Study of structural, morphological, optical, and

Applied Physics A (2018) 124:730 https://doi.org/10.1007/s00339-018-2139-7

Study of structural, morphological, optical, and dielectric behaviour of zinc-doped nanocrystalline lanthanum chromite Naima Zarrin1 · Shahid Husain1 Received: 1 June 2018 / Accepted: 25 September 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract The zinc (Zn)-doped-lanthanum chromite [LaCr1−xZnxO3 (0 ≤ x ≤ 0.3)] samples have been synthesised through sol–gel autocombustion process. The influence of Zn doping on micro and morphological structure as well as on optical and dielectric properties of LaCrO3 has been analysed. Micro-structural studies have been performed using X-ray diffraction and Fourier transform infrared spectroscopy. These studies confirm the formation of single-phase samples. Rietveld refinement employing FULLPROF software is used to obtain lattice parameters, unit cell volume, density, bond lengths, and bond angles. Crystallite size is calculated using Scherrer equation. In addition, Williamson–Hall analysis is used to calculate the crystallite size and lattice strain. Crystallite size and unit cell volume are found to increase with increase in Zn content. Surface morphology is examined using the SEM–EDX analysis, which ratifies the formation of regular and homogeneous samples. The optical energy bandgap, Eg, decreases, while Urbach energy increases with the increase in Zn doping. Dielectric constant (ɛʹ) decreases with the increase in frequency, but increases with increase in the Zn doping. All the samples follow universal dielectric response model in the low-frequency range. The increase in ac conductivity with the increase in frequency indicates that the conduction mechanism is governed through small polaron hopping between localized states.

1 Introduction Perovskites or distorted perovskites are the emphasis of several studies since long because of their numerous fascinating features such as high conductivity, high superconducting transition temperature (Tc), multiferrocity, colossal magnetoresistance (CMR), stability, etc. [1–4]. In multiferroic perovskite systems, two or more ferroic orders (ferroelectricity, ferromagnetism or ferroelasticity) appear in the same phase [5]. Commonly, they are materials that associate magnetism and ferroelectricity in the same phase due to magnetoelectric (ME) effect [6]. This ME effect offers an extra degree of freedom in the design of actuators, transducers, and nextgeneration memory devices. Rare-earth chromates R eCrO3 belong to the perovskite family (ABO3), where the Cr3+ ions are at B-site, and any one of the rare-earth ions (Re = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb) at A site. LaCrO3 is a GdFeO3-type distorted perovskite material having orthorhombic crystal structure with Pnma space * Shahid Husain [email protected] 1

Department of Physics, Aligarh Muslim University, Aligarh 202002, India

group [7, 8]. The chemical unit cell of LaCrO3 is made up of 20 atoms (4 lanthanum, 4 chromium, and 12 O atoms) per unit cell. Each chemical unit cell of L aCrO3 has cornerlinked octahedra in the form of CrO6, in which the centre is occupied with centro-symmetric Cr ions. The corner positions of the octahedra are taken by oxygen ions with two inequivalent positions, viz., the apex oxygen (O1) and planar oxygen (O2) ions. Lanthanum ions occupy the in between space of the octahedra. The distortion in L aCrO3 is the consequence of the tilting of CrO6 octahedra in opposite directions (a−b+a− in Glazer notation) that give rise to various interesting properties in these orthochromites. Lanthanum chromite (LaCrO3) has been explored in the recent past, as a multiferroic material, owing to their remarkable properties and crucial technological applications in solid oxide fuel cells [9], catalytic converters [10], electrode materials in magneto-hydro-dynamic (MHD) power generators [11], magneto-optical properties [12], and oxygen sensors [13]. Doped-lanthanum chromites have been investigated for their possible use as ceramic interconnects [14] or as coatings for metallic interconnects [15] in high-temperature solid oxide fuel cells (SOFCs) as they possess excellent mechanical and electrical properties and exhibit higher chemical stability even at higher temperatures in oxidizing and reducing

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atmospheres [16, 17]. From application point of view, a particular emphasis has been given to solid oxide fuel cells (SOFCs) these days as they transform chemical energy of a fuel gas directly into electrical work, and are efficient and environmental friendly, since combustion is not required. In addition, fuel cells are employed in large numbers due to their apt size for commercial electricity generation. L aCrO3 is a p-type conductor with very low conductivity which makes it unsuitable to be used as interconnect materials for SOFCs [18]. The electrical conductivity can be controlled with the tuning of the energy bandgap. Various doping approaches have been employed to enhance its electronic conduction which is achieved by the replacement of divalent ions on either the A- or B-sites [19, 20]. The appearance of divalent cations supplements extra holes in the valence band which results in sinking of the energy bandgap and, therefore, boosting the conductivity of lanthanum chromite and, hence, making the realization of L aCrO3 possible as an interconnect material in fuel cell. Therefore, band-gap engineering is one of the most burning issues considered for research purpose these days. Furthermore, ferroelectrics are the materials composed of permanent electric dipoles even after the applied electric field is withdrawn, such as the well-known perovskite materials BaTiO3, P bTiO3, etc. [21]. They are the best applicants for designing novel devices like transducers, next-generation memory devices, etc., as they are appropriate for fast non-volatile information storage on account of their bistable properties which exist even in the absence of electric field. The search for the existence of alternative ferroelectrics with relatively higher (colossal) dielectric constants is very intriguing and imperative topic to be searched for the application purpose [22]. It is important to remark that, in earlier studies done on LaCr1−xZnxO3 (0 ≤ x ≤ 0.3) samples, the influence of doping content on the crystal structure, morphology, and electrical and thermal behaviour have been investigated in detail by Ilham Chadli et al. [23]. However, to our best awareness, its optical and dielectric properties have not been yet explored. The optical analysis will convey vital information such as the band structure, the Urbach energy, and the steepness parameter, and, hence, elaborate the electrical conduction process in these orthochromites. Hence, this paper is intended to present a systematic study of the optical and dielectric properties along with the structural and morphological attributes of LaCr1−xZnxO3 (0 ≤ x ≤ 0.3) system. In view of above, we have synthesised L aCr1−xZnxO3(0 ≤ x ≤ 0.3) samples in nanocrystalline form using the sol–gel auto-combustion process and studied the effect of Zn doping on the structural, morphological, optical, and dielectric properties of LaCrO3.

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N. Zarrin, S. Husain

2 Experimental Nanocrystalline samples of L aCr 1−xZn xO 3 (0 ≤ x ≤ 0.3) are synthesised by the sol–gel auto-combustion process using the precursor solutions obtained from stoichiometric calculations employing lanthanum nitrate hexahydrate (La(NO3) 3⋅6H2O), chromium nitrate nanohydrate (Cr(NO 3 ) 3 ⋅9H 2 O), zinc nitrate hexahydrate (Zn(NO3)2⋅6H2O), and distilled water. The reagents were mixed in the molar ratio of 1:1 and heated with constant stirring at 80 °C on a magnetic stirrer. Citric acid and ethylene glycol are added in the molar ratio of 1:1 in a separate beaker and stirred for 10 min on the magnetic stirrer. It is then added dropwise to the above solution containing metal nitrates and the resulting solution mixture is stirred continuously till it becomes a gel. The obtained gels are ground and kept for heating in the furnace at 200 °C for 4 h where the combustion reaction took place to form the primary dried powders. Finally, the synthesised powders are ground again and calcinated at 600 °C for 2 h to get the samples in final form. The X-ray diffraction (XRD) patterns are recorded using Shimadzu Lab XRD-6100 advance diffractometer (Cu-K α radiation) at room temperature in the 2θ range of 20°–80° with the 0.02° step size. Fourier transform infrared (FTIR) spectra are recorded at room temperature using Bruker Tensor-37 spectrometer in the range of 400–4000 cm−1. The appropriate mixture of samples and KBr is compressed to prepare the pellets for the FTIR analysis. KBr is used here due to its optically transparent nature in the range of wavelengths used in this analysis. Surface morphology is studied using scanning electron microscopy (SEM) (JEOL, JSM.6510LV) in the energy range of 0–20 keV. Diffuse Reflectance UV–Vis (DRUV–Vis) spectra of the samples have been recorded at the room temperature in the range of 200–800 nm using the Lambda 950 UV–Vis–NIR spectrophotometer (Perkin Elmer). The dielectric properties are measured using Agilent 6300A precision LCR meter (accuracy of set frequency ± 0.005% with Frequency step size: ≤ 1 mHz) as a function of frequency of the applied ac field in the range of 75 kHz–5 mHz.

3 Results and discussion 3.1 Structural analysis Powder X-ray diffraction (PXRD) patter ns for LaCr1−xZnxO3 (0 ≤ x ≤ 0.3) show that all the samples are formed in single phase with no measurable secondary

Study of structural, morphological, optical, and dielectric behaviour of zinc-doped…

Fig. 1 XRD patterns of LaCr1−xZnxO3 (0 ≤ x ≤ 0.3)

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phases, as shown in the Fig. 1. The measured PXRD patterns for all the samples confirm the mono-phase primitive orthorhombic structure having Pnma space group as revealed after matching peaks with the reported (JCPDS card-62) data [12]. All the samples reveal characteristics peaks for orthorhombic structure at 23.24°, 32.88°, 40.54°, 47.14°, 53.02°, 58.24°, 68.26°, 73.21°, and 77.96° which arise due to diffraction from (101, 020), (121), (22 0), (202), (141, 301), (321, 240), (242), (060, 341), and (402, 161) planes, respectively. The Rietveld refinement of XRD data of LaCr1−xZnxO3 (0 ≤ x ≤ 0.3) samples are shown in Fig. 2. The refinement was carried out using the FULLPROF software for the orthorhombic crystal structure with space group Pnma (#62). We refined the cell parameters, background profile shape, peak shape, and desired orientation to minimize the difference between the observed XRD profile and theoretically obtained profile. Furthermore, the small value of χ2 certifies apt fitting between experimental and calculated XRD data.

Fig. 2 Observed and Rietveld refined X-ray diffraction patterns of LaCr1−xZnxO3 (0 ≤ x ≤ 0.3)

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The difference profile between the observed and calculated diffraction pattern is shown at the bottom of the plot. The obtained values of χ2 and other structural parameters are in good agreement with earlier reported values [7]. The peak broadening can be used to estimate the average crystallite size using Debye–Scherer’s formula [24]: (1) where symbols have their usual meaning. We make use of the Williamson–Hall plots to calculate the crystallite size and lattice strain of these samples. Williamson–Hall plots (βCosθ versus 4Sinθ) with straight line fitting are shown in Fig. 3. Crystallite size (DW–H) and lattice strain are calculated from the y-intercept and slope of the fitted line, respectively. The structural parameters as obtained from the refinement process, crystallite size and lattice strain have been tabulated in Table 1. The lattice parameters (Fig. 4) and, hence, the unit cell volume (Fig. 4, inset) of L aCr1−xZnxO3 (0 ≤ x ≤ 0.3) increase

D = K𝜆∕𝛽Cos(𝜃) ,

Fig. 3 Williamson–Hall plots for L aCr1−xZnxO3 (0 ≤ x ≤ 0.3)

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with the increase in Zn concentration. This is attributed to the smaller ionic radius of C r3+ (0.062 nm) as compared to 2+ Zn (0.074 nm) ion, and hence, when substituted at the Cr3+ site, Z n2+ may set itself into the lattice site with an average radius suitable for perovskite structure leading to an increase in their respective unit cell volume. The increase of lattice parameters results in the shift of most intense peak towards lower angle (2θ), as shown in Fig. 5. In addition, there is an increase in the crystallite size with the increase in Zn concentration which may be due to oxygen vacancies produced by the replacement of Cr3+ ions with Zn2+ ions in the LaCrO3 lattice. Furthermore, Zn doping at Cr site will cause a distortion in C rO6 octahedron, and hence, Cr–O–Cr bond angle decreases, while Cr–O and Zn–O bond lengths increase with the increase in Zn concentration, as tabulated in Table 1. Lattice strain refers to the distortion in the lattice appearing because of several crystal inadequacies. It results from the slight translations of atoms compared to their normal lattice positions, and is usually instigated by crystalline faults

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Study of structural, morphological, optical, and dielectric behaviour of zinc-doped… Table 1 Structural parameters, crystallite size, and lattice strain of LaCr1−xZnxO3 (0 ≤ x ≤ 0.3)

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Composition

LaCrO3

LaCr0.9Zn0.1O3

LaCr0.8Zn0.2O3

LaCr0.7Zn0.3O3

a (Å) b (Å) c (Å) V (Å)3 χ2 DS (nm) DW–H (nm) Lattice strain Density (g cm−3) Cr–O–Cr (°) Average Cr/Zn–O (Å)

5.4711 7.7602 5.5149 234.15 1.22 20.78 59.08 3.34 × 10−3 6.465 160.59 2.0154

5.4797 7.7672 5.5193 234.91 1.12 22.60 61.47 3.62 × 10−3 6.483 158.43 2.0439

5.4976 7.7859 5.5213 236.33 1.44 23.37 62.87 3.86 × 10−3 6.541 157.59 2.0799

5.5029 7.8009 5.5262 237.23 1.85 23.85 64.15 4.23 × 10−3 6.939 155.98 2.1030

Fig. 4 Lattice parameters and unit cell volume (inset) of LaCr1−xZnxO3 (0 ≤ x ≤ 0.3)

such as dislocations, interstitial impurity atoms, stacking faults, coherency stresses, etc. [25]. The Zn doping induces a lattice strain that increases with the increase in doping concentration as displayed in Table 1. This, in turn, increases the structural defects and imperfections which are confirmed by the widening as well as shifting of diffraction peaks towards lower diffraction angles, as shown in Fig. 5. The SEM micrographs of L aCrO 3 , L aCr 0.9 Zn 0.1 O 3 , and LaCr0.7Zn0.3O3 are shown in Fig. 6. In these samples, particles demonstrate even morphology with a particle dispersal which conform the synthesis process. The samples display uniform particle distribution and have the tendency of forming agglomerates. The EDX spectra for LaCrO3, LaCr0.9Zn0.1O3, and LaCr0.7Zn0.3O3 as shown in

Fig. 7 indicate the percentage elemental composition of lanthanum, chromium, oxygen, and zinc. Since there is no extra peak present in the spectra, hence, it endorses the purity of the samples. However, to get a distinct picture, the sample surface should be conducting, and hence, they are coated with a thin layer of gold. Therefore, some gold peaks also appear in these spectra to obtain clear pictures by escaping the accumulation of charges on these samples [26]. The atomic percentage of Cr in pristine sample is 12.58% which decreases as the doping content increases and becomes 8.64% in 30% doped sample. It shows that Zn has been incorporated at the Cr site in the crystal lattice. The weight and atomic percentages of constituent elements are shown in the inset of Fig. 7.

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Fig. 5 Shift of most intense peak of L aCr1−xZnxO3 with Zn doping

3.2 FTIR analysis The FTIR spectra of L aCr1−xZnxO3 (0 ≤ x ≤ 0.3) have been recorded at room temperature in the range of 400–4000 cm−1 to study the vibration bands present in our samples and are shown in Fig. 8a. The L aCrO3 formation is confirmed by the presence of vibration bands at around 420 cm−1 and 590 cm−1. The band appeared at 590 cm−1 corresponds to Cr–O-stretching vibration (ν1 mode), whereas band at 420 cm−1 is assigned to O–Cr–O bending (deformation) mode of vibration (ν2 mode) [27]. The Zn doping shifts these bands slightly towards higher wave number, as shown in Fig. 8b. The esterification between citric acid and ethylene glycol leads to the presence of ester groups in our samples. These ester groups give rise to the bands around 1100 cm−1 to 1700 cm−1 for the C=O and C–O–C-stretching vibration modes. The peak around 3450 cm−1 is associated with the stretching mode of vibration due to the hydroxyl group of water bound molecules.

3.3 UV/Vis analysis The absorption spectra of LaCr1−xZnxO3 (0 ≤ x ≤ 0.3) have been shown in Fig. 9. The optical activity of rare-earth chromates RCrO3 (R = La, Gd, Sm, Y) is due to its slightly distorted CrO6 octahedral complex [28]. The two prominent peaks are observed for L aCrO3 at around 275 nm and 360 nm in the UV region corresponding to charge transfer from O2− to Cr3+ ion. While the peaks around 450 nm and 630 nm in the visible region are linked to ligand field transitions [28, 29]. It is evident from the spectra (Fig. 9.) that the absorption capacity of Zn-doped samples has been increased

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as compared to LaCrO3. All the samples exhibit a broad absorption spectrum in the visible region, which illustrates that all the samples can absorb considerable amounts of visible light and, hence, can act as photo-catalysts. To determine the absorption coefficient, the reflectance data have been converted into the absorbance using the relation: A = − logRd, where ‘Rd’ signifies diffuse reflectance and ‘A’ denotes absorbance. Then, the absorption coefficient is directly obtained from the absorbance as: α = 2.303 (A/d), where ‘d’ indicates the length of cuvette (here, it is 1 cm). Furthermore, the optical bandgap of the samples is determined using the Tauc’s equation as follows [30]:

( )n (𝛼h𝜈) = A h𝜈 − Eg ,

(2)

where α,ν, A, and Eg represent absorption coefficient, frequency of light, band tailing parameter and energy bandgap, respectively. Furthermore, n is the parameter that characterizes the type of the optical transition process whether it is direct or indirect, i.e., n takes the value 1/2 for direct and 2 for indirect band-to-band transition [31]. The graphs are plotted between (αhν)2 and hν to determine the energy bandgap (Eg). The energy bandgap is determined by taking the intercept of the extrapolation in the linear portion of the graph to zero absorption with photon energy axis, i.e., (αhν)2 → 0 as shown below in Fig. 10. We have plotted the graphs for several n values, but the best plot is obtained when n = 1/2. The obtained band-gap values are tabulated in Table 2. The energy bandgap for LaCrO3 is estimated to be about 2.23 eV which supports the earlier work [32], and for other samples, the bandgap is found to decrease with the increase


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Fig. 6 SEM micrographs of a LaCrO3, b LaCr0.9Zn0.1O3, and c LaCr0.7Zn0.3O3

in the doping content, as shown in Fig. 10. The absorption edges of Zn-doped L aCrO3 show a red shift. The decrease in bandgap is may be due to shifting of Fermi level close to the valence band. Due to increase in the carrier concentration as a result of distortion of the crystal lattice caused due to doping, the high-energy transitions are obstructed and the bandgap decreases. These results indicate that band-gap engineering is possible with Zn doping at the Cr site in LaCrO3. Urbach empirical rule relates the absorption coefficient (α) with the photon energy (hν) in the low-frequency region and is stated through the following equations: ( ) 𝛼 = 𝛼0 exp h𝜈∕Eu (3) ( ) ln 𝛼 = ln 𝛼0 + h𝜈∕Eu , (4)

where α0 is a proportionality constant, (hν) is the energy of the incident photon and Eu identified as band-tail width (Urbach energy) of the localized states in the optical energy gap. Eu is an indicative of the thermal disorder or the occupancy level of phonon states in crystals. Thus, ln(α) versus hν plot (Fig. 11) exhibit the linear dependence and the inverse of the slope of this straight line gives the Eu. It has been observed that Eu increases with the increase in Zn-doping content [33]. This reveals that there is increase in the structural and thermal disorder in the crystal with increase in doping. It may be ascribed to the presence of localized states near the conduction band on account of disordered atoms and defects in these samples. The Zn doping increases the structural defects and isolated centres of these defects launch states at or near the band

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Fig. 7 EDX spectra with weight and atomic percentages (inset) of a LaCrO3, b LaCr0.9Zn0.1O3 and c LaCr0.7Zn0.3O3

Fig. 8 a FTIR spectra for LaCr1−xZnxO3 (0 ≤ x ≤ 0.3). b Enlarged view of slight shifting of Cr–O-stretching vibration bands towards higher wave number

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edges. These states lead to an enhancement in the band-tail width values [34]. In insulating and semiconducting crystals, absorption coefficient exhibits the following exponential dependence on energy [35]: [ ( )] 𝛼 = 𝛽 exp 𝜎 h𝜈 − − E0 ∕kB T, (5)

Fig. 9 UV/Vis. absorption spectra of L aCr1−xZnxO3 (0 ≤ x ≤ 0.3)

where β and E0 are characteristic constant parameters of the material, σ is another constant called steepness parameter, kB is the Boltzmann constant, and T is the temperature. Equation (5) suggests that plot between logarithm of “α” and “E” can be approximated by a straight line in energy range just below the fundamental absorption edge. The steepness parameter, σ, is a measure of the width of the straight line near the absorption edge. Alternatively, σ is a temperaturedependent parameter which designates the broadening of the absorption edge [36]. Urbach’s rule describes the broadening of the absorption edge and the formation of a band tail, and hence, Urbach energy is inversely proportional to σ [37]:

Fig. 10 Plots of (αhν)2 versus hν for LaCr1−xZnxO3 (0 ≤ x ≤ 0.3)

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Fig. 11 ln(α) versus hν plots of LaCr1−xZnxO3 (0 ≤ x ≤ 0.3)

(6) Using Eq. (6), the value of σ for different Zn content is calculated from the slope of the associated straight lines, as shown in Fig. 11. The calculated values of band-gap energy, Urbach energy and steepness parameter are tabulated in Table 2. As evident from Table 2, that Urbach energy increases and, hence, steepness parameter decreases with increase in the doping content. It is due to the increase in the structural and thermal defects in the samples, since both parameters measure the disorder of the crystal lattice and are inversely related to each other.

Eu = kB T∕𝜎.

3.4 Dielectric properties The frequency dependence of dielectric constant of LaCr1−xZnxO3 (0 ≤ x ≤ 0.3) at room temperature is shown in Fig. 12. All the samples exhibit the usual dielectric

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behaviour, where dielectric constant decreases rapidly at lower frequencies and remains constant at higher frequencies. In general, this type of behaviour is explained in the framework of space charge polarization model of Maxwell [38] and the Koop’s phenomenological theory [39]. The higher values of dielectric constant at lower frequencies find its basis in the assumption that solid is composed of well-conducting grains separated by poorly conducting

Table 2 Calculated values of energy bandgap, Urbach energy, and steepness parameter of L aCr1−xZnxO3 (0 ≤ x ≤ 0.3) Composition

Band-gap energy, Eg (eV)

Urbach energy, Eu (eV)

Steepness parameter

LaCrO3 LaCr0.9Zn0.1O3 LaCr0.8Zn0.2O3 LaCr0.7Zn0.3O3

2.23 2.06 1.92 1.65

2.43 3.22 5.44 8.27

0.0106 0.0080 0.0047 0.0031


Fig. 12 Variation of real part of dielectric constant (εʹ) with frequency for L aCr1−xZnxO3 (0 ≤ x ≤ 0.3)

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They should show a linear behaviour, but, in the present case, the UDR behaviour is followed only in the lowfrequency region, and as the frequency increases further, it shows a deviation from linear response which may be due to the relaxation behaviour as the electrons are not able to follow the alternating field completely. Therefore, we deduce that UDR phenomenon is responsible for dielectric response in these samples at lower frequencies only. Ac conductivity may increase or decrease with frequency depending on the type of polaron hopping. In case of large polaron hopping, the ac conductivity exhibit a decrease with frequency, while, in the event of small polaron hopping, conductivity enhances with frequency [41]. To analyze the conduction mechanism and the nature of polarons responsible for conduction, ac conductivity is determined using the following relation:

𝜎ac = 𝜀� 𝜀0 𝜔 tan (𝛿), grain boundaries. The electrons arrive at the grain boundary through hopping pile up there only if the resistance of the grain boundary is high enough, and, hence, produce polarization, which, consequently, increases its dielectric constant. However, as the frequency of the applied field is increased, the electrons are not able to follow the alternating field completely. Therefore, less number of electrons reaches the grain boundary and that amount to decrease in polarization and thereby decrease in dielectric constant with increase in frequency. Furthermore, at much higher frequencies, dielectric constant remains constant and becomes independent of frequency as the electrons cannot follow the alternating applied electric field. We have found that the values of dielectric constant in the Zn-doped samples are higher as compared to pristine LaCrO3, as shown in Fig. 12. This may be attributed to the dipoles resulting from changes in valence states of cations. A chemical pressure is created in the LaCrO3 lattice on doping with Zn2+. This may result in the conversion of Zn2+ to Zn3+ ions and hence conversion of Cr3+ ions to Cr2+ ions in proportionate amount to preserve charge neutrality in the system. Hence, Zn doping gives rise to the formation of Cr2+ ions at the octahedral sites. Consequently, electron hopping starts between C r3+ and Cr2+ ions leading to increase in orientational polarization, and hence, the dielectric constant also increases. To appreciate the nature of the dielectric response of our samples, we have analysed the frequency-dependent dielectric constant data at room temperature in the light of universal dielectric response (UDR) model [40]. According to this model, localized charge carriers hopping between spatially fluctuating lattice potentials not only give rise to the conductivity but also produce the dipolar effects. We have plotted log (εʹ × f) versus log (f) graphs, as shown in Fig. 13, to verify the UDR behaviour.

where ε0 is the permittivity of air (8.854 × 10−12 F m−1), εʹ is the real part of dielectric constant of the sample, tanδ is the loss factor and ω is the angular frequency of electrical signal of the applied electric field. The total conductivity is given by

𝜎tot (𝜔) = 𝜎ac (𝜔) + 𝜎dc , where σac (ω) is the ac conductivity that depends on frequency as well as temperature and σdc is the dc conductivity that depends only on temperature. We have plotted the graphs for the variation of ac conductivity with the frequency and found a normal behaviour that ac conductivity increases on increasing frequency as it is evident from the plots shown in Fig. 14. The behaviour of ac conductivity suggests that the conduction occurs by the hopping of charge carriers between localized states. In our case, plots are of linear nature confirming the small polaron type of conduction mechanism.

4 Conclusions We have synthesised the L aCr1−xZnxO3 (0 ≤ x ≤ 0.3) samples by the sol–gel process and studied their structural, optical, dielectric, and FTIR properties. This study shows a considerable effect of Zn doping on Cr site. Structural studies suggest that the crystal system is orthorhombic with Pnma space group. Lattice parameters, unit cell volume, crystallite size, lattice strain, bond length, and bond angle have been calculated using XRD data. FTIR spectra shows two vibrational bands at 600 cm−1 and 420 cm−1 confirming the formation of lanthanum orthochromite. In addition, the optical absorption measurements for these samples are carried out in the UV–visible region (200–800 nm). The value of the optical gap decreases monotonically, while the band-tail

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Fig. 13 log (εʹ × f) versus log (f) plots with a linear fit for L aCr1−xCoxO3 (0 ≤ x ≤ 0.3)

increase in frequency. All the samples deviate from the UDR behaviour at higher frequencies. We have also studied the variation of ac conductivity with frequency, and observed that ac conductivity increases with the increase in frequency of applied field. This indicates that small polaron hopping mechanism is responsible for conduction in these samples. The present study clearly shows that the physical properties of LaCrO3 can be modified with Zn doping depending on the concentration of dopant.

References Fig. 14 Variation of ac LaCr1−xZnxO3 (0 ≤ x ≤ 0.3)

conductivity

with

frequency

for

width increases with increasing Zn content. The absorption coefficient exhibited exponential dependence on photon energy following Urbach’s rule. In the dielectric analysis, we have found that dielectric constant decreases with the

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