Dielectric and optical spectroscopy of new polycrystalline ceramic for device applications

The polycrystalline double perovskite Li2GdFeTiO6 was synthesized through the solid-state mixed oxide method and its preliminary crystal structure was investigated by the XRD technique. The structure of the material was identified to be tetragonal with space group P4bm using POWD and MATCH software. The morphology of the sample was investigated through a scanning electron microscope (SEM) and the average grain size was found to be 3.82 μm using the intercept technique. The investigation of the perovskite phase and various vibrational modes were carried out through FTIR spectroscopic technique. The bandgap (Eg = 1.73 eV) and visible light sensitivity of the material were identified by UV–Visible spectroscopic operation carried in the range 200–700 nm. The dielectric and related properties were investigated as a function of frequency and temperature using an impedance analyzer (LCR meter). Room-temperature dielectric investigation suggests it may be useful for storage application. The transport activities investigated through conductivity, impedance, and modulus technique illustrate the significant influence of grains on transportation of charges.


Introduction
Over the most recent couple of decades, multifunctional-multiferroic materials accumulate the attention of researchers working in the field of material science as a result of their fascinating physical properties, for example, ferromagnetic and ferroelectric includes at the same time in a single phase. These materials are a wide scope of use for devices, for example, piezoelectric sensors, photovoltaic/solar cells, arbitrary access memory, and many more [1,2]. In this classification, perovskite materials are seen as valuable and promising applicant. Perovskites are also found to be useful in improving the efficiency and performance of solid electrolytes. It is reported that lithium titanate-based perovskites are a promising candidate for solid electrolytes because of their relatively high ionic conductivity and negligible electronic conductivity at room temperature [3][4][5][6]. In the framework of discovering new multifunctional material, we focus our attention on Gadolinium (Gd)-based orthoferrites. In Gd-based orthoferrite, the exchange interaction Gd 3? $ Fe 3? causes lattice distortion which triggers large electric polarization around anti-ferromagnetic Neel temperature [7,8]. In the system of examination on material development, material specialists have figure out some derivatives of perovskite. Among the derivatives, double perovskite oxide (DPO) with general recipe A 2 BB 0 O 6 (where A = alkali/alkaline earth or rare-earth ion, B and B 0 = Transition metal ions and O = oxygen ion) has drawn the consideration of researchers due to their utilization as a cathode in moderate temperature solid oxide fuel cells. The accessibility of various distinct cations alongside oxygen anion in DPO widens their application for device fabrication. Various theoretical and experimental investigations on DPO reveals that the different physical properties such as electrical, magnetic, optical etc. are very much influence by the size as well as the valence of the cations A, B and B 0 .
Although the research on DPO was long back, the actual progress in this field starts after the discovery of high tunneling resistance in Sr 2 FeMoO 6 at room temperature by Kobayashi et al. and Ueda et al. [9,10]. The other fascinating features of this class of materials are half-metallicity, colossal magnetoresistance, high ferromagnetic Curie temperature, etc. [9,11]. These class of materials are found auspicious for displaying magneto-electric coupling which enables their use in spintronic devices like low-field magnetoresistive sensors or tunneling magnetic junction [12]. Besides magneto-electric features, they are also found to possess a high value of dielectric constant (e r ) and dielectric relaxation which enhances their demand in technological applications such as multi-layer storage memory device, photovoltaic devices, optoelectronic devices, and many more [13,14]. In some of the work on perovskites [15][16][17][18], it was reported that Fe-based perovskites, A(Fe 0.5 B 0.5 )O 3 (A = Ca, Sr, Ba; B = Nb, Ta, Sb), possess a high dielectric constant with unique relaxation features besides their fascinating magnetic and magneto-transport activities. The involvement of iron (Fe) at the octahedral B-position of the investigated material is expected to generate fascinating multifunctional/multiferroic features.
Among the double perovskites, some members of the rare-earth family are found to exhibit very fascinating physical properties. The magnetic and transport investigation of La 2 CoMnO 6 done by Sahoo et al. [19] reveals the existence of semiconducting features in the vicinity of ferromagnetic (FM) curie temperature. It is reported that on substitution of rare-earth (Sm and Gd) with small ionic radii at La-site induce structural instability and destroy the long-range FM ordering [20]. It is also reported that La 2 CoMnO 6 and Sm 2 CoMnO 6 system possesses two FM transition, while Gd 2 CoMnO 6 has only one FM transition [19]. The double perovskite Lu 2 CoMnO 6 shows magnetically tunable electric polarization due to the breaking of spiral inversion symmetry [21]. The double perovskite system A 2 NiMnO 6 (where A = La, Lu) exhibits polar behavior associated with lattice frustration due to variation of ionic radii of rare-earth site ion [22]. Filho et al. reported the spin-phonon coupling in Y 2 NiMnO 6 due to expansion/contraction of the octahedral NiO 6 and MnO 6 [23]. Because of these fascinating and wide range spectra, we have focused our attention on rare-earth to develop double perovskite further improving properties. The double perovskites material can be obtained by combining two perovskite structures in proper stoichiometry. Based on this, we have synthesized double perovskite Li 2 GdFeTiO 6 by combining the elements of gadolinium ferrite and lithium titanate in a suitable ratio. In this work, we have reported the structural, optical, dielectric, and transport properties of Li 2 GdFeTiO 6 in detail.

Experimental technique
The investigated sample was synthesized through solid-state route method by taking the raw chemicals Li 2 CO 3 , Gd 2 O 3 , TiO 2 , and Fe 2 O 3 in proper stoichiometry ratio as shown in Fig. 1. These chemicals were graded with 99% of purity from M/S LOBA Chemie Corporation. The proportionality of the raw chemicals was estimated by the following relation: another 1-2 h. The grounded powder sample was then put in an alumina crucible and placed in a hightemperature furnace for calcination. After repeated firing technique, finally, a hard lump of the sample was found to form at 825°C which was considered as calcinations temperature. The lump sample was then broken and converted into homogeneous calcined powder using Agate Mortar and Pestle. For microstructure and electrical characterization, some portion of the calcined powder was pelletized into a circular disc of suitable dimension by exerting pressure through hydraulic press of the order 10 6 N/m. To improve the strength of the pellet sample, polyvinyl alcohol (PVA) was added as a binder in the calcined powder before pelletization. Finally, the pellet sample was sintered at around 875°C.
The room-temperature XRD technique was incorporated for preliminary investigation of structure. The XRD was conducted on the calcined powder using an X-ray diffractometer (Model: RIGAKU Japan ULTIMA IV) with CuK a as incident radiation in the Bragg's angle (2h) range 20°B 2°B 80°at a scanning rate 2°/min. The scanning electron microscope (SEM) (Model: JEOL JSM-5800) was incorporated for the investigation of surface morphology of the pellet sample at room temperature. Investigation on different modes of vibration, functional group, etc. was done through FTIR spectroscopic technique using JASCO-FTIR/4100 infrared spectrometer. 3 Results and discussion

Structural investigation
The preliminary room-temperature structural investigation was carried out in the diffraction angle (2h) ranging from 20 to 80°using X-ray diffraction (XRD) technique and depicted in Fig. 2. The observed sharp and unique peaks in the XRD profile differ from raw chemical suggesting a new structure has formed. The structural formation is also clarified from the characteristics diffraction peaks corresponding to JCPDS file no. 00-053-1045 (inset in Fig. 2). The structural identification was done by utilizing standard programming software ''POWD.'' In this technique, all the XRD peaks were refined in the framework of the seven crystal system. The deviation between experimental and computational value of interplanar spacing (shown in Table 1) was found minimum (r = 0.024) for tetragonal structure, which suggests the investigated sample crystallize in a tetragonal structure. The lattice parameters obtained are a = b = 7.804 Ȧ , c = 20.751 Ȧ , c/a = 2.6591, and V = 1263.81 (Ȧ ) 3 . As all the XRD peaks were index well for tetragonal structure with the above unit cell parameters, it suggests the formation of single-phase compound. The appearance of strong intensity XRD peak with Miller index (2 2 0) along 2h = 32.3°affirms that majority of the crystal is growing along [2 2 0]. The observed slight broadening in the XRD profile was expected due to titling of the octahedral FeO 6 and TiO 6 from their ideal position. Further investigation on structural parameters, atomic positions, and reliability factors was done by Rietveld refinement technique using MATCH software (version 2.O). The refinement profile and detail atomic position obtained through rietveld technique are illustrated in Fig. 3 and Table 2, respectively. The observed least value of reduced (chi) 2 (v 2 = 2.3) and average Bragg R-factor (R B = 12.8%) for tetragonal system (space group = P4bm) once again clarify that the investigated sample crystallizes in tetragonal structure.
The surface morphological investigation of the prepared sample Li 2 GdFeTiO 6 was carried out on pellet sample at room temperature using a scanning electron microscope (SEM) is shown in Fig. 4. The polycrystalline nature was revealed from the micrograph as it consists of grains of varying size and shape distributed non-uniformly throughout the pellet sample. Certain sort of clustering of grains observed in the micrograph may be due to hightemperature sintering of the pellet sample. Even after sintering at high temperature, certain amounts of voids are noticed on close observation which can trigger the hopping conduction mechanism of charges [24]. The relatively high concentration of small grains in the micrograph was expected due to collapsing of large grains during the transport of oxygen ion vacancies through the grain boundaries. The average grain size (3.82 lm) evaluated from the SEM image through the intercept method was found less as compared to the La-based equivalent sample (reported earlier) [25], which suggest the present sample has relatively fewer voids and more dense. In some of  [24,26], it is reported that the grains with rectangular geometry impart ferroelectric features. The observed richness of rectangular shape grains in the investigated sample suggests it can also possess the ferroelectric property with large spontaneous polarization.

FTIR spectroscopy
The investigation of different modes of vibration and functional groups present in the sample was done by FTIR spectroscopic technique as shown in Fig. 5. The FTIR spectrum was found to consist of some characteristic bands located at around 453, 567, 876, 927, 1000, 1134, 1433, 1505, and 3405 cm -1 . The perovskite-based materials are generally found to possess some characteristic band linked with lattice    [29]. The absorption of OHradicals attributes to the band at 3405 cm -1 in the investigated sample [29].

UV-Visible spectroscopy
The optoelectronic response of the prepared sample was investigated through the UV-Visible spectroscopic technique. The absorbance and reflectance spectra of the investigated sample are depicted in Fig. 6. It was noticed from Fig. 6a and c that the response of the sample was relatively weak in the UV range, whereas a reverse trend was observed in the visible range. The absorbance cut-off of the sample was found to be nearly 650 nm which suggest the sample absorb visible radiation in the range of 380-650 nm quite strongly. To calculate the energy bandgap (E g ) we have utilized the relation (ahm) 1/ n = A (hm -E g ) [30] proposed by Tauc, Mott, and Davis. Where a = absorbance coefficient, m = frequency of incident radiation, A = proportionality constant, and n = index ascribing different electronic transition. For n = 1/2, 3/2, 2, and 3, the transition is direct allowed, direct forbidden, indirect allowed, and indirect forbidden, respectively. In the present investigation, we take n = 1/2 as perovskite materials generally undergo direct allowed transition. The bandgap (E g = 1.73 eV) of the material was extracted from the Tauc plot (Fig. 6b) by extrapolating the tangent line on the hm axis. Besides Tauc function, we have also utilized Kubelka-Munk function [31] F (R) = (1 -R)/2R (where R = reflectance coefficient) to calculate the bandgap from reflectance data. The estimated bandgap (E g = 1.87 eV) from the reflectance plot (Fig. 6d) was found to be comparable with the value obtained from absorbance data.

Dielectric spectroscopy
The frequency-dependent variation of relative permittivity/dielectric constant (e r ) and loss tangent (tand) is depicted in Fig. 7a and b, respectively. It was found that both the parameters e r and tand decrease with an enhancement of frequency for all the selected temperatures. As per literature, the dielectric property of ceramic is very much influenced by four kinds of polarization, namely, electronic, ionic, dipolar/ orientation, and space charge polarization [25,32]. At low frequency, all the polarizations contribute significantly, whereas at high frequency only electronic polarization attributes towards the total dielectric of the ceramic [33]. The gradual disappearance of different polarizations with an enhancement of frequency is the significant cause of dielectric dispersion  Koop's phenomenological theory [34] was found quite consistent with the observed dielectric anomaly in the investigated sample. As per the theory, ceramic dielectrics consist of two types of layers (i) semiconducting grains and (ii) insulating grain boundaries. The grain boundaries are more prominent in the low-frequency region, whereas the grains are more prominent in the high-frequency region. Due to the insulating nature of grain boundaries, the charge carriers (like electrons) get to accumulate on them which increase the trapped charge density and hence e r value [35][36][37]. To move the charge carriers via grain boundaries, the energy required is more and hence high tand value. On increasing the frequency, the density of trapped charges on grain boundaries keeps on decreasing and charges start to slide over the grain by dissipating less energy and hence e r and tand are also low. Also, it is noticed from Fig. 8a and b that the values of dielectric parameters e r and tand almost attain saturation level below 350°C and above it, both of them start to rise sharply without encountering any transition (magnetic and/or ferroelectric) in the specified temperature range 25-525°C. Such observation suggests that the transition may lie beyond the experimental constraint temperature. The asymptotic variation of e r and tand above 350°C may be assigned to thermally activated hopping conduction of mobile charges in the system [25,38]. As the B-site of the investigated sample was occupied by multiple valency ions Fe and Ti, it was expected that the creation of oxygen vacancies during high temperature calcination and sintering can cause valence fluctuation and transforms Fe 3? /Ti 4? into Fe 2? /Ti 3? . The involvement of Fe 3? /Ti 4? along with oxygen vacancies is the possible cause for activation of mobile charges and hence dielectric parameters with enhancement of temperature. The other possibilities of high value of dielectric parameters at elevated temperature are (i) electron-phonon interaction at the lattice site, (ii) presence of some imperfection/dislocation in the crystal, and (iii) domination of conductivity [35][36][37][38].

Impedance study
The non-destructive impedance spectroscopy method was adopted to study the influence of grains, grain boundaries, and electrodes in the characterization of electrical properties. In this method, an electrical perturbation was induced in the dielectric system and its output response was recorded over a varying range of frequency and temperature. To evaluate the resistive (Z 0 ) and reactive (Z 00 ) components of complex impedance (Z*), the following equations were utilized [35][36][37] where s is the relaxation time and is defined as s = RC. The frequency-temperature-dependent variation of resistive (Z 0 ) and reactive (Z 00 ) is depicted in Fig. 9a and b, respectively. From Z 0 versus frequency spectra, it was noticed that Z 0 value falls in a sigmoidal manner below 10 kHz, which suggests the lowering in density of trapped charges at grain boundaries [39]. The overlapping of all the curves above 10 kHz irrespective of temperature signifies the release of space charges and domination of ac conductivity in the material at high frequency [40]. It is observed from Z 00 versus frequency spectra, the value of Z 00 raises proportionally with frequency and attains maxima at a characteristics frequency (commonly known as relaxation frequency) and then gradually falls and attains saturation in high frequency. The shifting of maxima peak in the direction of increasing frequency with enhancement of temperature suggests that the relaxation in the material is temperaturedependent and is non-Debye type [41]. The broadening of maxima peak in Z 0 spectra with enhancement of temperature suggests the spread of relaxation and fall of relaxation time in the investigated material. The low-temperature relaxation in the material can be ascribed to involvement of immobile charges through hopping between (Fe 3? -Fe 2? ) and (Ti 4? -Ti 3? ) at the octahedral site while that at high temperature is due to oxygen vacancies and/or some intrinsic defect. The NTCR behavior in the material is also reflected from both Z 0 and Z 00 spectra.
The change of Nyquist plots (i.e., Z 00 vs Z 0 ) at various temperatures is depicted in Fig. 9c. The observed single semicircular arc in the Nyquist plot suggests that the resistive and capacitive property was highly influenced by the grains in the material. As per Debye hypothesis, an ideal semicircular arc with center that lies on the Z 0 axis corresponds to a single relaxation process and homogeneity in the material. The depressed semicircle with center lies below the Z 0 axis suggesting the non-Debye type of relaxation and inhomogeneity in the investigated sample [42]. To correlate the electrical and microstructural properties, an equivalent circuit model consists of capacitor (C) and resistor (R) incorporated. The experimental data were fitted with the theoretical ones using software ZSIMWIN (version 2.O). In order to counter the observed depression in the semicircular arc, a new element, namely constant phase element (CPE) Q was introduced in the RC network. It was noticed that the experimental data were fitted well for the equivalent circuit (C || Q || R) (inset in Fig. 9c). Such observation suggests a significant contribution of grains in the electrical and transport mechanism [43]. The slight deviation observed in the semicircular arc from the model generated curve at low frequency might be due to weak contribution of grain boundaries.

Modulus study
The complex modulus spectroscopic method is also incorporated in addition of impedance technique to have a better understanding of different processes such as (i) relaxation, (ii) conduction, and (iii) transport occurring in the investigated sample. The advantage with modulus technique is that it can extract the contribution of small capacitance in the material which sometimes gets suppressed in impedance technique due to the inhomogeneous distribution of grains [44]. The real (M 0 ) and imaginary (M 00 ) components of complex modulus (M*) were extracted using the following equations [35][36][37]: where C0 is the geometrical capacitance and is defined as C 0 = e 0 A/d (e 0 = permittivity of free space, A and d are, respectively, area and thickness of the circular pellet). It is observed from the variation of M 0 versus frequency spectra (Fig. 10a) that M 0 has a negligibly small value in the low-frequency region, which suggest an insignificant contribution of electrode polarization. The monotonic dispersion observed in M 0 spectra at intermediate frequency region attributes to the short-range mobility of charge carriers influencing the conduction process. The mobility is due to the lack of restoring force of charge carriers in external electric perturbation. The merging of all curves irrespective of temperature ascribes to the lack of space charges in high-frequency region [45,46].
From M 00 versus frequency spectra (Fig. 10b), it is found that M 00 value increases with frequency and reach a maximum. The relaxation in the material is once again clarified from M 00 spectra. The temperature-dependent relaxation is observed from the shifting of relaxation peak towards high frequency which is due to activation of hopping conduction through thermal agitation. The asymmetric broadening of M 00 spectra signifies non-Debye type of relaxation [47,48].
In order to illustrate, the response of small capacitance and large resistance in the material, the relative variation of Z 00 and M 00 with frequency ( Fig. 11a) is studied at a particular temperature. It also enables to distinguish whether the relaxation in the material is dominated by short-range or long-range charge carriers. For long-range process, Z 00 and M 00 ' relaxation peaks appear at nearly common frequency, whereas for short-range process, they appear at different frequencies. The observed mismatching of Z 00 and M 00 peaks in the investigated sample suggest that shortrange charge carriers are dominating the relaxation mechanism [49,50]. The domination of short-range charge carriers, also noticed in dielectric spectroscopy investigation, for the prepared sample is expected due to the hopping of electrons between (Fe 3?-$ Fe 2? ) and (Ti 4? $ Ti 3? ) at different lattice sites.
The relaxation time (s) obtained from Z 00 and M 00 spectra are studied as a function of temperature as depicted in Fig. 11b. In order to estimate the value of s, we have utilized the relation s = 1/2pf r , where f r corresponds to the frequency of relaxation. The observed values of s are found to fit well with the Arrhenius relation [51] s = s 0 exp (-E a /K B T), where E a = activation energy. The E a = 1.109 eV value estimated from Z 00 spectrum corresponds to localized conduction, while E a = 1.087 eV obtained from M 00 spectrum corresponds to delocalized conduction [50,51]. The observed closeness of E a value illustrates that similar sort of charge carriers participates in both the conduction processes.

AC conductivity study
The frequency-dependent variation of ac conductivity (r ac ) at selected temperatures is depicted in Fig. 12a. It is noticed that the variation of r ac is relatively small in low-frequency range, whereas at high frequency it rises sharply. The observed dispersion in r ac spectra can be ascribed to the presence of space charges as well as disorderliness of the cations at A site and B site [52]. The conductivity spectrum was found to be very much consistent with Jonscher's power law r ac = r 0 ? Ax n [53]. As per the law, the origin of frequency-dependent conductivity is related to the relaxation phenomenon of mobile charges. Also, it is noticed that the slope of the ac conductivity spectrum is relatively high at high-frequency than that at low-frequency region. Such observation suggests that the hopping mechanism of charges is quite dominating in the conduction process. The presence of multi-valent ions Fe and Ti at B-site can initiate the hopping conduction of electron between (Fe 3? $ Fe 2? ) and (Ti 4? $ Ti 3? ) in the investigated sample.
The temperature-dependent variation of r ac at selected frequencies is shown in Fig. 12b. The NTCR behavior of the material was confirmed as r ac increases with temperature. The high value of r ac at high-temperature region attributes to higher mobility of charges due to hopping between localized sites [54]. The activation energy (E a ) was calculated in high-temperature region by fitting the Arrhenius equation r ac = r 0 exp (-E a /K B T) [36] in the experimental data. The obtained values of E a were 1.027 eV, 0.791 eV, 0.475 eV, 0.329 eV, and 0.295 eV at frequencies 1 kHz, 10 kHz, 100 kHz, 1 MHz, and 5 MHz, respectively. The E a value was found to be high at low frequency than that of high frequency. With the increase in frequency, the transportation of charge carriers between localized sites enhances and hence activation energy decreases.

Conclusion
The XRD investigation on double perovskite Li 2-GdFeTiO 6 synthesized through solid solution technique reveals that the formation of single-phase new compound crystallizes in tetragonal structure (space group = P4bm). The appearance of grains of varying size and shape with a little amount of porosity in SEM morphology reveals the formation of highdensity polycrystalline material. Also, the observed rectangular shape grains in SEM micrograph indicate that the material may possess ferroelectric features with large spontaneous polarization. The confirmation of perovskite phase and involvement of various modes of vibration were identified through FTIR Fig. 11 a Combined variation of Z 00 and M 00 with frequency b Variation of relaxation time with temperature Fig. 12 a Frequencydependent variation of r ac b Temperature-dependent variation of r ac spectroscopy. The optical property investigated through UV-Visible absorbance and reflectance data reveals visible light sensitivity of the material. The optical bandgap evaluation from both Tauc plot and Kubelka-Munk plot suggests the usefulness of the material for the photovoltaic device. The room-temperature dielectric parameters suggest that it can be utilized for storage application. The impedance and modulus spectroscopy analysis clarifies the non-Debye-type relaxation mechanism in the material. The AC conductivity plot was found to be consistent with Jonscher's universal power law. The basic conduction/transport phenomenon in the material was found to be dominated through hopping of immobile charges at low temperature while at high temperature is due to oxygen vacancies/intrinsic defects.