Structural and Electrical Properties of Ca Doped LaFeO3: The Effect of A-site Cation Size Mismatch

Physics Department Faculty of Science Mugla Sitki Kocman University Mugla, Turkey ekberirmak@gmail.com Abstract—In this study, nanosized La1-xCaxFeO3 (0.00≤x≤0.40) compounds prepared via sol-gel method followed by heat treatment at 1100C for 24 hours are studied. Crystal structure, microstructure, surface morphology and temperature-dependent resistivity of the samples are investigated. TEM investigation reveals nanoparticles with an average size of 35nm produced from the sol-gel process. The crystal structure of the compounds belongs to an orthorhombically distorted perovskite structure with Pbnm space group. Lattice distortion and cation size mismatch increase with an increase in Ca and particle and grain growth are suppressed by Ca doping. Electrical conduction is explained via thermally activated hopping of small polarons. Unit cell volume, charge ordering temperature, and activation energy for small polarons decrease linearly with an increase in cation size mismatch. Room temperature resistivity decreases with Ca doping and gets its minimum value for 30% Ca at which the orthorhombic distortion is maximum.

INTRODUCTION Rare-earth (Re) transition metal perovskite oxides attract attention due to their electronic and magnetic properties, such as insulator to metal and paramagnetic to ferromagnetic phase transitions, magnetoresistance, electroresistance, magnetocaloric effect and charge order properties. LaFeO 3 is a semiconductor/insulator perovskite oxide and its derived compounds by replacement of some of La atoms by other Re or alkaline earth (Ae) elements give rise to significant physical and chemical properties with promising applications in advanced technologies as in electronics, magnetics, fuel cells, gas sensors, and catalysts [1]. By partially exchanging La in the parent compound with other Re or Ae (La 1-x A x FeO 3 , A: Re or Ae) lead to structurally distorted compounds, and induce different lattice parameters and unit cell volumes [2][3][4]. In addition, Ae doping has an influence on particle size (PS) and grain size (R G ). The former is calculated using XRD data and the later is calculated using surface images taken by Scanning Electron Microscope (SEM) or Atomic Force Microscope (AFM). PS has an effect on electronic, magnetic and chemical properties and is an important parameter in determining the performance of the material.
Lack of holes or a trace of holes due to nonstoichiometric oxygen undoped compound has high resistivity at room temperature. Ae doping increases the number of holes in the compound and the polyvalent nature of the Fe compensates the created charge imbalance by oxidation. Ae with a valance state of + oxidizes two Fe +3 to two Fe +4 and Ae with a valance state of 2+ oxidizes one Fe +3 to Fe +4 . Therefore, the charge imbalance created by Ae doping is removed, and this process also increases holes in the compound leading to lower resistivity. Besides, oxygen content plays an important role in charge compensation. Oxygen deficiency leads to decrease the number of Fe 4+ , and excess oxygen leads to increase the number of Fe 4+ . Furthermore, doping at La site and O vacancy, have a direct impact on the local environment of Fe ions [4] and thereby resistivity. In addition, the difference of ionic radii of La-site ions in the compound and the difference of ionic radii of Fe +3 and Fe +4 have an influence on lattice and electrical properties. The measure of distortion due to La-site ionic radius difference is the cation size mismatch, ߪ ଶ = ∑ ‫ݔ‬ ‫ݎ‬ ଶ ‫ݎ〈−‬ 〉 ଶ , where x i and r i are the concentration and ionic radius of the i th A-site ion and ‫ݎ〈‬ 〉 is the average A-site ionic radius. The electrical transport in doped LFO compounds usually takes place by the "polaron hopping". An electron or a hole is trapped by a potential well resulting from the ionic displacements it created. Moreover, oxygen vacancy, which is a defect site, traps an extra electron and leads to polaron like bound states [5]. Charge Order (CO) is another property in some of these compounds which takes place in a material by a localization of charge carriers below a certain temperature, T CO , giving rise to long-range order throughout the crystal structure leading a sudden increase in resistivity.
The electrical transport and the structural properties of La 1x A x FeO 3 have been studied extensively. In ReFeO 3 oxides having an orthorhombic perovskite structure with Pbnm space group, the structural distortion increases with decrease in Re 3+ ionic radii [6]. It was shown that a decrease in ionic radii of Re 3+ leads to decrease in lattice parameters and unit cell volume. Authors in [7] reported that doping the LFO with Li + destroys the perfection of crystallinity and lead to decrease of PS. Authors in [8], contrary to other studies, reported that hightemperature synthesis of K + doped LFO doping with an ion having larger ionic radii than that of La, leads to a decrease of unit cell volume. An increase in Mg 2+ doping in LFO leads to lowered PS and doping with Mg 2+ prevents PS from growing up during high temperature treatment [2]. However, despite the smaller ionic size of Mg 2+ there was no considerable change in unit cell volume up to 70% doping. A study on Ba 2+ doped LFO revealed that an increase in doping decreased the PS and contrary to the larger ionic size of Ba 2+ the unit cell volume decreased and appropriate Ba-doping restrained the growth of grains [9]. Moreover, the effect of Pb 2+ doping on the structural properties of LFO was conducted in [10] with no change in the unit cell volume and a decrease in the PS with an increase in Pb 2+ content [10]. An increase in Ca 2+ in LFO leads to decrease in PS [11,12] and in grain size [13]. Structural and electrical properties of simultaneously doping LFO with Ca 2+ and Pb 2+ [14] showed that doping with larger Pb 2+ ions up to 20% did not change the principal phase, but lattice parameters, unit cell volume and PS increased. However, another study reported that Pb 2+ doping lead PS to decrease [15]. Electrical transport properties of LFO can be tuned by alkaline ion substitution. The incorporation of Ca 2+ ions into the La sub-lattice decreased the lanthanum ferrite's electrical resistivity [16,17]. Moreover, doping the parent compound LFO with another divalent ion, Mg 2+ , led to increase the resistance of LFO due to secondary phases and nonstoichiometric oxygen in the structure [2].
Although there are studies involving the effect of divalent ion doping on the structural properties of the LaFeO 3 compound, a detailed and combined study on the effect of divalent ion doping on structural parameters, microstructure, and electrical properties is required. Therefore, in this study, the effect of cation size mismatch on the unit cell volume, charge order temperature, compound activation energy, microstructure, particle size, and grain size evaluation are discussed in detail. Using divalent Ca 2+ as a dopant ion, crystal structure, microstructure, and the electrical properties of La x Ca 1-x FeO 3 (x=0. 10 3 .9H 2 O with the desired stoichiometry. Pellets pressed using the fine powders were sintered at 1100 o C for 24h and cooled down to room temperature in the furnace. Close cycle cryostat was used to perform temperature dependent resistivity measurement using four-point probe from 320K down to 140K. Details of the experimental procedure can be found in [18].

A. Crystal Structure Analysis
The room temperature structures of the La 1-x Ca x FeO 3 (0.0≤x≤0.4) samples were investigated using their respective X-ray diffraction profiles. To explore the effect of Ca doping in detail, the structural parameters of all the samples were refined by Rietveld's profile-fitting using freely available FullProf Suit software [19]. The given structural model was refined with the peak shapes of the experimental patterns were assumed to be a Thompson-Cox-Hastings (TCH) pseudo-Voigt profile functions. Lattice parameters, particle size and lattice strain were refined to fit the peak shifting and broadening of the experimental data. The values of goodness of fit (GoF) for all of the refinement lie between 0.87 and 1.3. GoF was calculated by the ratio R e /R wp , where R e and R wp are the expected weighted and weighted profile factors. The experimental and calculated profiles with their differences were figured out along with Bragg positions (see Figure 1). Rietveld refinement reveals that the samples crystallize in orthorhombically distorted perovskite structure with Pbnm space group. Inspecting on main peak, in Figure 1 (XRD pattern of LCFO40) and in Figure 2, there emerges another peak (marked with a * ) in the pattern of LCFO40. Further investigation revealed that this peak was due to the trace of the rhombohedrally distorted perovskite Fe 2 O 3 (hematite) with ܴ3 ത ܿ space group (Crystallographic Open Data (COD) base card # 96-901-0140). Refined lattice parameters, unit cell volumes, average A-site radii, ‫ݎ〈‬ 〉, average distortion ratio (D), cation size disorder (σ 2 ), and Rietveld refinement parameters are summarized in Table I. Inspection on the XRD patterns of the samples makes clear that following Ca doping, main-peak of parent compound LFO at 32.17 o (Figure 2) is rendered broader and shifted to higher angles. It is known that the former is due to decrease in particle size and the latter is a change of the lattice constants.  Table I. Unit cell volume calculated for the parent compound LFO is 242.72Å 3 . A 10% increase in Ca, results to smaller unit cell with volume 239.85Å 3 . Further increase in Ca leads to decreased unit cell volumes: 238,04Å 3 , 235.26Å 3 , and 235.12Å 3 for 20%, 30%, and 40% Ca respectively. Therefore, an increase in Ca amount decreases the unit cell volume which agrees with the replacement of La 3+ having 12 coordinated ionic radii of 1.36Å with the smaller Ca +2 ion with 12 coordinated ionic radii of 1.34Å. Doping the parent compound with smaller ion decreased ‫ݎ〈‬ 〉 thus unit cell volume decreases. Moreover, there is another contribution on shrinkage of the unit cell which can be explained by parent compound doping, LFO, with Ca 2+ ion resulting to oxidation of Fe 3+ to Fe 4+ . An increase in doping leads to a decrease in concentration of Fe 3+ (0.645Å) with larger ionic radii, and an increase of concentration of Fe 4+ (0.585Å) with smaller ionic radii. Hereby, there is a decrease in size around Fe-site which may also contribute to a decrease of unit cell volume [20]. Even expressing the decrease in unit cell volume with Ca doping, it will be better to express the change in the unit cell volume with respect to A-site cation size mismatch (σ 2 ) which is an inherent parameter for doped perovskite structures and it measures the size disorder of the structure [21]. To represent the change of unit cell volume, V is plotted with respect to ߪ ଶ which is given in Figure 3. It is clear from the Figure that as the cation size mismatch increases the unit cell volume decreases linearly. Therefore, fitting the data with following linear equation in σ 2 was performed: where V 0 represents the volume of the sample at which ߪ ଶ is zero (namely V 0 is the volume of the parent compound, LFO) and m is the slope of the line. Fitting results to χ 2 =0.98, V 0 and m, 242.81±0.41Å 3 and -82373±6268 Å respectively. The calculated unit cell volume for the parent compound using linear fitting is almost equal to the value (242.72Å 3 ) from Rietveld refinement. It is seen from Table I and Figure 3 that there is no considerable change in the volume of LCFO40 as it is expected due to 10% more Ca with respect to LCFO30. For LCFO40, the amount of Ca in the structure may be lower than the expected. This can be explained with the appearance of Fe 2 O 3 as an impurity phase in LCFO40 ( Figure 1). If some Fe atoms are not in the main phase, then there should be the compounds or the oxides of Ca and/or La. However, there is no trace of the compound or the oxide of La and/or Ca in the XRD pattern. An amount of impurity phase which should be dispersed in the main perovskite phase and the precipitates with low concentration usually exhibit particle sizes in the range of a few nm, invisible to the XRD [22].
Doping an orthorhombic perovskite component at the Asite with an element having different ionic radii results to deviation from the cubic symmetry. The measure of deviation is an average distortion ratio, D, which is defined as [23]:

B. Microstructural Analysis: Particle Size and Strain
Particle size and lattice strain (s) are parameters which can be extracted from the peak width analysis. Particle size generally has been calculated using Scherrer equation and Williamson-Hall (W-H) method. The full width at half maximum of the most intense peak for a given pattern is used in Scherrer's equation ቀ‫ܦ‬ = ‫ߣܭ‬ ‫ߠݏܿߚ‬ ൗ ቁ. Without correction for the lattice strain, this gives a rough particle size. One can say that, Scherrer's equation gives only an approximate estimate of the mean particle size. But, the peak broadening due to size and strain is expressed in Williamson-Hall method as: where ߚ is the full with at half maximum of the corresponding reflections in XRD pattern, K is the shape factor, λ is the X-Ray wavelength, D is particle size and ε is strain.
Plotting β hkl cosθ values with respect to 4sinθ is called a Williamson-Hall plot. Fitting the data with a linear equation gives the strain and particle size from the slope and y-intercept of the fitted line respectively [24]. The FullProf Suite program was used to calculate the microstructural parameters of the sample. The microstructural effects were handled using the Voigt approximation: both instrumental and sample intrinsic profile are supposed to be described approximately by a convolution of Lorentzian and Gaussian components [19]. The parent compound LFO has the largest particles with average size of 77.18±0.08nm. The doping parent compound with 10% Ca, had an average PS decrease to 56.43±0.01nm. PS gets its minimum value for LCFO40 at 24.06±0.02nm. As doping increases, the average PS decreases. The average strain for the parent compound is 1.95 which is the smallest, while 10% Ca doping increased strain to 18.25. Further increase in Ca with 10% leads strain to attain its maximum for LCFO20. Doping more Ca decreases strain. The average strain is calculated as 6.48 for the LCFO40 sample with 40% Ca. The calculated particle size and strain for the samples are given in Table II, and the plot representing the change in these parameters with respect to Ca is given in Figure 4. It is clear from the plot that as Ca doping increases, PS size decreases. The particle size of the doped oxide becomes smaller than the pure host oxide, as a consequence of the restriction of the motion of particles at the boundaries between host and dopant particles [25]. The results obtained in this study are consistent with findings in [2,[8][9][10][11][12]26], even if these studies have concluded to a decrease in average PS with an increase in doping. The method used in these studies to calculate average PS is only taking the contribution of the main peak in the XRD pattern. It is well established that, as the particle size decreases, surface and interface between the particles increase. And, surfaces are the place of broken bonds and oxygen vacancies which increase stress and strain on the surface and interface of the particles [27].

C. Atomic Force Microscopy Analyss
Surface scanning of the samples was performed by AFM in non-contact mode with a resolution of 5µm×5µm. Scanned images of all samples are given in Figure 5. These images reveal that larger grains are surrounded by smaller ones and they are tightly connected with each other. This introduces that the grain growth process is not finalized yet. The average grain size calculated for the undoped sample is 940nm. Grain size decreases from 940nm, as nominal Ca increases in the samples up to 30% Ca for which grain size is 450nm. The grain size of the doped sample becomes smaller than the pure host sample [9,13,28], and the sample with 40% Ca has an average grain size of 540nm. A decreasing trend in grain size up to 40% Ca is consistent with the decreasing trend of particle size with Ca content. However, the average grain size of the sample LCFO40 was calculated to be 540nm. This increase in grain size (from 450nm to 540nm) may result from a Ca deficiency in the sample LCFO40 and impurity phase La 2 FeO 3 . The change in R G with Ca content is given in Figure 4. The largest particles calculated for the parent compound are 77.18±0.08nm. The sample with the largest average PS has the largest average grain size (940nm). Average PS is smaller than the average grain size calculated from AFM images (Table II). This suggests that, the grains viewed by AFM images are agglomerates of almost a few thousands ቀ ோ ಸ ௌ ቁ ଷ of particles [29]. Grain size calculated using the AFM image is a local average over tens of grains, but particle size calculated using XRD data is an average namely over 10 10 particles. One can say that particle size calculated using XRD pattern with W-H analysis is a more accurate method. The change of microstructural strain with respect to Ca is given in Figure 4 as an inset. Since the sign of the strain is positive, it stands for compressive strain. Generally, there is a trend of increasing and decreasing strain with Ca. The samples undergo increasing compressive strain up to 20% Ca and then decrease up to 40% Ca.

D. High-resolution TEM Analysis
Surface morphology, particle size distribution and structure of the nanoparticles were studied by High-Resolution Transmission Electron Microscopy (HRTEM) using a JEOL-JEM 2010 operated at 200kV. Powder specimens were dispersed into acetone and underwent an ultrasonic bath for 20 minutes. A drop of solution was taken on a carbon grid to carry out HRTEM analysis. TEM investigation was performed to clarify the nanosized particle distribution and perfect crystallinity of LCFO20 precursor after calcination of the solgel route for 12hs at 600 o C. A general view of the particle distribution of LCFO20 precursor is given in Figure 6(a). It is clear from the image that nanoparticle distribution with size between 20nm and 50nm was produced from the sol-gel process. Though TEM images are not necessarily representative of the whole sample, the average value of particle size calculated from XRD analysis (Table II) was closely represented by them. For further structural investigation one of the nanoparticle's surface was focused (Figure 6(b)) and HRTEM technique was applied. Inverse Fast Fourier Transform (IFFT) of the real image indicated by a square in Figure 6(b) was taken in order to filter the unwanted noise ( Figure 6(c)). The perfect crystalline structure of LCFO20 precursor before heat treatment is clear. Figure 7(a). IFFT of the R-ROI of real image is given in the upper right inset of Figure 7(a). Five spots were identified which correspond to the distance between different lattice planes as 0.5929, 0.4122, 0.3124, and 0.2048nm. These planes, having plane distances of 0.2601, 0.3124 and 0.2048nm, labeled as 1, 2 and 3 respectively, were indexed using lattice parameters of LCFO20 calculated from XRD data. The planes were indexed as follows: plane 1 was indexed as (0 2 0), (1 1 2), (2 0 0), plane 2 was indexed as (1 1 1) and plane 3 was indexed as (0 0 4) and (2 2 0). Theoretical calculation using lattice parameters of the sample LCFO20 gives an angle of 5.86 o between the planes (2 2 0) and (1 1 1), and 50.89 o between the planes (2 0 0) and (1 1 1). The two planes shown in Figure 7(a) form an angle of 50.06 o which was calculated by IFFT analysis. This result suggests that high-quality crystalline structure was obtained in this study. The line profile is given in Figure 7(b) to emphasize interatomic distances. The average distance between the atoms was found to be 5.1Å which closely represents the lattice parameters a and/or b of the LCFO20 (Table I).

E. Electrical Properties
Temperature dependence of the samples' resistance is given in Figure 8. The change of the resistance of the samples shows the same trend with temperature which exhibits insulating properties for the studied temperature range (140-320K). Moreover, all samples exhibit strong insulating behavior at low temperatures. Due to the compliance limit of the measuring device, the resistance of the parent compound LFO could not be measured. At high temperature, the resistance of the sample changes slightly and increases as the temperature decreases. However, at low temperatures, resistance increases abruptly. This abrupt increase in resistivity may indicate that the samples are charge ordered (CO) insulators. This phenomenon is another property of mixed valence perovskite oxide. The onset of CO phase can be triggered by temperature and causes a sudden increase in the transport properties of the perovskite and lattice degrees of freedom [30]. The charge order temperature, T CO , is a temperature at which the onset of CO is observed. T CO can be calculated by taking the derivative of ln(ρ/T) against the 1/T curve (d(lnρ)/d(1/T)) and plotting the derivative as a function of temperature ( Figure 9). The temperature at which a sharp peak within the derivative plot observed is the T CO . The calculated values of T CO for all the samples are shown in Table III and the plot of the variation of T CO with σ 2 is given in Figure 9. For the samples LCFO10, LCFO20, LCFO30, and LCFO40 the calculated values are 197K, 177K, 161K, and 164K. There is a decreasing trend in T CO with increase in Ca except for LCFO40. Ca deficiency and Fe 2 O 3 as an impurity phase in LCFO40 may lead to an increase of T CO for this sample.  The resistivity of all samples increased rapidly after CO took place, due to the localization of electronic states which characterize the CO state. Changing the number of charge carriers by hole doping (Ca 2+ amount in the sample) has an effect on T CO , but hole doping alone cannot describe the change of CO temperature. The structural factors including structural distortion or cation size disorder influence the electrical transport properties of these compounds. Electrical properties can be modified by changing the type and the concentration of trivalent Re, divalent or monovalent Ae cations, which led distorted crystal structure due to ionic size differences [31]. In our study, La 3+ and Ca 2+ have different ionic radii coordinated by 12 nearest O ions in the perovskite structure (〈r ୟ 〉=1.36Å and 〈r େୟ 〉=1.34 Å). The concentration of the cations and their ionic radii differences determine the distortions of crystal structure [31,32]. The plot of T CO with σ 2 is used to express the influence of a measure of this distortion at the A−site on T CO (Figure 9). A linear decrease of T CO with σ 2 is clear. Linear variation of T CO versus σ 2 was analyzed with [33]: where ܶ ை ሺ0ሻ represents the estimated value of the T CO of a parent compound in the given series and m is the proportionality factor which was obtained from the slope of the corresponding figure. Fitting gives ܶ ை ሺ0ሻ=224.20±1.53K, and slope m=-18.69×10 −4 K/Å 2 with reduced chi-square of 0.97.
Due to the compliance of the measurement devices ρ(T) for the parent compound, LFO was not performed. But, for the parent compound, T CO was estimated to be 224.20K with the help of (4) and fitting results. 224.20K is the estimated highest possible CO temperature of the parent compound with no mismatch, which is consistent with the results of [34]. With a linear decrease in T CO with σ 2 we may conclude that upon increasing A-site disorder, i.e. an increase in σ 2 from 0.0 to 1.0×10 -4 Å 2 , the CO is gradually suppressed. Since ionic radii of Ca 2+ are close to ionic radii of La 3+ (〈r ୟ 〉=1.36Å and 〈r େୟ 〉=1.34Å, the change of σ 2 even at high doping with Ca 2+ will be small. However, using dopant elements with larger ionic size may give high disorder at A-site, which may lead to collapse of charge order for a given composition. Typical plots of temperature variations of electrical resistivity for all samples are shown in Figure 8. ln(ρ/T) and temperature axes with 1/T scale. All samples exhibit insulating behavior. Thermally activated hopping of small polarons is a model which describes the resistivity of perovskite oxides [35,36]. Therefore, the resistivity was analyzed with the use of the Small Polaron Hopping (SPH) model [37]. According to the SPH model, the expression for the temperature dependence of the electrical resistivity is given by [38]: where ρ 0 is a pre-exponential factor, T is the absolute temperature, k B is the Boltzmann constant and E a represents the activation energy for small polarons. Calculated Debye temperatures are given in Table III (the temperature at which resistivity deviates from linearity is θ D /2). In the high temperature region, linear increase of ln(ρ/T) with 1/T is clear for all samples (Figure 8). Therefore, resistivity data in the given temperature range, (temperatures higher than θ D /2) fit to  [2,16,17]. The perovskite oxides are classified in terms of their conduction mechanism based on the values of E a . If E a >1eV then that material is oxide ion conductor [39,40]. Whereas, it is p-type polaronic insulator if 900meV>E a >200meV and it is an n-type polaronic insulator if E a ≤200meV [41,42]. Therefore, the activation energies calculated for samples in this study reveal that they are p-type polaronic insulators.
To explore the effect of cation size mismatch on activation energy, E a is plotted against cation size mismatch ( Figure 10).
From the plot, the inverse linear relation with E a and σ 2 is clear. The highest value of E a occurs at the lowest σ 2 and vice versa. As the cation size mismatch increases, activation energy decreases. It is well known that the electronic properties of perovskite oxides are often crucially connected with structural distortions around the Re site and/or transition metal sites [43,44]. Linear fitting was performed to represent the variation of E a with σ 2 and the following relation was written from the fitting result: where E a (0) represents the activation energy at which σ 2 =0, or the activation energy of the parent compound LFO which was not calculated in this study due to the compliance limit of the measuring devices, and m is the slope of the best fitted line. Fitting results are: E a (0)=367.87±5.49meV and m=934502.54K/Å 2 . E a (0) is the activation energy of the undoped sample LFO which was estimated with the use of (6) and the fitting results.
It is clearly evident (Figure 10) that room temperature resistivity decreases with increasing Ca and gets its minimum value at 10.47Ωcm for sample LCFO30. As Ca 2+ increases, the p-type carriers in a doped compound increase. This results to an increase in conductivity or equivalently a decrease in resistivity. Moreover, increasing p-type carriers causes E a to decrease, leading to a decrease in the energy gap of the doped compound. Furthermore, the decrease in resistivity possibly suggests that the Fermi level shifts to the nearer edge of the conduction band [45]. The room temperature resistivity of LCFO40 increased to a value of 29.47Ωcm. This may be the result of oxygen vacancy and appearance of impurity phases in that compound. Oxygen vacancies can provide electrons which compensate some of the holes created with Ca doping. This results to filling the d band of Fe 4+ ions and transforming them to Fe 3+ . In addition, Ca deficiency and impurity phase La 2 FeO 3 in LCFO40 leads to decrease of the Fe 4+ ions. As a result, the number of holes contributing to conduction decreases and therefore resistivity increases.

IV. CONCLUSION
The structural and electrical properties of nanosized La 1x Ca x FeO 3 compounds prepared via sol-gel method have been studied. Rietveld refinement of the XRD pattern of the samples indicates that all the samples have distorted orthorhombic structure with Pbnm space group, except the sample doped with 40% Ca which is single phase. Increase of Ca doping leads to increase of the average distortion ratio. There is a drastic increase of average distortion ratio from parent compound LFO to LCFO10 and to LCFO20. Moreover, particle and grain growth are suppressed with Ca. There is an inverse linear relation between unit cell volume and σ 2 .
It was shown that electrical conduction in these compounds is thermally hooping of small polarons. The studied compounds are p-type polaronic insulators considering the conduction mechanism based on the values of E a . As the Ca amount increases, E a and room temperature resistivity of the samples decreases. Inverse linear relation between E a with σ 2 and T CO with σ 2 were introduced. Moreover, charge ordering temperature, T CO , decreases with increasing cation size mismatch.