The pure BaTiO₃ and Ho doped BaTiO₃ (Ba_1-xHo_xTiO₃ with x = 0, 0.25, 0.50, 0.75, 1, 1.5 and 2%), powders were prepared through the sol-gel process and structurally characterized by Thermogravimetric analysis (TGA), Differential thermal analysis (DTA), X-Ray diffraction (XRD), Fourier Transform Infrared (FT-IR) and Raman spectroscopy. The optical properties have been investigated using Ultraviolet-Visible (UV-Vis) transmittance-reflectance spectroscopy. X-ray diffraction (XRD). The results revealed that the prepared powders, calcined at 1000 °C for 4 hours, crystallized in the pure perovskite structure without the presence of secondary phases and showed a slight transition from the quadratic phase (pure BT) to the pseudo-cubic phase for the doped samples. From these results, we can also notice that Ho may occupy both Ba and Ti crystallographic sites. Raman and Fourier Transform Infrared (FT-IR) results are in accordance with those obtained from XRD characterizations. The values of the bandgap energies for the doped samples are lower than that of the pure BaTiO₃ (3.26 eV), thus confirming energy softening effect of Ho

Keywords: Sol-gel, Ba1-xHoxTiO3 ceramics, Structural analysis, Gap energy

Perovskites (ABO₃) are among the most fascinating categories of oxide materials. This is owing to their distinct and numerous significant characteristics, which include a high dielectric constant, the capacity to exhibit ferroelectric activity under their Curie temperature, inherent polarization, and non-linear optical coefficients [1, 2]. In the ABO₃ structure, the cations in the A and B-site adopt a total valence of +6 with 12 and 6-fold coordinated geometry, respectively. The flexibility of this structure allows it to host a variety of iso- and aliovalent cations, thus opening a wide horizon for applications. Among these materials is the Barium Titanate, BaTiO₃ (BT), which presents high dielectric properties that can be systematically tailored by chemical substitution of Barium and/or Titanium. The current market share of capacitor business based on this powder represents 80-90% [3]. For example, BaTiO₃ doped with the rare earths Ho³⁺, Y³⁺ or Er³⁺ is used as a dielectric material in ceramic capacitors [4, 5]. Most ceramic capacitors have a multi-layered structure which is known as a multi-layer ceramic chip capacitor (MLCC) [6]. Common electronic devices contain large numbers of MLCCs: a cell phone 250, a laptop 400 and an automobile with over 1,000 [7]. Studies have demonstrated that the electrical characteristics of BaTiO₃ sublattices are influenced by the position of rare earth ions within them [8]. Tsur and Randall [9] found that when elements with ionic radius values between 0.87 Å and 0.94 Å (such as Er, Y, Ho, Dy, Gd) are used as substitutes, the compounds display amphoteric traits. This means that these elements can occupy either of the (A, B) cation lattice sites in the BaTiO₃ structure, with their specific location being dependent on factors like the quantity of dopants, the Ba/Ti ratio, and solubility. For Ho³⁺ ions, the ionic radius of Ho³⁺ is about 0.90 Å, they could replace Ba²⁺ (1.35 Å) or Ti⁴⁺ (0.64 Å) ions. When Ho³⁺ ions are substituted into the Ba sites, the charge imbalance is compensated by Ba²⁺ vacancies, while when Ho³⁺ ions are substituted into Ti sites, charge compensation is provided by oxygen vacancies. In terms of the structure, Lu et al. [10] showed that Ho-doped BaTiO₃ crystallized in a tetragonal structure, while Vega et al. [11] reported that this compound may adopt a cubic perovskite structure. Moreover, it has been found that doping with Holmium (Ho) leads to the creation of defects in the BaTiO₃ structure, manifesting as a pyrochlore-like secondary phase, Ho₂Ti₂O₇. This occurs in samples where the concentration of Holmium (x(Ho)) exceeds 3%, according to the research conducted by Jeong et al. [12]. Additionally, Marjanović et al. [13] demonstrated that this effect is also observed when the concentration of Ho is 0.5% or more. These established findings prompted us to restrict the Ho concentration, denoted as x, within the range of 0 to 2%. Moreover, the occupation of both cationic sites in BaTiO₃ by Ho resulted ina lowering of the Curie temperature (T_C) [14], and the decrease of the Curie constant with increase of Ho- concentration [12]. Despite these reported results, there is still a lack of our understanding on the: (i) effect of Holmium on the physical-chemical properties of BaTiO₃, (ii) effect of occupation (of Ba or Ti sites) on the optical properties .
In this study, we report the effect of the Ho doping in BaTiO₃ at the Ba site on the structural and optical properties of BaTiO₃ ceramics obtained with the sol-gel method and compare our results with those found in the literature. In particular, we found that the samples exhibited a pure perovskite structure and a shift from quadratic to pseudo-cubic phase in the doped samples. It can be noticed that, at room temperature (RT), BaTiO₃ adopts the tetragonal structure and is in its ferroelectric phase (Polarized state). With increasing temperature and around Tc = 130 °C (Curie temperature) the permittivity of the material reaches its maximum value and the phase begins to transform from ferroelectric to paraelectric phase. The latter is reached above Tc (Depolarized state) and the structure becomes cubic. The doping influences both the sturctural and dielectric properties of the material. In particular, due to the difference between ionic radii of Ba and Ti ions compared to that of Ho, the calculated values of the parameter quadracity (c/a), at room temperature , show a decrease with increase in Ho concentration without equaling 1. Indeed, at RT (< Tc), the material is in its ferroelectric state (non centro symmetric structure) and the corresponding structure is pseudo cubic (quadratic)(c/a is near 1). Moreover, under doping the physical properties of the materials are affected. It is obeserved from dielectric measurements a shift of Tc, a variation of the value of the permittivity around Tc, and the calculated parameters such as the piezoelectric coefficient and electromechanical coupling vary.
In particular, the shift of Tc to lower values , near RT, is suitable for applications of the materials at low temperatures and high values of the permittivity are favorable for the use of these materials for enrgy storage [15, 16]. A high piezoelectric coefficient and permittivity make the materials to have potential applications in multilayer piezoelectric devices [17].
UV-Vis spectroscopy demonstrated reduced bandgap energies in doped samples, confirming the energy-softening effect of Ho.We can also notice that In addition to the known applications of rare earth (La, Er, Ho, Sn, …)-doped BaTiO₃ [3-7], attempts are still underway to improve the optical properties of this material for possible technological applications [18].

Synthesis
We produced Holmium-doped Barium Titanate powders, corresponding tothe chemical formula Ba_1-xHo_xTiO₃ (BH_xT) with x values ranging from 0 to 2%, through the sol-gel technique. Precursors for this process included Barium acetate trihydrate (Ba(CH₃CO₂)₂∙3H₂O), Holmium acetate (C₆H₉HoO₆), and Titanium isopropoxide Ti[OCH(CH₃)₂]₄. Lactic acid (CH₃CH(OH)COOH) was used as a peptizing agent while acetic acid and distilled water served as solvents. The initial stage involved creating a TiO₂ colloidal solution. This was done by adding Titanium isopropoxide to a lactic acid and H₂O mixture while maintaining continuous stirring at 70 °C. A white precipitate formed after 72 hours, which then converted into a uniform, clear solution. In the subsequent stage, the colloidal solution was mixed with Holmium and Barium acetates in stoichiometric quantities. The resulting clear sol transformed into a translucent gel upon stirring at 80 °C. This gel was then dried at 80 °C and ground to produce fine powders. The resulting nanopowders underwent calcination in open air at a temperature of 1000 °C for 4 hours inside a programmable oven. A detailed illustration of the entire synthesis procedure is given in Fig. 1.
Characterization techniques
The structure of the BH_xT samples was determined by X-ray diffraction (XRD) usingan X-PERT PRO diffractometer with Cu-k (alpha) radiation. Raman and Fourier transform infrared (FT-IR) spectroscopies were measured for all samples in backscattering and transmission geometries, respectively. Differential Thermal Analysis (DTA) and Thermogravimetric Analysis (TGA) were applied to the BH₁T sample, which was selected as a representative sample from the BH_xT series. Ultraviolet-visible (UV-vis) reflectance spectroscopy (Lambda 25 Perkin-Elmer) was used to investigate the optical properties of the synthesized BH_xT samples.

Thermal analysis
The thermal stability of the BH₁T precursor-gel was examined using thermogravimetry (TG) and differential thermal analysis (DT), as illustrated in Fig. 2. The thermogravimetric assessment was carried out in an air atmosphere, with a heating rate of 5 °C per minute, and temperatures between 30 and 1000 °C. The TGA diagram (Fig. 2) suggests that the sample’s decomposition of the sample occurs across four distinct stages, over temperature intervals of 30-180 °C, 180-500 °C, 500-780 °C, and 780-980 °C. In the initial stage, we observed a mass reduction of 4.87%.This mass loss was accompanied by a small endothermic peak in the DTA curve around 56.56 °C and has been attributed to the elimination of water and excess lactic acid [19]. During the second phase, the TGA graph showed a substantial mass reduction of approximately 24%, which took place between 180 and 500 °C. This reduction can be attributed to the decomposition of acetate and isopropoxide groups associated with Titanium, along with the pyrolysis of the remaining organic compounds, leading to the elimination of CO₂ and any residual H₂O [20]. This mass loss was accompanied by two exothermics peaks on the DTA curve around 304 and 381 °C, respectively. In this temperature range, the gel is converted into a polymeras a result of the rearrangements of chemical bonds [21]. The third step occurs between 500 and 780 °C with a mass loss of 3%, which corresponds to the decomposition of small quantities of barium carbonate BaCO₃, formed by the decomposition of barium acetate [19]. Before 600 °C, the decomposition of the metallic organic framework has started and amorphous TiO₂ and BaOare produced from the metallic organic pyrolysis. A last part of mass loss ranging between (780-980 °C) was detected with a mass loss of 5%, accompanied by an exothermic peak in the DTA curve due to organic polymer degradation and the production of inorganic compounds (the formation of BH_xT) [20]. The results indicate that the onset of crystallization occurs at 980 °C, which is relatively low compared to other studies using different synthesis techniques. This low temperature is attributed to the sol-gel preparation method [22] as compared to the conventional ceramic method [23, 24].
X-ray Diffraction study
Fig. 3a presents the XRD spectra of the BH_xT powder samples (x = 0, 0.25, 0.50, 0.75,1, 1.5 and 2%), calcined at 1000 °C for 4 hours. All these powders adopt the perovskite type structure without the presence of secondary phases, thus confirming the results observed by the thermal analysis (TGA-DTA). A zoom on the peak (101) (Fig. 3b) shows a displacement of its position towards lower 2θ angles for small concentrations x of Ho (x = 1.5), followed by a shift towards higher angles for x = 2%, which highlights the incorporation and effect of Ho on the change in the structure of BT. Moreover, the presence of the peaks (200) and (002) (Fig. 3c) for the pure sample (x = 0) are signature of the quadratic BT-phase [25]. Thus, the increase in holmium content causes a merging of both peaks, which therefore shows a subtleshift from the quadratic phase (pure BT) to the pseudo-cubic phase for the doped samples. These findings are consistent with those reported by Marjanovic et al. [13], where the BH_xT samples (x = 0.01, 0.1, 0.5%) were prepared using the solid-state reaction method and sintered at 1380 °C for a duration of 4 hours. In a similar study, Chang et al. [26] concluded that the overall structure of the tetragonal lattice was unaffected by Ho doping up to x = 1.2%, and the diffraction peaks shifted slightly to lower values of 2θ as the holmium concentration increased. Secu et al. [18] observed that the composition Ba_0.97Ho_0.03TiO₃, crystallized in the tetragonal BaTiO₃ lattice, with the presence of traces of the second Ti-rich Ho₂Ti₂O₇ phase. In fact, it is commonly recognized that when Ba is replaced by holmium, there is a consequent decrease in the unit cell volume. Conversely, when Titanium is substituted with Holmium, there is an increase in the unit cell volume. This is due to the ionic radius of Ho³⁺ (0.90 Å), which is smaller than that of Ba²⁺ (1.35 Å), larger than that of Ti⁴⁺ (0.64 Å). Table 1 shows the lattice parameters (a and c) along with the c/a ratio and unit cell volume of Ba_1-xHo_xTiO₃ (x = 0, 0.25, 0.50, 0.75,1, 1.5 and 2%) calcined at 1000 °C-4 h.
The unit cell volume contracts with increasing Holmium concentrations up to 1.5%, then expands for the sample (BH_xT, x = 2%). When Ho³⁺ cations occupy the Ti⁴⁺ sites (in an octahedral environnement), oxygen vacancies are generated to compensate for the charge imbalance, which is expected to result in the expansion of the cell volume due to an increase in cell parameters (a andc). Furthermore, if these oxygen vacancies primarily align along the c-axis, this leads to a significant reduction in the c lattice parameter, which could explain the changes in the lattice parameters and cell volume in relation to the Ho(x) content. Contrastingly, due to the differences in ionic radii between Ba²⁺ and Ho³⁺, the replacement of Ba sites with Ho³⁺ ions introduce compression of the unit cell. In addition, the behavior of in the quadracity, c/a, reveals that as the Holmium content increases, the tetragonality of the phase diminishes, signifying a shift from the quadratic phase to the pseudo-cubic phase.The size of the crystallites (D) in our BH_xT samples was determined from the X-ray diffraction patterns, specifically the (101) peak, with the help of the Debye-Scherrer equation [27]:



Where D represents the crystallite size, λ is the X-ray wavelength (1.5406 Å), θ is the diffraction angle and β is the Full Width at Half Maximum (FWHM) of the peak (101). The estimated values for the samples are given in Table 1. The latter shows that when the Holmuim concentration increases the crystallite size decreases.

Ba_1-xHo_xTiO₃ ceramics (x = 0, 0.25, 0.50, 0.75,1, 1.5 and 2%) were successfully prepared using the sol-gel process, and their structural and optical properties investigated. The structural analysis (DRX, Raman and FTIR) revealed that all powders crystallized in a pure perovskite structure, with no secondary phases present, and a transition from the quadratic phase (pure BT) to the pseudo-cubic phase was observed under doping. From the same analysis, it was also observed that the Ho³⁺ ion can replace both Ti⁴⁺ and Ba²⁺ ones.This result was confirmed by Raman and Fourier transform infrared (FT-IR) analyses. For optical measurements, the values of the bandgap energies for the doped ceramics are lower than those of the value in the pure case, and it was shown that Ho doping increases the structural disorder within the BT lattice, giving rise in particular to a narrowing of the forbidden gap.