Improved Dielectric and Nonlinear Electrical Properties of Fine‐Grained CaCu3Ti4O12 Ceramics Prepared by a Glycine‐Nitrate Process

Pure CaCu₃Ti₄O₁₂ was successfully prepared by a glycine‐nitrate process using a relatively low calcination temperature and short reaction time of 760°C for 4 h. Fine‐grained CaCu₃Ti₄O₁₂ ceramics with dense microstructure and small grain size were obtained after sintering for 1 h. The nonlinear coefficient of a fine‐grained CaCu₃Ti₄O₁₂ ceramic calculated in the range 1–10 mA/cm² was found to be very high of ~16.39 with high breakdown electric field strength of 1.46 × 10⁴ V/cm. This fine‐grained CaCu₃Ti₄O₁₂ ceramic also exhibited a very low loss tangent of 0.017 at 20°C with temperature stability over the range ?55°C to 85°C. The grain growth rate of the CaCu₃Ti₄O₁₂ ceramics was found to be very fast after increasing the sintering time from 1.5 to 3 h, leading to formation of a coarse‐grained CaCu₃Ti₄O₁₂ ceramic with grain size of about 100–200 μm. The dielectric permittivity of this coarse‐grained ceramic was found to be as high as 1.03 × 10⁵ with a low loss tangent of 0.054.     

Giant dielectric behavior of monovalent cation/anion (Li+, F−) co-doped CaCu3Ti4O12 ceramics

Giant dielectric behavior and electrical properties of monovalent cation/anion (Li⁺, F⁻) co-doped CaCu₃Ti₄O₁₂ ceramics prepared by a solid-state reaction route were systematically investigated. Substitution of Li⁺ and F⁻ led to a significantly enlarged mean grain size. A reduced loss tangent (tanδ ~0.06) with the retainment of an ultra-high dielectric permittivity (ε′ ~7.7-8.8 × 10⁴) was achieved in the co-doped ceramics, while the breakdown electric field and nonlinear coefficient of CaCu₃Ti₄O₁₂ ceramics were increased by co-doping with (Li⁺, F⁻). The variations in nonlinear electrical properties and giant dielectric response, as well as the dielectric relaxation, were well explained by the Maxwell-Wagner polarization model for an electrically heterogeneous microstructure, in which a Schottky barrier height at the grain boundaries (GBs) was formed. ε′ was closely correlated to the GB capacitance. Significantly decreased tanδ value and enhanced nonlinear properties were related to a significant increase in the GB resistance, which was attributed to the significantly increased potential barrier height and conduction activation energy at the GBs. The semiconducting nature of the grains was also studied using X-ray photoelectron spectroscopy and found to originate from the presence of Cu⁺ and Ti³⁺ ions.     

Low temperature preparation of CaCu3Ti4O12 ceramics with high permittivity and low dielectric loss

Low temperature preparation of CaCu₃Ti₄O₁₂ ceramics with large permittivity is of practical interest for cofired multilayer ceramic capacitors. Although CaCu₃Ti₄O₁₂ ceramics have been prepared at low temperatures as previously reported, they have rather low permittivity. This work demonstrates that CaCu₃Ti₄O₁₂ ceramics can not only be prepared at low temperatures, but they also have large permittivity. Herein, CaCu₃Ti₄O₁₂ ceramics were prepared by the solid state reaction method using B₂O₃ as the doping substance. It has been shown that B₂O₃ dopant can considerably lower the calcination and sintering temperatures to 870 °C and 920 °C, respectively. The relative permittivity of the low temperature prepared CaCu₃Ti_4−xB_xO₁₂ ceramics is about 5 times larger than the previously reported results in the literature. Furthermore, the dielectric loss of the CaCu₃Ti_4−xB_xO₁₂ ceramics is found to be as low as 0.03. This work provides a beneficial base for the future commercial applications of CaCu₃Ti₄O₁₂ ceramics with large permittivity for the cofired multilayer ceramic capacitors.     

Grain boundary engineering that induces ultrahigh permittivity and decreased dielectric loss in CdCu3Ti4O12 ceramics

Dielectric materials with ultrahigh permittivity are attracting attention due to the increasing demand for these types of materials for microelectronics and energy storage applications. In this work, we successfully synthesized Zn-doped CdCu₃Ti₄O₁₂ (CdCTO) ceramics with low dielectric loss and large permittivity via an ordinary mixed-oxide technique. Remarkably, at a Zn doping level of 0.10, a CdCu_2.9Zn_0.1Ti₄O₁₂ ceramic exhibited both decreased dielectric loss tangent of ~0.058 and large dielectric permittivity > 4.0 × 10⁴, as well as a good frequency stability over a wide frequency range from 40 Hz to 10⁶ Hz. The high dielectric performance was attributed to the enhanced grain boundary resistance and internal barrier layer capacitor (IBLC) effect due to the fine and uniform grains that formed upon Zn doping. The findings reported in this work provide valuable insights into how to simultaneously realize a low dielectric loss and high permittivity in CdCTO and other related dielectric ceramics.     

Structural and dielectric properties,and nonlinear electrical response of the CaCu3-xZnxTi4O12 ceramics: Experimental and computational studies

CaCu_3-xZn_xTi₄O₁₂ ceramics (x = 0, 0.05, 0.10) were successfully prepared by a conventional solid-state reaction method. Their structural and dielectric properties, and nonlinear electrical response were systematically inspected. The X-ray diffraction results indicated that single-phase CaCu₃Ti₄O₁₂ (JCPDS no. 75–2188) was obtained in all sintered ceramics. Changes in the lattice parameter are well-matched with the computational result, indicating an occupation of Zn²⁺ doping ions at Cu²⁺ sites. The overall tendency shows that the average grain size decreases when x increases. Due to a decrease in overall grain size, the dielectric permittivity of CaCu_3-xZn_xTi₄O₁₂ decreases expressively. Despite a decrease in the dielectric permittivity, it remains at a high level in the doped ceramics (~3,406–11,441). Besides retention in high dielectric permittivity, the dielectric loss tangent of x = 0.05 and 0.10 (~0.074–0.076) is lower than that of x = 0 (~0.227). A reduction in the dielectric loss tangent in the CaCu_3-xZn_xTi₄O₁₂ ceramics is closely associated with the enhanced grain boundary response. Increases in grain boundary resistance, breakdown electric field, and conduction activation energy of grain boundary as a result of Zn²⁺ substitution are shown to play a crucial role in improved grain boundary response. Furthermore, the XPS analysis shows the existence of Cu⁺/Cu²⁺ and Ti³⁺/Ti⁴⁺, indicating charge compensation due to the loss of oxygen lattice. Based on all results of this work, enhanced dielectric properties of the Zn-doped CCTO can be explained using the internal barrier layer capacitor model.     

Dielectric properties of CaCu3Ti4O12 ceramics with Zn substitution for Cu

Abstract

CaCu_3–xZn_xTi₄O₁₂ (x is from 0 to 1·0) polycrystalline samples were fabricated via a two-step solid state reaction process. The lattice parameter of the monophasic CaCu₃Ti₄O₁₂ phase increased as Zn content increased. Scanning electron microscopy (SEM) images of the CCTO ceramic show bimodal grain size distribution and the grain size decrease largely with the appearance of Zn₂TiO₄ second phase. The dielectric permittivity of pure CCTO ceramic is ～1·5×10⁴ at f?=?100 Hz. The dielectric constant of the sample largely increased with Zn substitution in the frequency range f<10⁴ Hz. The highest dielectric constant was 6·2×10⁴ at f?=?100 Hz with Zn substitution of x?=?0·8. The improved dielectric properties are believed to be related to the presence of a thin grain boundary barrier layer. The resistivity of the grain boundary decreased largely with Zn substitution as evidenced from the impedance plots.     

Microstructural evolution,non‐Ohmic properties,and giant dielectric response in CaCu3Ti4−xGexO12 ceramics

The microstructural evolution, non‐Ohmic properties, and giant dielectric properties of CaCu₃Ti_4?xGe_xO₁₂ ceramics (x=0‐0.10) are systematically investigated. The Rietveld refinement confirms the existence of a pure CaCu₃Ti₄O₁₂ phase in all samples. Significantly enlarged grain sizes of CaCu₃Ti_4?xGe_xO₁₂ ceramics are associated with the liquid phase sintering mechanism. Enhanced dielectric permittivity from 6.90×10⁴ to 1.08×10⁵ can be achieved by increasing Ge⁴⁺ dopant from x=0‐0.10, whereas the loss tangent is remarkably reduced by a factor of ≈10. Non‐Ohmic properties are enhanced by Ge⁴⁺ doping ions. Using impedance and admittance spectroscopies, the underlying mechanisms for the dielectric and nonlinear properties are well described. The improved nonlinear properties and reduced loss tangent are attributed to the enhanced resistance and conduction activation energy of the grain boundaries. The largely enhanced permittivity is closely associated with the enlarged grain sizes and the increase in the Cu⁺/Cu²⁺ and Ti³⁺/Ti⁴⁺ ratios, which are calculated from the X‐ray absorption near‐edge structure.     

Dielectric properties with high dielectric permittivity and low loss tangent and nonlinear electrical response of sol-gel synthesized Na1/2Sm1/2Cu3Ti4O12 perovskite ceramic

Giant dielectric ceramic, Na_1/2Sm_1/2Cu₃Ti₄O₁₂, was successfully prepared by a modified sol-gel method. X-ray diffraction experiments indicated that a body-centered cubic structure with a space group of Im3 was obtained. Our density functional theory calculations revealed that codoping Na and Sm in the CaCu₃Ti₄O₁₂ structure resulted in charge compensation between Na and Sm ions in this structure, whereas the oxidation states of Cu and Ti were unaltered. Giant dielectric permittivity ～7.21 × 10³ - 8.04 × 10³ and low dielectric loss tangent ～0.045–0.049 were accomplished at a sintering temperature of 1050 °C for 12–18 h. Nonlinear J - E property with breakdown electric field ～5.13 – 5.78 × 10³ V/cm and nonlinear coefficient ～6.08–6.82 were also achieved. The n-type semiconducting grain originated from short-range migrations of mixed Cu⁺/Cu²⁺ and Ti³⁺/Ti⁴⁺ charges. Finally, our charge analysis showed that the occurrence of Cu⁺ and Ti³⁺ was related to the existence of oxygen vacancy in these ceramics.     

Enhancing giant dielectric properties of Ta5+-doped Na1/2Y1/2Cu3Ti4O12 ceramics by engineering grain and grain boundary

Various strategies to improve the dielectric properties of ACu₃Ti₄O₁₂ (A = Sr, Ca, Ba, Cd, and Na_1/2Bi_1/2) ceramics have widely been investigated. However, the reduction in the loss tangent (tanδ) is usually accompanied by the decreased dielectric permittivity (ε′), or vice versa. Herein, we report a route to considerably increase ε′ with a simultaneous reduction in tanδ in Ta⁵⁺–doped Na_1/2Y_1/2Cu₃Ti₄O₁₂ (NYCTO) ceramics. Dense microstructures with segregation of Cu– and Ta–rich phases along the grain boundaries (GBs) and slightly increased mean grain size were observed. The samples prepared via solid-state reaction displayed an increase in ε′ by more than a factor of 3, whereas tanδ was significantly reduced by an order of magnitude. The GB–conduction activation energy and resistance raised due to the segregation of Cu/Ta–rich phases along the GBs, resulting in a decreased tanδ. Concurrently, the grain–conduction activation energy and grain resistance of the NYCTO ceramics were reduced by Ta⁵⁺ doping ions owing to the increased Cu⁺/Cu²⁺, Cu³⁺/Cu²⁺, and Ti³⁺/Ti⁴⁺ ratios, resulting in enhanced interfacial polarization and ε′. The effects of Ta⁵⁺ dopant on the giant dielectric response and electrical properties of the grain and GBs were described based on the Maxwell–Wagner polarization at the insulating GB interface, following the internal barrier layer capacitor model.     

Enhancement of giant dielectric response in Ga-doped CaCu3Ti4O12 ceramics

The influences of Ga³⁺ doping ions on the microstructure, dielectric and electrical properties of CaCu₃Ti₄O₁₂ ceramics were investigated systematically. Addition of Ga³⁺ ions can cause a great increase in the mean grain size of CaCu₃Ti₄O₁₂ ceramics. This is ascribed to the ability of Ga³⁺ doping to enhance grain boundary mobility. Doping CaCu₃Ti₄O₁₂ with 0.25 mol% of Ga³⁺ caused a large increase in its dielectric constant from 5439 to 31,331. The loss tangent decreased from 0.153 to 0.044. The giant dielectric response and dielectric relaxation behavior can be well described by the internal barrier layer capacitor model based on Maxwell?Wagner polarization at grain boundaries. The nonlinear coefficient, breakdown field, and electrostatic potential barrier at grain boundaries decreased with increasing Ga³⁺ content. Our results demonstrated the importance of ceramic microstructure and electrical responses of grain and grain boundaries in controlling the giant dielectric response and dielectric relaxation behavior of CaCu₃Ti₄O₁₂ ceramics.     

Dramatically enhanced non-Ohmic properties and maximum stored energy density in ceramic-metal nanocomposites: CaCu3Ti4O12/Au nanoparticles

Non-Ohmic and dielectric properties of a novel CaCu₃Ti₄O₁₂/Au nanocomposite were investigated. Introduction of 2.5 vol.% Au nanoparticles in CaCu₃Ti₄O₁₂ ceramics significantly reduced the loss tangent while its dielectric permittivity remained unchanged. The non-Ohmic properties of CaCu₃Ti₄O₁₂/Au (2.5 vol.%) were dramatically improved. A nonlinear coefficient of ≈ 17.7 and breakdown electric field strength of 1.25 × 10⁴ V/m were observed. The maximum stored energy density was found to be 25.8 kJ/m³, which is higher than that of pure CaCu₃Ti₄O₁₂ by a factor of 8. Au addition at higher concentrations resulted in degradation of dielectric and non-Ohmic properties, which is described well by percolation theory.     

Extremely Enhanced Nonlinear Current–Voltage Properties of Tb‐Doped CaCu3Ti4O12 Ceramics

Nonlinear current–voltage properties of CaCu₃Ti₄O₁₂ ceramics were extremely enhanced by doping with Tb. Substitution of Tb to CaCu₃Ti₄O₁₂ resulted in a decrease in grain size due to the ability of Tb ions to inhibit grain boundary mobility. The dielectric properties of CaCu₃Ti₄O₁₂ ceramics were degraded after doping with Tb. Surprisingly, the nonlinear electrical properties were strongly enhanced. The best properties with a nonlinear coefficient of ~29.67 and breakdown electric field strength of ~1.52 × 10⁴ V/cm were obtained in the Ca_0.775Tb_0.15Cu₃Ti₄O₁₂ ceramic. These extremely enhanced properties were attributed to modification of grain boundary electrical response due to the effect Tb substitution.     

Electrical properties of Co-doped CaCu3Ti4O12

Co-doped CaCu₃Ti₄O₁₂ samples were synthesized by solid-phase reaction. Electrical properties were studied by impedance spectroscopy in wide temperature (25–450 °C) and frequency (10 Hz–10 MHz) intervals. It was shown that the presence of the copper oxide interlayer significantly reduces the value of the dielectric constant. The amount of impurity copper in the CaCu₃Ti_4-хCo_хO_12-δ samples (x = 0.06; 0.12; 0.24) rise with an increase in the cobalt content. The samples are characterized by a granular microstructure, with an average grain size ranging from 2 to 10 μm. The impedance of the samples was simulated at a temperature of 25 °C and in the range of 100–450 °C. It was found that the samples are characterized by low- and high-frequency polarization. The conductivity activation energy varied from 0.94 to 0.87 eV depending on the cobalt content. The CaCu₃Ti_3.94Co_0.06O_12-δ sample are characterized by the best values of the dielectric permittivity and the dielectric loss tangent, ε = 400 and tanδ = 0.2 (at 1 MHz and room temperature), respectively.     

Origin of significantly enhanced dielectric response and nonlinear electrical behavior in Ni2+-doped CaCu3Ti4O12: Influence of DC bias on electrical properties of grain boundary and associated giant dielectric properties

CaCu_3-xNi_xTi₄O₁₂ (x?=?0, 0.05, and 0.10) powders were synthesized using a solid state reaction method. Phase structure and microstructure analyses revealed that all sintered CaCu_3-xNi_xTi₄O₁₂ ceramics were of a pure phase. The CaCu₃Ti₄O₁₂ ceramics had a dense microstructure and grain sizes were enlarged by doping with Ni²⁺. Interestingly, the dielectric permittivity was significantly enhanced, whereas the loss tangent was greatly suppressed to ～0.046–0.034 at 1?kHz. All sintered ceramics exhibited non-Ohmic characteristics. Clarification of the influences of DC bias showed that the dielectric permittivity and loss tangent values were increased by DC bias. The resistance of grain boundaries and the associated conduction activation energy of CaCu_3-xNi_xTi₄O₁₂ ceramics were reduced as the DC bias voltage increased. Therefore, the observed non-Ohmic behavior and significantly enhanced dielectric properties should be closely related to variation in the Schottky barriers at the grain boundaries.     

A novel strategy to enhance dielectric performance and non-Ohmic properties in Ca2Cu2−xMgxTi4O12

A novel strategy to improve the dielectric and non-Ohmic properties of CaCu₃Ti₄O₁₂ ceramics that deliberately created a binary-phase system of CaCu_3−xMg_xTi₄O₁₂/CaTiO₃ was proposed and can be performed with a starting nominal formula of Ca₂Cu_2−xMg_xTi₄O₁₂. Mg²⁺ doping ions were preferentially incorporated only into the CaCu₃Ti₄O₁₂ phase. Substitution of Mg²⁺ into CaCu₃Ti₄O₁₂/CaTiO₃ can cause a significant increase in dielectric permittivity and a large reduction of the loss tangent to <0.015 at 1 kHz; while, retaining excellent temperature dielectric-stability. Sintering time had a slight influence on the dielectric properties, but remarkable effects upon the nonlinear electrical properties of CaCu_3−xMg_xTi₄O₁₂/CaTiO₃ ceramics. Degradation of nonlinear properties with increased sintering time is suggested to be the result of the dominant effect of oxygen vacancies. Impedance spectroscopy analysis demonstrated that improved dielectric and nonlinear properties could be attributed to the enhanced electrical responses of CaCu₃Ti₄O₁₂–CaTiO₃ and CaCu₃Ti₄O₁₂–CaCu₃Ti₄O₁₂ interfaces resulting from Mg²⁺ doping ions.     

Thermal stability improvement of dielectric properties and non-ohmic characteristic of CaCu3+xTi4O12 ceramics via a Cu-nonstoichiometric approach

In this work, the effects of Cu composition on the thermal stability of the dielectric and nonlinear properties of CaCu_3+xTi₄O₁₂ (?0.2 ≤ x ≤ 0.2) ceramics obtained via a polymer-pyrolysis chemical process were studied. The mean grain sizes of Cu-stoichiometric (x = 0), Cu-deficient (x < 0) and Cu-excess (x > 0) CaCu_3+xTi₄O₁₂ ceramics were found to be ~3.2, ~3.4 and ~3.7 μm, respectively. Interestingly, very good dielectric properties (0.020 ≤ tanδ ≤ 0.038 and 4000 ≤ ε′ ≤ 7065) were attained in CaCu_3+xTi₄O₁₂ (?0.2 ≤ x ≤ 0.1, excluding x = 0.2) ceramics. Moreover, the variation of dielectric constant (ε′) within a limit of ±15% (Δε′_{± 15%}) over a wide temperature range (T_R) of ?70 – 220 °C with low tanδ < 0.05 (tanδ_<0.05) over a T_R of ?70 to 80 °C were achieved in a CaCu_2.8Ti₄O₁₂ ceramic. These results suggest that this ceramic could be applicable for X9R capacitors and energy storage devices that require high thermal stability. Additionally, the nonlinear properties of Cu-nonstoichiometric ceramics could be improved when compared with those of the Cu-stoichiometric material. The incremental changes of dielectric and nonlinear properties of CaCu_3+xTi₄O₁₂ (?0.2 ≤ x ≤ 0.2) ceramics revealed the significant role of Cu composition on grain boundary resistance (R_gb), which was confirmed by impedance spectroscopy analysis. In addition, XANES results revealed the proper ratios of Cu⁺:Cu²⁺ and Ti³⁺:Ti⁴⁺ found in these ceramics, indicating the semiconducting behavior of these grains.     

Dielectric properties of CaCu3Ti4O12 improved by chromium/lanthanum co-doping

The dielectric properties of Cr + La co-doped CaCu₃Ti₄O₁₂ ceramics prepared by a solid-state reaction method were evaluated and compared to Cr-doped, La-doped, and parent CaCu₃Ti₄O₁₂ (CCTO). Their structure and grain size were evaluated by X-ray diffraction and scanning electron microscopy, respectively. No secondary phase was detected based on the XRD analysis. The results show that, the room temperature dielectric loss of the co-doped samples is reduced to 43% compared to CCTO and their dielectric permittivity is higher than the un-doped, Cr-doped, and La-doped samples at frequencies over 325 kHz, 30 kHz, and 12 Hz, respectively. Furthermore, the temperature stability of the co-doped sample is significantly more convenient than that of CCTO, and its dielectric loss is three times lower. The results also indicated that the co-doping method is effective in reducing the dielectric loss, still maintaining the high dielectric permittivity.     

Effect of oxygen sintering atmosphere on the electrical behavior of CCTO ceramics

The CaCu₃Ti₄O₁₂ ceramics were sintered in air and pure O₂ atmosphere, respectively, and the effect of pure O₂ atmosphere on the electrical behavior of the CaCu₃Ti₄O₁₂ ceramics was investigated. It was found that the dielectric properties of the CaCu₃Ti₄O₁₂ ceramics displayed a Debye-like relaxation between 20 Hz and 1 MHz, but the permittivity of the sample sintered in pure O₂ atmosphere was decreased drastically. Moreover, the I-V behavior of the ceramic sintered in pure O₂ atmosphere presented a linear feature. With XPS analysis, it was illustrated that the valence of Cu and Ti elements in the CaCu₃Ti₄O₁₂ ceramics had obviously been influenced by the O₂ concentration. Based on the experimental comparison of CaCu₃Ti₄O₁₂ ceramics sintered in air and pure O₂ atmosphere, it was suggested that the valence of metallic elements and defects played key role for the origin of the giant permittivity and I-V nonlinear feature in the CaCu₃Ti₄O₁₂ ceramics.     

Colossal dielectric properties of Na1/3Ca1/3Sm1/3Cu3Ti4O12 ceramics: Computational and experimental investigations

A modified sol?gel technique was used to synthesize a high dielectric ceramic, Na_1/3Ca_1/3Sm_1/3Cu₃Ti₄O₁₂. The crystal structure of this sintered ceramic matches the standard pattern of a body?centered cubic (bcc) system within the Im3 space group (JCPDS No. 75–2188). No impurity phases were observed. Interestingly, a high dielectric permittivity of ～1.14–1.35 × 10⁴ and a low loss tangent of ～0.027–0.039 were achieved in this sintered Na_1/3Ca_1/3Sm_1/3Cu₃Ti₄O₁₂ ceramic. Our DFT calculations disclosed that substitution of Na⁺ ions at Cu²⁺ sites causes an observed excess Cu concentration. As a result, metastable insulating phases were formed at a relatively high sintering temperature. Additionally, our electron density calculations revealed that Na ions lose their electrons to Sm ions, whereas the oxidation states of Cu and Ti are unaltered. Our results show that Cu⁺ and Ti³⁺ were observed after introducing an oxygen vacancy into this lattice. Significantly different values of R_g, R_gb, and E_g, E_gb support an internal barrier layer capacitor as the most likely origin of the giant dielectric properties of this ceramic. XPS results show mixed Cu⁺/Cu²⁺ and Ti³⁺/Ti⁴⁺ in all ceramics, suggesting that electron hopping between Cu⁺?Cu²⁺ and Ti³⁺?Ti⁴⁺ is the probable origin of the n?type semiconducting state inside the grains.     

Enhanced intrinsic permittivity and bulk response in Y2/3Cu3Ti4+xO12 ceramics

Considering the contribution of the mixed valence structure of Ti³⁺ and Ti⁴⁺ to the semiconductivity of grain, compositions with the formula of Y_2/3Cu₃Ti_4+xO₁₂ were designed and prepared. The dielectric bulk responses of Y_2/3Cu₃Ti_4+xO₁₂ ceramics were explored in detail. Changing Ti stoichiometry gives rise to an increase of the intrinsic permittivity. Y_2/3Cu₃Ti_3.925O₁₂ ceramic exhibits a higher intrinsic permittivity of ~120 at 60 MHz than that of pure Y_2/3Cu₃Ti₄O₁₂ ceramics (87 at 60 MHz). Additionally, the activation energies of bulk responses are significantly enhanced by changing Ti stoichiometry, which is closely linked with the increase of Ti³⁺/Ti⁴⁺.