Fe3+-substitution effect on the thermal variation of J–E characteristics and DC resistivity of quadruple perovskite CaCu3Ti4O12

Kunal B. Modi, Pooja Y. Raval, Dolly J. Parekh, Shrey K. Modi, Niketa P. Joshi, Akshay R. Makadiya,Nimish H. Vasoya, and Utpal S. Joshi

1Department of Physics, Saurashtra University, Rajkot 360005, India

2Department of Physics, C. U. Shah University, Wadhwan City, Surendranagar 363030, India

3Department of Environment Engineering, L. D. Engineering College, Ahmedabad 380015, India

4Department of Balbhavan, Children′s University, Sector – 20, Gandhinagar 382015, India

5Department of Physics, University School of Sciences, Gujarat University, Ahmedabad 380009, India

Abstract: The electrical properties of cubic perovskite series, CaCu3–xTi4–xFe2xO12 with x = 0.0, 0.1, 0.3, 0.5, and 0.7, have been studied by employing current density as a function of electric field characteristics registered at different temperatures and thermal variations of direct current electrical resistivity measurements. All of the compositions exhibit strong non-ohmic behavior. The concentration dependence of breakdown field, the temperature at which switching action takes place, and maximum value of current density (Jmax) has been explained on account of structural, microstructural, and positron lifetime parameters.The highest ever reported value of Jmax = 327 mA/cm2 has been observed for pristine composition. The values of the nonlinear coefficient advise the suitability of ceramics for low-voltage varistor applications. The Arrhenius plots show typical semiconducting nature. The activation energy values indicate that electric conduction proceeds through electrons with deformation in the system.

Key words: perovskites; magnetic materials; J–E characteristics; capacitor

1.Introduction

In 2000, Subramanianet al.[1]and Ramirezet al.[2]noticed that the dielectric permittivity (ε′) of a microcrystalline sample of perovskite derivative calcium-copper-titanate(CaCu3Ti4O12) abruptly jumps by a factor of 100 when heated aboveT= 90 K (at 1 kHz frequency). This material atT=100 K exhibits a huge value ofε′ of the order of 104andε′ becomes weakly dependent on temperature forT= 100–320 K.These unusual and fascinating properties make them suitable for potent applications, such as in multilayer ceramic capacitors, devices for memory and high-density energy storage[3]. In 2003, Kretlyet al.[4]successfully used CaCu3Ti4O12substrates for microwave devices and antennas. In 2004, Chunget al.[5]observed highly non-ohmic current–voltage characteristics in CaCu3Ti4O12with nonlinear coefficient ≈ 912. This leads to the use of this material as an efficient switching (varistor-type device) and gas sensing device. In 2012, Felixet al.[6]investigated thin films of CaCu3Ti4O12for potential applications, such as gas sensing, rectification, and resistive switching. In 2016, it was demonstrated that this material could serve as photocatalytic and photoelectrochemical materials with an excellent performance in visible light[7]. Since then,pure and substituted CaCu3Ti4O12and related materials in monocrystalline, microcrystalline, nanophasic, nanocomposites, and thin-film forms have been extensively researched for potential use in a wide range of applications. In 2020, Chhetryet al.[8]revealed a novel possibility for the easy design and development of superior CaCu3Ti4O12based capacitive sensors with versatile characteristics. Chattopadhyayet al.[9]suggested the possible use of CaCu3Ti4O12nanopowder for application in a humidity sensor. Many research reports describing the fundamentals of experimental and theoretical researches on CaCu3Ti4O12based ceramic materials are available in the literature.

Varistors are voltage-dependent resistors that demonstrate strong nonlinear current versus voltage (I–V) characteristics. The electrical properties of varistors are chiefly influenced by grain-boundary interface states. The principal function of a varistor is to sense and control transient voltage surges. When a varistor is subjected to a high applied voltage, its impedance changes from a near open circuit to a highly conducting state, which results in the clamping of the transient voltage to a safe level and thus electronic components of high-cost electronic devices may be protected.Between 2016 and 2021, a limited number of research reports were published onJ–Echaracteristics of CaCu3Ti4O12cubic perovskites substituted with different metallic cation/cations. For example, the nonlinear electrical properties with high-performance dielectric behavior of CaCu2.95Cr0.05Ti4.1O12have been studied by Prompaet al.[10]. The improvement of the breakdown field and the dielectric properties of Bi3+-Al3+co-doped CaCu3Ti4O12have been investigated by Renet al.[11]. The dielectric properties, nonlinear electrical response,and microstructural evolution of CaCu3Ti4–xSnxO12ceramics prepared by a double ball-milling process have been investigated by Boonlakhornet al.[12]. Corteset al.[13]performed dielectric and non-ohmic properties of Ca2Cu2Ti4–xSnxO12multiphasic ceramic composites. Comparative studies on pure and Sr2+and Ni2+doped and co-doped ceramics with special emphasis on the enhancement of dielectric properties have been published by Rhoumaet al.[14]. Wuet al.[15]accomplished the effect of Ba2+substitution on microstructure and electrical properties of Ca1–xBaxCu3Ti4O12ceramics. Enhanced nonlinearI–Vresponse of Te4+substituted CaCu3Ti4O12ceramics has been studied by Barmanet al.[16]. Meanwhile, the improvement in varistor properties of aliovalent Cr3+substitution for Ti4+in CaCu3Ti4–xCrxO12–δseries has been investigated by Grezebieluckaet al.[17]. Sunet al.studied improved dielectric properties of In3+and Ta4+co-substituted CaCu3Ti4O12ceramics prepared by spark plasma sintering[18].Very high-performance dielectric and non-ohmic properties of X and R-type Ca1–1.5xHoxCu3Ti4O12/TiO2ceramics have been investigated by Sriakdeeet al.[19]. Finally, enhanced giant dielectric properties and improved electrical response in acceptor–donner (Al and Ta)-substituted CaCu3Ti4O12polycrystalline ceramics have been carried out by Boonlakhornet al.[20].Unfortunately, these studies carry very limited and similar information, and were performed atT= 300 K. The same is the case with the thermal variation of dc electrical resistivity,ρdc(T),study. To the best of our knowledge, only a handful of research articles describingρdc(T) characteristics of bulk[21?24]and thin films[25]of CaCu3Ti4O12are available in the literature.This gap has motivated us to carry out a systematic study of current density versus electric field characteristics over a wide temperature range and thermal variation of dc resistivity study of polycrystalline samples of quadruple perovskite series, CaCu3–xTi4–xFe2xO12withx= 0.0, 0.1, 0.3, 0.5, and 0.7.

Based on the following facts, the work presented in this communication is important as well as different from the existing literature. The electrical properties,J–Echaracteristics and dc resistivity of CaCu3–xTi4–xFe2xO12withx= 0.0, 0.1, 0.3, 0.5,and 0.7 have been studied over a wide temperature range ofT= 313 to 773 K as a function of Fe-concentration (x). The compositional variation of various electrical parameters (e.g., maximum current density, breakdown electric field, the temperature at which switching action takes place, Schottky barrier height, non-linearity coefficient, and activation energy) are determined and correlated with structural parameters (i.e., lattice constant, cationic distribution), microstructural parameters (i.e., grain size, microstrain, dislocation density) and positron annihilation lifetime (PAL) parameters (i.e., defect-specific positron lifetime, the concentration of vacancy defect).We have thoroughly investigated various physical properties of pristine and Fe3+-substituted CaCu3Ti4O12ceramics,CaCu3–xTi4–xFe2xO12withx= 0.0–0.7, in recent years (2018–2021)[26?37]. In the system, divalent, weak magnetic (1 Bohr magneton), Jahn-Teller Cu2+ions, and tetravalent, non-magnetic Ti4+ions are simultaneously replaced by highly magnetic (5 Bohr magneton), trivalent Fe3+ions in the series of quadruple perovskites, CaCu3–xTi4–xFe2xO12wherexvaries from 0.0 to 0.7. Thus, interesting improvements in electrical behavior are expected. This work blends fundamental and applied research.

2.Experimental details

A series of cubic perovskites, CaCu3–xTi4–xFe2xO12withx=0.0, 0.1, 0.3, 0.5 and 0.7, was prepared by the mixed oxide route. The complete details regarding the synthesis, crystallographic phase identification, and structural parameters including cationic distribution determination by employing Rietveld refinement of X-ray powder diffraction data and average grain size (D) estimation by analyzing scanning electron micrographs are given elsewhere[27,33]. The measurements of current (I) versus applied signal voltage (V) (V= 0–400 V) (I–Vcharacteristics) were carried out with the help of an Aplab made high-voltage dc regulated power supply (model no.?7332) at temperatures ranging fromT= 300–673 K using the two probe pressure contact method and a horizontal electric furnace. The cylindrically pelletized samples were rubbed with fine glass paper to give mirror-polished surfaces, and then cleaned with dilute hydrochloric acid and dimethyl ketone. To have perfect ohmic contact, microcracks on the surfaces were filled with a rubbing of graphite, and finally Alfoil was also kept on the surface. Instead ofI–Vcharacteristics, the traces ofJversusEare taken into consideration,which eases the comparison between theI–Vcharacteristics of the samples with varying thickness and surface area. A biterminal pressure contact method was employed to carry out the dc electrical resistivity measurement. The same set of the ceramic pellets, sample holder, vertical electric furnace, temperature indicator with thermocouple, and temperature controller used for thermal variation ofIversusVcharacteristics was used to carry out temperature-dependent dc resistivity measurement. The resistance was directly measured using a megaohm meter supplied by BPL India. The thermal variation of resistance was obtained by keeping a sample holder containing a cylindrically pelletized sample in a horizontal electric furnace. ForI–Vcharacteristics and dc resistivity measurements as a function of temperature, an indigenously designed and fabricated sample holder was used. The holder consists of two ceramic beads with supporting metal roads. The springloaded brass electrode is introduced into the ceramic beads and pressed hard against the surface of the pellet. The second brass electrode is fixed at the other end. GELCO electronics private limited, India made PTS-7201 temperature indicator attached with K-type chromal-alumel thermocouple were used to measure the temperature of the pellet. The temperature of the furnace was controlled by maintaining the current passing through the heater employing a current controller (Bharat electrical Mumbai, India, made single phase autotransformer). The resistance was noted during the cooling cycle at an interval of 20 °C in the temperature range of 300–773 K. A single set of temperature-dependentI–Vcharacteristics and dc resistivity measurements have been performed.

3.Results and discussion

A careful structural analysis demonstrates that thex=0.0–0.5 compositions are formed in the single phase with cubic perovskite crystal symmetry in the space group Im3.For the composition withx= 0.7, the aciculate but low intensity(～ 4.0 %) peak centered at 2θ= 25.6° is due to a trivial amount of anatase structure of well-crystallized TiO2[33]. The secondary phase is randomly distributed within the primary CaCu3Ti4O12matrix. Thus, Fe3+substitution is restricted tox=0.7 in the present study. In Tables 1 and 2, the structural and microstructural parameters are compiled to illustrate the compositional and temperature-dependentJ–Echaracteristics.

Table 1. Structural, microstructural, and electric parameters for a series of cubic perovskites.

Table 2. Distribution of metallic cations (Ca+2, Cu+2, Ti+4 and Fe+3)among the available crystallographic sites determined from Rietvield refinement of X-ray powder diffraction data ( T = 300 K) for CaCu3–xTi4Fe2xO12 ( x = 0.0–0.7) system.

Fig. 1 gives the plots ofJagainstEregistered at different temperatures ranging fromT= 300–773 K for the series CaCu3–xTi4–xFe2xO12. The samples exhibit strong non-ohmic characteristics. In the lowEregion, the dominant conduction mechanism is thermal excitation and as a result theJ–Ecurve is nearly ohmic. Nonlinear behavior is observed whenEis beyond the particular threshold value or breakdown value(Es) (E>Es). In this regime, tunneling action via grain-boundary barrier is responsible for the electric conduction. It is seen in Fig. 1 that the lowest temperature at which switching action takes place (TsL) decreases with Fe-content (x). The compositions withx= 0.0, (0.1, 0.3, 0.5) and 0.7 show switching action forT ≥473 K, (T≥ 373 K),T ≥313 K, respectively. Meanwhile,Esdecreases withxforx= 0.0 to 0.5 compositions,while forx= 0.7 compositionEsshows small enhancement(Table 1). The compositional variation ofEsmay be described by considering the structural and microstructural parameters.The strain values have been deduced from the simple and widely employed Williamson-Hall plot method[38]. The negative slope for all of the compositions suggests that a compressive strain has been produced (Fig. 2). The strain increases from –4.54 × 10–4forx= 0.0 composition to –6.77 × 10–4forx= 0.3 composition, it then decreases to –5.96 × 10–4forx=0.5 composition and further increases to –6.95 × 10–4forx=0.7 composition. It has been reported elsewhere that strain is directly proportional toTsLandEs, values[26]but no such correlation has been observed in this work. Huet al.[39]have shown that for ceramically prepared compositions,Esis inversely proportional to aggregate grain size (D) (Es∝1/D). For the series under investigation,Dincreases from 3.7μm forx= 0.0 composition to 7.9μm forx= 0.5 composition and then abruptly decreases to 3.4μm forx= 0.7 composition[33]. The increase ofDmeans that there is a decrease in the number of grainboundary barriers. Accordingly,Esdecreases from 978 V/cm forx= 0.0 composition to 261 V/cm forx= 0.5 composition and then forx= 0.7 compositionEsslightly increases to 300 V/cm, as shown in Table 1. Furthermore, observed decrease inTsLandEsforx= 0.0 – 0.3 compositions may be correlated with a subsequent decrease in lattice parameter (a(?))[38](Table 1). The observed decrease inawith Fe-substitution (x) for the compositionx= 0.0–0.3 infers that charge carriers need a small amount of energy for the conduction and thusTsLandEsdecrease forx= 0.0–0.3 compositions. The observed dependence ofEswith Fe- content (x) can also be explained based on defects that occur during the sintering process.There are three types of defects: vacancy, dislocation, and grain boundary. The presence of these defects effectively modifies the material’s optical and electrical properties. It has been reported that interface defect density or dislocation density on grain boundaries (δ) ∝ 1/D2∝Es2[26,38]. Thus, on increasing grain size fromx= 0.0–0.5 compositions and observed grain size reduction forx= 0.7 composition turned into decrease in δ andEsvalues (x= 0.0–0.5) and increase inδandEsvalues forx= 0.7 composition as observed (Table 1). The concentration of vacancy defects (Cd) determined from highly sophisticated PAL spectroscopy measurements[29]decreases rapidly within the crystallites forx= 0.0–0.3 compositions and then saturates gradually forx= 0.5 and 0.7 compositions. The variation ofCdis consistent with the variation ofEswith Fe3+-content (x). This leads to a very important conclusion that theEsis mainly controlled byCdandδ.

Fig. 1. (Color online) Plots of J–E characteristic recorded at different temperatures for a series of cubic perovskites, CaCu3–xTi4–xFe2xO12 (x =0.0–0.7).

Another interesting observation from Fig. 1 is that maximum current density (Jmax) decreases from 327 mA/cm2forx=0.0 composition to 270 mA/cm2forx= 0.1 composition to 225 mA/cm2forx= 0.3 composition and remains constant with further Fe3+-substitution. In the design of electronic and electrical devices, current density has a very significant role.Over the last few years, there has been a movement towards having a higher current density to achieve a higher number of devices in an ever-smaller chip area. As discussed earlier,with an increase inDforx= 0.0–0.5 compositions, the contribution from poorly conducting grain boundaries decreases as compared to semiconducting grains; thus,Jmaxis expected to increase with Fe- substitution, but this is not the case. This suggests that besides grain size, other microstructural parameters are also expected to affectJmax. Zhenget al.[40], following the density functional theory, have shown that in CaCu3Ti4O12the conduction mechanism is an adiabatic hopping conduction of small polarons and electron transport among CuO4square-planar (A′-site) clusters. Furthermore,the conduction band is chiefly contributed by the antibonding states of Cu 3delectrons. Usually, metal oxide series containing Jahn-Teller ions (high-spind4Cr2+and Mn3+ions, lowspind7Co2+andd9Cu2+ions) are referred to as the most likely candidates to demonstrate switching action. Based on the above findings, it is clear that cupric ions on the A′-site play a governing role in switching phenomenon and electric conduction. It is now feasible to elucidate the compositional variation ofJmax. The occupancy of metallic cations such as Ca2+, Cu2+, Ti4+and Fe3+among the crystallographic interstitial sites determined from Rietveld refinement of X-ray diffraction patterns revealed that with Fe- substitution the Cu2+-ion concentration at the A′ decreases from 3.0 forx= 0.0 composition to 1.53 forx= 0.7 composition[29,33], as displayed in Table 2. This results in the curtailment of electric conduction through the square-planar site, and thusJmaxdecreases rapidly forx= 0.0–0.3 compositions and then levels off for the compositions withx= 0.5 and 0.7, as shown in Table 1. The observed reduction inJmaxforx= 0.7 composition can also be explained based on the formation of a minor secondary insulating TiO2-phase and reduced grain size. The percentage formation of these secondary phases is well below the theoretical percolation threshold (～16%) and experimental percolation threshold (～20%) values. This would ensure that electric behavior such asEsandJmaxwould always be dominated by the CaCu3Ti4O12phase[33]. An effort has been undertaken to correlate the previous outcome of the PAL spectroscopy study[29]and present electric parameters as a function of composition(x). The magnitude of defect-specific positron lifetime (τ2) reflects the contributions from the grain boundaries, vacancies,and vacancy clusters in grains. Earlier, it was found thatτ2gradually increases from 0.2317 ns forx= 0.0 composition to 0.4449 ns forx= 0.5 composition and then level off forx=0.7 composition to 0.4379 ns. The subsequent increase inτ2suggests that the thickness of grain-boundary layers increases with Fe-substitution forx= 0.0–0.5 compositions and saturate forx= 0.7 compositions. This limits the conduction of charge carriers from one conducting grain to the adjacent conducting grain separated by the highly resistive grain boundary. This is thought to be the cause of the observed initial reduction ofJmaxwithx. On the same line of argument,Esis expected to increase withxbut no such trend has been observed. This suggests that as far asEsvalue is concerned, an increase in grain size and decrease in defect density in grains dominant over the grain boundary broadening with Fe3+- substitution in the system, CaCu3–xTi4–xFe2xO12.

Fig. 2. Williamson-Hall plots for all the samples of a series CaCu3–xTi4–xFe2xO12.

To the best of our knowledge, these values ofJmaxfor the pure and Fe-substituted CaCu3Ti4O12ceramics are the highest ever reported values, except for those reported for Nb5+and Ta5+-substituted CaCu3Ti4O12(Jmax≈ 275 mA/cm2)[41]. Earlier,we have foundJmax= 254 mA/cm2and 234 mA/cm2for quenched and microwave-assisted samples of CaCu3Ti4O12, respectively[26]. The nanocrystalline and microcrystalline samples of CaCu3Ti4O12synthesized by distinct routes (solid-state reaction, sol-gel, modified sol-gel, thermal decomposition, spark plasma sintering etc.) and treated with different conditions (atmoshphere, sintering temperature and duration etc.) have shown thatJmaxvaries from 0.1–32 mA/cm2[3,42?48]. Meanwhile, Y and Mg co-doped samples of CaCu3Ti4O12have shownJmax≈ 28 mA/cm2[49], Sr-Ni substituted CaCu3Ti4O12have exhibitedJmax≈ 15 mA/cm2[14], Pr-substituted CaCu3Ti4O12have demonstratedJmax= 15 mA/cm2[50], while Zn + Zr co-doped CaCu3Ti4O12thin films showJmaxin the range of 5–6 mA/cm2[51]. Finally, the composites, (1–x)(CaCu3Ti4O12)–(x)(0.1 Na0.5Bi0.5TiO3–0.9 BaTiO3) withx= 0.02,0.04, 0.06, 0.08 and 0.10, have shownJmaxranging from 13–20 mA/cm2[52].

Fig. 3. (Color online) ln J against E1/2 plots at different temperatures for polycrystalline samples of quadruple perovskite series,CaCu3–xTi4–xFe2xO12.

The existence of the Schottky barrier at the grain boundaries is signified by the observed linear relationship for lnJagainstE1/2traces[53–55](Fig. 3). The Schottky barrier height(?B) values determined from the slopes of the fitting lines of lnJ0(J0is the value ofJextrapolated toE= 0 V/cm) against reciprocal of temperature 1000/Tgraphs (Fig. 4) decreases from 0.25 eV forx= 0.0 composition to 0.21 eV forx= 0.5 composition while?Bvalue increases to 0.28 eV forx= 0.7 compositions. The electric potential barrier height for the pristine composition, CaCu3Ti4O12is consistent with the reported value[56].Huanget al.[54]have shown that the?Bis influenced by the residual impurities and impurities from decomposition. The?Bdemonstrates a close linear relationship to the microstrain andδ.

The coefficient of determination (R2) of a statistical model describes how well it fits a set of observations. A measure of this goodness-of-fit typically summarizes the discrepancy between the observed values and the values expected under the model in question. TheR2value between 0.70–1.0 indicates that there is a strong correlation between the dependent and independent variables. In general,R2value at or above 0.60 is considered to be worthwhile[57].

Fig. 4. (Color online) Plots of ln Jo against temperature for the different compositions.

Fig. 5. (Color online) Arrhenius plots for a quadruple perovskite series,CaCu3–xTi4–xFe2x O12.

On fitting lnJ0versus reciprocal of temperature (1000/T)plots with linear relation, theR2value forx= 0.0 composition is found to be 0.91, forx= 0.1 composition,R2= 0.94, forx= 0.3 composition,R2= 0.97, forx= 0.5 composition,R2=0.95 and for the composition withx= 0.7,R2comes to 0.90.These values ofR2are near the ideal value of 1.0, which suggests that the applied carrier transport model is able to successfully and accurately model the experimental data.

When we think about the varistor-type device, two parameters (i.e., non-linearity coefficient (α) andEs) are considered as a figure-of-merit. A large value ofαis always desirable because it allows the device to withstand the surges atEs. Theαvalues at different temperatures were calculated for the compositions withx= 0.0–0.7 using the standard definition. Theαvalue is found to vary from 2.09–4.51, 0.45–1.14,0.60–1.64, 0.76–2.34, and 1.27–6.88 forx= 0.0, 0.1, 0.3, 0.5 and 0.7 compositions, respectively, in the studied range of temperature. Furthermore, the value ofαis found to increase with temperature and Fe-substitution (x) (x= 0.1–0.7). This can be explained as follows.

The nonlinear coefficient (α) is defined by the standard relation:α= (logJ2– logJ1) / (logE2– logE1), whereJ1andJ2are calculated analogous toI1= 1 mA andI2= 10 mA, respectively, andE1andE2are the corresponding values of the electric fields. The electric field (E) and threshold voltage (Es) decrease with increasing Fe3+-substitution (x) in the system,CaCu3–xTi4–xFe2xO12, forx= 0.0–0.5 compositions. This is attributed to the decrease of the number of grain boundaries due to the increase of average grain size[58]from 3.7μm forx=0.0 composition to 7.9μm forx= 0.5 composition, as depicted in Table 1. Meanwhile, with an increase in temperature and the concentration of highly magnetic Fe3+-ions (5μB) for non-magnetic Ti4+(0μB) in the system, the degree of Fe3++e-→ Fe2+conduction that occurs on the square-planar site of the cubic perovskite structure is enhanced. Thus,IandJare expected to increase. These combined effects result in an increase in the value ofαwith temperature and Fe3+-substitution (x). The ranges ofαvalue advise that these perovskites are best suited for low-voltage varistor applications. In the literature, a wide range ofαvalues ranging fromα= 1.91 toα= 912 have been reported for pristine composition,CaCu3Ti4O12, registered at different temperatures, and synthesized with different sintering temperatures, preparative parameters, preparation routes, thermal history, voltage rise time in bulk, nanocrystalline and thin-film forms[26].

The high-temperature synthesis process of oxide ceramics that is employed here leads to the inevitable formation and existence of pores. Thus, X-ray density (dx) is always higher than the bulk density (d). These voids decisively affect the electric, dielectric, and elastic properties of the material. Thus,it is essential to correct such parameters for a void-free state,especially for compositional dependent investigation. The dc resistivity values in the void-free state (ρdc) for the different compositions have been determined from the experimental values of dc resistivity (ρp) recorded at different temperatures and void fraction values (f= 1 – (d/dx)) with the help of the following relation[59]?

This relation is effectively applied for the materials havingf< 0.4. The different compositions of the system under study possessfvalues that are much less than 0.4, as shown in Table 1. Theρdcvalues forx= 0.0–0.7 compositions lie in the range105–108Ω·cm atT= 300 K, advising that these are good insulating materials. Fig. 5 portrays log ρ versus temperature plots (Arrhenius plot). All of the compositions reveal usual semiconducting behavior (i.e., a decrease of resistivity with temperature). In the low-temperature regime, 300 K ≤T≤573 K, a linear variation of resistivity with temperature is observed; while forT> 573 K, a discontinuity or change of slope occurs, suggesting a change in the mechanism responsible for conduction in the studied materials. This may be correlated with the diffuse anomaly that takes place atT= 630 K[60]or may be associated with high-temperature structural phase transition reported occurring betweenT= 726–732 K for pure CaCu3Ti4O12composition[61]. The activation energy values (Ea1andEa2) were calculated for regions below and above the transition temperature, respectively, from the well-known Arrhenius equation and are shown in Table 1. In the low-temperature region,T= 300–573 K,Ea1decreases from 0.33 eV forx= 0.0 composition to 0.22 eV forx= 0.3 composition,and then increases to 0.25 and 0.27 eV forx= 0.5 and 0.7 compositions, respectively. The lattice constant (a) value decreases from 7.391 ? forx= 0.0 composition to 7.387 ? forx= 0.3 composition, and then increases to 7.400 and 7.411 ? forx= 0.5 and 0.7 compositions, respectively (Table 1). The observed reduction inawithxsuggests a corresponding decrease in interionic distances and as a result a decrease in barrier height encountered by the hopping charge carriers. Thus,Ea1is supposed to decrease forx= 0.0–0.3 compositions. The same argument is applicable for the observed increase inEa1with an increase inaforx= 0.5 and 0.7 compositions. The average size of grains (D) also affectsEa1[62]. A bigger grain size insinuates increased grain-to-grain contact area for the charge carrier to flow and consequently a lower barrier height, and vice versa. As discussed above,Dincreases from 3.7μm forx= 0.0 composition to 7.9μm forx= 0.5 composition and then decrease to 3.4μm forx= 0.7 composition. This explains the observed dependence ofEa1with Fe-content (x).TheEa1values ranging from 0.22–0.33 eV are much higher than the ionization energy of acceptors and donors (i.e., 0.1 eV), and thus band-type conduction may not be possible.These values lie between the activation energy of a small polaron (≥ 0.5 eV) and the energy needed for the electron hopping mechanism (0.2 eV). Thus, the conduction proceeds by electrons with deformation. TheEa2for the high-temperature regime are 0.43, 0.29, 0.21, 0.15, 0.21 eV, respectively, forx=0.0, 0.1, 0.3, 0.5 and 0.7 compositions. Commonly, the resistivity of oxide ceramics is essentially dependent on the mobility and concentration of the carrier, but at such relatively low temperature it cannot be ascribed to oxygen depletion or absorption. The observed high-temperature deviation may be the result of the vacancy-disorder transition. Oxygen vacancies become ordered in the low-temperature regime, considerably enhancing the resistivity and thus higher activation energy. In the high-temperature regime, the conduction process is contributed by the oxygen ions and the oxygen vacancies are disordered, which allows oxygen ions to migrate with lower activation energy[25]. Furthermore, in the temperature range studied, resistivity decreases with Fe3+-concentration(x). The incorporation of highly magnetic Fe3+ions which take part in the process of conduction, for non-magnetic Ti4+ions, enhances the degree of Fe3++ e–= Fe2+conduction that occurs on the A′ - site of the cubic perovskite structure.Thus, dc resistivity decreases with Fe3+-substitution.

4.Conclusions

The following conclusions can be drawn based on the electrical properties studies of a series of quadruple perovskites,CaCu3–xTi4–xFe2xO12wherex= 0.0–0.7. The switching action is chiefly due to the concentration of Jahn-Teller Cu2+ion engendered distortion in the system. The variation of switching temperature and threshold field is principally governed by grain size, interface defect density, and vacancy defects but not by compressive strain. TheJmaxvalue is controlled by a change in Cu2+ion concentration on the A′-site and the thickness of the grain-boundary layer on Fe3+-substitution. It is possible to tailor electrical parameters by controlling the structural and microstructural parameters, which is important from an application's point of view. The system is found to be suitable for low-voltage varistor applications. The compositional dependence of dc resistivity is governed by ferric ion concentration on the square-planar site of cubic perovskite structure and the activation energy values are suggestive of conduction through electrons with deformation.

Acknowledgements

One of the authors (DJP) is thankful to the Education Department, Gujarat state for providing financial assistance under ScHeme of developing high-quality research (SHODH).