoulders (T_S) were observed for the temperature range 120–170 °C, which are associated with the generation of the polar nano-regions created due to the presence of different ionic radii and varying electrovalence states of cations at the A-site of the ceramics [21]. These cations not only cause distortion of the lattice structures of the materials but also harvest variable electrovalence states in the sub-nano area, leading towards the creation of domains with diverse polarization activities. Jia et al., proposed such distorted units to be polar units [16]. The shifting of ɛ_m towards a higher temperature by varying the frequency relates to the relaxation polarization of the ceramics [22]. For the BNKLBT ceramic, the ɛ_m for 1 kHz, 100 kHz and 1 MHz were 1281 at 233 °C, 1179 at 244 °C and 1071 at 269 °C, respectively (Figure 4a). Similar behavior was observed for the BNKMBT ceramic; the ɛ_m for 1 kHz, 100 kHz and 1 MHz being 1474 at 249 °C, 1342 at 260 °C and 1222 at 270 °C respectively (Figure 4e). The temperature dependent dielectric loss curves of BNKLBT (Figure 4b) and BNKMBT (Figure 4e) ceramics are presented where the values of tanδ were less than 0.003 and 0.016, respectively, at room temperature. At low frequencies, the sharp increase in the values of tanδ occurred after crossing 300 °C for both ceramic samples, which can be related to space charge polarization [23]. The modified Curie−Weiss law can be used to evaluate the relaxation degree of the fabricated ceramics [24]:

$$\frac{1}{{\epsilon }_r}-\frac{1}{{\epsilon }_m}=\frac{{(T-T_m)}^{\gamma }}{C}(1\le \gamma \le 2)$$

(2)

where C refers to the Curie-Weiss constant, γ refers to the diffusion co-efficient, whose value lies between 1 (Ferroelectric) and 2, the ideal relaxor ferroelectric. For both ceramic samples, 100 kHz curves from ε_r−T were simulated, and values calculated for the diffusion co-efficient using Equation (2) for BNKLBT and BNKMBT ceramics were 1.617 (Figure 4c) and 1.753 (Figure 4f), respectively.

Figure 5 shows the ferroelectric analysis (P−E) of BNKLBT and BNKMBT ceramic samples at room temperature with a frequency 10 Hz under a critical electric field of 100 kV/cm. Both P−E loops are slimmer, which is a characteristic of relaxor ferroelectrics compared to normal ferroelectrics that are widely open on the electric field axis. The values entered in

Table 2. Dielectric capacitive performance of high-entropy BNKLBT and BNKMBT ceramics.

Entropic Ceramics	Pmax µC/cm2	Pr µC/cm2	Wrec J/cm3	WST J/cm3	Ƞ %
BNKLBT	21.24	4.19	0.8525	1.062	80.27
BNKMBT	17.71	3.12	0.7295	0.8855	82.38

were calculated by using the following relations [15]:

$$W_{rec}={\int }_{Pr}^{Pmax}Edp$$

(3)

$$W_{st}={\int }_0^{Pmax}Edp$$

(4)

$$\eta =\frac{W_{rec}}{W_{st}}\times 100$$

(5)

where the values of P_max, P_r, and E were obtained from measured P−E loops. The maximum polarization (P_max) for the BNKLBT ceramic was 21.24 µC/cm², while for the BNKMBT ceramic the P_max was 17.71 µC/cm² at 100 kV/cm. Dielectric capacitive analysis in terms of stored (W_ST) and recoverable (W_rec) charge densities and energy conversion efficiency (ƞ) of both ceramic samples are presented in Table 2 depending on maximum polarization (P_max) and remnant polarization (P_r) for an electric field of 100 kV/cm. The W_rec, W_ST and ƞ of the fabricated BNKLBT ceramic were 0.8525 J/cm³, 1.062 J/cm³ and 80.27%, respectively, while for the BNKMBT ceramic were 0.7295 J/cm³, 0.8855 J/cm³ and 82.38%, respectively.

It was seen that high entropy BNKLBT and BNKMBT ceramics showed relatively high energy conversion efficiencies >80%, which is associated with the relaxor ferroelectric behavior of the ceramics. The dielectric energy storage performance of these high-entropic ceramics is not as high as traditional perovskites [25,26,27], but much better as reported high entropic ceramic systems (

Table 3. Energy Storage comparison study of BNKLBT and BNKMBT ceramics with other reported high entropy ceramics.

Sr. No	Lead Free Ceramics	Recoverable Energy Density, Wrec (J/cm3)	Energy Conversion Efficiency, η (%)	Applied Electric Field, E (kV/cm)	Ref.
1	NBN-BNTBT	1.36	73.9	136	[29]
2	BNT- NT-BT	1.2	74.8	100	[30]
3	AN-BNBLT	1.697	82.3	130	[31]
4	6KS-NBT	0.57	53.2	90	[32]
5	BNT-BA-BKT	1.15	73.2	105	[8]
6	BNTBT-NN-SZ	0.95	66	110	[33]
7	KNN-NBSLT	1.234	74.7	90	[34]
8	BNKLBT	0.8525	80.27	100	This work
9	BNKMBT	0.7295	82.38	100	This work

). Low dielectric loss <0.3, even at high temperature, (300 °C) indicates the existence of highly dense ceramics, which suggests there are no holes or cracks, as was evident from the SEM analysis. Low dielectric loss also results in the low leakage current of the ceramics [28], resulting in better ferroelectric and dielectric capacitive performance of the ceramics. A comparison among the different reported high-entropic ceramics and our results is shown in Table 3. Our results clearly indicate the potential of the high-entropy ceramics for dielectric capacitors.

Temperature dependent ferroelecytic analysis of the prepared BNKLBT and BNKMBT ceramics is illustrated in Figure 6 (a and c respectively). The values of P_max were reduced with the variation of temperature from 30 to 120 °C. The P−E loops became slimmer with the influence of temperature; however, the energy storage efficiency value was retained (Figure 6b,d) for BNKLBT (80.27% at 30 °C and 80.21% at 120 °C) and BNKMBT (82.38% at 30 °C and 82.295% at 120 °C). The temperature range 30–120 °C had not influenced the ferroelectric and dielectric energy storage properties because of the high T_C > 265 °C for both ceramic systems.

4. Conclusions

High-entropy BNKLBT and BNKMBT ceramics were fabricated successfully. XRD and Rietveld refinement confirmed their cubic structure with the space group $Pm\overline{3}m$. Tolerance factors showed that the perovskite structure of the ceramics is highly tolerant for various ions, which supports expanded compositional space and practical applications. With the elemental complexity of BNKLBT and BNKMBT ceramics, temperature dependent relative dielectric analysis showed diffuse phase evolution for a wide temperature range with diffusion coefficients of 1.617 and 1.753, respectively. BNKLBT and BNKMBT ceramics had P_max values of 21.24 µC/cm² and 17.71 µC/cm², W_rec values of 0.8525 J/cm³ and 0.7295 J/cm³, and ƞ values of 80.27% and 82.38%, respectively. Ferroelectric analysis performed at a high temperature of 120 °C confirmed the energy storage efficiencies of the ceramics at >80%. The high values of energy efficiencies of the high-entropy ceramic samples indicate the potential of the samples to be used in pulsed power dielectric capacitors.