Effect of grain size on the dielectric properties of lanthanum-doped lead titanate perovskite ceramics

1. Introduction

Ferroelectric perovskite oxides have been widely investigated owing to their outstanding dielectric, piezoelectric, and ferroelectric properties, which render them promising candidates for various advanced electronic and multifunctional device applications [1]. These qualities make them very well-suited for use in non-volatile memory devices, transducers, and actuators. The compound known as lead titanate (PbTiO₃) has garnered considerable attention among these materials because of its prominent spontaneous polarization and high Curie temperature, which is around 490^ᵒC [2]. Pure lead titanium oxide (PbTiO₂), on the other hand, has a number of limitations that restrict its practical uses. These shortcomings include poor sinterability, brittleness, a strong coercive field, and thermal instability [3, 4]. For their exceptional dielectric, piezoelectric, electrooptic, electrostrictive, and pyroelectric properties, Lead Lanthanum Titanate (PLT) materials have been extensively investigated for their potential applications in multilayer capacitors, actuators, electro-optical modulators, ultrasonic transducers, and infrared detectors. There is a unique attribute of the PLT that may be improved by adding different ions at the "A" or "B" locations. "Donor" dopants, like La^+3, Nb⁺⁵, Ce⁺³, and Ta⁺⁵, create "soft" Lead Zirconate Titanate (PZT), whereas "acceptor" dopants, such as Fe⁺³, create "hard" PZT. Soft dopants improve electrical characteristics over undoped PLT by easing domain wall motion. The integration of La into PbTiO₃ results in modifications to the material's physical characteristics, including enhanced permittivity and reduced tetragonality [5, 6].

The use of nanoscale particles in the production of ferroelectric materials has garnered heightened interest in recent years, since these particles have unique features relative to their bulk equivalents. Diverse synthetic techniques, including hydrothermal approaches such as sol-gel processing and the tartrate precursor technique have been developed to synthesize a diverse array of chemicals at the nanometric scale [1-4]. Lanthanum (La) is one of the most prevalent doping agents in ferroelectric materials, significantly influencing the characteristics of perovskite-structured compounds. Doping at the A-sites of lead titanate leads to a decrease in tetragonality, an enhancement in permittivity and transition temperature (Tc), and a widening of the Curie point temperature [5-9]. The modified materials exhibit a broad spectrum of potential applications across various domains, including dynamic random-access memory, electro-optic systems, and actuator technologies [10-13].

The current work aims to prepare \(\mathrm{Pb(La}_{x}\mathrm{Ti}_{1-\frac{3}{4}x}\mathrm{)O}_{3}\) (x = 0, 0.02, 0.04, 0.06, 0.08 and 0.1) nanopowders using tartrate precursor technique and studying the impact of the La3+ substitution ratio on the morphology, structure, and ferroelectric characteristics of PLT was examined. It also emphasizes the potential applications of this material in various electrical and optoelectronic devices.

2. Materials and methods

The powders of \(\mathrm{Pb(La}_{x}\mathrm{Ti}_{1-\frac{3}{4}x}\mathrm{)O}_{3}\), where x is 0, 0.02, 0.04, 0.06, 0.08 and 0.1, were prepared using the tartrate precursor method. The materials used were titanium dioxide (TiO₂), tartaric acid (C₄H₆O₆), lead nitrate (Pb(NO₃)₂) with 99% purity, and lanthanum nitrate (La(NO₃)₃.6H₂O) with 98% purity. The precise stoichiometric quantities of these chemicals were carefully determined to correspond with the desired La content. The chemicals were weighed in a stoichiometric ratio and mixed with 250 ml of distilled water. The mixture was heated on a magnetic stirrer at 80°C until dry and then dried at 100°C overnight. The powder was collected and annealed at 600°C for 2 hours. It was then pressed into tablets using a compressor at 5MPa. The crystallite size of the prepared samples was measured using X-ray diffraction (XRD) with a Philips model (PW-1729) diffractometer using a wavelength of 1.540598 Å in the 2θ range of (20 to 80°). The morphology of the prepared samples was characterized by the grain size, which was obtained using scanning electron microscope (SEM) with a JEOL model JSM-5600 in the National Research Center, Cairo, Egypt. The grain size was determined from SEM micrographs using the image analysis software ImageJ. The SEM images were first calibrated using the scale bar provided in each micrograph. Individual grains were manually outlined, and the equivalent circular diameter was calculated for each grain. A total of N grains (≈ 25–35 grains per sample) were measured to ensure statistical reliability. The average grain size was calculated as the arithmetic mean, and the standard deviation was used to estimate the size dispersion. Grain size distribution histograms were constructed to illustrate the statistical distribution of grain sizes for each sample. The dielectric constant (ε) of the produced samples at various temperatures was measured using an RLC bridge of type BM591 (Solid Lab, Tanta University, Egypt). The weight loss for the prepared ferrite samples was estimated using a thermogravimetric analyzer (TGA-50) with a heating rate of 10 °C/min in the range of room temperature to 800 °C.

3. Results and discussions

3.1. XRD analysis and discussion

Figure 1 presents the XRD diffraction patterns of \(\mathrm{Pb(La}_{x}\mathrm{Ti}_{1-\frac{3}{4}x}\mathrm{)O}_{3}\), which has been subjected to annealing at 600°C for a duration of 2 hours, exhibiting varying La content. The various phases of tetragonal perovskite are observable for La concentrations of x = 0.0, 0.02, 0.04, and 0.06, which correspond to the space group (P4mm).

The perovskite structure is shown by pronounced peaks at 2θ = (21.07°, 31.1°, 38.8°, 49.54°, 55.2°, and 65.49°) for the tetragonal phases. The numbers are (001), (101), (111), (102), (112), and (202). XRD patterns indicate the presence of tetragonal, cubic (predominantly at elevated La concentrations), α-PbO, and rhombohedral phases. The fluctuation in lattice parameters, namely a and c, results from two primary factors: the difference in ionic radii between La and Ti and the simultaneous existence of many contending phases [14. 15].

The Scherrer equation (1) is used to determine the crystallite size (DXRD) from the XRD data of each sample [22].

\(D=\frac{k\lambda}{\beta\cos\theta}\)                                   (1)

Here, "θ" signifies the location of the diffraction peak, "β" indicates the full width at half maximum (FWHM), and "λ" refers to the X-ray wavelength for Cu-Kα radiation (λ = 1.540598 Å). An observable reduction in crystallite size, as shown in Table 1, occurs with increasing La concentration, reaching a maximum at x = 0.06. The tetragonality factor \(\frac{c}{a}\) decreases by increasing La content, except for sample x=0.1 due to the formation of a new phase (α-PbO). Figure 2 shows the La content dependence of the a and c cell parameters and the \(\frac{c}{a}\) ratio. The ‘a’ parameter remains almost constant, whereas the ‘c’ parameter increases up to 0.06, then decreases. Figure 3 shows that the X-ray density was calculated by using equation (2):

\(\rho_{x}=\frac{ZM}{N_{\mathrm{A}}V}\)               (2)

M represents the molecular weight, Z denotes the number of molecules per unit cell (Z=1 for the tetragonal phase), N signifies Avogadro's number (N_A=6.022×10²³ mol⁻¹), and V indicates the volume of the unit cell. In Figure 3, we can see the density, which decreases with increasing La content up to 0.06 and then increases for samples with x=0.08 and 0.1. This is related to the higher atomic weights of La (138.9 a.m.u.), Ti (47.9 a.m.u.), and Pb (207 a.m.u.), and to the formation of a cubic phase at x=0.1.

As La³⁺ ions substitute Pb²⁺, the average A-site ionic radius decreases from 1.49 Å for Pb²⁺ to 1.36 Å for La³⁺, leading to a slight decrease in the tolerance factor with increasing La concentration.

3.2. Scanning Electron Microscopy (SEM) micrographs

The morphology of PbTiO₃ doped with La ions at various concentrations (x= 0, 0.02, 0.04, 0.06, 0.08, and 0.10) is shown in Figure 4. As listed in Table 1, the grain size ranges from 145 to 277 nm. The decrease in grain size with increasing La content up to x= 0.06 indicates that La ions inhibit grain growth, likely due to lattice distortion and grain boundary pinning effects. For higher La concentrations (x = 0.08 and 0.10), La ions become partially insoluble in the lattice, segregating at grain boundaries or occupying interstitial sites. This results in a slight increase in grain size, which can be attributed to reduced inhibition and coalescence of neighboring grains.

These SEM observations are consistent with the trends obtained from XRD, where crystallite size initially decreases and then slightly increases at higher La concentrations. It is important to note that SEM grain size reflects the physical grains, which may contain multiple crystallites, while XRD crystallite size represents coherent diffraction domains. Thus, the comparison is qualitative, highlighting the influence of La doping on microstructural evolution.

Table 1. The values of crystallite size from XRD and grain size as a function of lanthanum content for \(\mathrm{Pb(La}_{x}\mathrm{Ti}_{1-\frac{3}{4}x}\mathrm{)O}_{3}\) samples.

3.3. Dielectric properties

3.3.1. Dielectric spectroscopy

Figure 5 (a and b) show the variation of the dielectric constant real part (ɛˊ) and its imaginary part (ɛˊˊ) as a function of our perovskite sample for different La content. It is clearly seen from the figure that the dielectric constant (ɛˊ and ɛˊˊ) has a high value at low frequency and decreases sharply at high frequency [23, 24]. The hopping electrons between the A-site and B-site are responsible for high polarization at low frequency, leading to a high value of the dielectric constant, whereas at high frequency the electrons are hard to flow the external field frequency, resulting in a decrease of polarization and dielectric constant. At low La content (x=0.02 and 0.04) the tetragonality of these samples are less than that of the lead titanate sample, leading to a decrease of polarization and dielectric constant. For high La content (x=0.06 ,0.08 and 0.1), an interfacial polarization is formed due to the interaction of La and PbTiO_3, leading to an increase in the polarization and dielectric constant.

Figure 5 (c) illustrates the variation of tan(δ) as a function of frequency, indicating a relaxation peak for samples with elevated La content. The peak identified as the relaxation frequency (F_m) indicates that for frequencies greater than F_m, the charge carriers are confined within their potential well and exhibit short-range movement. On the other hand, the hopping charge carriers are moving over long distances [25, 26]. This material exhibits a transition from long-range to short-range mobility, as indicated by the relaxation frequency derived from equation (3), and is given in Table 2.

\(T_{m}=\frac{1}{2\pi F_{m}}\)                                (3)

Sample (X)	Fm (Hz)	Tm (Sec) *10-3
0	100	1.59
0.02	14.8	10.78
0.04	21.4	7.44
0.06	94.6	1.68
0.08	170	0.936
0.1	288.4	0.551

3.3.2. Electric modulus study

Electric modulus spectra for PbTiO₃ doped with La ions are shown in Figure 6 (a and b) as a function of frequency for all La samples. The modulus spectra are useful for understanding of the response of the material, as the electrode polarization effect becomes minimized. The complex electric modulus from equation (4) [27]:

\(M^{*}=\frac{1}{\varepsilon^{*}}+(M^{\prime}+jM^{\prime\prime})\)                           (4)

where M` and M`` are the real and imaginary part of electrical modulus and ɛ^* is the complex dielectric constant.

From the figure, it was noticed that at low frequency, the modulus equals zero. up to certain frequency, as given in Table 3, the value for all samples at low frequency is close to zero due to the presence of electrode polarization. After a certain frequency, the modulus begins to increase above the zero value for all samples with La content.

The real part of modulus M` still increases and reaches a maximum at higher frequency because the space charge impact is less. The saturation value is reached at high frequency, suggesting that the electric property of the material is frequency independent [28].

The imaginary part of modulus M`` is shown in Figure 6 (b); at low frequency it has the similar nature of frequency dependance of M`, with the presence of relaxation peak at high frequency which shifts to higher frequency value. The relaxation peak time shifts to lower value by increase La content and was calculated from equation (5):

\(T_{m}=\frac{1}{2\pi F_{m}}\)             (5)

The plot of M` and M`` of our samples can be classified as Debye type and non-Debye type as shown in Figure 6 (c), the relaxation is Debye type if the semi-circle is formed with its center line of the real axis (M`) and non-Debye type if the semi-circle is deformed.

In our case, the center of semi-circle is deviated from the M` axis and hence our relaxation process is attributed to a non-Debye type.

The electrical modulus has physical significance in relation to the relaxation mechanism of the electric field, wherein the electric displacement remains constant.

As shown in Table 4, the Cole–Cole plots clearly differentiate the relaxation contributions arising from grains (the more conductive regions) and grain boundaries (the more resistive regions). As shown in Figure 6 (c), the samples with X = 0, 0.02, and 0.06 display a single relaxation peak, indicating that grain boundary effects dominate the conduction mechanism. In contrast, samples with x = 0.04, 0.08, and 0.10 exhibit two relaxation peaks, corresponding to two distinct relaxation times. The first semicircle is attributed to the grain boundary contribution, while the second semicircle arises from the grains themselves [29, 30].

This behavior clearly demonstrates that the observed dielectric relaxation is non-Debye in nature, reflecting the combined influence of grains and grain boundaries on the electrical response of the material. The dielectric relaxation observed in the La-doped PbTiO₃ samples exhibits a non-Debye behavior, which is attributed to a distribution of relaxation times rather than a single characteristic time. This is a common feature in polycrystalline materials, where structural heterogeneities such as grain boundaries and defects create multiple relaxation pathways.

The computed value of the relaxation time is shown in Table 5. The existence of two relaxation peaks in the Cole-Cole diagram (x=0.08 and 0.1) corroborates the presence of two structural phases, as shown by the X-ray pattern of the sample (cubic and tetragonal phases).

Table 3. The relaxation frequency of the real part of electrical modulus for \(\mathrm{Pb(La}_{x}\mathrm{Ti}_{1-\frac{3}{4}x}\mathrm{)O}_{3}\).

Sample (X)	F (Hz)
0	100
0.02	94.589
0.04	14.7585
0.06	288.397
0.08	1000
0.1	1848.55

Table 4. The relaxation time and frequency of the imaginary part of electrical modulus for \(\mathrm{Pb(La}_{x}\mathrm{Ti}_{1-\frac{3}{4}x}\mathrm{)O}_{3}\).

Sample (X)	F1 (Hz)	F2 (Hz)	Τ1 (Sec) *10-5	Τ2 (Sec) *10-5
0	5636.52	—	2.825	—
0.02	52377.2	—	0.304	—
0.04	44.9935	606.354	353.9	26.26
0.06	3886.56	—	4.097	—
0.08	5636.52	231534	2.83	0.0688
0.1	8171.5	52377.2	1.95	0.3

Table 5. The relaxation time and frequency for Cole-Cole diagram of \(\mathrm{Pb(La}_{x}\mathrm{Ti}_{1-\frac{3}{4}x}\mathrm{)O}_{3}\).

Sample (X)	F1 (Hz)	F2 (Hz)	Τ1 (Sec) *10-5	Τ2 (Sec)*10-5
0	5636.52	—	2.825	—
0.02	52377.2	—	0.304	—
0.04	65.2406	606.354	244.07	26.26
0.06	3886.56	—	4.097	—
0.08	3886.56	231534	4.097	0.0688
0.1	5636.52	75946.9	2.83	0.209

3.3.3. Impedance spectroscopy

The dielectric relaxation process in polycrystalline perovskite samples is explained by the impedance spectroscopy, which coincidence as an important to analyze the relationship between the microstructure and electrical properties of the material and can be distinguished by semi-circles and can study the effect of grains, grain boundary and the electrode interface to the electrical properties of the sample [31].

Figure 7 shows the real part (Z`) and imaginary part (Z``) of impedance (Vs) as a function of frequency. The figure shows that Z` is very high at low frequency, then starts to decrease with increasing frequency to reach a constant value and becomes frequency independent at high frequency. The imaginary part of the impedance Z`` has an inverse character to the real part Z`. At low frequency, the grain boundary resistance is high and dominates the grain resistance, which plays an important role at high frequency.

The impedance Z` of the sample with La content (x=0.02 and 0.04) has a higher value than the sample with zero La content, whereas the other samples (x=0.06, 0.08 and 0.1) have a lower Z` value than the sample that is free of La content.

The grain size of both samples (x=0.02 and 0.04) are 170 and 150 nm, respectively, which is greater than the samples (x=0.06, 0.08 and 0.1) as given in Table 6.

Depending on the value of grain size, the grain boundary resistance at low frequency for the abovementioned sample (x=0.02 and 0.04) are greater than the grain boundary resistance for samples (x=0.06, 0.08 and 0.1), which explains the behavior of real part of impedance for our sample at low frequency [32, 33].

Table 6. Impedance (Z`) and grain size of \(\mathrm{Pb(La}_{x}\mathrm{Ti}_{1-\frac{3}{4}x}\mathrm{)O}_{3}\).

Sample(X)	Grain size (nm)	Z` at 100Hz
0.02	240.13	6.84237*107
0.04	147.02	4.54123*107
0.06	138.36	1.3254*107
0.08	131.98	1.3254*107
0.1	116.11	5.59205*107

3.3.4. AC conductivity for \(\mathrm{Pb(La}_{x}\mathrm{Ti}_{1-\frac{3}{4}x}\mathrm{)O}_{3}\)

The variation of σ` and σ`` for the perovskite samples \(\mathrm{Pb(La}_{x}\mathrm{Ti}_{1-\frac{3}{4}x}\mathrm{)O}_{3}\) as a function of frequency is shown in Figure 8.

The conductivity exhibits a uniform response at low frequencies and is nearly independent of frequency and La content. The conductivity displays considerable dispersion at higher frequencies [28].

Above a certain frequency, the σ` increases with increasing frequency, which confirms the presence of hopping conduction.  σ`` has the same trend as σ` and rebel the same behavior.

4. Conclusion

In summary, the La doping in PbTiO₃ affects the structure, microstructure, and dielectric properties in a correlated manner. XRD analysis shows that doping modifies the crystallite size and lattice parameters, while SEM reveals the corresponding evolution in grain size and morphology. Smaller grains at moderate doping levels (x= 0.02–0.06) result in enhanced grain boundary contributions, which dominate the dielectric relaxation as confirmed by Cole–Cole analysis. At higher doping levels (x = 0.08–0.10), partial solubility of La and grain coalescence lead to increased grain contributions, giving rise to dual relaxation times. This structure–microstructure–property relationship highlights that controlled La doping can tune both the conduction and relaxation behavior of PbTiO₃. Based on these findings, the materials exhibit enhanced dielectric and electrical response, making them promising candidates for capacitors, sensors, and microelectronic devices where tailored dielectric relaxation and microstructural control are crucial.

Conflict of interest statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Funding

No funding was received for writing this manuscript.

Authors’ contributions

Eman N. Serag: Data collection, analysis.

Aseel M. Altarawneh: Writing – original draft.

 Osama M. Hemeda: Discussion data & editing.

 S. A. Abdel Gawad: Writing – review.