Dielectric properties of the Ca0.25Cu0.75-xAlxTiO3 ceramics: experimental and computational investigations

In this study, we employed a solid-state reaction method to synthesize Ca0.25Cu0.75-xAlxTiO3 ceramics, investigating the impact of Al doping at concentrations of x = 0 and 0.0125. Notably, all ceramics exhibited a primary phase of Ca0.25Cu0.75TiO3. The addition of Al3+ induced a significant increase in grain size. Density functional theory analyses revealed a preferential occupation of Cu sites by Al, leading to liquid-phase sintering processes attributed to excess Cu. Moreover, it was also found from DFT that the Al dopant cannot induce an oxygen vacancy in the lattice. Charge density analysis revealed that Cu+ and Ti3+ observed via XPS originate from the presence of an oxygen vacancy. The Ca0.25Cu0.7375Al0.0125TiO3 ceramic exhibited a very high dielectric permittivity of 9.23 × 104 and a low dielectric loss tangent of 0.057 at 1 kHz and room temperature. Importantly, the dielectric permittivity exhibited impressive stability over a temperature range of −60 °C to 110 °C, perfectly meeting the practical requirements for utilization in X5R ceramic capacitors. Our investigation indicates that the improved dielectric properties may be attributed to enhanced grain boundary responses, influenced by oxygen enrichment and the presence of metastable insulating layers at grain boundaries. Combining experimental findings with theoretical evidence, our study elucidates that the excellent dielectric properties of the Ca0.25Cu0.7375Al0.0125TiO3 ceramic originate from an extrinsic effect arising from grain boundary enhancement. This work not only contributes to advancing the understanding of the underlying mechanisms governing dielectric behavior in doped ceramics, but also emphasizes the potential of Ca0.25Cu0.7375Al0.0125TiO3 as a promising material for applications demanding superior dielectric performance.


Introduction
In recent years, increased interest in dielectric materials, attributed to their potential technical uses in microelectronic systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14], has encouraged the development of numerous compounds with very high dielectric permittivity (ε′), including co-doped TiO 2 [6], ACu 3 Ti 4 O 12 (A = Ca, Cd, Y 2/3 , Na 1/2 La 1/2 ) [1-5, 10-12, 14], co-doped SnO 2 [7], and others, contributing to recent achievements in dielectric research.Ca 0.25 Cu 0.75 TiO 3 or CaCu 3 Ti 4 O 12 (CCTO) perovskite oxide is one of the most alluring materials.It has been established via impedance spectroscopy experiments that electrical heterogeneity exists in CCTO ceramics with semiconducting grains separated by insulating grain boundaries [15].As a result, an enormous dielectric phenomenon might be created by an internal barrier layer capacitor (IBLC), which is a distinctive microstructural characteristic [1-5, 8-12, 14].During the sintering process, intergranular oxygen in the CCTO lattice is displaced, resulting in the formation of oxygen vacancies (V O ) in the ceramic lattice.It is necessary to employ O 2− throughout the cooling process to fill some V O sites, notably those located at the GB layers.As a result, V O was discovered inside the grains.According to general principles, the presence of V O in the oxide lattice triggers a charge compensation process, resulting in a small conductivity in the oxide lattice due to charge carrier hopping [10].According to the substantial investigations of the aforementioned studies, the dielectric characteristics of CCTO ceramics are significantly impacted by V O [5,13].Researchers have discovered that nanocluster defects, such as nanoscale domain boundaries and micro-insulating barriers, when present in conjunction with the V O that already exists in the CCTO lattice, can significantly influence the dielectric response of ceramics [9,16,17].This understanding helps advance CCTO and similar oxides with enhanced dielectric and electrical characteristics in practical applications for research and development.
Undoped CCTO has a high energy loss from an application aspect.Further study is required to lower the loss tangent (tanδ) for use in microelectronic device fabrication.Thus far, elemental doping has been shown to be the most effective method for improving the dielectric characteristics of oxides [1, 3-5, 8, 9, 12].This is because doping causes point defects and possible vacancies in anion and cation sites.Hence, dielectric properties of these materials are altered.Various research groups have investigated the repercussions of metal ion doping.Improved dielectric properties, especially lowering tanδ, can be achieved in Sr 2+ [3], Lu 3+ [5], Mg 2+ [8], Al 3+ [1,12,18,19], Cd 2+ /F − [9], Bi 3+ /Al 3+ [20], and Al 3+ /F − [4] doped CCTO.When doping with various elements, the origins of a decreased tanδ might result from several distinct sources.For example, replacement of Mg 2+ in Cu 2+ sites of the CCTO lattice may reduce oxygen losses during sintering at high temperatures.As a consequence, oxygen enrichment at grain boundaries (GBs) is the most likely source of the low tanδ in Mg doped CCTO, according to the literature [8].The enhanced ε′ associated with a decreased low-frequency tanδ in Aldoped CCTO is most likely the result of microstructural evolution and alteration of the electrical properties of GBs [1,12].Cu-rich phases could be detected in the microstructure of Al-doped CCTO in these instances.These Cu phases may be critical in suppressing tanδ values [21].Previous investigations indicated that various ions have been doped into multiple sites within the complex lattice structure of CCTO [22][23][24][25], and Al 3+ is one of these ions.Considering factors such as coordination numbers, valent charges, and the ionic radius of Al 3+ , it was discovered that Al 3+ can effectively occupy either Cu 2+ or Ti 4+ sites.Several reports focus on substitution of Al 3+ ions into the Ti 4+ sites of CCTO [18,20,26] and mixing CCTO with Al 2 O 3 [12,20,26].However, there is no work addressing the impact of Al 3+ ion substitution specifically into Cu 2+ sites within the CCTO lattice.As demonstrated in earlier studies, substitution of the same type of ion at different sites within the CCTO lattice yielded diverse outcomes in terms of structural factors, dielectric properties, and electrical behavior [27].Previous work on Al 3+ doped CCTO has shown that identifying Al 3+ substitutions at Ti 4+ sites is challenging due to the observed liquid phase sintering (LPS).Hence, Al 3+ might occupy Cu 2+ sites, but there is no report focusing on this point.Therefore, a comprehensive understanding of the structural and dielectric characteristics of Al 3+ doped CCTO, specifically within Cu 2+ sites, through integration of both experimental and computational methods, is required.
In this work, Ca 0.25 Cu 0.75-x Al x TiO 3 (x = 0 and 0.0125) ceramics were fabricated using a traditional solidstate reaction (SSR) method.The study made use of both experimental and computational methods.We examined crystallographic and microstructural characteristics in detail.The most stable location and V O density were estimated using first-principles calculations.Additionally, the charge density inside the lattice was investigated.Experimental and computational findings including discussion are presented below.

Experimental details
In our synthesis, the molar ratios of the original raw metallic components consist of CaCO 3 (Sigma-Aldrich, 99.0% purity) with a mean particle size of ∼13 μm, CuO (99.0%purity, Sigma-Aldrich) with a mean particle size of ∼1 μm, Al 2 O 3 (Sigma-Aldrich, 99.99% purity) with a mean particle size of ∼16 μm, and TiO 2 (99.99% purity, Sigma-Aldrich) with a mean particle size of ∼0.6 μm.Scanning Electron Microscopy (SEM) images of the initial raw powders for CaCO 3 , CuO, TiO 2 , and Al 2 O 3 , are respectively provided in figures S1(a)-(d) of the supplementary information.These components were mixed with C 2 H 5 OH in plastic bottles and the resulting suspension was ball-milled at a speed of 150 rpm for 12 h.After mixing the essential ingredients, they were dried for 24 h at 80 °C in a heated oven.After crushing the dried powders, all mixed powders were calcined for 12 h at 900 °C.According to figure S1(e) in the supplementary information, SEM images of the mixed powder before calcination reveal cracked particles from each raw material.Additionally, figures S1(f) and (g) demonstrate particle agglomeration with a mean particle size of approximately 1 μm in all calcined powders, both with and without grinding.The change of coefficient method was used to create balanced equations for preparation the final products.The resulting balanced equations for the preparation of Ca 0.25 Cu 0.75 TiO  ( ) where δ is excess oxygen, which is 0.00625.The calcined powders were crushed until smooth particles were produced for each condition.All the calcined powders were compressed into disk shapes using uniaxial compression at a pressure of 200 MPa.The final product consisted of disks measuring 9.5 mm in diameter and 2 mm in thickness.Ca 0.25 Cu 0.75 TiO 3 (CCTO) and Ca 0.25 Cu 0.7375 Al 0.0125 TiO 3 (Al0125) disks were sintered in air for 6 h at 1040 °C.
This research examined the phase and microstructures of all samples in detail using standard methods.An x-ray diffractometer (XRD, PANalytical, model EMPYREAN) was used to determine the original crystalline structure of the materials.According to our XRD measurements, 2θ ranging from 20°to 80°in 0.01°/step increments was employed.Rietveld quantitative phase analysis was done using PANalytical's X'Pert High Score Plus v3.0e software.For Rietveld refinements, all parameters are given in [28].Scanning electron microscopy (MiniSEM, SEC, and SNE-4500M) was utilized to study the surface morphology of the samples.Energy dispersive x-ray spectroscopy (EDS) analysis was conducted using Field Emission Scanning Electron Microscopy (FE-SEM, FEI Helios NanoLab G3 CX model).ImageJ software was utilized to estimate sample grain sizes based on a line intercept method.The lengths of the intersections of eight lines per grain were determined.Additionally, the grain size distributions were examined using a frequency function.The valence structures of the Cu and Ti elements were analyzed using x-ray photoelectron spectroscopy (XPS) with the Axis Ultra DLD model.
To make metal electrodes, surfaces of sintered ceramics were coated with conductive silver paint (Heraeus, PCC11889) and they were heated at 600 °C in air for 30 min.The dielectric characteristics of all ceramics were determined using a KEYSIGHT E4990A at an oscillation voltage (V rms ) of 0.5 V. Additionally, the stability of dielectric properties was examined across wide frequency and temperature ranges, spanning 40 to 10 7 Hz and −60 to 210 °C, respectively.
The local environment of Al in the Al0125 structure was computed using density functional theory (DFT) with the Vienna Ab initio Simulation Package (VASP) [29].Moreover, the most stable position of an oxygen vacancy (V O ) in the Al0125 host was determined.In DFT calculations, several exchange-correlation functionals, such as the Local Density Approximation (LDA), Generalized Gradient Approximation with a Perdew-Burke-Ernzerhof (PBE) functional [30], hybrid functionals, and others, have been used to determine the structural parameters of materials.For the cubic phase of PbTiO 3 [31], it was observed that the errors in lattice constants obtained from LDA and PBE functionals, compared to experimental values, are 2.0% and 0.09%, respectively.Moreover, in the case of SrTiO 3 , the error derived from the PBE functional is less than 2% [32].In the BiAlO 3 structure, it is evident that the error in lattice parameters obtained from the PBE functional is the lowest, followed by the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional and LDA [33].Based on these results, structural parameters obtained from the PBE functional are highly accurate for TiO 3 -and AlO 3 -based structures.Therefore, the PBE functional was selected for our calculations.Valence states of Al, Ca, Cu, Ti and O are given in our previous works [34,35].Based on our total energy convergence test, a 470 eV plane wave cut-off energy and 1 × 3 × 5 k-points meshes of the reciprocal lattice were employed.All crystal structures and electron density plots were drawn using VESTA software [36].

Results and discussion
A summary of the structural characteristics that were determined using XRD is presented in table 1.The XRD patterns of the CCTO and Al0125 ceramics are shown in figure 1.Our XRD results disclosed that the primary phase of the CCTO structure (JCPDS No. 75-2188) was obtained [37].In the Al0125 ceramic, trace levels of Cu 2 O and TiO 2 were present as impurities.In the case of the CCTO/MgO composite [38], it was observed that Mg 2+ preferentially occupies Cu 2+ sites, resulting in the generation of several impurities, namely MgTiO 3 , Cu 2 O, and CuO.Consequently, the excess Cu decomposes due to the replacement of Mg, inducing formation of a eutectic liquid CuO-TiO 2 at 950 °C [39].Simultaneously, TiO 2 is formed from the decomposition of the small Ti content during this process.Similarly, the TiO 2 observed in our XRD pattern of the Al0125 ceramic may be produced in a similar manner.Regarding formation of Cu 2 O, it was found that decomposed copper ions may combine with oxygen in an oxygen limited environment during the cooling process, hindering CuO formation [40].The formation of Cu 2 O can be described via the following reaction: Additionally, each sample shows evidence of the presence of a body-centered cubic structure that can be found in the Im3 No. 204 space group [37].The Rietveld method was used for all of the XRD data to conduct the analyses.Figure 2 depicts the Rietveld profile fit of the Al0125 ceramic, which was selected as a sample to demonstrate the fitting.According to table 1, all R-factors, namely the profile residual (R p ), expected residual (R exp ), weighted profile residual (R wp ) are less than 8%, and the goodness of fit (GOF) factor spans the values of 1.2 and 3.These are appropriate settings for Rietveld fitting [28].In the case of CCTO and Al0125 ceramics, the lattice parameters (a) are 7.392 and 7.390 Å, respectively.Comparable results are reported in other studies [1][2][3][4].
The a of the Al0125 ceramic showed a considerable reduction in value.A small amount of Al 3+ , which has a smaller ionic radius, might be substituted into the larger host sites of Ti 4+ .This could explain the reduced unit cell size [41].In the CCTO lattice, Al 3+ may also act as a replacement for Cu 2+ [41].The size of the unit cell may shrink as a consequence of this replacement.3(a) that the CCTO sample has a fine-grained ceramic microstructure.The average grain size of this sample is around 7.49±1.67μm.Moreover, the particle size distribution ranged from 3 to 14 μm.For the Al0125 sample, the average grain size was found to be 210.39±86.20 μm.It is notable that the grain sizes of the Al0125 ceramic became much larger compared to those of the CCTO ceramic.Regarding grain size, Choi et al [18] previously observed that substituting Al 3+ into the Ti 4+ sites of CCTO, sintered at 1100 °C for 12 h, resulted in an unchanged grain size.In contrast, our research demonstrates a significant 28-times increase in grain size even at a lower sintering temperature of 1040 °C for 6 h when Al 3+ is substituted into the Cu 2+ sites of CCTO.Even when the average grain size of the Al0125 sample increased, the grain size remains homogenous.The large grains formed by a low concentration of dopant is in excellent agreement with other doped CCTO ceramics [9,12,42].The impact of Al might be the principal source of grain size growth in the doped material.Generally, at low sintering temperatures, liquid phase sintering (LPS) processes may result in a significant grain growth rate [9,12,42].For a CCTO system doped with Al 3+ , the CuO-Al 2 O 3 , CaO-TiO 2 , and Al 2 O 3 -TiO 2 phases form at high temperatures (about 1100 °C) [43].In contrast, the CuO-TiO 2 phase can be generated in the atmosphere at a lower temperature, 950 °C [39].Hence, the system might have an excessive amount of either the Cu or Ti elements.The presence of excessive Cu is almost certainly due to the substitution of Al 3+ at Cu 2+ sites.Therefore, the liquid phase was produced in our samples owing to Al 3+ substitution at the Cu 2+ sites that occurred during calcination at 900 °C.
EDS mapping images of the Al0125 ceramic, indicating the distribution of Ca, Cu, Ti, Al, and O, are shown in figure 4.Moreover, it was found that the Al element in the Al0125 ceramic exhibited uniform dispersion within the grain.Also, the grain area showed a homogeneous distribution of Ca and Ti, while there is a very limited presence of these two elements at the GBs.It is noteworthy that significant quantities of Cu-rich phases were found within the GB layers.The results derived from this EDS mapping are consistent with the findings documented in earlier studies exploring the LPS mechanism [44,45].
The dielectric characteristic of CCTO and Al0125 samples was studied.In the C p -tanδ measuring method, ε′ is computed as dC p /ε 0 A, where d and C p are the sample thickness and the relative capacitance, respectively.ε 0 is the permittivity of a free space and A stands for the electrode area.The ε′ and tanδ values at room temperature at various frequencies for the CCTO and Al0125 samples are shown in figure 5 and its inset, respectively.The dielectric properties of Al-doped samples reveal that the ε′ in the frequency range of 40-10 5 Hz is almost unchanged, while the CCTO ceramic displays a stronger frequency dependence.As frequency increases, the lowfrequency region of the dielectric dispersion of the CCTO sample seems to change greatly.There is a low-frequency dielectric relaxation process that is overlaid by DC conduction as illustrated in the dielectric spectra of CCTO.This relaxation process greatly adds to the instability of the low frequency ε′, illustrating the relationship between charge movement and space charge polarization.It has been established that conduction takes place when carriers go to the electrode surfaces and combine.Space charge polarization takes place when carriers move to the electrodes without combining [46,47].This is a significant discovery since the ε′ value of the Al0125 ceramic is much greater than that observed in the undoped CCTO sample.Greater grain sizes in the Al0125 sample in comparison to undoped CCTO ceramics are substantially linked to increases in the ε′ value of the Al0125 ceramic.It has been shown in the literature [5,12] that grain size and ε′ values are closely related.The ε′ of undoped CCTO and doped Al0125 ceramics measured at a frequency of 1 kHz were 2.83 × 10 4 and 9.23 × 10 4 , respectively.One purpose of the current study was to investigate the impact that doping has on suppression of tanδ.It is noteworthy that the Al0125 sample has a reduced low-frequency tanδ compared to the undoped CCTO ceramic.The tanδ values of CCTO and Al0125 ceramics at 1 kHz are 0.096 and 0.057, respectively.For Al-doped CCTO, the dielectric properties of our work are compared with those reported in the literature.It was found that the Al0125 ceramic, sintered at a lower temperature of 1040 °C for 6 h, achieves a remarkably high ε′ of approximately 9.23 × 10 4 and a low tanδ of approximately 0.057.Moreover, the dielectric property of our Al0125 ceramics is better than that of other works as summarized in table 2. Additional investigations are required to explain the significant decrease in tanδ.
The ε′ values at a frequency of 1000 Hz as a function of temperatures for all samples is clearly displayed in figure 6.As seen in this figure, dielectric temperature stability was observed for all samples at temperatures below   room temperature.In contrast, when the temperature is increased, the value of ε′ climbs significantly.Interestingly, the Al0125 sample exhibited stronger dielectric temperature stability than the CCTO sample.The inset of figure 6 illustrates the temperature coefficient (Δε′/ε′ @RT ) of ε′ compared to ε′ at room temperature for both CCTO and Al0125 ceramics.The temperature range where Δε′/ε′ @RT is less than 15% for the Al0125 sample is between −60 and 110 °C.The dielectric stability with temperatures for the Al0125 ceramic satisfies the primary practical requirements for incorporation into X5R capacitors over the temperature range of −55 to 85 °C, where Δε′/ε′ @RT < 15% [48].There was a significant increase in ε′ at temperatures over 110 °C.Other effects seen in these studies include long-distance charge carrier migration inducing DC conduction and sample-electrode impacts [49].Regarding their dielectric-temperature relationships, the findings for all ceramics were comparable to previously reported values [5,50,51].Doping with Al 3+ can improve dielectric stability.This is associated to lowering tanδ at low frequency.Also, variation of ε′ with temperature is very low.The complex of ε′ obtained from Impedance spectroscopy (IS) can be computed via the following equation [52]: where i = 1 , -ε″ = ε′tanδ, C 0 = ε 0 A/d, and ω is the angular frequency.Z′ and Z″ represent the real (Z′) and imaginary (Z″) parts of impedance.It is well known that the Z′-intercept is the grain resistance (R g ).The wide semicircular arc represents the resistance of grain boundary (R gb ) value.All ceramics displayed a larger resistive component, indicating R gb , and a lower resistive component, indicating R g , as seen in figure 7 and its inset.The R g of the Al0125 sample is higher than that of undoped CCTO, as seen in the inset.As observed in the Al0125 specimen, R g increases when an Al 3+ dopant is added.The R g values were 74 and 113 Ω for CCTO and Al0125, respectively.Unfortunately, R gb cannot be determined because the large semicircle cannot be observed at ambient temperature.The slopes of the Z * spectra, on the other hand, may be utilized to infer the trend of R gb changes.Interestingly, like R g , the R gb value increases when an Al 3+ dopant is added.Metal-ion doping caused increased R g and R gb values that are similar to those in previous reports [3,8,14].The enhanced dielectric characteristics, inducing increased R gb in the Al0125 ceramic, may be attributed to greater grain boundary responses generated by metastable insulating layers and oxygen enrichment at grain boundaries.
Since the sample-electrode contact has the most effect at low frequencies, it is not possible to determine R gb values from the Z * spectra of CCTO and Al0125 ceramics.A complex electric modulus, denoted by M * , was considered to exclude the influence of a sample-electrode contact from the calculation of R gb .It is possible to generate an M * plot using the following equations [53]: The maximum value of M″ is denoted as M″ max , while the variation of relaxation time is signified by the notation τ gb = 1/ω max .Capacitance of GBs is C gb .The frequency dependence of M″ for sintered samples is depicted in figures 8(a) and (b).Both CCTO and Al0125 ceramics displayed comparable patterns with similar shifts in the M″ max position.As temperature increased, the M″ max location rapidly shifted to a higher frequency, demonstrating that thermal activity can activate dielectric relaxation [54].The following equation was used to determine the activation energies of relaxation (E a ) for CCTO and Al0125 ceramics: where f max is a critical frequency at which M″ max occurs, and f 0 is a constant value.As shown in figures 8(c) and (d), the temperature dependence of f max for each ceramic material followed equation (8).The E a values of undoped CCTO and doped Al0125 samples were found to be 0.617 and 0.658 eV, respectively.It was found that the M″ spectra indicated that R gb decreased as temperature increased using equations (2)-( 4).M * plots were employed to determine the R gb values of the CCTO and Al0125 ceramics at room temperature, which were 2.41 × 10 6 and 3.35 × 10 7 Ω, respectively.In the low-frequency range, the R gb values of all samples followed those of tanδ.The activation energy of grains (E g ) and GBs (E gb ) can be determined using the Arrhenius law for resistances.
where R 0 is a pre-exponential constant term.As shown in figures 9(a)-(d), the variation of R gb (solid symbols) and R g (open symbols) followed the Arrhenius relation for all samples, and the slopes of linear fitted curves can be used to estimate E g and E gb .CCTO and Al0125 ceramics exhibit E g values of 0.094 and 0.110 eV, respectively.The Arrhenius equation was used to calculate the values of E gb .They are 0.621 and 0.665 eV for CCTO and Al0125 ceramics, respectively.If the difference in values of E g and E gb is greater than 0.5 eV, this suggests that the microstructure is heterogeneous with both semiconductive and insulative components [55].When the calculated E a value of each sample was compared to the E gb of that sample, it was discovered that the E a and E gb values have the same tendency.The GB response is thought to cause dielectric relaxation at low frequencies and high temperatures [54].Finally, the ε′ and tanδ at 1 kHz and room temperature, R g , R gb , E g , E gb and E a of CCTO and Al0125 ceramics are summarized in table 3.
In our preparation process, we successfully fabricated Al0125 samples using a conventional solid-state reaction approach.Subsequently, these samples underwent calcination for 12 h at 900 °C and sintering for 6 h at 1040 °C.The resulting samples were analyzed for their crystal structure using the XRD technique.Our XRD results (figure 1) revealed that the crystal structure of Al0125 after the calcination and sintering processes matches the CCTO structure (space group Im3), identical to the initial structure used in our simulations.Consequently, the effects from heat treatments, such as calcination and sintering during synthesis, have been incorporated into our initial structure.According to our DFT calculations, we would like to emphasize that the  total energy calculated by us incorporates the effects of all thermal treatments and the occupation of Al at a specific site in the CCTO lattice.As previously mentioned, the CCTO structure is used as the initial structure.
When comparing the total energy between two structures (ΔE), the effects from the heat treatments during synthesis are canceled out.In other words, the obtained ΔE represents the energy difference due to the distinct positions of Al in the CCTO lattice.It is well known that the stable structure is the one with the lowest total energy.The most stable position of Al in the CCTO lattice corresponds to the structure with the lowest ΔE.In other words, the ΔE value can be utilized to determine the most preferable positions of Al in the CCTO host.
In our previous study [34], we performed calculations on the formation energies associated with substitution of an Al atom at Ca, Cu, or Ti sites within CaCu 3 Ti 4 O 12 .Our findings revealed formation energies of +4.41 eV, −3.25 eV, and +1.44 eV for Al substitution at the Ca, Cu, and Ti sites, respectively.A lower formation energy indicates a more stable structure [56].Therefore, in this case, the Al atom is likely to be inserted the Cu site in CaCu 3 Ti 4 O 12 .Moreover, previous experimental studies [19,57] reported that doping Al 3+ into the CCTO lattice, with the chemical formula CaCu 3 Ti 4-x Al x O 12 (substituting Al 3+ into Ti 4+ sites), and compositing CCTO with Al 2 O 3 [12,20,26], can induce a CuO impurity.This suggests the possibility that Al 3+ may preferentially occupy Cu 2+ sites rather than Ti 4+ sites.Also, our SEM measurements revealed liquid phase sintering in the samples.These observations are associated with placement of Al In principle, the presence of Vo is always found during the sintering process.This leads us to determine the most preferable position of Vo in the Al0125 lattice.Using Structure A as an initial structure, a Vo is created at Consequently, the n-type semiconductive region inside the grains originates from the presence of Vo inside this structure.
In the present work, XPS measurements were conducted to investigate the charge compensation mechanisms in the CCTO and Al0125 structures.Figures 13(a)-(d) depict the XPS spectra of Ti and Cu ions, offering insights into the oxidation states of these two elements.The XPS spectra of Cu2p and Ti2p were measured in the binding energy (BE) ranges of approximately 926-970 eV and 448-470 eV, respectively.In figures 13(a)-(b), both Ti 3+ and Ti 4+ states were identified in the Ti2p 3/2 and Ti2p 1/2 peaks.In the Ti2p 3/2 peak, the main peak position suggests the presence of the Ti 4+ state at a BE value of approximately 458.17-458.19eV.Concurrently, a minor peak corresponding to Ti 3+ was observed at around 456.29-456.41eV.Illustrated in figures 13(c)-(d), the Cu2p 3/2 peaks of the CCTO and Al05 ceramics exhibited a blend of Cu + and Cu 2+ ions.The pronounced peak indicative of Cu 2+ was identified at a BE value of approximately 933.91-934.10eV.Simultaneously, a minor peak observed at a BE of around 932.05-932.28eV signifies the presence of Cu + .The presence of Cu + and Ti 3+ in the ceramic lattice indicates the presence of V O , prompting the charge compensation mechanism to achieve a balanced charge.This observation is in excellent agreement with our charge density analysis, depicted in figures 12(b)-(c).The XPS study further reveals that the potential origin of an n-type semiconductive region within the grains may result from charge carrier hopping between Cu + ↔ Cu 2+ and Ti 3+ ↔ Ti 4+ .Consequently, the colossal dielectric permittivity observed in the material originated from an extrinsic effect, namely the IBLC effect.

Conclusions
This study explored the structural parameters, dielectric, and electrical responses of Al 3+ doped Ca 0.25 Cu 0.75 TiO 3 .XRD analysis unequivocally validated the presence of the Ca 0.25 Cu 0.75 TiO 3 primary phase in all sintered ceramics.From DFT investigations, preferential occupation of Cu 2+ sites by Al 3+ dopant ions was revealed, leading to a substantial increase in grain size facilitated by the liquid-phase sintering process.Furthermore, DFT analysis indicated that the introduction of the Al dopant does not lead to generation of oxygen vacancies within the lattice.Charge density analysis further disclosed that the presence of oxygen vacancies is responsible for the observed Cu + and Ti 3+ states in the XPS analysis.Notably, the Ca 0.25 Cu 0.7375 Al 0.0125 TiO 3 ceramic demonstrated exceptional dielectric properties, with a high dielectric permittivity of approximately 9.23 × 10 4 and an impressively low dielectric loss tangent of about 0.057 at 1 kHz and room temperature.Significantly, the high dielectric permittivity demonstrated remarkable stability across a wider temperature range, from −60 °C to 110 °C, with a dielectric permittivity change of less than 15% compared to the value observed at room temperature.This characteristic perfectly meets the practical requirements for utilization in X5R ceramic capacitors.Our findings suggest that the giant dielectric properties of these samples can be attributed to an internal barrier layer capacitor model, providing insight into the underlying mechanisms governing the remarkable dielectric performance of Al 3+ doped Ca 0.25 Cu 0.75 TiO 3 .

Figure 1 .
Figure 1.X-ray diffraction patterns of CCTO and Al0125 ceramics relative to a standard CCTO.

Figures 3 (
Figures 3(a) and (b) show SEM images and grain size dispersion of CCTO and Al0125 ceramics, respectively.It can be clearly seen in figure3(a) that the CCTO sample has a fine-grained ceramic microstructure.The average grain size of this sample is around 7.49±1.67μm.Moreover, the particle size distribution ranged from 3 to 14 μm.For the Al0125 sample, the average grain size was found to be 210.39±86.20 μm.It is notable that the grain sizes of the Al0125 ceramic became much larger compared to those of the CCTO ceramic.Regarding grain size, Choi et al[18] previously observed that substituting Al 3+ into the Ti 4+ sites of CCTO, sintered at 1100 °C for 12 h, resulted in an unchanged grain size.In contrast, our research demonstrates a significant 28-times increase in grain size even at a lower sintering temperature of 1040 °C for 6 h when Al 3+ is substituted into the Cu 2+ sites of CCTO.Even when the average grain size of the Al0125 sample increased, the grain size remains homogenous.The large grains formed by a low concentration of dopant is in excellent agreement with other doped CCTO ceramics[9,12,42].The impact of Al might be the principal source of grain size growth in the doped material.Generally, at low sintering temperatures, liquid phase sintering (LPS) processes may result in a significant grain growth rate[9,12,42].For a CCTO system doped with Al 3+ , the CuO-Al 2 O 3 , CaO-TiO 2 , and Al 2 O 3 -TiO 2 phases form at high temperatures (about 1100 °C)[43].In contrast, the CuO-TiO 2 phase can be generated in the atmosphere at a lower temperature, 950 °C[39].Hence, the system might have an excessive amount of either the Cu or Ti elements.The presence of excessive Cu is almost certainly due to the substitution of Al 3+ at Cu 2+ sites.Therefore, the liquid phase was produced in our samples owing to Al 3+ substitution at the Cu 2+ sites that occurred during calcination at 900 °C.EDS mapping images of the Al0125 ceramic, indicating the distribution of Ca, Cu, Ti, Al, and O, are shown in figure4.Moreover, it was found that the Al element in the Al0125 ceramic exhibited uniform dispersion within the grain.Also, the grain area showed a homogeneous distribution of Ca and Ti, while there is a very limited presence of these two elements at the GBs.It is noteworthy that significant quantities of Cu-rich phases were found within the GB layers.The results derived from this EDS mapping are consistent with the findings documented in earlier studies exploring the LPS mechanism[44,45].The dielectric characteristic of CCTO and Al0125 samples was studied.In the C p -tanδ measuring method, ε′ is computed as dC p /ε 0 A, where d and C p are the sample thickness and the relative capacitance, respectively.ε 0 is the permittivity of a free space and A stands for the electrode area.The ε′ and tanδ values at room temperature at various frequencies for the CCTO and Al0125 samples are shown in figure5and its inset, respectively.The dielectric properties of Al-doped samples reveal that the ε′ in the frequency range of 40-10 5 Hz is almost unchanged, while the CCTO ceramic displays a stronger frequency dependence.As frequency increases, the lowfrequency region of the dielectric dispersion of the CCTO sample seems to change greatly.There is a low-frequency

Figure 3 .
Figure 3. SEM images of surface morphologies and grain size distributions of (a) CCTO, and (b) Al0125 ceramics.

Figure 5 .
Figure 5. ε′ of CCTO and Al0125 ceramics as a function of frequency at ambient temperature.The inset in the figure illustrates the frequency dependence of tanδ for these two ceramics.

Figure 6 .
Figure 6.ε′ as a function of temperature at 1 kHz in CCTO and Al0125 ceramics.The inset shows the temperature coefficient of ε′ at 1 kHz of these two ceramics in comparison to room temperature.

Figure 7 .
Figure 7. Impedance complex spectra of CCTO and Al0125 ceramics at room temperature.The inset depicts the spectra of these two samples at a high frequency.

Figure 8 .
Figure 8. (a)-(b) M″/M″ max of CCTO and Al0125 ceramics as a function of frequency across a wide temperature range.(c)-(d) Arrhenius plots of the f max values for these two samples.
3+ at Cu sites.In other words, Al atoms occupied Cu sites in the CCTO lattice.In our simulation, we used a 5 × 2 × 1 supercell for the CCTO lattice.This supercell has the chemical formula, Ca 20 Cu 60 Ti 80 O 240 .The chemical formula of the Al0125 structure is Ca 0.25 Cu 0.7375 Al 0.0125 TiO 3 or Ca 20 Cu 59 AlTi 80 O 240 .Therefore, the Al0125 structure corresponds to substitution of Al atoms at the Cu sites of this supercell.In this supercell, there are two possible positions for Al substitution, illustrated as Structures A and B in figure 10.In Structure A, an Al dopant is in the Ca-Cu line.Al is in the Cu line displayed as Structure B. As clearly seen from figure 10, we found that the total energy difference between these structures is 4.08 meV.In other words, the total energy of Structure A is lower than that of Structure B by 4.08 meV per formula unit.Consequently, the Al0125 structure is Structure A.

Figure 10 .
Figure 10.Total energy of Structures A and B. For Structure A, Al is located at a Cu site on the Ca-Cu line in the CCTO lattice.Position of an Al occupied Cu site on the Cu line is presented as Structure B.

Figure 12 .
Figure 12.(a) Al-Cu and Ti planes for the r ( ) r D projection.The positive r ( ) r D is projected on the (b) Al-Cu and (c) Ti planes.

Table 1 .
Crystallographic and microstructural parameters of CCTO and Al0125 ceramics.

Table 2 .
ε′ and tanδ values at 1 kHz for this work and previous studies.

Table 3 .
ε′ and tanδ at 1 kHz and room temperature, resistances of grains (R g ) and GBs (R gb ) at room temperature, activation energies of grains (E g ) and GBs (E gb ), and activation energy of GB relaxation (E a ) for CCTO and Al0125 ceramics.