Ba-doped LaFeO₃ [La_1-xBa_xFeO₃ (0 ≤ x ≤ 0.4)] ceramics were synthesized using the solid-state reaction method. The phase purity and structural characteristics were confirmed by X-ray diffraction, revealing that all samples exhibit a cubic structure with a Pm-3m space group. X-ray photoelectron spectroscopy was used to identify the chemical state of the component elements. The dielectric properties and conductivity measurements have been carried out. It was found that doping Ba into the ferrite LaFeO₃ resulted in an enhancement of dielectric constant, with the dielectric loss showing Debye-type dipolar relaxation behavior. This behavior is linked to the polarization from small polarons caused by electron hopping between Fe²⁺ and Fe³⁺ ions.

Keywords: Ceramics, Dielectric properties, Conductivity.

Oxide materials with high dielectric constants coupled with low losses hold crucial value in the advancement of microelectronics, facilitating the downsizing of electronic components. As opposed to complex oxide structures, the RFeO₃ system, where R represents a rare-earth element, offers a simpler framework that is well-suited for investigating properties associated with superior dielectric capabilities. LaFeO₃, as a typical perovskite-type material, has attracted considerable attention for its unique physico-chemical properties and susceptibility to significant changes with alterations in their composition [1, 2]. Many research achievements on LaFeO₃ have been reported in various state-of-the-art fields such as solid oxide fuel cells, photocatalysis, chemical sensors, magnetic material advancements, and the innovation of electrode materials [3-9].
Furthermore, the cation doping technique has been proved to be an effective method to modify the desirable properties of LaFeO₃. Several studies reveal that doping can result in changes in lattice distortions and electronic configuration, which in turn affect the dielectric properties of LaFeO₃ [10-13]. Huang et al. reported that the creation of oxygen vacancies in
La_1-xSr_xFeO₃ nanoparticles were crucial for the charge compensation during the substitution of high-valence cation ions with low-valence ones [14]. Similarly, Cao et al. discovered that La_1-xNa_xFeO₃ crystals exhibited a dielectric constant as high as 10⁵ at low frequencies [15]. Additionally, it was observed by L. H. Omari et al. that the solid solution of 0.97(PbTiO₃)-0.03(LaFeO₃) showed an optical bandgap of 2.032 eV, indicating it as a potential material for solar cell technologies [16]. Up to now, cation ions with different valence states, such as monovalent elements Na [15], K [17], Ag [18]; divalent elements Pb [19], Sr [20], Zn [21]; trivalent elements Co [22], Cr [23], Al [24]; and tetravalent elements Ti [25] have been reported as dopants entering into LaFeO₃ crystal lattice, and their effects on magnetic or electrical and optical properties have been investigated.
However, there are few reports on the dielectric properties of Ba-doped LaFeO₃ ceramics. In this work, a seris of La_1-xBa_xFeO₃ ceramic samples were synthesized using the solid-state reaction method, and the effect of Ba doping on the dielectric properties of LaFeO₃ was investigated. Our results show that the use of Ba ions as A-site dopants contributes to the increase of dielectric constant, which can be explained by the dipolar effect originate from the Fe³⁺/Fe²⁺ ion pairs.

By employing high-purity chemical reagents La₂O₃ (≥99.9%), Fe₂O₃ (≥99.5%), and BaCO₃ (≥99.5%), the La_1-xBa_xFeO₃ ceramics were synthesized using the solid-state reaction method. The raw chemical materials were meticulously weighed according to the stoichiometric ratio and thoroughly mixed. Five La_1-xBa_xFeO₃ ceramics were prepared with setting x = 0, 0.1, 0.2, 0.3, 0.4, and the corresponding samples were denoted as LBFO0, LBFO1, LBFO2, LBFO3, LBFO4, respectively. The mixed powders were finely ground, proceeding with a solid-state calcination process at 1350 °C in a muffle furnace for a duration of 6 hours. Subsequently, the derived materials were reground in an agate pestle and mortar for a period of 1 hour, and then pressed into cylindrical pellets of uniform thickness using a pellet press. These pellets were sintered at 1400 °C for 6 h to form ceramic samples. Finally, silver paste was uniformly applied to both sides of the pellets, and silver wires were connected. After thorough drying, the samples were subjected to appropriate characterization and dielectric measurements.
The crystal structure of the prepared samples was investigated using X-ray diffraction (XRD) with Cu Kα radiation (λ = 1.5418 Å) over a 2θ range of 10°~80°, employing an X'Pert3 Powder diffractometer (PANalytical, The Netherlands). Structural analysis of the XRD data was performed using the General Structure Analysis System (GSAS) and VESTA (JP-Mineral.org, Ibaraki, Japan) software. X-ray photoelectron spectroscopy (XPS) analysis was performed utilizing a monochromatic Al Kα X-ray source from the ESCALAB 250Xi, a device manufactured by Thermo Electron Corporation in the USA. To investigate the dielectric properties, a HIOKI 3532-50 LCR HiTester and an HP4194A analyzer were utilized for measurements over a frequency range of 100 Hz to 1 MHz.

The XRD patterns of the prepared samples are shown in Fig. 1. All the diffraction patterns demonstrate excellent crystalline quality and the presence of iron-based perovskite phases. The diffraction peaks were confirmed and indexed with the standard reference pattern of LaFeO₃ in the Pm-3m space group (PDF#75-0541). No impurities or alternative phases can be detected. With increasing doping concentration, the peaks slightly shifted to lower angles, as shown in Fig. 1(b), indicating an expansion of the lattice parameters. This is mainly because the ionic radius of Ba²⁺ is approximately 135 pm, whereas that of La³⁺ is approximately 103 pm. Doping with larger ions accounts for the low-angle shift of the diffraction peaks.
The Rietveld refinement was carried out using the GSAS program to analyze the XRD data. The refinement results of the five samples are shown in Figs. 2(a-e). All the samples crystallize in cubic perovskite structure with the Pm-3m space group. The lattice parameters for all samples were refined using the least-squares method. The obtained lattice parameters (a, b, c), unit cell volume (V), and reliability factors (R_wp, R_p) for different doping concentrations are presented in Table 1. With the increase of doping concentration x, the expansion of lattice parameters and unit cell volume is confirmed.
The chemical state of the component elements of the prepare samples was investigated using XPS analysis. Fig. 3 displays the XPS spectra for LBFO2 as a typical case. The high-resolution scan of the La 2p spectra [Fig. 3(a)] exhibit peaks for La 2p_5/2 and La 2p_3/2 at 883.7 eV and 850.7 eV, respectively, with characteristic satellite peaks in accordance with the standard La³⁺ [26]. The Fe 2p spectra [Fig. 3(b)] display a doublet assigned to 2p_3/2 and 2p_1/2, respectively. The 2p_3/2 peak is resolved into two peaks at 710.7 eV and 713 eV, attributed to Fe²⁺ and Fe³⁺, respectively. This is in agreement with the reports by Martine Mullet et al. [27], indicating a mixed-valence state of iron in the samples. The Ba 3d high-resolution XPS spectra [Fig. 3(c)] suggest that the Ba ions are in Ba²⁺ states. Generally, doping a lower valence state cation into ABO₃ oxides can lead to the reduction of oxygen ions and the subsequent formation of vacancies [28, 29]. When Ba²⁺ is introduced as a dopant, it substitutes for La³⁺, leading to charge compensation mechanisms that influence the iron oxidation states. The existing oxygen vacancies provide additional electrons, reducing Fe³⁺ to Fe²⁺. The relative concentrations of these valence states are calculated to be 34.8% (Fe²⁺), and 65.2% (Fe³⁺) for the sample LBFO2. As the concentration of Ba²⁺ increases, more Fe³⁺ ions are reduced to Fe²⁺ to balance the additional positive charge introduced by oxygen vacancies. This results in an increased Fe²⁺/Fe³⁺ ratio. The transfer of charge carriers between Fe²⁺-Fe³⁺ ions induces electron-pinned defect-dipoles which align to a varying electric field, resulting in the increased dielectric properties. The oxygen vacancies were confirmed by the O 1s XPS spectra, as shown in Fig. 3(d). The broad peak is deconvoluted into three Gaussian peaks at 529.8 eV, 530.7 eV, and 531.8 eV, which can be ascribed to lattice oxygen, oxygen vacancies, and surface-adsorbed oxygen, respectively. These findings are in line with the results reported by C. C. Wang et al. on BaFeO_3-δ ceramics [30].
The dielectric properties were analyzed over a frequency range of 100 Hz to 1 MHz under the room temperature. The dielectric constant, denoted as ε', was determined using the following equation:



where C represents the capacitance, S is the cross-sectional area of the pellet, d is the thickness of the pellet, and ε₀ is the permittivity of free space. Fig. 4 shows the variation of the dielectric constant ε' with frequency for the prepared samples. At low frequencies ( f < 10⁴ Hz), the dielectric constant is large due to the dipolar polarization in the dielectric material. As frequency increases, the dielectric constant tends to reduce because electron movement may not synchronize with the fluctuations of the external electric field, potentially resulting in saturation and minor alterations [31]. Similar trends have been reported in the dielectric properties of other oxide materials [32, 33].
It is likely that the Ba doping can help to increase the dielectric constant although the values reduce a little in the low-frequency range ( f < 5 kHz). This enhancement may originate from the dipolar effect arising from the Fe³⁺/Fe²⁺ ion pairs, as shown in the XPS analysis (Fig. 3(b)), within the perovskite framework of iron. The transfer of electrons between these ions induces dipolar polarization which aligns the dipoles in response to a varying electric field, resulting in the increased dielectric properties. In addition, the introduction of Ba²⁺ into LaFeO₃ structure may also cause distortion of the FeO₆ octahedra, leading to the formation of oxygen vacancies, which could weaken the interaction between the A-site and B-site sublattices, thereby reducing polarization resistance. Therefore, polarization and the dielectric properties increase consequently [34].Moreover, the presence of oxygen vacancies can lead to the formation of defect dipoles, where the vacancy itself acts as a negative charge center and neighboring atoms or ions redistribute to form a positive charge center. These defect dipoles can align with the external field, contributing to the overall polarization [35, 36].
Figure 5 shows the frequency dependence of tanδ for the prepared samples. It is obvious that when La³⁺ is replaced by Ba²⁺ ions, the curves of samples LBFO1, LBFO2, LBFO3, and LBFO4 exhibit relaxation peaks, leading to a Debye-type dipolar relaxation response. The Debye relaxation is characteristic of a group of non-interacting ideal dipoles that have the same waiting period before transitioning or a set of dipoles that lose energy at a rate proportional to frequency. As is known, dielectric relaxation is influenced by the mobility and alignment of charged species within the material. The presence of Ba²⁺ ions can lead to partial charge transfer or redox reactions and modify the local electric field experienced by Fe²⁺/Fe³⁺ pairs, influencing their relaxation behaviors. This type of relaxation can be simulated by combining capacitance (C) and resistance (R) in various ways, resulting in a peak frequency of f_p​ = (RC)^-1. The peaks in the dielectric loss are indicative of a significant link between the dielectric response and the conduction mechanisms in ferrites [37, 38]. The occurrence of a peak is anticipated when the frequency of electron hopping between Fe²⁺ and Fe³⁺ ions is roughly equivalent to the external field frequency, satisfying the condition ωt = 1, where t is the relaxation time for the hopping process and ω is the angular frequency of the external field [39].
To further investigate the transport mechanism, the conductivity s of the prepared samples was studied. Fig. 6 shows the results at room temperature. In the low-frequency region, there are almost no noticeable changes for the values of s. In the high-frequency range, there is a significant increase of conductivity with the increasing frequency. As is known, the conductivity can be described by Mott’s law, s(w, T) = s_dc(T)+s_ac(w, T), where s_dc and s_ac denote the DC and AC conductivity, respectively. At lower frequencies, the DC conductivity is the dominant process, which remains constant regardless of frequency and is dependent on the mobility of free charge carriers. As the frequency increases, the alternating electric field is applied to the electron hopping between Fe²⁺ and Fe³⁺ ions within the samples, which in turn enhances the AC conductivity. Meanwhile, oxygen vacancies introduce defects acting as traps or donors, which can facilitate the movement of charge carriers. When an external AC field is applied, these defect states can capture and release electrons more readily, enhancing the material’s AC conductivity at high frequencies. The improving AC conductivity is responsible for the increased values of s in the high-frequency range. Similar results have been reported by many literatures [40]. It seems that the introduction of Ba²⁺ can reduce polarization resistance due to the weakening interaction between the A-site and B-site sublattices. Lower polarization resistance leads to higher response times and decreased energy losses, which are favorable for the device performance. The reduction in polarization resistance directly benefits sensors by enhancing sensitivity and improving response time. In the same way, a lower polarization resistance can improves capacitor characteristics through increasing density and efficiency [41].

Ba-doped LaFeO₃ ceramics were synthesized using a conventional solid-state method. Different valence state of Fe irons and oxygen defects were revealed. Dielectric measurements suggest that the dielectric constant and loss are influenced by the Ba doping concentration. The doping of Ba²⁺ increases the dielectric constant, results in the Debye-type relaxation peaks. The conductivity data suggest that the observed Debye-type response may be associated with polaronic relaxation due to electron movement between Fe²⁺ and Fe³⁺ ions.

This work was supported by the National Natural Science Foundation of China (No. 12374031) and the Graduate Innovation Foundation of Yantai University (No. GGIFYTU2315).