Effect of magnesium substitution on structural and dielectric properties of LiNiPO₄

The X-ray diffraction was used to obtain information about the structure, composition and the state of polycrystalline materials. Fig. 1 shows the X-ray diffraction patterns of the LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15) cathode materials synthesized by solid state reaction method. It was found that all the peaks could be indexed to a single phase of ordered olivine type structure belonging to orthorhombic Pnma space group. No peaks related to alternative phases have been detected in the pattern. Thus, it can be concluded that the series of high purity LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15) cathode materials was synthesized from the LiNiPO₄ material described previously. Similar to the pure LiNiPO₄, in the doped LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1, and 0.15) samples, the transition metal ion still occupied the octahedral M²⁺ site homogeneously, in a ratio determined by the precursor material. All diffraction peaks are sharp and distinguishable [16–18].

Based on the XRD graphs, lattice parameters for prepared compounds were calculated using Unit cell (1991) software and summarized in Table 1. A linear correlation between lattice parameters and the content of magnesium in the composition has been found. Lattice parameters a and b decreased linearly with the increasing ratio of magnesium due to the smaller Shannon radii of Ni (0.69 Å) compared to Mg (0.71 Å). The lattice parameter c remained unchanged. For the magnesium doped LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15) cathode materials, lattice parameters a and b are slightly larger than those of pure LiNiPO₄ sample with the same composition [19–22].

Table 1

Lattice parameters, space group and cell volume for different compounds.

The powder morphology of the samples at different magnifications was determined for a series of olivine structures of LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15) prepared by solid-state reaction method. As shown in Fig. 2, the powder samples exhibit relatively uniform grain size distribution, revealing the well-developed crystallinity, confirmed also by the XRD patterns. In addition, the synthesized samples exhibit porous structure, which facilitates faster penetration of the electrolyte through the cathode material.

However, some exceptionally large particles are observed in addition to the smaller ones. From the grain size, morphological changes resulting from the variation of the composition of the substituted cations Li and Mg in the samples are clearly seen [23–25]. The average grain size is in the range of 10 µm for all samples. It has also been revealed that when the amount of substituted Mg increases, the grain size decreases, which is consistent with the crystallinity nature observed by XRD.

The compositional homogeneity of nickel, magnesium, oxygen and phosphorous has been examined by EDS. As shown in Fig. 3, there are no other impurity peaks in the spectra besides Ni, P, Mg and O. Since the titration of the light element lithium is difficult with this spectroscopic technique, it was not possible to assess the lithium content.

Fig. 4 shows the FT-IR spectra of the LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15) compounds.

From the Fourier transform study, we observe that the fundamental frequencies of PO₄ polyanions are split due to the correlation effect which, in turn, is induced by the coupling of M–O bonds. As a result, the vibrational spectra of LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15) are dominated by the fundamental vibrations of PO₄ polyanions, which is not unusual. Fig. 4 shows four fundamental vibrations of PO₄, such as stretching mode around ν₁: 940 cm^–1, a doublet at around ν₂: 525 cm^–1 and two triplets viz., ν₃ and ν₄ in the region of 1059 cm^–1 to 1102 cm^–1 and at 732 cm^–1. Further, the peaks observed at the 547 cm^–1 and 580 cm^–1 region are attributed to the asymmetric stretching modes of NiO₆ octahedra, thus, confirming the formation of LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15). Basically, ν₁ and ν₃ modes involve the symmetric and antisymmetric stretching vibration of the P–O bonds, where as ν₂ and ν₄ modes involve mainly O-P–O symmetric and antisymmetric bending modes with a small contribution of P vibration [26]. The vibrational modes and band assignments in LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15) are presented in Table 2.

Table 2

Vibrational spectra data (cm^–1) and band assignments in LiNi_1–xMg_xPO₄(x = 0, 0.05, 0.1 and 0.15).

The complex impedance spectroscopy (CIS), sometimes called AC impedance spectroscopy, is a useful characterization technique for investigating the electrical properties of materials. Moreover, the CIS measurement technique is also useful to investigate the temperature and frequency dependent behavior of AC conductivity and dielectric constant. The results obtained from these analyses can provide information about the electrical behavior of the samples [27, 28]. In the present study, the electrical properties of LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15) compounds were studied in the temperature range of 30 °C to 150 °C in the frequency range of 50 Hz to 5 MHz. The measured impedance data can be represented in different forms, using the inter relations as follows:

– complex impedance Z* = Z′ - jZ″,

– complex modulus M* = M′ +jM″ = jωC₀Z*,

– complex permittivity ε* = ε′ – jε″

where j=−1,${\text{j}} = \sqrt { - 1} ,$ C₀ is the vacuum capacitance and ω = 2πf is the angular frequency. (Z′, M′, ε′) and (Z″, M″, ε″) are the real and imaginary components of impedance, modulus and permittivity.

The cole-cole/Nyquist plots of LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15) samples measured at various temperatures are shown in Fig. 5.

There are two semicircles in each impedance spectrum. The low frequency semicircle is due to the grain boundary and the high frequency semicircle depicts the bulk (grain) effect. The obtained curves for each sample appear in the form of single semicircles at various temperatures. No other curves are observed in the lower frequency region. Therefore, the semicircles of each sample are attributed to bulk conductivity, suggesting that the conductivity is of mixed electronic and ionic character. As shown in the figure, in the plots of Z′ (the real part of the impedance) against Z″ (the imaginary part of the impedance), each arc begins from lower frequencies to the right direction of the Z′-axis and ends to the left direction of Z′-axis at higher frequencies. It is observed that resistivity of the samples dramatically decreases with the increase in temperature. As a result, the diameter of the semicircle decreases with increasing temperature. On the other hand, it is observed that all arcs in the impedance plots are not perfect semicircles, which means that the highest frequency arcs do not intersect with the Z′ axis [29–31].

The variations of real (Z′) and imaginary (Z″) part of impedance with frequency at different temperatures of LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15) are shown in Fig. 6 and Fig. 7.

The value of Z′ decreases with an increase in frequency at low temperatures. The peak position shifts towards higher frequency side with a rise in temperature, as well as the width of the peak is also broadened with increasing temperature. The asymmetric broadening of the peaks in Z′ with frequency suggests that there is a spread of relaxation time. Also the shifting of relaxation peak indicates the existence of a temperature dependent electrical relaxation phenomenon in the material. The use of the imaginary part of the impedance (Z″) is particularly appropriate for resistivity and/or conductivity analysis (when the long range conductivity is dominant) [32, 33].

The variation of the dielectric constant (ε′) as a function of frequency (50 Hz to 5 MHz) at room temperature to 150 °C for LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15) samples is shown in Fig. 8.

From the frequency dependent plot of ε′, it is observed that the value of ε′ decreases sharply as the frequency increases and attains a constant limiting value, at which ε′ becomes almost frequency independent. The higher values of dielectric constant at low frequencies can be due to pile-up of charges at the interfaces between the sample and the electrode. This can be explained based on the behavior of dipole movement as follows. Dielectric behavior of samples with frequency is related to the applied electric field. An alternating electric field changes its direction with time. With each direction reversal, the polarization components are required to follow the field reversal. So, the polarization depends on the ability of dipoles to orient themselves in the direction of the field during each alternative change of the field. At low frequency regions the dipoles will get sufficient time to orient themselves completely along the direction of the field, resulting in larger values of ε′ of the samples. As the frequency increases further, the dipoles in the sample cannot reorient themselves fast enough to respond to the applied electric field, resulting in the decrease in ε′ of the samples and becoming almost constant [34, 35].

The dielectric loss can be divided into three parts: conduction losses, dipole losses and vibrational losses. The loss that is attributed to conduction presumably involves the migration of ions over large distances. This motion is the same as that occurring under direct current conduction. The variation of dielectric permittivity (ε″) with frequency is shown in Fig. 9. The variation of the dielectric loss tanδ with the frequency at different temperatures is shown in Fig. 10 for the compound LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15). The magnitude of the dielectric loss increases with an increase in temperature. At low temperature, conduction losses have minimum value. As the temperature increases AC conductivity also increases, so the conduction losses increase. This leads to an increase of the value of tanδ with temperature. The increase of the dielectric loss at low frequency is due to dipole polarization [36–38].

The electrical conductivity studies of the synthesized compounds have been carried out over a frequency range of 50 Hz to 5 MHz in the temperature range of 30 °C to 150 °C. The conductivities are found to be ~10^–6 S/cm at room temperature and higher temperature respectively for all the doped samples. The AC conductivity is calculated from dielectric data using the relation: (1)σac=ωεrε0tan⁡δ$$\begin{align}{\sigma _{ac}} = \omega {\varepsilon _r}{\varepsilon _0}\tan \delta\end{align}$$ where ω = 2πf.

The calculated conductivity results for all samples at different temperature ranges are compared in Table 3. The obtained results are found to be dependent on temperature as well as concentration of substituted Mg ions. It is observed that the conductivity of each sample increases with an increase in temperature, indicating that the electrical conduction in the samples is a thermally activated process. Thus, the observed electrical conductivity is found to occur due to the hopping of small polarons associated with the behavior of changeable oxidation state of the transition metal ions. As the temperature increases, the polarons have sufficient thermal energy to get activated and jump over the barrier and that is why larger values of conductivity of the samples are observed at higher temperatures. Also, the room temperature conductivity is found to be 9.47 × 10^–10, 2.95 × 10^–9, 9.62 × 10^–10, 9.80 × 10^–10 S/cm for LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15), respectively. These results are in the range of the electrical conductivity of semiconductors (10^–10 S/cm to 10^–9 S/cm), indicating the semiconductor behavior of the samples [39, 40].

Table 3

Activation energies for different compounds at 100 kHz.

The variation of the AC conductivity as a function of frequency (from 50 Hz to 5 MHz) at room temperature to 150 °C for LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15) samples is shown in Fig. 11. It is clearly observed that the AC conductivity curves show two distinct regions. The first one is the low frequency region in which the conductivity is almost frequency independent, which corresponds to the random hopping of charges. The second one is the high frequency region in which the conductivity increases rapidly and reaches the highest value at 5 MHz, corresponding to frequency dependent conductivity. This behavior is characteristic of hopping of charges between the trap levels situated in the band gap. These two types of conductivities are observed in all samples.

The electric modulus data were calculated using the real and imaginary parts of the measured impedance data and the pellet dimensions. The relaxation behavior was analyzed using the complex electric modulus (M* = M′ + jM″) formalism. The calculated M as a function of frequency for LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1, and 0.15) samples were fitted to the Kohlrausch-William-Watts (KWW) expression. Fig. 12 shows the imaginary part of electric modulus M′ vs. logf spectra obtained from RT to 150 °C for the synthesized compounds. From the figure, it is observed that the shape of each curve is of asymmetric non-Lorentzian type, exhibiting a peak at the relaxation frequency with a long tail extending in the region of shorter relaxation time and a shift in peak height and frequency.

A comparison of the experimental data in the M* and ε* formalism is useful to distinguish the long-range conduction process from the localized dielectric relaxation. To visualize this, we have plotted the imaginary part of complex dielectric permittivity (ε″) and modulus (M′) as a function of frequency for olivine LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15) cathode materials. Dielectric relaxation is a result of the reorientation process of dipoles in the metal-ion chains, which shows a peak in ε″ spectra. For cathode materials (with higher ionic concentration), the movement of ions from one site to another will perturb the electric potential of the surroundings. Motion of the other ions in this region will be affected by the perturbed potential. Such a cooperative motion of ions will lead to non-exponential decay, or a conduction processes with distribution of relaxation time. It has been observed that in the real part of modulus spectra, a relaxation peak occurs for the conductivity processes, whereas no peak is observed in the dielectric spectra. This suggests that the ionic motion and electronic segmental motion are strongly coupled, manifesting as a single peak in the M′ spectra with no corresponding feature in dielectric spectra. So, the conduction in cathode materials takes place through charge migration of ions between coordinated sites of the polymer along with the segmental relaxation of polymer. An enhanced ionic conduction is a natural consequence of a type of cathode material [41, 42].

The increase in conductivity with increasing temperature indicates a characteristic activated behavior in the studied temperature range. Analysis of the frequency-dependent conductivity suggests that the electrical conduction in lithium orthophosphates is presumably caused by the hopping of lithium ions between octahedral sites of the olivine framework. At room temperature, conductivity is found to be 10^–8 S/cm, since the increased repulsion between Li⁺ and M²⁺ cations reduces the strength of the Li–O bonds resulting in higher conductivity. From impedance measurements, the activation energies E_a was derived from Arrhenius equation, yielding activation energy in the range of 4 eV for LiNi_1–xMg_xPO₄ (x = 0, 0.05, 0.1 and 0.15). Fig. 13 shows that the activation energy decreases with the increasing magnesium concentration. The change in the activation energy is due to the lattice shrinkage [43].