The impact of Gd on structural, morphology, dielectric behavior of BaTiO₃

Abstract

Barium Titanate (Gd_xBa_(1−x)TiO₃) modified with replacing Barium (Ba) with Gadolinium (Gd) (x = 0, 0.25, 0.50, 0.625, 0.75, 0.875, and 1 mol%) were synthesized via the a modified solid-state reaction method. This study elucidates the substitution mechanism of Gd³⁺ ions into Ba²⁺ ions sites, leading to the creation of Ba and oxygen vacancies to maintain charge neutrality. Structural analyses, including X-ray diffraction (XRD), FT-IR spectroscopy, FE-SEM, and Raman spectroscopy, provided insights into the compositional and structural characteristics of the composites. A structural phase transition from near cubic tetragonal to orthorhombic was observed in Gd-modified BaTiO₃, with coexisting phase noted in (Gd/Ba)TiO₃ samples. FE-SEM analysis revealed reduced particle size and particle shape morphology with increasing Gd content. Photoluminescence (PL) confirmed the impact of the immersion of Gd ions on the BaTiO₃. Dielectric properties were examined across varying frequencies (100 Hz–10 MHz) and temperatures (30–500 °C), showing a decrease in dielectric constant with increasing Gd content and frequency. This study offers an effective modulation of electronic and dielectric properties through the controlled incorporation of Gd in BaTiO₃ material, which offers valuable insights for the development of advanced functional materials tailored for various technological applications.

Introduction

The advancements in materials science contribute to the development of microelectronics and communications, particularly in high-energy–density storage devices¹. These developments provide the foundation for enhancing the efficiency, performance, and reliability of such technologies. In microelectronics and communications, obtaining dielectric materials with high permittivity is crucial for enhancing high-energy–density storage devices^2,3. These materials enable energy storage, signal transmission, and voltage regulation within devices⁴. High permittivity dielectrics could store more energy per unit volume, boosting energy density and device performance. Advancing such materials is vital for improving the capabilities and efficiency of microelectronic and communication systems, paving the way for smaller devices, higher energy efficiency, and enhanced functionality^5–10.

Perovskites, with their distinctive ABO₃ structure, play a crucial role as essential dielectric materials with a wide range of applications spanning various fields. They consistently exhibit exceptional performance and adaptability in a variety of applications, spanning from gas sensors and capacitors to photocatalysts, solar cells, and Li-ion batteries³. In light of their inherent structural flexibility, which permits precise property modifications, they are highly appropriate for modern technological applications. Among the numerous perovskite variants, compositions such as ATiO₃ (where A = Ba, Sr, La, and Gd) have emerged as particularly promising candidates, demonstrating outstanding characteristics suitable for both research and practical application. Moreover, rare earth/transition metal oxide hybrids exhibit excellent thermal stability and an insulator-to-metal transition property, dependent on the amount of rare earth material^4–6.

The most suitable material for ferroelectric capacitors is rare-earth (RE) element modified BaTiO₃ (RE: BaTiO₃), due to its colossal dielectric constant. The incorporation of trivalent RE ions (such as La³⁺, Gd³⁺, and Nd³⁺) effectively enhances the physical properties of BaTiO₃, thereby enhancing the performance of energy storage devices^9,10. The enhancement can be achieved through chemical modification and/or grain-size engineering. The ferroelectric properties of BaTiO₃ can be finely tuned by adjusting the grain size; specifically, as the grain size decreases, the permittivity initially increases and then decreases after reaching a maximum value at a critical grain size of the BaTiO₃. The dielectric constant of BaTiO₃ is closely associated with structural distortion and chemical defects near the dopants^11–13.

The application of tolerance factor calculations reveals that the incorporation of exotic ions in the crystal structure is contingent upon their respective radii. Where the radius of rare earth (RE) ions falls within the range between Ba²⁺ (1.35 Å) and Ti⁴⁺ (0.68 Å)¹⁴. Larger RE³⁺ ions, like La³⁺ (1.15 Å) and Nd³⁺ (1.08 Å), exhibit a preference for substituting the Ba²⁺-site (A-site). Conversely, smaller ions such as Yb³⁺ (0.87 Å) tend to be exclusively located at the Ti⁴⁺-site (B-site). Intermediate-sized ions like Y³⁺ (0.93 Å) and Er³⁺ (0.96 Å) are capable of occupying both the A- and B-sites. In the context of specific doping, chemical inhomogeneity frequently occurs^13,15. For instance, when the A-site in BaTiO₃ is partially replaced by La³⁺, it can lead to the creation of Ti vacancies and the reduction of Ti content. These defects significantly impact the dielectric properties of ceramics based on BaTiO₃¹⁶. Typically, Ba_0.95La_0.05TiO_3−x ceramics exhibit a room-temperature colossal permittivity (ε_eff ~ 800,000), with Ti³⁺/Ti⁴⁺ serving as polaron carriers¹⁷. Additionally, doping Nd into BaTiO₃ has been shown to enhance permittivity (~ 300,000). The samples in this study were synthesized using the solid-state reaction method at approximately 800°C, resulting in large grain sizes and limited sintering activity^18–20.

One of the rare-earth (RE) elements, gadolinium (Gd), exhibits various oxidation states including Gd⁰, Gd¹⁺, Gd²⁺, and Gd³⁺, with an ionic radius of 0.935 Å^11,12. The Gd ions are considered an intermediate radius size among RE ions, which are commonly utilized to dope BaTiO₃ in commercial applications such as Multilayer Ceramic Capacitors (MLCCs). However, the insertion of a considerable amount of Gd to Ba ions is anticipated to alter the structure and induce a magnetic state with the ferroelectric state. Liubin Ben and Derek C. Sinclair explored the effects of Gd³⁺ doping on the structural and ferroelectric properties of BaTiO₃. Their findings indicated that Gd ions induce local strain in the lattice, causing the decrease in the (c/a) ratio and cell volume, thereby causing the rate of decrease in T_c¹³.

It is established that doping BaTiO₃ with large ions such as La can result in the formation of Ti vacancies and a decrease in Tc. Conversely, introducing smaller ions with ionic radii such as Ca²⁺ into the A-site leads to complex behavior. Where at 8 mol% doping, T_c increased to 138 °C, whereas it decreased to 118 °C at 24 wt%. The rise in Tc is attributed to a mismatch in the A-cation ionic radius between Ba²⁺ and Ca²⁺ ions, inducing strain in the lattice and raising T_c^14,15. Similar behaviors have been observed in structural and electronic phase transitions in other perovskite-related materials^16–18.

Achieving high bulk density and optimal dispersion within the inorganic matrix demands the production of ultrafine Gd: BaTiO₃ nanoparticles with uniform particle size and pure phase, a task that poses significant challenges¹⁹. While thermal synthesis methods are known for yielding high-purity nanoparticles, they often result in a wide-size distribution. Surprisingly, reports on the synthesis of RE: BaTiO₃ nanoparticles are scarce. Recently, it successfully synthesized both BaTiO₃ and modified BaTiO₃ nanoparticles using the solid-state reaction method, applicable in ceramic and thin film forms. These nanoparticles find application across various fields including memory devices, Multilayer Ceramic Capacitors (MLCCs), and ferroelectric RAM, presenting promising trends for the industrial utilization of ferroelectric composites^20,21.

This study aims to explore the synthesis and characterization of gadolinium-replacement the barium in Barium Titanate (BaTiO₃) with varying Gd content (0–1 mol%) using the solid-state method. This work lies in systematically investigating the structural, optical, and dielectric properties as a function of Gd content. Advanced characterization techniques, including XRD, FE-SEM, and Raman spectroscopy, were employed to analyze the structural modifications induced by Gd content. Additionally, the photoluminescence behavior of the samples was examined to gain insights into their optical properties. Furthermore, the frequency- and temperature-dependent dielectric properties were comprehensively studied, highlighting the influence of Gd incorporation on the material’s performance. This research provides valuable contributions to the understanding and potential applications of Gd-replacement in the BaTiO₃ structure.

Experimental work

Materials synthesis

BaTiO₃ and Gd-substitute Ba ions Gd_xBa_1−xTiO₃ (x = 0, 0.25, 0.5, 0.625, 0.75, 0.875 and 1.0 mol%) were synthesized through a solid-state reaction method as the samples labeled in Table 1. A raw material of BaCO₃ (3N), Gd₂O₃ (4N) and TiO₂ (3N) which are purchased from Al-Gomohriyia Chemical Reagent Co., Ltd (Cairo-Egypt) and Sigma Aldrich and were weighted to be used. The powders were prepared using a modified solid-state reaction method. Initially, they were mixed with ethanol and ball-milled for 12 h to enhance homogeneity and reduce particle size. The mixture was then dried and calcined at 600 °C for 3 h, followed by grinding for 30 min in an agate mortar. A second calcination was performed at 1150 °C for 6 h, after which the powders were crushed and ball-milled again for 12 h to ensure fine particle distribution. The dried powders were sieved and uniaxially pressed at 8 MPa into green pellets with a diameter of 10 mm and a thickness of approximately 1–2 mm at room temperature. Finally, the pellets were sintered at 1250 °C for 12 h in air with a controlled heating rate of 100°C/h to achieve the desired phase formation and microstructure. Finally, the sintered ceramics were polished and coated with silver electrodes for electrical measurements. The pellets used for FE-SEM were polished and heated at 400 °C for 15 min in air, with a heating rate of 100 °C/h, to remove humidity absorbed during the polishing process and to reveal the grain details.

Table 1.

Composition of prepared samples with labels.

No.	Sample name	Sample labelled
1	BaTiO3	S1
2	Gd0.250Ba0.750TiO3	S2
3	Gd0.500Ba0.500TiO3	S3
4	Gd0.625Ba0.375TiO3	S4
5	Gd0.750Ba0.250TiO3	S5
6	Gd0.875Ba0.125TiO3	S6
7	GdTiO3	S7

Characterization techniques

The X-ray diffraction (XRD) patterns of all prepared samples were obtained using the Bruker D8 Advance diffractometer with Copper Kα radiation (radiation wavelength = 1.54056 Å) operating at 40 kV and 40 mA. The samples were scanned in the 2θ range of 10–80° in step-scan mode (0.02° per step). High-resolution scanning electron microscopy (FE-SEM) images were acquired using the FEI Quanta 200 microscope operated at 200 kV. Raman spectra were recorded in the wavenumber range of 100 ~ 1100 cm⁻¹ using a Jobin Yvon T64000 instrument.

Photoluminescence (PL) spectra were collected at room temperature by exciting the samples with a 325 nm He–Cd laser using a QM40-NIR (PTI, USA) setup. The dielectric characteristics were measured as a function of temperature (25–500 °C) and frequency (100 Hz–10 MHz) using an LCR meter (Hioki 3533, Japan) at a potential difference of 1 mV.

Results and discussion

X-ray diffraction

The XRD analysis was conducted on the synthesized composites to evaluate phase purity and crystallinity, as shown in Fig. 1. In Fig. 1a, all diffraction peaks correspond to the planes indexed according to ICSD card No: 05-0626, confirming the formation of pure Barium Titanate (BaTiO₃).

Fig. 1.

XRD patterns of Gd_xBa_)1−x(TiO₃ (x = 0 ~ 1.0 mol%). (a) XRD of pure BaTiO₃ sample, (b) XRD patterns of samples with varying Gd-content, right and lift inbox graph is the peaks for (222), and (200) plans, respectively.

Figure 1b displays the XRD patterns for various Gd contents in Gd_xBa_1−xTiO₃. Analysis of these patterns indicates the presence of two distinct phases: Gd_xBa_1−xTiO₃ and Gd₂Ti₂O₇, as shown in the figure. The diffraction peaks for Gd₂Ti₂O₇ are indexed according to JCPDS 23-0259. The two inset graphs in Fig. 1b highlight the (200) plane of the Gd_xBa_1−xTiO₃ phase and the (222) plane of the Gd₂Ti₂O₇ phase. A clear shift in the (200) peak towards higher diffraction angles is observed with increasing Gd content, accompanied by peak splitting, indicating lattice changes associated with Gd incorporation.

The peak shift of the (200) plan to higher angles indicates a reduction in the lattice parameter along that direction, which occurs as Gd³⁺ (ionic radius = 0.938 Å) replaces Ba²⁺ (ionic radius = 1.35 Å) in the BaGdTiO₃ structure, leading to lattice contraction. This trend is supported by Table 2, which shows the decrease in lattice parameters and unit cell volume with increasing Gd content. The splitting of the (200) peak suggests the presence of lattice strain or distortion as more Gd is incorporated, possibly indicating the formation of multiple domains or phases within the structure. Furthermore, the shift of the (222) peak for Gd₂Ti₂O₇ to a higher angle also indicates a reduction in lattice parameter along that direction with increasing Gd content. This could be a result of tighter packing or structural adjustments as the composition changes. Since Gd₂Ti₂O₇ has a pyrochlore structure, the presence of more Gd may enhance the phase’s stability or reduce unit cell size due to the overall chemical pressure.

Table 2.

Crystal lattice parameters for different sample compositions.

Samples	a (Å)	b (Å)	c (Å)	angles	System	symmetry	c/a	Volume (Å)3
S1	3.9995	3.9995	4.02375	90	Tetragonal	P4mm	1.006	64.36391
S2	5.9685	3.6471	2.5781	90	Orthorhombic	Pmmm	0.432	56.11935
S3	5.9262	3.6542	2.5521	90	Orthorhombic	Pmmm	0.431	54.24943
S4	5.8955	3.6077	2.5531	90	Orthorhombic	Pmmm	0.433	54.30238
S5	5.9180	3.6216	2.5594	90	Orthorhombic	Pmmm	0.432	54.85467
S6	5.927	3.592	2.5582	90	Orthorhombic	Pmmm	0.432	54.46353
S7	2.5594	3.6216	5.9180	90	Orthorhombic	Pnma	2.3123	34.18254

It is notable that, at specific Gd content levels (x = 0.625 and x = 0.875), an additional peak appears at 32° in the XRD pattern. This peak is not due to a shift or displacement of any other indexed peaks but is unique to these Gd concentrations. The emergence of this peak at 32° may suggest an ordering effect, likely caused by regions of Gd₂Ti₂O₇ phase developing in close proximity to the Gd_xBa_1−xTiO₃ lattice. This interaction potentially generates a superlattice reflection that does not typically appear in either phase independently but arises from their specific structural interplay at these concentrations. By analyzing the XRD data using FullProf software (https://www.ill.eu/sites/fullprof/php/downloads.html)²², the lattice parameters and symmetry of the prepared samples were determined, as shown in Table 2. The pure BaTiO₃ phase has a tetragonal structure with P4mm symmetry and a c/a ratio of 1.0061. However, as Gd is added to BaTiO₃, the structure transitions to an orthorhombic phase with Pmmm symmetry.

In pure BaTiO₃, the structure is nearly cubic with a slight tetragonality, where subtle distortions can contribute to measurable local strain. However, when BaTiO₃ is doped with Gd, the crystal structure transforms to an orthorhombic phase (samples S2–S7), as evidenced by the distinct lattice parameters and lower unit cell volumes. This structural change is accompanied by a decrease in local strain, which might seem counterintuitive since lower-symmetry phases are often associated with higher strain. In this system, the transition to the orthorhombic phase appears to promote strain relaxation through improved accommodation of lattice distortions and more efficient redistribution of defects. Additionally, the contraction of the unit cell upon Gd doping suggests that the lattice relaxes, reducing residual stresses. The concomitant increase in crystallite size in the Gd-doped samples further contributes to the decrease in local strain by minimizing the impact of grain boundaries and other defect-related stress concentrators. Thus, while the undoped BaTiO₃ exhibits a near-cubic tetragonal structure with inherent distortions, Gd doping stabilizes an orthorhombic structure that is more effective at relieving internal strain.

Additional important parameters can be derived from XRD analysis, including crystallite size (D), local strain, and dislocation density. The crystallite size was calculated using the Scherrer equation, the local strain was evaluated using the Williamson–Hall equation, and the dislocation density, representing the number of dislocations per unit volume, was determined as the inverse of the square of the crystallite size. The calculated strain from the XRD data shows a decrease in strain with increasing Gd content, as shown in Table 3.

Table 3.

XRD and SEM analysis parameters for different sample compositions.

Samples	Crystalline Size(D) (nm)	Local strain(ε) X (10–4)	Grain size from SEM (μm)	Dislocation density(δ) X (10–4)
S1	38.42 ± 0.62	9.42 ± 0.24	6.10	6.78
S2	45.81 ± 0.50	7.90 ± 0.15	3.23	4.77
S3	52.64 ± 0.70	6.12 ± 0.11	3.31	2.61
S4	60.84 ± 0.70	5.95 ± 0.11	1.381	2.40
S5	71.61 ± 0.85	5.05 ± 0.13	1.281	2.35
S6	65.20 ± 1.03	5.55 ± 0.18	0.523	2.35
S7	67.28 ± 0.88	5.38 ± 0.14	0.512	2.21

The preparation conditions could significantly influence the material’s structural characteristics. The coexistence of phases, such as GdTiO₃ and Gd₂Ti₂O₇, could promote this structural evolution. The interaction between these two phases could create a localized strain field or alter the average energy of the crystal structure, thereby facilitating the phase transition or changing the crystal symmetry. The presence of multiple phases may also lead to changes in the overall crystal symmetry, causing the material to exhibit different structural properties than it would in a single-phase state^23,24.

Substituting Ba²⁺ ions in the A-site with Gd³⁺ ions led to structural phase transitions depending on the Gd content. Specifically, with Gd content at x = 0.25, the structure exhibited an orthorhombic phase with a Pmmm space group, resulting in a reduction of unit cell volume from 64.37 to 56.12 Å³ (as shown in Table 2). Furthermore, the crystallite size increased while the local strain and dislocation density decreased, as presented in Table 3. Notably, these results demonstrate a clear trend of structural phase transitions with increasing Gd content in the BaTiO₃ matrix.

Field emission scanning electron microscopy (FE-SEM) analysis

The field emission scanning electron microscopy (FE-SEM) images provide a detailed analysis of the changes in shape and size of the grains of the ceramics containing Gd_xBa_1−xTiO₃ with varying Gd content. Initially, at x = 0 (pristine BaTiO₃), the sample exhibit a morphology dominated by long rod-shaped grains, interspersed with smaller irregular-shaped particles. This morphology suggests a certain level of crystallographic orientation and grain growth during synthesis (higher temperature and time interval, 1250 °C for 12 h in air). As the Gd content increases, starting at x = 0.25 mol%, the rod-shaped grains transform into irregular-shaped particulates. This indicates that the introduction of Gd ions influenced the grain structure, potentially causing disruptions or distortions in the crystal lattice. As Gd ions are introduced into the BaTiO₃ lattice, they replace some of the Ba²⁺ ions in the A-site positions. This substitution process modifies the material’s composition and impacts the local symmetry and charge distribution within the crystal lattice. These changes can lead to distortions in the crystal structure and modifications in the grain morphology, as observed in the FE-SEM images in Fig. 2.

Fig. 2.

FE-SEM analysis of the different Gd content of Gd_xBa_(1−x)TiO₃: (a) x = 0, (b) x = 0.25, (c) x = 0.5, (d) x = 0.625, (e) x = 0.75, (f) x = 0.84 and (g) x = 1.0 wt%).

This trend continues as the Gd content rises to x = 0.5 mol%, where the grains become smaller and display a higher degree of irregularity in shape. This suggests a more pronounced effect of Gd doping on the grain morphology, potentially leading to changes in the crystalline structure. At x = 0.625 mol%, a significant transformation occurs, with the grains adopting spherical structures and the size getting smaller. Although these grains are smaller than the original rod-shaped grains, they maintain a certain level of irregularity in shape, indicating ongoing changes induced by Gd doping. As the Gd content further increases, observed at x = 0.75 mol% and x = 0.84 mol%, the grains continue to exhibit a spherical morphology with a further size reduction. This suggests a continued influence of Gd doping on the grain structure, leading to the formation of finer, more uniform spherical particles. Finally, at x = 1.0 mol%, the microstructure is dominated by numerous smaller spherical grains. The grain size of the prepared samples is tabled in Table 3. This indicates that the highest concentration of Gd has induced the most significant morphological changes, resulting in the formation of smaller, spherical grains throughout the material. Therefore, the observed morphological transformations, including the transition from long rod-shaped grains to irregular-shaped particulates and ultimately to smaller spherical grains, can be attributed to the doping of Gd and its substitution into the Ba A-site positions in BaTiO₃.

One important observation in our study is that BaTiO₃ typically forms equiaxed grains, grains that are nearly equal in all dimensions, when prepared by conventional solid-state reaction methods. In contrast, our modified solid-state reaction synthesis method, performed at 1250 °C for 12 h, promotes anisotropic grain growth. We argue that the high synthesis temperature significantly enhances diffusion processes, which in turn favor preferential, unidirectional growth over isotropic growth. This results in the formation of rod-shaped grains, as clearly evidenced by our SEM images. A key factor supporting this observation is the near-cubic nature of the unit cell in our sample, as indicated by XRD analysis, where the c/a ratio is approximately 1.006. In conventional solid-state synthesis, BaTiO₃ adopts a more pronounced tetragonal structure due to the off-center displacement of Ti atoms, which induces internal strain and restricts anisotropic grain growth. However, in our case, the reduced Ti displacement leads to minimal tetragonal distortion, lowering internal strain and allowing for more uniform grain growth along specific crystallographic directions. The anisotropic grain growth observed here deviates from the norm, underscoring the critical influence of synthesis conditions on the microstructural evolution of BaTiO₃. Such a distinct morphology not only illustrates the effectiveness of our method but also suggests that controlled high temperature modified solid-state reaction synthesis method can be used to tailor the microstructure, and potentially the functional properties, of BaTiO₃.

The Raman spectra analysis

Raman vibrational spectra were recorded to elucidate the structure of both BaTiO₃ and Gd-BaTiO₃ ceramics at room temperature, as depicted in Fig. 3a, b. In Fig. 3a, Raman scatters spectra of three samples—BaTiO₃, Gd_0.25Ba_0.75TiO₃ and Gd_0.5Ba_0.5TiO₃.—are presented. For the BaTiO₃ perovskite, distinctive bands are observed at 193.3, 226.8, 417, 463, 512, 621, and 862 cm⁻¹, representing vibrational modes intrinsic to the BaTiO₃ system²⁵. The presence of bands at 193 cm⁻¹ indicates a decoupling between the A1(TO) phonons²⁶, possibly induced by internal stress or lattice defects. The sharp peak at 417 cm⁻¹, corresponding to [B1, E(TO + LO)] modes, suggests non-centrosymmetric regions arising from titanium atom displacements within the TiO₆ octahedra, signifying essential structural distortion in tetragonal BaTiO₃. Irregularities in the bands at 521 cm⁻¹ suggest coupling of TO modes associated with the tetragonal phase. Additionally, the presence of a peak at 713 cm⁻¹ is attributed to the highest frequency longitudinal optical mode (LO), with the higher relative intensity of this band possibly linked to Ba vacancies in BaTiO₃^27,28.

Fig. 3.

Raman spectra of Gd_xBa_(1−x)TiO₃, where x ranges from 0 to 1.0 mol%. (a) Raman spectra for S1, S2, and S3, (b) Raman spectra for S4, S6, and S7.

Upon adding Gd ions to BaTiO₃, peak positions shift, with three prominent peaks observed in both Gd_0.25Ba_0.75TiO₃ and Gd_0.5Ba_0.5TiO₃ ceramics at 324, 568, and 865 cm⁻¹. The first peak, related to GdTiO₃, shifts to a lower frequency from 300 to 324 cm⁻¹, likely associated with oxygen atom movements rather than Gd. This peak is accompanied by increasing linewidth and asymmetry. The second peak at 568 cm⁻¹ exhibits strong resonant enhancement, indicating changes in the electronic structure of BaTiO₃ as corroborated by XRD data²⁹. Furthermore, peak intensities increase with increasing Gd-content concentration.

In Fig. 3b, Raman spectra of higher Gd-ion contents in BaTiO₃ ceramics reveal two main peaks and two smaller peaks. The first main peak, initially at 314 cm⁻¹, shifts to 528 cm⁻¹ with increasing Gd content, while the second main peak shifts from 516 to 532 cm⁻¹. Overall, there is a trend of peak shifting to higher frequencies and increasing intensity with higher Gd content. XRD data suggests the crystal structure of these composites to be orthorhombic. There is one small peak at 682 shifted to 732 cm⁻¹ with the increasing of Gd-contents (Fig. 2SU). Raman spectra of BaTiO₃ with tetragonal P4mm space group exhibit eight Raman active modes described by:

It is known that the bands at 314, 516 and 682 cm⁻¹ are assigned to the fundamental TO mode of A1 symmetry, which mostly occurs both in cubic and tetragonal phases^29,30. The isotropic distribution of electrostatic forces made all phonons of cubic Pmεm symmetry inactive to Raman modes. The presence of a free-carrier component in these insulators in which the electrons are believed to exist in localized states is unexpected and presumably due to an unintentional doping mechanism. Based on recent work that has shown that LaTiO₃ is susceptible to doping by rare-earth vacancies, this suggests that there is a systematic increase from Ba to Gd in the number of R31 vacancies³¹, which provides a small, but increasing number of free carriers across the series^32,33.

The photoluminescence (PL)

Room temperature photoluminescence (PL) emission spectra were excited by laser with the wavelength of 355 nm investigated for the BaTiO₃ and Gd-BaTiO₃ ceramics PL emission typically occurs in structures featuring polarization and/or localized states within the band gap, such as self-trapped excitons, free exciton levels, and impurity or defect levels. The emission spectra of BaTiO₃ and Gd-BaTiO₃ composites are depicted in Fig. 4a, b. For pure BaTiO₃, a small peak at 554 nm is observed, attributed to direct band excitation closely linked to the distortion of TiO₆ (detailed in supplementary information Fig. 1 SUB)¹⁶.

Fig. 4.

Photoluminescence (PL) emission spectra of Gd_xBa_(1−x)TiO₃, where x ranges from 0 to 1.0 mol%. (a) PL spectra and (b) Normalized PL spectra.

There is a sharp peak (much broader) appeared at the wavelength (λ ~ 700–860 nm) for the ceramics with higher Gd-contains (Gd > 0.25 mol%). The analyzed and normalized PL emission is presented in Fig. 4b. This sharp peak is attributed to the defects state within the band gap of the composites. The electrons trap from the valance band and interact with the holes to form self-trapped excitations behind this is the oxygen vacancies which are considered as highly localized sensitive centers³⁴. The gradual increase of the emission intensity is evidence of the increase in oxygen vacancy defects due to the incorporation of Gd ions. With the analysis of the above data, When Gd is introduced into BaTiO₃, both Ba vacancies and oxygen vacancies would concurrently form to recompense the charge balance as described in the following Eq. (1)

1

A similar occupation mechanism has been considered for RE-modified BaTiO₃ ceramics, but, the Ba-vacancy induced by the donor-doping mechanism demonstrated experimentally due to the mixtures of Ba_1−yLa_yTi_1−y/4O₃^18,35 and other Ti–rich phase(s) such as Ba₆Ti₁₇O₄₀³⁶. In our data vacancy of Ba is due to the thermal treatment conditions during preparation, where vacancy of Ba can be generated due to the Gd-ions^37–39.

From the normalized PL spectra, the bandgap energies for the samples were determined. The band gap energy of Barium Titanate (BaTiO₃) varies depending on factors such as phase, particle size, and doping⁴⁰. At room temperature, the band gap values of bulk BaTiO₃ are 3.254 eV, 3.894 eV, 3.694 eV, 3.519 eV, and 3.388 eV for the cubic, rhombohedral, tetragonal, and hexagonal phases, respectively⁴¹. This variation explains the undetectable photoluminescence (PL) peaks observed in both samples S1 and S2. For sample S3 (50% Gd and 50% Ba), the band gap is calculated as 1.6 eV, while samples with higher doping levels (S4, S5, S6, and S7) exhibit an average band gap of approximately 1.62 eV.

Dielectric properties as functions of temperature

The dielectric constants are a reliable tool for examining the electrical properties of the materials, encompassing parameters such as the real part (ε′) which represent the value of dielectric constant, the imaginary part (ε″) which represent the dielectric loss of the dielectric constant, and the alternating current (AC) conductivity (σ_AC). Data on frequency-dependent dielectric properties provide insights into various aspects, such as bulk material characteristics, grain boundaries, and electrode effects. The complex dielectric constant (ε*) of a material is defined as Eq. 2²³:

2

where , are the real part and imaginary part of the complex dielectric constant, respectively. The real part () and imaginary part (ε″) of the complex dielectric constant (ε*) represents the energy stored and energy dissipated within the dielectric sample between the conductive electrodes, respectively. Grain boundaries contribute to energy dissipation as the sample experiences loss when subjected to an applied electric field, preceding polarization. Additionally, this loss occurs due to three primary factors: molecular dipole movement, dipole loss, space charge migration, and direct current conduction.

In this study, the dielectric properties as a function of temperatures were investigated at three different frequencies (10 kHz, 100 kHz, and 1 MHz). The temperature dependence of the dielectric constant (ε′) for all prepared samples, including BaTiO₃ (S1) and various samples of Gd_xBa_1−xTiO₃ (S2 to S7), is illustrated in Fig. 5.

Fig. 5.

Variation of the dielectric constant with temperature for the Gd_xBa_1−xTiO₃ samples, where x ranges from 0 to 1.0 mol%.

The experimental data of S1 (BaTiO₃: parent compound) demonstrates frequency independence at lower temperatures (T < 300 °C), with a pronounced peak observed at the Curie temperature (T_C), corresponding to the well-known crystal structural phase transition of BaTiO₃ from tetragonal to cubic phases. In addition, for sample S1, the ε′-value initially increases (ε′ peak value 6500) at T_C = 130 °C, followed by a subsequent decrease with increasing temperature up to 300 °C. Beyond this temperature threshold (T > 300 °C), the ε′-values exhibit an upward trend, with the magnitude influenced by the applied frequency; lower frequencies yield higher ε′-values across the temperature range.

Upon replacing Ba-ions with Gd-ions in samples S2 and onwards, T_C shifts to a lower temperature (100 °C), accompanied by a decrease in ε′-values (543) compared to S1. Furthermore, a frequency-dependent behaviour of the dielectric constant (ε′) is observed, starting at a temperature of 180 °C, indicating a decrease in temperature from 300 °C (S1) to 180 °C (S2 data). This finding aligns with recent reports suggesting that partial substitution of Ba²⁺ by RE³⁺ results in the reduction of T_C, corresponding to a transition from a tetragonal to a cubic structure phase⁴².

From the XRD data, replacing Ba ions in the A-site with an additive of the Gd-ions exhibited structural phase transitions depending on the amount of Gd. The additive of Gd = 1.0 changed the structure from tetragonal to orthorhombic phase and, as a result, decreased the cell volume from 64.3667 to 56.12 (Ǻ)³ as seen in Table 2. This is the main reason behind the decreeing both T_C and -values. The results confirmed that the introduction of Gd ions decreased into tetragonality and convinced the transition. Moreover, the FE-SEM specifies that ceramic grain size decreased with the increasing of Gd content as shown in Fig. 3. Both the experimental data of XRD and FE-SEM display the clear compact microstructure and their grain sizes. The other composites for example (S3: Gd_0.5Ba_0.5TiO₃) show decreasing T_C (80 °C). In addition, the values of the dielectric constant (= 575) shows frequency dependence at lower temperatures (room temperature (25 °C)).

The experimental dielectric data of sample S3 (Gd_0.5Ba_0.5TiO₃) confirms the introduction of RE ions in BaTiO₃ reduced the T_C. With increasing Gd-contents (S4, S5, S6, S7), the T_C disappeared and the dielectric constant shows independent of applied frequency as displayed in Fig. 5. Our interpretation of this phenomenon is that introducing Gd-ions may create a leakage current inside the composites and break down the dielectric behavior of the original perovskite BaTiO₃. Further, similar behaviors for all samples with higher contents of Gd-ions (S4, S5, S6, S7) were observed. The introduction of Gd can create electron hopping conduction phenomena and increase the conductivity of the ceramics as in AC conductivity data (Fig. 7). One point here, It is well known that BaTiO₃-based ceramics exhibit a dielectric peak around 500°C, primarily due to oxygen vacancy-related effects, grain boundary polarization, and thermally activated charge carriers^43,44. This is clearly evident from these two references. Although for our dielectric–temperature dependence measurements were not extended to higher temperatures (> 500 °C), the introduction of Gd doping in BaTiO₃ caused the peak to shift to 450 °C. This shift is attributed to relaxor-like behavior.

Fig. 7.

Variation of the AC conductivity with temperature for the Gd_xBa_1−xTiO₃ samples, where x ranges from 0 to 1.0 mol%.

In combination with XRD data and SEM, the defects (both the Ba vacancies and O vacancies) induced by the replacing Ba with Gd maybe act as additional carriers⁴⁵. The dielectric constant shows a decrease with the increase in frequency values, such a polarization cannot follow the alternating field at high frequency. This is the reason behind the decrease in the permittivity values of the Gd_xBa_1−xTiO₃ samples with increasing frequency (Fig. 5).

The sharp peaks seen in S1 and S2 around 125°C indicate a ferroelectric-to-paraelectric phase transition, typical of BaTiO₃-based materials. S3, S5, and S6 show more gradual transitions, possibly indicating a diffuse phase transition or relaxor-like behavior. Samples S1, S2, S6, and S7, there is a significant increase in the dielectric constant above 400°C. This could be attributed to leakage currents or conduction effects, which become more prominent at high temperatures, especially at low frequencies⁴⁶. The sharp increase in ε′ could also indicate space charge polarization or defect-related processes^47,48. All the samples show frequency dispersion, with the dielectric constant being higher at lower frequencies. This is a common behavior in dielectric materials, where slower polarization mechanisms (like ionic or space charge polarization) can follow the applied electric field at low frequencies, but not at high frequencies⁴⁹. Samples S3, S5, and S7, exhibited broad peaks and gradual changes in dielectric constant, suggesting relaxor-like behavior, where the phase transition is more diffuse and not as sharp as in classic ferroelectrics. This can occur due to compositional disorder or the presence of defects. The dielectric properties of these samples show a range of behaviors, from classic ferroelectric transitions in S1 and S2 to more relaxor-like behavior in S3, S5, and S7. The high-temperature rise in dielectric constant for several samples suggests the presence of conduction or space charge effects, especially at lower frequencies⁵⁰. Understanding the specific material compositions and synthesis conditions would help provide deeper insights into the observed dielectric responses. The interfacial polarization in the dielectric samples shows Maxwell–Wagner-type relaxation, mainly caused by the hopping of oxygen vacancies⁵¹. Further, the polaron hole hopping have been found responsible for conduction and relaxation processes through the grain and grain boundaries⁵¹, same behavior was reported by Mandal with the doping Gd in YFe_0.6Mn_0.4O₃⁵².

Figure 6 illustrates the dielectric loss (ε″) as a function of temperature at three distinct frequencies (10kHz, 100kHz, and 1MHz). Analysis of the experimental data reveals that the introduction of Gd-ions induces relaxation, as evidenced in panel S2 of Fig. 6. This relaxation phenomenon is observed solely in the composites with Gd contents of 0.25 and 0.5, whereas it diminishes with higher Gd-content samples (S4, S5, S6, and S7). The relaxation is attributed to DC conduction at low frequencies and electrode polarization, occurring at temperatures above T_C⁵⁰. In samples with higher levels of Gd-ions, the ε″ indicates leakage current, compromising the dielectric behavior within the samples⁵³. This behavior is consistent across samples S4, S5, S6, and S7, beyond S3 (Gd_0.5Ba_0.5TiO₃), as the predominant carriers arise from barium and oxygen vacancies resulting from the substitution of Ba with Gd ions. Notably, in the temperature dependence of dielectric loss, lower frequencies (10kHz) correspond to lower T_C and higher values of ε″. The dielectric loss versus temperature plots for the samples (S1–S7) reveal significant frequency-dependent behavior. In all samples, the ε″ increases with temperature, with larger losses observed at lower frequencies (10 kHz) compared to higher frequencies (100 kHz and 1 MHz). S1, S2, and S3 exhibit prominent peaks between 100 °C and 300 °C, suggesting polarization or relaxation processes occurring at these temperatures, potentially linked to phase transitions or defects⁵⁴. Notably, S4 shows a dispersed pattern with high variability at lower temperatures, which might indicate unstable relaxation dynamics. For S5 and S6, the ε″ dramatically rises above 400 °C, particularly at lower frequencies, likely due to increased conductivity or space charge polarization effects at high temperatures. Sample S7 shows relatively low ε″ across the entire temperature range, indicating better dielectric stability compared to the other samples. The overall frequency dispersion suggests that each sample experiences increased dielectric relaxation or conduction effects as temperature rises, with lower frequencies more affected by these mechanisms^49,54,55.

Fig. 6.

Variation of the dielectric loss with temperature for the Gd_xBa_1−xTiO₃ samples, where x ranges from 0 to 1.0 mol%.

The AC conductivity (σ_AC) as a function of Frequency

Figure 7 depicts the relationship between conductivity (σ_AC) and frequency (f) for all samples under investigation. Initially, in S1 (BaTiO₃), conductivity exhibits a linear increase with frequency. However, in samples containing Gd, conductivity demonstrates an increase as frequency rises, attributed to the replacement of Ba ions by Gd ions²⁷. Notably, the conductivity of Gd-containing samples is markedly lower values compared to the parent BaTiO₃ (S1) sample, influenced by various factors including changes in crystal and electronic structures, as well as variations in impurity or oxygen vacancy concentrations. As elucidated in the structural analysis of this study, the introduction of Gd into BaTiO₃ disrupts the parent lattice’s crystal structure, leading to variations in the density of states near the Fermi level and affecting charge carrier mobility. Furthermore, the distorted structure of Gd-containing samples may introduce additional defects or impurities, consequently hindering charge carrier mobility and reducing conductivity compared to the more regular structure of BaTiO₃⁵⁶. The lower conductivity values observed at lower temperature ranges are attributed frozen dipoles, with increasing freqency and temperature, the conductivity values incraesed, due to the thermal motion of the ions on the surface of the samples^57,58. Though, the can be expressed according to Jonscher’s universal power law:

3

where is the at , is a constant that depends on temperature, is the total conductivity, and is called the exponent of the frequency. The conductivity versus frequency plots for the samples (S1 to S7) show a general trend of increasing conductivity with frequency and temperature. At lower frequencies (below 10 kHz), the conductivity is relatively constant, but as the frequency increases, all samples exhibit a notable rise in conductivity. This frequency dependence is more pronounced at higher temperatures, indicating the activation of charge carriers with increasing thermal energy. Samples S1, S2, S5, and S6 exhibit a stronger increase in conductivity at high temperatures, likely due to thermally activated conduction mechanisms such as hopping or defect-related charge transport^58,59.

In contrast, S3 and S4 show more stable conductivity over the measured frequency range, suggesting better frequency stability. Sample S7 displays lower overall conductivity, indicating superior insulating properties compared to the other samples. The observed behavior aligns with common dielectric and semiconducting materials, where conductivity increases at higher temperatures and frequencies due to enhanced mobility of charge carriers^25,60,61.

Conclusion

In conclusion, our study successfully synthesized a series of Gd_xBa_1−xTiO₃ ceramics and conducted a comprehensive investigation of their structural, morphological, optical, and electrical properties. X-ray diffraction (XRD) and morphological analyses confirmed the transition from near cubic tetragonal to orthorhombic phases in our samples, while photoluminescence (PL) and Raman spectroscopy revealed distinct features in samples with Gd concentrations exceeding 0.5. The introduction of Gd ions induced the formation of Ba and O vacancies to maintain valence equilibrium, as evidenced by our experimental data. Dielectric studies revealed intriguing trends, with AC conductivity increasing with frequency for pure BaTiO₃. However, as the Gd-ion concentration increased, the samples exhibited increasing conductivity with frequency and temperature, likely due to the induced Ba and Oxygen vacancies. Our findings provide insights into the substitution mechanism of Gd³⁺ ions into Ba²⁺ sites and highlight the potential of controlled gadolinium incorporation for tuning the electronic and dielectric properties of BaTiO₃-based materials. This study contributes valuable knowledge to the design and development of advanced functional materials for diverse technological applications, ranging from electronics to energy storage and sensing.

Author contributions

Ahmed I. Ali fabricated the composites, R. K. Hussein and Jong Yeog Son, Ahmed. I. Ali, A.B. El Basaty characterized the samples, investigated the experimental results, investigated the dielectric properties data, S. Abu Alrub, A.B. El Basaty and Jong Yeog Son: contributed to an analysis of the data, writing the draft of the manuscript, and Ahmed I. Ali, A.B. El Basaty, and Jong Yeog Son: reviewing the manuscript.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Ethical approval

No ethical approval was granted to conduct the experiments involved in the manuscript.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-93014-4.