Dielectric and impedance analysis of Li_0.5La_0.5Ti_1-xZr_xO₃(x = 0.05 and 0.1) ceramics as improved electrolyte material for lithium-ion batteries

The X-ray diffraction analysis investigates different types of phases present in materials. It is a technique for the study of crystal structure and spacing between the atoms. The principle of X-ray diffraction is constructive interference of monochromatic X-rays from the sample which is crystalline. The X-rays are produced by a cathode ray tube, which produces monochromatic radiation, which is directed toward the sample. This diffraction only occurs when the Bragg's law is satisfied. This law relates the wavelength of electromagnetic radiation to the diffraction angle and the lattice spacing in a crystal.

The XRD patterns of the calcined powder of Li_0.5La_0.5Ti_1-xZr_xO₃ (x = 0.05 and 0.1) at room temperature are shown in Fig. 1. The presence of sharp diffraction peaks in the patterns, which are different from that of the ingredients, suggests the formation of a new single phase compound. The crystal structure of the synthesized compounds is found to be a cubic structure with an expected pm3m space group [12, 13]. The lattice parameters and unit cell volume of the Li_0.5La_0.5Ti_1-xZr_xO₃ decrease with an increase in Zr concentration. As the Zr concentration increases, the XRD peak shifts to lower 2θ values (higher d spacing). This may be due to the higher ionic radius of Zr as compared to Ti. In addition to identifying crystalline phases, X-ray diffraction can also be used to determine crystallite size. This can be obtained from the broadening of the peaks according to the Scherer's formula. The calculated crystallite sizes, lattice parameters and volume of both the compounds are given in Table 1.

Fig. 1

The scanning electron microscope (SEM) is a type of electron microscope that produces images of a sample by scanning it with a focused electron beam. The beam of electrons interacts with electrons in the sample, which produces various signals that can be detected and that contain information about the sample's surface morphology and composition. The beam of electrons is generally scanned by the method of raster scan pattern, and the position of the beam is combined with the detected signal to create an image.

Fig. 2 shows the SEM micrographs of Li_0.5La_0.5Ti_1-xZr_xO₃ (x = 0.05 and 0.1) electrolyte materials. The SEM micrographs show the polycrystalline microstructure with nearly rectangular grains of different grain sizes that are homogeneously distributed throughout the sample surface [14, 15]. The grains and grain boundaries are well defined and clearly visible. Grains of slightly unequal sizes appear to be distributed throughout the sample. The microstructure is overall dense, but a few scattered pores are observed which indicates that there is a certain degree of porosity in the sample. The average grain size ranges between 1 μm to 3 μm.

Fig. 2

The Raman spectra of Li_0.5La_0.5Ti_1-xZr_xO₃ (x = 0.05 and 0.1) in Fig. 3 show five bands which is in good agreement with that of La_(2-x)/3Na_xTiO₃ except for the up shift of the bands due to the lighter Li atom compared to Na. The Li_0.5La_0.5Ti_1-xZr_xO₃ (x = 0.05 and 0.1) has five atoms and fifteen degrees of freedom per unit cell. In cubic phase it has O_h symmetry and 15 degrees of freedom divided into twelve optical representations 3F_1u+F_2u, while another three F_1u symmetry mode corresponds to acoustical branch [16, 17]. 145 cm^-1, 237 cm^-1 and 528 cm^-1 modes come from the F_1u cubic phase modes. The 303 cm^-1 mode comes from the splitting of the cubic F_2u mode and the somewhat broader 858 cm^-1 resuls also from F_1u mode. Hence, the spectra represent the characteristic peaks of perovskite phase and confirm that TiO₆ octahedra have been formed at 858 cm^-1. No appreciable change in bands corresponds to the characteristic TiO₆ A-site of the compound.

Fig. 3

The impedance spectroscopy is a nondestructive method used to analyze the electrical response of polycrystalline sample in a wide range of frequencies and temperatures. Fig. 4 shows typical impedance diagrams of Li_0.5La_0.5Ti_1-xZr_xO₃ (x = 0.05 and 0.1) compounds at different temperatures. The nature of the plots with the change in temperatures ensures a distinct effect of the material on the characteristic impedance spectrum by the appearance of single semicircular arc arising due to increase in temperature [18–20].

Fig. 4

The impedance (Nyquist) studies exhibit two overlapping semicircles terminating to a straight line at low frequency. The observed depressed semicircular arcs have a center lying below real impedance (Z′) axis. The relaxation process associated with this observation is non-ideal in nature. This non-ideal behavior may originate from several factors such as grain orientation, grain size distribution, grain boundaries and atomic defect distribution. The presence of a single semicircular arc indicates that the electrical processes in the material may be due to bulk properties. The impedance patterns appear to be overlapping of two semicircular arcs with a rise in temperature which indicates the appearance of grain boundary contribution [21-24]. An equivalent electrical circuit can be modeled for the observed electrical phenomena in the material, according to brick layer model. It has been observed that both the grain and grain boundary resistances decrease with the rise in temperature.

From the plots (Fig. 5), it is seen that at lower temperatures Z′ decreases monotonically with increasing frequency up to a certain limiting range (^100 kHz) above which it becomes almost frequency independent. The higher values of Z′ at lower frequencies and higher temperatures indicate that the polarization in the test material is larger. The temperature, at which this frequency-dependent to frequency-independent change of Z′ occurs, varies with frequency in the material composition [25-28]. This also signifies that the resistive grain boundaries become conducting at these temperatures and that the grain boundaries are not relaxing even at the highest measurement ranges of frequency and temperature.

Fig. 5

Fig. 6 shows the imaginary parts of impedance (Z″) versus frequency plot at different temperatures. It is evident from this figure that the Z′ value increases with frequency. At high frequency side all the curves merge. Apart from this, the values of Z′ is found to decrease with increasing temperature indicating the increase in conductivity. Further Z′ maxima appear to shift towards the high frequency side with increasing temperature and the peak becomes broader. This indicates that the relaxation in these materials is a thermally activated process. The merger of all the curves at high frequency indicates the depletion of space charges at those frequencies [29-31].

Fig. 6

The AC conductivity is calculated from dielectric data using the relation: σac=ωεrε0tanδ$$\sigma_{ac} = \omega \varepsilon_r \varepsilon_0 \; \text{tan}\delta$$(2) where ω = 2πf.

The variation of AC electrical conductivity of Li_0.5La_0.5Ti_1-xZr_xO₃ (x = 0.05 and 0.1) as a function of frequency at different temperatures is shown in Fig. 7. The conductivity spectrum displays characteristic conductivity dispersion throughout the frequency up to 100 °C. The AC conductivity of the material is frequency independent in the low frequency region and frequency dependent in the high frequency region [32–34]. The AC conductivity values calculated by the above formula at different temperatures are given in Table 2.

Fig. 7

Fig. 8 presents the experimental results of the electrical conductivity for all the synthesized compounds in standard Arrhenius plots: σ=σ0exp−EakBT$$\sigma = \sigma_0 \exp \left[\frac {-E_a}{k_B T}\right]$$(3)

Fig. 8

where E_a is the activation energy. These results show an increase of the conductivity with increasing temperature for all compounds indicating a characteristic activated behavior over the complete temperature range studied. Furthermore, the plots of log a vs. 1/T are found to be linear in the considered temperature range. From impedance measurements, the total conductivity activation energies, E_a are derived, yielding the activation energy of 0.603 eV and 0.598 eV for Li0.5La0.5Ti1-_xZr_xO3 (x = 0.05 and 0.1) compounds, respectively. These results are similar to those found for other lithium fast-ion conductors [35, 36].

Dielectric analysis measures electric properties of a material as a function of frequency and temperature. This analysis measures two fundamental electrical characteristics of materials: (1) the capac-itive (insulating) nature, which represents its ability to store electric charge; (2) the conductive nature, which represents its ability to transfer electronic charge. Through this analysis, the dielectric constant £_r and dielectric loss t″ of a material can be determined [31-33]. The value of the dielectric constant (e′) of Li0.5La0.5Ti1-_xZr_xO3 (x = 0.05 and 0.1) are calculated using the formula: εr=C×dε0×A$$\varepsilon_r = \frac {C \times d}{\varepsilon_0 \times A}$$(4) where C is capacitance, A is area of the electrode and ϵ₀ is permittivity of the free space.

Fig. 9 compares the variation of relative dielectric constant (ϵ_r) with frequency for two compounds at different temperatures. For all the temperatures, a strong frequency dispersion of permittivity is observed in the low frequency region followed by a nearly frequency independent behavior above 100 kHz. The decrease of ϵ_r with increase in frequency may be attributed to the electrical relaxation processes, but at the same time the material electrode polarization cannot be ignored, as the samples used in our investigation are ionic conductors [37, 38]. The material electrode inter-facial polarization is superimposed with other relaxation processes at low frequencies. It is obvious that the dielectric constant decreases sharply with frequency at low frequency and is independent of frequency at high frequency. Generally, low frequency dispersion is believed to be associated with mobile charge carriers, electrons or ions. The presence of dielectric dispersion phenomenon at low frequency is believed to be due to the presence of trapping levels. The increase of dielectric constant with an increase of temperature is generally due to the increase of trapped charge carriers at the grain boundaries.

Fig. 9

The dielectric loss tanδ is given by tan δ=ε"ε′$\delta = \frac {\varepsilon^"}{\varepsilon^\prime}$.

The comparison of variation of tanδ with frequency of Li0.5La0.5Ti1__xZr_xO3(x = 0.05 and 0.1) at different temperatures is shown in Fig. 10. The increase in tanδ value of Li0.5La0.5Ti1__xZr_xO3 at x = 0.05 is very small up to 100 kHz and above this frequency there is a sudden increase in the tanδ value with a rise in temperature. But in the case of Li0.5La0.5Ti1__xZr_xO3 at x = 0.1, it has been observed that the dielectric loss increases with an increase in temperature at 500 kHz. The increasing trend in tanδ values at higher temperature region for all frequencies may be due to space charge polarization. Also the dielectric loss of Li0.5La0.5Ti1__xZr_xO3 (x = 0.05) is less in comparison to Li0.5La0.5Ti1__xZr_xO3 (x = 0.1) and at high frequency has been significantly reduced [39-41]. These results are due to the formation of cation vacancies which efficiently reduce the concentration of oxygen vacancies which in turn significantly reduce the dielectric loss.

Fig. 10

Fig. 11 shows the variation of modulus curve as a function of frequency over a range of temperature that enables us to have an insight into the dielectric processes occurring in the material. It is characterized by: (i) broad asymmetric pattern with a cross over from short range mobility to long-range mobility of ions with a rise in temperature, (ii) more or less the same shape and pattern with a slight variation in full width at half maximum (FWHM) with a rise in temperature and (iii) FWHM greater than the width of a typical Debye peak. These observations indicate that the dynamical processes occurring within the sample at different frequencies exhibit the same thermal activation energy and are independent of temperature with non-exponential type of conductivity relaxation [42–44].

Fig. 11

The variation of imaginary part of electrical modulus (M′) of Li_0.5La_0.5Ti_1-xZr_xO₃ (x = 0.05 and 0.1) with frequency at different temperatures is shown in Fig. 11. It is observed that M′ decreases with an increase in frequency. For all temperatures, variation of M′ with frequency attains a maximum value (peak) at a particular frequency and that peak is shifted to higher frequency with a rise in temperature. These peaks indicate the transition from long range to short range mobility with an increase in frequency and are asymmetric in nature indicating the spread of relaxation time. The asymmetric nature of the modulus peak indicates the stretched exponential character of the relaxation time. This behavior may be due to the non-exponential process, such as correlated diffusive motion of the ions or non-uniform microstructure in the material. The FWHM of the peak is observed to be larger than Debye peak. It also suggests that the relaxation process is of non-Debye type. The peaks are getting more broadened after phase transition with the increase of temperature showing the increase of non-Debye behavior. This temperature dependent relaxation time follows the Arrhenius behavior.

The shape of the spectrum remains unchanged but the frequency of the modulus maximum M_max shifts to high frequencies as temperature increases but the shape and full width at half maximum of M'/M'max do not change in the considered temperature range [45, 46]. It is also observed that M'/M'max curves are not symmetric, implying a non-exponential behavior of the conductivity relaxation as shown in Fig. 12.

Fig. 12

In order to investigate the extraction/intercalation properties of lithium-ions in the Li_0.5La_0.5Ti_1-xZr_xO₃ (x = 0.05 and 0.1) electrolytes, cyclic voltammetry (CV) analysis is performed. Fig. 13 illustrates the CV for Li_0.5La_0.5Ti_1-xZr_xO₃ (x = 0.05 and 0.1) cathode material recorded at room temperature, under a sweep rate of 10 mV·s^-1. In this technique, the potential window is fixed between -3.0 V and 4.0 V vs. Li/Li⁺. It can be seen from the figure that the electrolyte materials exhibits two pairs of well resolved cathodic and anodic (redox) peaks, which are characteristic of a typical perovskite phase [47]. This suggests the two-step reversible intercalation/de-intercalation of lithium-ions between lithium and metal ions.

Fig. 13