Electrical and impedance spectroscopy properties of hydrothermally synthesized Ba0.2Sr0.8-yLayFe12O19 (y = 0.2–0.8) nanorods

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Electrical and impedance spectroscopy properties of hydrothermally synthesized Ba0.2Sr0.8-yLayFe12O19 (y = 0.2–0.8) nanorods N. Raghurama, T. Subba Raoa, K. Chandra Babu Naidub,∗ a b

Dept. of Physics, Sri Krishnadevaraya University, Anantapuramu, 515003, A.P, India Dept. of Physics, GITAM Deemed to be University, Bangalore, 562163, Karnataka, India

A R T I C LE I N FO

A B S T R A C T

Keywords: Hexaferrites Nanorods Structure Electrical properties Impedance spectroscopy

The Ba0.2Sr0.8-yLayFe12O19 (y = 0.2, 0.4, 0.6 & 0.8) (BSLFO) nanorods were prepared via low temperature, and inexpensive hydrothermal method. The presence of hexagonal phases was confirmed using the X-ray diffraction (XRD) patterns. The surface morphology revealed the formation of rectangular nanorods for y = 0.2–0.8 contents. Especially, y = 0.8 content showed the complete formation of rectangular nanorods due to high La-content. Furthermore, the dielectric properties, ac-electrical properties, impedance and dielectric modulus parameters were described as a function of composition, frequency and temperature.

1. Introduction The magnetic hexaferrites were the good candidate materials for potential applications in telecommunications, RADAR system, permanent magnets, loudspeakers, transformers, microwave absorbers, wind turbines, high frequency electronic devices, electromechanical machines, capacitors, high-density magnetic storage devices, recording, microelectronics, etc owing to their significant electrical, magnetic (high Curie transition temperature, and coercivity), electromagnetic, and microwave properties [1–3]. Furthermore, the high corrosion resistance, and inexpensive for materials preparation were also noticed to be some reasons for achieving the above mentioned applications [1–3]. In general, these hexaferrites can exhibit the hexagonal structure. However, depending on the iron to oxygen ratio, and other elements, these hexaferrites were divided into different types like M, U, W, X, Y, and Z [1]. Among all the hexaferrites, the M-type (MFe12O19, where M = Sr, Ba, Pb etc.) hexaferrites were observed to be the easiest structure to understand [1]. Recently, among all the M-type hexaferrites, the barium hexaferrite, strontium hexaferrites, and barium strontium hexaferrites were studied extensively for different electrical, magnetic, microwave, and other properties [3]. In our previous work [3], the Ba0.2Sr0.8Fe12O19 material revealed the moderate formation of nanofibers like morphology. Likewise, in case of Pb0.8-yLayCo0.2TiO3 (y = 0.2–0.8), Pb0.8Co0.2-zLazTiO3 (z = 0.05–0.2), Ba0.2Cu0.8-xLaxFe2O4 (x = 0.2–0.6), and BaxCu1-xFe2O4 (x = 0.2–0.8) nanostructures, the complete nanofiber, and nanorods were noticed at high La and Ba-contents of high ionic radii [4–7]. This

∗

was evolved due to either horizontal or vertical distortions of particles of the resultant compound on doping/substituting the elements of high ionic radii [7]. In general, the nanofibers/nanorods will have the larger number of elongated grains with fewer grain boundaries (high resistive layers) [7]. Hence, the obstacles for the effective electrical properties can be reduced. Therefore, the above - mentioned materials showed prominent electrical properties owing to the formation of nanofiber/ nanorod like morphology [4–7]. In order to obtain these kinds of nanostructures, several scientists commonly adopted an expensive synthesis technique called electrospinning [8]. In addition, the refining method by Ma et al. [9], & Wang et al. [10], and thermal decomposition process by Sunaina et al. [11] were adopted to prepare the nanorods. But Raj et al. [12,13] prepared the nanostructures via the hydrothermal method. From the literature survey, it was planned to substitute the La rare earth element into the Ba0.2Sr0.8Fe12O19 moderate nanofiber system. After preparing the single-phase BSLFO hexagonal system, it was decided to study the electrical properties thereby forming the nanofibers/nanorods using the low-cost hydrothermal method. 2. Materials and method In order to synthesize the Ba0.2Sr0.8-yLayFe12O19 (y = 0.2, 0.4, 0.6 & 0.8), the Ba (NO3)2·6H2O, Sr (NO3)2, La (NO3)3.6H2O, and Fe (NO3)3·9H2O (each of 99.88% purity: Sigma-Aldrich) were selected as the raw materials in nitrate form. Furthermore, these nitrate materials were shifted to a glass beaker according to the desired stoichiometric ratio. These nitrate precursors were dissolved in distilled water to

Corresponding author. E-mail address: [email protected] (K. Chandra Babu Naidu).

https://doi.org/10.1016/j.ceramint.2019.11.042 Received 19 October 2019; Received in revised form 5 November 2019; Accepted 5 November 2019 0272-8842/ © 2019 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Please cite this article as: N. Raghuram, T. Subba Rao and K. Chandra Babu Naidu, Ceramics International, https://doi.org/10.1016/j.ceramint.2019.11.042

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Fig. 1. The synthesis process of BSLFO nanostructures.

obtain a resultant solution. In the next step, we added sodium hydroxide solution drop by drop into the resultant nitrate materials solution in order to reach the pH value 12. Later on, the whole solution was poured in a Teflon bowl of 300 ml capacity. This Teflon bowl was sealed and kept in a stainless steel autoclave. The whole autoclave was made tight and positioned in a conventional hot air oven to perform the hydrothermal reaction. The reaction temperature of the oven was set at 150 °C for 8 h. After completion of the hydrothermal reaction, the oven was cooled to room temperature. Then, we opened the autoclave carefully. At this moment, we observed the powder sample under the depth of distilled water. We removed this water using the centrifuge technique. Besides this, the sample was washed using distilled water and acetone for seven to ten times or till the pH reaches 7. This confirmed that the sodium was completely removed from the resultant sample. Afterwards, the powder sample was subjected to heat treatment at 60 °C/2 h. As a result, we obtained the BSLFO nanopowder. The synthesis process and steps were shown clearly in Fig. 1. This powder was grinded well and forwarded to various characterization techniques like X-ray diffractometer (Bruker, XRD, CuKα, λ = 0.15406 nm), Fieldemission Scanning Electron Microscope (Ultra 55 FE-SEM Carl Zeiss), and LCR HiTESTER (HIOKI 3532-50) for describing the structural, morphological, and electrical properties. 3. Results and discussion Fig. 2. X-ray diffraction patterns of BSLFO nanostructures.

3.1. XRD analysis The phase purity and the structure of the BSLFO nanomaterials were identified with the help of XRD patterns as shown in Fig. 2. It was apparently observed that the high crystallinity, as well as diffraction peak broadening, was acquired for the BSLFO. In Fig. 2, the reflection planes were indexed using the Miller indices (hkl). These planes were compared with the standard JCPDS: 84 – 1531 (hexagonal structure). From this, we observed that both experimental and standard JCPDS patterns were in good agreement. Therefore, the hexagonal structure of

the BSLFO nanomaterials was confirmed. Furthermore, the average crystallite size (D) was computed using the Scherrer equation: D = 0.9λCuKα/βcosθ, λCuKα is the CuKα wavelength (0.15406 nm), β refers to full-width half maxima (FWHM in radians), and θ is associated with the diffraction angle [14]. The results ensured that the ‘D’ value was increased from 25.7 to 83.8 nm as a function of ‘y’. This can be attributed to the decrease of internally developed microstrain during

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In addition, the temperature gradient involved in the autoclave can, in turn, lead to the formation of present nanostructure (nanorod). This was also observed in our previous work of PLCT (Pb0.8-yLayCo0.2TiO3 (y = 0.2–0.8)), PCLT (Pb0.8Co0.2-zLazTiO3 (z = 0.05–0.2)), BCLF (Ba0.2Cu0.8-xLaxFe2O4 (x = 0.2–0.6)), BCF (BaxCu1-xFe2O4 (x = 0.2–0.8)) [4–7]. In PLCT, PCLT and BCLF nanostructures, the complete nanofiber/nanorods were observed at high concentration of La+3 cations while BCF revealed the same at high concentration of Ba+2 cations of high ionic radii. As reported by Sunaina et al. [11], it was evidenced that these kinds of ions were responsible for the morphology consisting of nanofiber/nanorods/nanowires like structures. Likewise, in the present work, the BSLFO nanostructures showed the formation of complete nanorods covered by few linear nanofibers. Herein, the Ba+2 & La+3 cations of high ionic radii and the temperature within the autoclave were considered as the reasonable factors for the particle orientation thereby achieving the rectangular nanorods.

Table 1 Structural parameters of Ba0.2Sr0.8-yLayFe12O19 (y = 0.2 to 0.8) nanorods. x

0.2

0.4

0.6

0.8

D (nm) a = b, c (nm)

25.7 0.5869, 2.3168 3.948 691.09 5.199 1081.965

31.6 0.5872, 2.3170 3.946 691.86 5.242 1092.223

62.5 0.5877, 2.3174 3.942 693.16 5.282 1102.481

83.8 0.5879, 2.3178 3.943 693.75 5.326 1112.739

c/a V (Å)3 ρx (gcm−3) MW (gmol−1)

the hydrothermal reaction. Besides, the unit cell dimensions (or lattice constants a = b & c) were calculated using the formula 1/d2 = 1.333/ a2 [h2 + hk + k2 + l2c−2] [3] (see Table 1). The achieved results evidenced that ‘a = b’ and ‘c’ values were increased from 0.5869 to 0.5879 nm and 2.3168–2.3178 nm respectively with an increase of Lacontent. This kind of manner can be attributed to the dopant element and its ionic radius. In view of this, Shannon [15], earlier mentioned the ionic radii of the elements of the BSLFO compound. Thus, we noticed the ionic radii of Ba+2:1.35 Å, Sr+2: 1.27 Å, La3+: 1.22 Å, Fe+3: 0.645 Å and Fe+2 = 0.80 Å. From this report, it can be probably expected that the La-element may occupy either Ba or Sr-site. But in practice, La can prefer to replace Sr-site owing to almost comparable ionic radii of La with Sr element. However, in the literature [16–20], many scientists reported that the doping of trivalent/rare earth elements into the system consisting of divalent elements can lead to different consequences. Therefore, in the hexaferrite system, on doping the La element, the Sr-site will be replaced by La element. Subsequently, the ferric ions will be converted into the ferrous ions [16–20]. Hence, the lattice constants were increased with increase of La-content followed by the consecutive increase of number ferrous ions. Moreover, the material compositions, suppression of trivalent cations, and imperfections can cause to obtain this kind of variation [18,19]. As a result, the unit cell volume (V = 0.866a2c) was noticed to be increasing from 691.09 to 693.75 Å3 with an increase of ‘y’. The c/a ratio was noticed to be almost 3.94 for all samples. The X-ray density (ρx = ZMW/NAVcell, wherein Z = effective number of atoms per unit cell, MW = molecular weight, NA = Avogadro's number, and V = unit cell volume) was evaluated and the results were noticed to be increasing from 5.199 to 5.326 gcm−3. This was happened owing to the increase of compositional molecular weight from 1081.965 to 1112.739 g mol-1 with increase of ‘y’.

3.3. Dielectric properties The frequency variation (from 100 Hz–5 MHz) of dielectric constant (ε′) and dielectric loss (ε") of y = 0.2–0.8 contents of BSLFO nanostructures was depicted in Figs. 4 and 5 respectively. Fig. 4 expressed a fact that the ε′ was observed to be very high in magnitude at 100 Hz whereas ε′ was low at 5 MHz (see Table 2). Numerically, y = 0.4 & 0.8 contents offered high ε′ values of 114.2 and 261.9 respectively (at 100 Hz). But on the other hand, the ε′ of the same compositions (see Fig. 4 & Table 2) was noted as 4.1 and 0.39 respectively (at 5 MHz). Particularly, it was noticed that the y = 0.6 content showed the decreasing trend of dielectric constant at lower and higher frequencies. Numerically, it was seen that ε′ acquired 55.3 at 100 Hz while the same content revealed the ε′ of 2.7 at 5 MHz (see Table 2). In general, this kind of trend in ε′ of y = 0.8 content, was attributed to the response of charge carriers to the applied electric field. These charge carriers have no enough time to align in the direction of electric field (at the selected frequencies). Subsequently, the ε′ of y = 0.6 content expressed the decrease of ε′ which differed from other compositions. In the same fashion, the ε" values of y = 0.4 & 0.8 contents showed 105.7 and 261.6 respectively at 100 Hz while the same contents exhibited ε" values ~4.2 and 0.3 respectively at 5 MHz. This experimental data evidenced a fact that there were two different conditions working at low and high frequencies of ε' – log ω (Fig. 4) and ε" – log ω (Fig. 5) plots. In addition, a similar mechanism was reported earlier by Koop's theory [21] in the case of polycrystalline materials. Koop's theory suggested that each polycrystalline dielectric materials is composed of high conducting grains which can be separated by the high resistive layer called grain boundary. At lower electric field frequencies (≤102 Hz), the charge carriers will be activated rapidly. Therefore, all the charge carriers can align in the direction of the electric field and furthermore, the carriers can start conducting through grains (conducting layers). In course of the hopping process, these charges can reach the grain boundary (high resistive layers) interface and they will be piled up as well at the interface. Due to this pile-up nature of charges, huge amount of polarization will be developed. This kind of polarization was considered as the space charge polarization or Maxwell – Wagner's interfacial polarization [22]. This was, in general, happened due to the inhomogeneous dielectric structure. Hence, this could be responsible for the high magnitude of ε′ and ε" values at 100 Hz. Moreover, all these charge carriers may not have sufficient time in order to align in the direction of the electric field at high frequencies. That is, only a few charge carriers can respond to the applied electric field frequency. Therefore, the number of charge carriers which can be piled up at the interface will be diminished. This produced a small amount of polarization thereby obtaining the low ε′ and ε" values at high frequencies. The temperature variation of ε′ was depicted in Fig. 6. The y = 0.2–0.8 contents performed almost a constant variation of ε′ as a function of temperature from 300 to 520 K. This indicated a fact that

3.2. FESEM analysis The FESEM photos of BSLFO nanomaterials were shown in Fig. 3. The surface morphology of y = 0.2–0.8 samples revealed the interesting results in a stepwise manner. That is, for y = 0.2 content, the nanorods were hidden within the cluster of nanoparticles. At y = 0.4 content, the rectangular nanorods were formed which were hidden among the nanoparticles. However, interestingly, y = 0.6 content exhibited the formation of accumulated nanoparticles as well as cylindrical nanofibers on the rectangular nanorods. On the other hand, y = 0.8 content, clearly showed the presence of rectangular nanorods covered by few nanofibers. From the overall, analysis of surface morphology, it was understood that the lanthanum was the main element to reinforce the change in the shape of the BSLFO nanoparticles along with barium. In the case of BSFO nanomaterials (Ba0.2Sr0.8Fe12O19) [3], for particular content (x = 0.8), the partially oriented nanorods were formed by covering few flexible nanofibers and particles. This kind of orientation (by forming the nanorod) was attributed to the crystal structure of BSLFO, bonding preferences, and kind of ions as reported by Sunaina et al. [11]. Besides these, the external physical parameters like pressure, temperature, chemical environment (viz., surfactant, pH, etc.) can be responsible for the favorable orientation of nanostructures. 3

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Fig. 3. FESEM pictures of BSLFO nanostructures.

Fig. 4. ε' – log ω plots of BSLFO nanostructures.

Fig. 5. ε" – log ω plots of BSLFO nanostructures.

the very less number of electrons were thermally activated and contributed the hopping mechanism. However, beyond T = 520 K, most of the charges were thermally activated and therefore a gradual increasing trend of ε′ was observed. In view of this, y = 0.2 & 0.4 contents showed two transition temperatures (Te). That is, y = 0.2 performed Te1 at 573 K and Te2 at 733 K while y = 0.4 revealed Te1 at 513 K and Te2 at 713 K. Out of these transitions, the first transition indicated the ferroelectric relaxation temperature and the second one showed the dielectric transition temperature. Similar observations were reported by Tan et al. [23,24]. Likewise, y = 0.6 and 0.8 contents showed the

dielectric transition temperatures at 713 and 683 K respectively at 1 MHz. As a whole, it was understood that the dielectric transition temperature was decreased from 733 to 683 K as a function of ‘y’ from 0.2 to 0.8. Thus, the ferro to paraelectric transformation was occurred in case of BSLFO samples. This was attributed to a fact that the electron exchange interaction between Fe–O–Fe was decreased owing to the increase of bonding distance between iron and oxygen ions upon La substitution into the BSFO hexaferrite system.

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Table 2 The electrical parameters of BSLFO nanostructures. Composition (y) σac (S/cm) σdc (S/cm) exponent (n) ε′ at 100 Hz ε′ at 5 MHz ε" at 100 Hz ε" at 5 MHz EH (eV) EL (eV)

0.2

0.4 −5

7.716 × 10 2.424 × 10−8 0.706 97.4 3.8 47.1 1.9 0.776 0.185

0.6 −5

7.050 × 10 8.186 × 10−8 0.452 114.2 4.1 105.7 4.2 0.542 0.226

0.8 −5

5.674 × 10 5.962 × 10−8 0.585 55.3 2.7 82.4 2.7 0.838 0.053

4.896 × 10−5 1.462 × 10−7 0.747 261.9 0.39 261.6 0.3 0.859 0.170

this. Due to Te, the change in the slope of the gradient line was occurred on either side of the Te. As a result, two different activation energies were obtained within two regions thereby achieving two slopes. In addition, the change of conduction mechanism from polaron (HTR) to hopping (LTR) conduction on either side of Te can be responsible for different EH and EL values [3]. Furthermore, the ac-electrical conductivity was calculated using the equation σac = ωεoε", where ω = 2пf, εo is the permittivity of free space and the other symbols have their usual meaning [3]. The logσac versus logω (Fig. 8) plots were drawn and later on, the power-law fit was applied. Then, it was noticed that the total ac-electrical conductivity σac (f, T) was related to the inclusive of two terms such frequency-dependent σac (f) and frequency independent term (σdc). Furthermore, the logσac versus logω plots offered the parameters like dc-electrical conductivity (σdc) and exponent (n). These values were listed in Table 2. From the results, it was noticed that σac was decreased from

3.4. AC-electrical properties The lnσac versus 103/T plots (at 1 MHz) of BSLFO were drawn to evaluate the activation energies (see Fig. 7). The plots indicated two regions such as the high temperature region (HTR) and the low temperature region (LTR). The slopes were taken in both regions. The results expressed that the slope values of HTR plots were seemed to be larger than that of the slopes of LTR plots. Subsequently, the ac-activation energies of HTR (EH) and LTR (EL) plots of y = 0.2–0.8 were calculated and listed in Table 2. The obtained EH and EL values were observed to be different in magnitude for all samples. That is, the EH values were changed from 0.542 to 0.859 eV whereas the EL values were noted to be varying from 0.053 to 0.226 eV with an increase of ‘y’. This obviously established a fact that EH values were noted to be larger in magnitude than EL. Similar reports were noticed in the literature [3]. The dielectric transition temperature (Te) was one of the reasons for

Fig. 6. ε' – T plots of BSLFO nanostructures. 5

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Fig. 7. lnσac versus 103/T plots of BSLFO nanostructures.

Fig. 8. logσac versus log ω plots of BSLFO nanostructures.

7.716 × 10−5 to 4.896 × 10−5 S/cm (at 3 MHz) with an increase of ‘y’. In general, it was known that the increase of frequency can induce the oscillations of the electric dipoles. Consequently, a huge amount of heat will be developed. This heat dissipation could be responsible for the evolved dielectric loss. Therefore, σac was increased as well with frequency. In addition, the σdc and n were evaluated. It was observed that the σdc was varied from 2.424 × 10−8 to 1.462 × 10−7 S/cm (for y = 0.2–0.8). The high La-content recorded high dc-electrical conductivity due to having the complete formation of nanorods. The exponent (n) revealed a value varying from 0.452 to 0.747. In general, the ‘n’ value offers the ratio between back hop rate and site relaxation. As a result, it can attain the maximum value of ‘1’ and a minimum value of ‘0’. In the present work, the ‘n’ was achieved to be < 1 only for all contents. This confirmed a fact that the site relaxation existed in the BSLFO materials was faster than the polaron hopping [3].

Fig. 9. The Z′-log ω plots of BSLFO nanorods at various temperatures.

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Fig. 10. The Z″-log ω plots of BSLFO nanorods at various temperatures.

Fig. 9. (continued)

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3.5. Impedance spectroscopy In general, the impedance spectroscopy technique can segregate the grain, grain boundary, and electrode behavior within polycrystalline materials. According to this, the complex impedance (Z*) was considered to be the inclusive of Z' (real part of Z*) and Z" (imaginary part of Z*) parameters. The frequency (log ω) dependence of Z′ and Z″ as a function of composition (y = 0.2–0.8) during the temperature ranging from 313 to 723 K was investigated. The concerned plots (Bode plots) were shown in Figs. 9 and 10 respectively. In Fig. 9, it was clearly observed that all the BSLFO contents performed the usual dielectric behavior over 313–563 K temperatures. That is, the high Z′ was noticed at low frequencies and it was found to be decreased while going to the higher frequencies. This mechanism was attributed to the space charges accumulated at the interface. In addition, the high Z′ value at 100 Hz was happened due to the electrode polarization effect. However, for the temperatures (T) ranging from 553 to 723 K, all samples showed the peaking value of Z′ which can be considered as relaxation (resonance) frequency. The relaxation became predominant at very high ‘T’ values. Particularly, for y = 0.2 content, the relaxation was shifted towards the high log ω values. After relaxations, the Z′ values were observed to be small in magnitude. It was occurred owing to have less enough time to the charge carriers to align in the direction of the electric field. Also, this was attributed to the liberation of charge carriers due to the decrease in barrier height as reported by Salah et al. [25]. Similarly, y = 0.4, 0.6 & 0.8 contents revealed the relaxations at the constant angular frequencies (log ω) of 5.812, 5.675 and 5.412 respectively. This confirmed a fact that the relaxation frequency was decreased with the increase of La-content in the BSFO system. Likewise, in Fig. 10, the Z″log ω plots at different ‘T’ values showed the high Z″ at low angular frequencies and small Z″ values at high log ω (from 313 to 563 K). Besides this, the considerable relaxations were noticed at high temperatures just like in the case of temperature-dependent Z' – log ω plots. At the temperatures ranging from 553 to 723 K, these relaxations were shifted to high frequencies. This implied a fact that the hopping of localized charge carriers was increased with temperature as reported by Joshi et al. [26]. The observed relaxation peaks were seemed to be broad in nature and therefore, it reflected the non-Debye relaxation present in the materials [25]. The Cole-Cole plots of BSLFO nanomaterials at various temperatures (from 313 to 723 K) were shown in Fig. 11. This analysis usually can offer the contribution of grain and grain boundary as a part of the electrical conduction mechanism. In other words, one can understand the microstructure of BSLFO using the Cole – Cole plots analysis. In the case of y = 0.2 content, the plots showed the partial relaxation behavior over 313–503 K range. This was attributed to the partial relaxation strength and it could be happened due to the existence of charge carriers which can move longer distances [27]. Moreover, the complete semicircular arcs were formed beyond T = 503 K with asymmetric in nature. This asymmetry or distortions in the arcs were formed due to the grain size, strain, temperature, dislocations, and moisture effects [28]. The similar effects were noticed in the case of y = 0.4, 0.6 & 0.8 contents from 313 to 723 K. Therefore, the presence of complete semicircles of BSLFO at high ‘T’ values inferred that the present material compositions expressed the semiconducting nature [29]. In addition, it was evident that as the temperature was increased, the broad nature of semicircles was diminished. This implied that the relaxation was moved towards the high frequencies with increase of ‘T’. The charge carriers which were confined to the potential well can be responsible for this [30]. It was also observed that there was larger number of single semicircles which indicated the contribution of grains rather than grain boundaries in the electrical conduction mechanism [3]. The bulk conductivity or dc-electrical conductivity behavior was well understood by means of bulk resistance (grain resistance). In fact, one can apparently identify the intersecting position of arcs at the Z′-axis (real axis). This can bring us the bulk resistance. In the ColeCole plots of y = 0.2–0.8, the bulk resistance was decreased drastically

Fig. 10. (continued)

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Fig. 11. Cole – Cole plots (Z′ Vs. Z″) of BSLFO nanorods at various temperatures.

Fig. 11. (continued)

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Fig. 12. M′-log ω plots of BSLFO nanorods at various temperatures.

Fig. 12. (continued)

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Fig. 13. M″-log ω plots of BSLFO nanorods at various temperatures.

Fig. 13. (continued)

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with the increase of temperature. Thus, obviously, bulk conductivity was found to be increased by following the Arrhenius law as mentioned in Ref. [3]. In addition, the non-Debye types of relaxations were identified for all samples from the location of centers of arcs observed at the below position of real axis as reported in the literature [31–37]. 3.6. Dielectric modulus spectroscopy The complex dielectric modulus (M*) can be in general written as M* = M' + jM", whereas M' = (ε'/(ε′2 + ε"2)) and M" = (ε"/ (ε′2 + ε"2)). The electrical conduction, as well as the space charge polarization effect, can be well understood by means of studying the complex dielectric modulus formalism. The real (M′) and imaginary (M″) parts of complex dielectric modulus were discussed in the case of BSLFO nanostructures at different ‘T’ values. The related graphs were shown in Figs. 12 and 13. In Fig. 12, it was noticed that the M′ of all the contents was approximately zero (for all ‘T’ values) at small log ω values. This was attributed to the lack of strength that can control the mobility of charges via the input field frequency [25]. In addition, the charges were noticed to be more active (due to electrode polarization) at low-frequency region and hence they can move within a long-range regime. But, due to having less restoring force at small log ω values, M′ was recorded to be minimum. Further, it was found that the M′ was increased with frequency and decreased with temperature. During this continuous dispersion, the M′ approached the M'max. The reduction of M′ with ‘T’ was attributed to the temperature-dependent relaxation process as reported by Joshi et al. [26]. In the same way, the increase of M′ with log ω was due to short distance mobility of charge carriers [25]. In Fig. 13, the M″ versus log ω plots at distinct ‘T’ values were shown. The M″ was also increased with an increase in log ω and reached maximum values. In doing so, the small asymmetric relaxation peaks were found by revealing the non-Debye relaxation nature. Indeed, the asymmetric relaxation peak positions were shifted towards the high log ω values with an increase in temperature. This was happened due to the motion of mobile charges [26]. Below the relaxation, the M″ was achieved due to mobility of charges for longer distances. The M″ values beyond relaxation were established owing to the short-range mobility of charges which were confined to potential well [26]. Herein, the reason for the observed asymmetry in the relaxation peaks was the presence of stretching exponent parameter which can be responsible for the Debye and non-Debye relaxations. In general, the negligible dipoledipole interaction takes place within a material due to having the exponent equals to one. But for considerable dipole-dipole interaction, the exponent lies between 0 & 1. Thus, the low value of exponent indicated the deviation of Debye relaxation as suggested by Joshi et al. [26]. The M′ versus M″ plots at different temperatures were depicted in Fig. 14. Two semicircular arcs were found in the case of y = 0.2–0.8 contents. Obviously, it was noted that all the arcs were depressed and the centers were positioned below the M′-axis. This expressed the non-Debye relaxation mechanism as in the case of Z′ versus Z″ plots. The low-frequency arcs (first arcs) were formed due to the grain contribution whereas the high-frequency arcs (second arcs) were correlated to the grain boundary contribution. The second arcs were not visible in the Z′ versus Z″ plots. However, secondly formed arcs were partial and reverse in nature due to partial relaxation strength [26]. In addition, this (formation of reverse arcs) can be attributed to the high electrical conduction mechanism. In addition, the scattering of charge carriers from the scattering centers may be responsible for acquiring this kind of trend. Normally, the scattering of charges can occur owing to the disordered arrangement of atoms or grains at the grain boundary interface [32]. Fig. 14. M′ Vs. M″ of BSLFO nanorods at various temperatures.

4. Conclusions The BSLFO nanorods were prepared via the hydrothermal method. The hexagonal phase identification was confirmed using the XRD 12

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patterns. The FESEM pictures showed the formation of rectangular nanorods for y = 0.2–0.8 contents. The space charge polarization was observed within the ε′- log ω plots. Furthermore, the dielectric transition temperature was found to be decreased from 733 to 683 K with composition. In the Arrhenius plots, the high-temperature activation energies (EH) (0.542–0.859 eV) were observed to be higher than that of low-temperature region activation energies (EL) (0.053–0.226 eV) due to polaron hopping. Using the power-law fit, the calculated σdc was noted to be changing from 2.424 × 10−8 to 1.462 × 10−7 S/cm with an increase of ‘y’. The microstructure and electrical conduction mechanisms were analyzed by impedance study. In addition, the nonDebye relaxations were identified for y = 0.2–0.8 contents. The short range and long range polarization mechanisms were observed in the dielectric modulus plots.

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