Study of the influence of 2.5% Mg2+ insertion in the B-site of La0.8Ca0.1Pb0.1FeO3 on its structural, electrical and dielectric properties

This work involves the synthesis and study of physical properties of the La0.8Ca0.1Pb0.1Fe0.975Mg0.025O3 compound, which has been characterized by various experimental techniques, such as X-ray diffraction, SEM and complex impedance spectroscopy. The structural study showed that the La0.8Ca0.1Pb0.1Fe0.975Mg0.025O3 compound crystallized in the orthorhombic structure with the Pnma space group. The particle size and the surface morphology of this compound have been analysed using SEM. The particle size was found to be around 120 nm and we confirmed that one particle contains more than one crystallite. Importantly, the studied compound presented a giant dielectric permittivity (ε′ of around 9 × 104 at high temperature and low frequencies). An equivalent electric circuit has been deduced from the Nyquist plots of the complex impedance parts (Z′′ vs. Z′) to correctly describe the electrical behavior of the La0.8Ca0.1Pb0.1Fe0.975Mg0.025O3 compound. The chosen circuit consists of two cells mounted in series corresponding to the grain and grain boundary contributions. The electrode contribution has been detected from the frequency dependence of the imaginary part of modulus where the activation energy of each constitution has been calculated. The relaxation process and the electrical conductivity are attributed to the same type of charge carriers characterized by similar values of the activation energy determined from loss factor tangent (tg(δ)), the imaginary part of the permittivity and the modulus spectrum.


Introduction
Mixed valence oxides, of general formula A 1Àx M x FeO 3 , with A ¼ La, and M ¼ Ca and Pb, have attracted signicant attention due to their interesting structural and physical properties, such as ferromagnetism with metallic conduction, the order of charge, the Colossal magnetoresistance (CMR) 1-23 and the magnetocaloric effect (MCE). [4][5][6][7][8][9][10] In this context, a great effort has been made on the iron oxides of formula LaFeO 3 and their derivatives, both from the structural point of view and their physical properties, which have proved to be of interest, for example in the eld of gas sensors. Moreover, this kind of material offers a major advantage, which is the possibility of modifying their physical properties by substitutions based on a good choice of the dopant, of the doping site and of the concentration of the dopant. [11][12][13] Indeed, doped LaFeO 3 is known for its electrocatalytic activities.
In this regard, it is important to note that the substitution of LaFeO 3 compound generates new structural, magnetic and dielectric properties. For example, the insertion of Ca into the Asite, reported by Andoulsi et al. 14 and by Shi et al., 15 reduced the electrical resistance and improved the magnetic properties. Also, Benali et al. 16 studied the effect of the introduction of lead cations in the A-site of the compound La 0.8 Ca 0.1 FeO 3 , on the structural, dielectric and gas detection properties. They found that insertion of the Pb ion into the A-site can restrict grain size growth and improve the response to ethanol gas. The best response to ethanol was obtained for a level equal to 0.1 mol of Pb. These properties are further improved with the cobalt cation substitution in the B-site of the compound La 0.8 Ca 0.1 Pb 0.1 -FeO 3 ; 17 further more detailed investigations 18,19 have shown that La 1Àx Pb x FeO 3 systems are of interest for the study thanks to these important physical properties for many applications and their high functional properties.
For this reason, the substitution of this type of compound has attracted a great deal of interest in recent years and several researchers are concentrating on improving these properties by the process of substitution in one or both A and B-sites. [20][21][22] Here, we are looking essentially to enhance the electrical and dielectric properties of these materials by replacing the iron cations with those of magnesium. In fact, this is a continuation of the research conducted by our laboratory team to optimize the appropriate composition for a desired application. Therefore, the aim of this manuscript was to study the effect of the insertion of the 2.5% Mg cation into the B-site of the L a0.8 -Ca 0.1 Pb 0.1 FeO 3 compound, synthesized by the sol-gel method and annealed at 800 C, on the structural and dielectric properties.

Sample preparation
The sol-gel technique 23,24 is a process for developing solid nanopowder materials from an aqueous solution containing the starting precursors. This process is carried out under so-called so chemistry conditions (temperatures very close to room temperature). The reaction takes place according to the following chemical equation:  3 and Mg(NO 3 ) 2 in distilled water (all reagents are obtained from Sigma-Aldrich with a purity higher than 99.6%). The citric acid was added with maintaining a ratio of n (La 3+ , Ca 2+ , Pb 2+ , Fe 3+ , and Mg 2+ ) : n (citric acid) ¼ 1 : 2. The ethylene glycol was added to further assure the homogeneity of the solution. The obtained mixture was then heated at 70 C until a viscous brown gel was formed. Heated at 170 C, the gel was slowly transformed into a ne black powder and heated for 12 hours at 300 C in order to decompose the organic residuals. Then, the resulting powder was ground and using an uniaxial pressure system (approximately 2 tones per cm 2 ), pellets of approximately 8 mm in diameter and 1.8 mm in thickness were made and submitted to heat treatments at different temperatures of 600 C (12 hours) and 800 C (12 hours).The phase purity of the prepared compound was checked by X-Ray Diffraction (XRD) analysis (Siemens D5000 X-ray diffractometer, with monochromatic Cu-Ka radiation (l ¼ 1.5406Å)).

Characterization tools
The X-Ray Diffraction (XRD) patterns of the prepared powder were recorded at room temperature using a Siemens D5000 diffractometer with a copper anticathode over the 10 -100 Bragg angle range. The morphology of the sample was examined using a TES-CAN VEGA3 SBH scanning electron microscope (SEM) equipped with an EDS detector BrukerXFlash 410 M for analysing the elemental composition and homogeneity of the prepared sample.
For dielectric measurements, two conducting silver layers were coated on both sides of the prepared pellet. Then, the transport properties of the studied materials were measured using an Agilent 4294A in the frequency range 100 Hz-1 MHz and the temperature range 200 K-400 K using a nitrogen bath cryostat setup. During the measurements, the samples were kept under a helium atmosphere to minimize thermal gradients and the temperature of the samples was controlled using an Oxford Research IT-C4 and measured using a platinum sensor. [25][26][27] 3 Structural characterization

Structural study
The purity and good crystallization of our synthetized compound were systematically veried using a diffractometer driven from a copper anticathode and a back graphite monochromator. X-ray diffractogram recording was performed at room temperature. The angular range varies from 10 to 90 and the recording time is 10 seconds in steps of 0.02 . The used renement program, FULLPROF, 28 is derived from the Rietveld method. Recall that Benali et al. conrmed the existence of two Ca 2 Fe 2 O 5 and Fe 3 O 4 secondary phases in addition to the La 0.8 -Ca 0.1 Pb 0.1 FeO 3 main phase detected using X-pert Highscore phase identication soware. These secondary phases are at very low percentages compared to the main phase. We note that the substitution of iron by magnesium in the La 0.8 Ca 0.1 Pb 0.1 -Fe 0.975 Mg 0.025 O 3 compound does not modify the main phase and the secondary phases, which remain the same as those found for the case of the parent compound. As can be seen, the peak intensities of the two secondary phases decrease following the substitution of iron by magnesium.  Table 1. The substitution of iron by magnesium in the La 0.8 Ca 0.1 Pb 0.1 FeO 3 compound generates the reduction of the mesh parameters and of its volume.

Calculation of grain size
The grain size was calculated by Scherrer's formula 30 based on the X-ray diffraction data of the most intense peak: with l ¼ 1.5406Å, q: the most intense peak diffraction angle, and b: the width at mid-height (rad). The average crystallite size obtained from Scherrer's formula was found to be equal to DSC ¼ 40.87 nm while the grain size of the parent compound La 0.8 Ca 0.1 Pb 0.1 FeO 3 is DSC ¼ 37.42 nm. It is clear then that the insertion of magnesium with an atomic radius greater than that of iron, even at a low concentration, increases the grain size.

Calculation of porosity
In order to evaluate the porosity p of our compounds, we started by calculating the density d x of the compounds from the following relation: 31 where M is the molecular mass, N A is the Avogadro number, a is the lattice parameter, m is the mass of the powder used for characterization and V p is the total volume it occupies. The values are summarized in Table 2. The porosity for the studied compound is around 61.59%.

Morphological study
Aer preparation, a morphological study with a scanning electron microscope of the TESCAN VEGA3 SBH type is carried out on the La 0.8 Ca 0.1 Pb 0.1 Fe 0.975 Mg 0.025 O 3 compound, in order to have an overview on the particle size and the morphology of the compound surface. Fig. 3(a) shows that the grains are contiguous and present different polygonal and cubic shapes. The average particle size was calculated from these images using "Image J" soware which allowed us to plot a histogram of the average size as a function of the number of grains considered as shown in Fig. 3(c).
The average particle size determined from the SEM image is larger than that calculated using the Scherrer formula (DSC). This difference is probably due to the fact that each grain observed by the SEM is made up of a set of small-crystallized grains.
The elemental compositions of the synthesized sample were carefully analysed by energy dispersive spectroscopy (EDS), as shown in Fig. 3 60.120 (6) 60.218 (2) capacitors. 32 The equivalent circuit, therefore, makes it possible to establish a correlation between the electrochemical parameters and the characteristic elements of the impedance. Indeed, in order to take into account the physical phenomena responsible for conduction and relaxation phenomena, we analysed the real and imaginary parts of the impedance data using Z-view soware. 33 We show in Fig. 4 the variation of the imaginary part of impedance Z 00 as a function of the real part of impedance Z 0 for different temperatures. In accordance with literature results, the best t of the impedance Nyquist plots was found when using two combinations of two electrical cells; each one contains a resistance (R) connected in parallel with a capacitance (CPE) as described in Fig Note that the two contributions are the grain and grain boundary and that the error of all calculated parameters (Table  3) was less than 4%.
In the low frequency region, the semicircle with high diameter corresponds to the grain boundary contribution (R gb ) whereas at higher frequencies the electrical response is due to the grain contribution (R g ) as it previously conrmed. 34,35 From the results regrouped in Table 3, one can see that the grain boundary resistance (R gb ) values are much higher than those of the grains (R g ) and that both resistance values decreased by increasing the temperature. This conrms well the p-type semiconductor nature of the La 0.8 Ca 0.1 Pb 0.1 Fe 0.975 Mg 0.025 O 3 compound.
Furthermore, we present in Fig. 6 the logarithmic variation of both R gb and R g as a function of 1000/T. For both contributions, we found that the resistance linearly follows the increase in temperature, indicating an Arrhenius power law as can be described as follows: 36 It can be seen that the calculated activation energy value related to the grain boundary contribution is greater than that of the grain contribution.  Fig. 7, the real part of the impedance decreases with increasing frequency and temperature, indicating the increase in conductivity s ac . 37 At higher frequencies, the coincidence of impedance (Z 0 ) for all temperatures indicates a possible release of space charges. 38 Considering the equivalent circuit adopted we can write the characteristic equation of the variation of the real part of impedance Z 0 .

Variation of the imaginary part of impedance Z 00
To better understand the relaxation phenomenon in the La 0.8 -Ca 0.1 Pb 0.1 Fe 0.975 Mg 0.025 O 3 compound, we have presented in Fig. 8 the variation of the imaginary part of impedance (Z 00 ) as a function of the frequency at different temperatures. By examining these curves, we observe the appearance of a relaxation peak (Z 00 max ), which moves towards high frequencies when the temperature increases. According to the literature, 39-42 the displacement of the relaxation peak conrms the existence of a Debye relaxation phenomenon within the material. This process is probably due to the presence of electrons and/or stationary space charges at low temperatures. 43 The thermal variation of log(f max ) (Fig. 9) is linear which follows Arrhenius' law: From this variation, we have deduced that the activation energy is around E a ¼ 0.149 eV.

Complex modulus analysis
The complex modulus can be written as a real component M 0 and an imaginary component: where 3 0 is the electrical permittivity of vacuum, S is the surface of the sample (0.503 cm 2 ), e is the thickness of the sample (e ¼ 1.25 mm) and u ¼ 2pf: pulsation. Fig. 10 shows the variation of M 0 as a function of frequency for different temperatures. The curves clearly show a very low M 0 value in the low frequency region and an increase in the value of M 0 in the high frequency region. In addition, the value of M 0 decreases with increasing temperature and the curves are well dispersed in which the region of dispersion shis towards higher frequencies with an increase in temperature. This behavior supports the long-distance mobility of charge carriers. The dispersive nature of the modulus implies a well-dened relaxation mechanism over several decades of frequency for all temperatures. Fig. 11 shows the variation of the imaginary part of the complex modulus (M 00 ) with frequency at different temperatures. The M 00 (f) curves are characterized by well resolved peaks in the pattern occurring at a single frequency for each temperature. Those at low frequencies are associated with grain boundary effects and the peaks observed towards high frequencies are correlated with grain contribution.
The logarithmic variations of the frequencies corresponding to the peaks as a function of the inverse of the temperature are given in Fig. 12. These variations represent straight lines following the Arrhenius law, whose slopes will be used to calculate the activation energy: We deduce from the slopes of the lines of log(f) as a function of temperature the activation energies of grains (E g ¼ 0.140 eV) and grain boundaries (E gb ¼ 0.152 eV). These two values are very close to those determined previously from the resistances of two contributions and from Z 00 curves. This proves the good t of the Nyquist and that the equivalent circuit is the most adequate (Fig. 13).

Loss factor variation as a function of frequency
The dissipation factor tg(d) is a complementary element for the study of the permittivity in order to determine the presence of the relaxation phenomenon in the material. Fig. 14   variation of the loss factor tg(d) as a function of the frequency at different temperatures. These curves clearly show the increase in dielectric losses in the low frequency region and the decrease in the latter in the high frequency region.

presents the
To determine the activation energy (E a ) we plot the curves of log(f) ¼ f(1/T) (Fig. 15). The E a values, calculated from the slopes of these curves, are found to be equal to E g ¼ 0.144 eV for the grains and E gb ¼ 0.159 eV for the grain boundaries.

Dependence of conductivity on frequency
The measurement of the conductivity sac (Fig. 16) was carried out using impedance spectroscopy in the frequency range of 40 Hz-1 Mz and a temperature range of 100 to 400 K.
We notice that at low frequency, the conductivity is independent of the frequency and has a wide plateau corresponding to a uniform conductance dependent on the temperature. In this case, only the diffusive aspect of ionic transport is Table 3 Parameters of the equivalent circuit    considered and the conductivity s ac is equal to the static conductivity (s ac ¼ s dc ). On the other hand, we note that the value of s ac increases with increasing temperature which is a characteristic of a thermally activated conduction process. However, at high frequencies the value of conductivity increases with frequency according to a power law Au s . This regime represents the displacement current, and the conductivity is equal to the dynamic conductivity s dc . Consequently, the conductivity s ac of our compound is described according to the approach of Jonscher's law 44 by the sum of two terms and is then written as s ac ¼ s dc + Au s (11) where u is the frequency, and s dc is the low frequency conductivity which depends on the temperature and s (0 # s < 1).
The exponent s is related to the variation of the polarizability induced in the material. This dimensionless parameter is generally used to characterize the electrical conduction mechanism throughout the material. In the high frequency range, the conductivity s ac obeys the type of law: s ac (u) ¼ Au s (12) This type of variation is characteristic of the jump conduction process. The increase in conductance with temperature indicates thermal activation of the conduction process in this material.
We performed an adjustment of the curves as shown in Fig. 16 using eqn (12) with ORIGIN8.0 soware. The renement results are shown in Table 4.    By examining the values of the parameter "s" we notice that it increases with increasing temperature. 45 Hence, the small tunnel polaron jump model (NSPT) is the most suitable model. According to this model, the variation of this parameter as a function of the temperature can be written as follows: [46][47][48] where W m is the binding energy of the charge carrier in its localized sites and k B is the Boltzmann constant.
For large values of W m /k B T, this equation becomes In order to determine W m , we have plotted in Fig. 17 the variation of S as a function of temperature.
Based on equation eqn (14), the values of W m (polaron energy) are determined using the slope of the curves S(T) and the obtained value was found to be around 0.161 eV.

Conclusion
This work focused on the development and study of the physical properties of the La 0.8 Ca 0.1 Pb 0.1 Fe 0.975 Mg 0.025 O 3 compound, which has been characterized by various experimental techniques such as X-ray diffraction, SEM and complex impedance spectroscopy. The XRD study showed that this compound crystallized in the orthorhombic structure with the Pnma space group. It is found that the grain sizes, determined from the SEM images, are much greater than those calculated by the Scherrer formula (DSC). This difference was related to the fact that each grain observed by the SEM is made up of a set of small crystallized grains. The study of the variation of the real part Z 0 and imaginary Z 00 of the complex impedance of the La 0.8 Ca 0.1 Pb 0.1 -Fe 0.975 compound as a function of the frequency allowed us to dene the equivalent circuit. The circuit chosen is made up of two cells connected in series. The rst circuit is formed by a parallel combination of a resistance R 1 and a fractal capacitance CPE 1 related to the contribution of the grains. The second one consists of a resistor R 2 and a fractal capacitor CPE 2 mounted in parallel, which corresponds to the contribution of the grain boundaries. From the impedance spectroscopy measurements, we determined the different dielectric parameters to know the conductivity s ac , the complex impedance Z, the complex modulus M and dielectric losses. The electrical properties of our materials have been found to be highly dependent on temperature and frequency.

Conflicts of interest
There are no conicts to declare.