Impedance spectroscopy analysis of double perovskite Ho₂NiTiO₆

The complex perovskite oxide of Ho₂NiTiO₆ (HNT) was synthesized by solid state reaction technique. Nanopowders of Ho₂O₃ (Aldrich, 99.9+%), NiCO₃ (Loba Chemie, 99%) and TiO₂ (Laboratory reagent, 98%) were taken as primary raw materials and mixed in stoichiometric ratio in the presence of acetone (MERCK) for 12 h. The mixture was calcined in a Pt crucible at 1200 °C in air for 10 h and brought to room temperature under controlled cooling. The calcined powder was analyzed by X-ray diffraction technique and it was found to have monoclinic structure. The calcined sample was palletized into a circular disc (of thickness 1.6 mm and dia. 10 mm) using PVA as binder which was burnt out during high temperature sintering at 1250 °C for 5 h, and cooled slowly to room temperature by adjusting the cooling rate. The sintered pellets were polished to make both their faces parallel, electroded by high purity ultrafine silver paste and then connected to the LCR meter for their electrical characterization. In order to dry the paste the samples were evaporated onto both sides of the disc at 200 °C for 2 h prior to conducting experiment. Capacitance (C), impedance (Z), phase angle (φ) and conductance (G) of the sample were measured both as a function of frequency (100 Hz to 1 MHz) and temperature (300–420 °C) using a computer-controlled LCR meter (HIOKI-3552, Japan). The temperature was controlled with a programmable oven. All the electrical data were collected while heating at a rate of 0.05 °C/min. These results were found to be reproducible.

The X-ray diffraction pattern of HNT measured at room temperature is shown in Fig. 1. All the reflection peaks of the X-ray profile are indexed and lattice parameters are determined using a least-squares method with the help of a standard computer programmed (Crysfire). Good agreement between the observed and calculated interplanner spacing (d-values) suggests that the compound crystallizes in monoclinic phase at room temperature with β = 119.863° (A = 8.772741, B = 7.687233, C = 5.691668) and unit cell volume V = 332.87 Å³.

Figure 2 shows the angular frequency dependence of Z′(ω) and Z″(ω) of HNT as a function of temperature. In Fig. 2a, Z′ decreases with increase in frequency for all temperatures implies relaxation process in the sample. The magnitude of Z′ decreases at lower frequencies with increasing temperature which indicates increase in the ac conductivity and this can also be attributed to the fact that Z′ values decrease with increase of temperature indicating reduction of grains, grain boundaries and electrode interface resistance. This indicates the negative temperature coefficient of resistance (NTCR) in the sample. At higher frequencies (above 11 kHz) the value of Z′ merges for all the temperatures indicating release of space charges. From Fig. 2b it is clear that the position of the peak in Z″ is centred at the dispersion region of Z′ and it shifts to higher frequencies with increase in temperature which is mainly due to change in relaxation in the sample. The asymmetric broadening of the peaks suggests the presence of electrical process of the material with a distribution of relaxation times as indicated by the peak width. The relaxation species may be possibly due to presence of electron at low temperature and defects at higher temperature. In such a situation, the most probable relaxation time τ_m (= 1/ω_m) from the position of the peak in the Z″ versus log ω plots can be determined (ω_m = relaxation frequency, i.e. frequency at which Z″ is found to be maximum). The most probable relaxation time follows the Arrhenius law given by the relation:where τ₀ is the pre-exponential factor, E _a is the activation energy, k is Boltzmann constant and T is the absolute temperature. The variation of relaxation time (log τ) with inverse of absolute temperature (10³/T) is shown in the inset of Fig. 3, where the circles are the experimental data and the solid line is the least-squares straight-line fit. The activation energy E _a calculated from the least-squares fit to the points is 0.129 eV. It is observed that the value of relaxation time is found to be decreasing with increasing temperature which indicates semiconductor behaviour of the sample.

In polycrystalline samples, grains are semiconducting while the grain boundaries are insulating [7]. The semiconducting nature of the grains in ceramics is believed to be due to the loss of oxygen during high temperature sintering process.

If we plot the Z″(ω,T) data in the scaled coordinates, i.e. Z″(ω,T)/Z″_max and log (ω/ω_m), where ω_m corresponds to the frequency of the peak value of Z″ in the Z″ versus log ω plots, the entire data of imaginary part of impedance can collapse into one master curve as shown in Fig. 3. Thus, the scaling behaviour of Z″ clearly indicates that the relaxation mechanism is nearly temperature independent.

Figure 4 shows the complex-plane impendence plots (called Nyquist plots, i.e. Z″ vs. Z′ plot) of different temperatures for HNT compound. In this Z-plot, one can expect a separation of the bulk phenomena from the surface phenomena [8, 9]. The surface (electrode) polarization as a highly capacitive phenomenon is characterized by larger relaxation times than the polarization mechanism in the bulk (grain interior). This fact usually results in the appearance of two separate area of semicircle in the Z″ and Z′ plots in which one representing the bulk effect at high frequencies while the other represents surface effect in lower frequency range. It is observed from Fig. 4 that the values of impedance decreases sharply as the temperature increases which indicates that the conductivity increases sharply with increase in temperature and showing the semiconducting behaviour of the material. It is observed from the inset of Fig. 4 that in the temperature range from 300 to 340 °C both the grain and grain-boundary contribution are present in this material. With the increase of temperature the grain contribution shifted to the higher frequency side and not observed in the measured frequency window, i.e. after 340 °C only grain-boundary contribution is dominated. As obtained from the intercept of the low frequency semicircle with the X-axis, the grain-boundary resistance (R _gb) values at 300, 320, 340, 360, 380, 390, 400 and 420 °C are 3.234, 2.063, 1.221, 0.820, 0.670, 0.488, 0.372, and 0.315 MΩ, respectively. And the corresponding grain-boundary capacitance (C _gb) values are 12.3 × 10⁻¹¹, 9.21 × 10⁻¹¹, 8.95 × 10⁻¹¹, 7.67 × 10⁻¹¹, 6.49 × 10⁻¹¹, 6.17 × 10⁻¹¹, 5.60 × 10⁻¹¹ and 5.50 × 10⁻¹¹ F. The corresponding relaxation times (τ_g) in this temperature range are 3.97 × 10⁻⁴, 1.90 × 10⁻⁴, 1.09 × 10⁻⁴, 0.63 × 10⁻⁴, 0.44 × 10⁻⁴, 0.30 × 10⁻⁴ and 0.21 × 10⁻⁴ s.

Figure 5 shows the variation of grain-boundary resistance as a function of temperature. It is clear that the grain-boundary resistance decreases sharply with rise in temperature up to 360 °C and then decreases slowly (Fig. 5). The rate of increase of grain-boundary conductivity is different in different regions, which means different activation energies involved in different temperatures regions for the conductivity due to grain-boundary.

The complex impedance plots of HNT at three temperatures 340, 360 and 400 °C is shown in Fig. 6. The values of grain and grain-boundary resistances and capacitances can be obtained by an equivalent circuit of two parallel resistance–capacitance (RC) elements connected in series (inset of Fig. 6). This RC elements give rise to two semicircular arcs on the complex-plane plot, representing the grain and grain-boundary effect. The equivalent electrical equations for grain is where C _g and C _gb are the grain and grain-boundary capacitances and R _g and R _gb are the grain and grain-boundary resistances, respectively. We have fitted the experimental data using these expressions and the best fit of data at 340, 360 and 400 °C are shown by solid line in Fig. 6.

Figure 7 shows the log σ_ac–log ω plot of frequency dependence of ac conductivity for HNT sample at different temperatures. It is obvious that the conductivity increases with increasing frequency and increasing temperatures (Fig. 7). At higher temperatures, a plateau is observed in the conductivity plots at lower frequency range where σ_ac is frequency-independent. The plateau region extends to higher frequencies with the increase of temperature. Notice that at low frequencies, random diffusion of charge carriers via hopping gives rise to a frequency-independent conductivity. At higher frequencies, σ_ac exhibit dispersion, increasing in a power law fashion and eventually becoming almost linear. The real part of conductivity σ in such a situation can be given by Jonscher power law [10]:where σ_dc is the dc conductivity, ω_H is the hopping frequency of charge carriers and n is the dimensionless frequency exponent. The experimental data are fitted to Eq. 4 at various temperatures (300–420 °C) where n is 0.65–0.69. The best fit of conductivity spectra is shown by solid lines in Fig. 7.

Figure 8 shows the Arrhenius plot of ac conductivity of HNT at various frequencies. The activation energies calculated from the slopes of Arrhenius plots are given in Table 1. It is interesting to note that ac conductivity activation energy decreases with increasing frequency and different activation energies involved in different temperature regions in the conduction process.

The reciprocal temperature dependence of dc conductivity (σ_dc) is shown in Fig. 9 which obeys Arrhenius law. The activation energy for dc conductivity is found to be 0.130 eV. The values of activation energy indicate that the conductivity in HNT is mainly due to the hopping of charge carriers, because the activation energy corresponding to hopping process is small.