Structural and electrical properties of lithium substituted niobo vanadate glasses doped with nickel ferrite

This article reports on the impedance spectroscopic study of lithium substituted niobo vanadate glasses and their nickel ferrite doped counterparts using Cole–Cole (Nyquist) plots and electrical conductivity analysis. The glass samples were prepared using the melt quenching technique. Differential scanning calorimetry and x-ray diffractometry were used to determine the thermal properties and the amorphous nature of the glass samples, respectively. Using impedance spectroscopy, the nature and extent of inhomogeneity were investigated and cor-related with transport properties in the glasses at different temperature ranges (120–240 ○ C). Equivalent circuit analysis was adopted to study the glass materials further. The introduction of a constant phase element (Q) in a modified RQ circuit describes the Cole–Cole plot well, which accounts for the frequency dependence of dielectric response. The electrical conductivity analysis is performed using Jonscher’s law and Arrhenius plots. The exponent “ n ” was found to be a decreasing function of temperature. The DC part of the electrical conductivity is analyzed on the basis of alkali ion distance and alkali-oxygen distance. The activation energy estimated by the Arrhenius equation is found to decrease from 0.54 to 0.39 eV as lithium content increases. The estimated mobility of lithium ions was found to decrease as the lithium content increases in both doped and undoped cases.


I. INTRODUCTION
The demand for energy is ever increasing because of rapidly increasing worldwide population and urbanization. Developing different methods to produce energy sustainably is the need of the hour. Rechargeable batteries are one such method. Semiconducting transition metal oxides (TMOs) are candidates for this kind of energy source. Among TMO materials, vanadate glasses containing lithium ions are considered to be a potential entrant. 1,2 Lithium ion conducting solid electrolyte materials attract great attention from both scientific and technological perspectives because of their light weight, compact size, and highly electropositive characteristics, which are considered factors that contribute high energy densities and high voltages. 3,4 Vanadium based oxides are interesting among TMOs as they exhibit various oxidation states. On the basis of experimental techniques like solid state nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR), it is established that vanadium exhibits both four-and five-fold coordination in glasses. 5,6 Both polaronic and ionic conductivity are observed in vanadate glasses. It has been reported that the incorporation of V 2 O5 improved the lithium ion conductivity in Li 2 O-B 2 O 3 glass. 7 V 2 O5 is a conditional glass former. It needs a co-glass former like another transition metal oxide to form glass. Alkali or alkali earth oxides are usually used as glass modifiers. We preferred synthesizing ternary vanadate glasses with niobium oxide acting as a co-former since they widely differ in their valance state and atomic radius. Niobium has higher ionic radii (215 pm) than vanadium (205 pm). Hence, the effect of substituting niobium with lithium on conductivity is interesting. Furthermore, it is essential that ion conducting glasses should be chemically stable for any practical use. In a recent article, we have shown that doping nickel ferrite (NF) enhances the thermal stability of lithium substituted niobo vanadate glasses. 8 Impedance Spectroscopy (IS) is a better method for investigation of ion movement in the frequency range of a few Hz to a few MHz in glasses. 9 A better insight into conductivity and the transport mechanism can be obtained by varying the temperature because it has a link with the change in network structure and mobility of the modifying ions. The data from IS can be modeled in terms of equivalent circuits that can give insight into the transport mechanisms of materials and device operation. For a dielectric with a single relaxation mechanism with a corresponding single relaxation time, the Cole-Cole plot is expected to be a semicircle.
This work presents a detailed analysis of temperature and frequency dependence on conductivity and Cole-Cole analysis of lithium substituted niobo vanadate (VNL) glasses and their nickel ferrite (NF) doped counterparts (VNLFe). Cole-Cole plots and equivalent circuits were used to estimate the contribution from various relaxing elements. Jonscher's equation was used to extract the values of exponent "n." Arrhenius plots are used to calculate the activation energy for DC conductivity. Conductivity variation vs ion separation is plotted to check how the distances between ions affect the conductivity.

II. EXPERIMENTAL DETAILS
Glasses having a general formula 70 V 2 O5-(30-x) Nb 2 O5-x Li 2 O and 68 V 2 O5-(30-x) Nb 2 O5-x Li 2 O-2NiFe 2 O 4 were prepared by the melt quenching technique. 10 Nickel Ferrite (NiFe 2 O 4 ) (NF) was prepared via the combustion technique (a mixture of nickel nitrate and ferric nitrate in ethyl alcohol was used as the dopant 11 ). 2 mol. % of NF was doped at the expense of V 2 O5. The glasses were opaque and were dark brown in color [ Fig. 1(b)]. Table I details out the glass content for ready reference.
Electrical properties were analyzed in terms of the Cole-Cole plot (Nyquist plot) and electrical conductivity formalism. Impedance measurements were recorded for temperatures ranging from 120 ○ C to close to Tg of the glass samples. Frequency dependent complex conductivityσ = k /Ẑ, whereẐ is the frequency dependent complex impedance measured from the impedance analyzer and k, the cell constant given by d/A (where d is the thickness and A is

A. Basic characterization of glass and nickel ferrite
The amorphous nature of the glasses was confirmed by XRD [ Fig. 1(a)]. Differential scanning calorimetry (DSC) was used to find the glass transition temperature (Tg). Archimedes' technique was used (with xylene as the immersion liquid) to determine the density of the prepared glass samples (details are provided in the supplementary material). The values of Tg and density are listed in Table I, and DSC isotherms of the samples are shown in Fig. 2. The prepared NF was subjected to XRD and FTIR (see Figs. S1 and S2 in the supplementary material). When doped, NF mixes homogeneously in glass and does not separate out as a different phase. This can be confirmed from perusal of Fig. 1 where along with the undoped glasses, XRD of NF doped glass is also shown for comparison. Figure 3 shows the high resolution SEM image of the prepared NF. A closer look reveals that the sample is uniform, with almost spherical structural morphology and narrow size distribution but with agglomeration to some extent. Other low resolution SEM images are presented in the supplementary material.
Since the doped glasses did not show any inhomogeneity in XRD, it felt unnecessary to record SEM or TEM images of those glasses. The presence of NF in glass was confirmed by the presence of the Fe-O bond using FTIR. Figure 4 shows clearly that the Fe-O bond present in NF is retained in the doped glass as well, whereas in the undoped counterpart, the vibrational band is absent.
Nickel ferrite present in the doped samples acts to enhance the thermal stability of the doped glasses. As can be seen from Fig. 2, the difference between Tg and the onset of crystallization is larger in doped glasses than their undoped counterparts. This is a measure of thermal stability. The increase in thermal stability in doped ARTICLE scitation.org/journal/adv glasses may be due to the increased packing density as the addition of nickel ferrite settles in the voids of the glass network. 8 In Ref. 8, it was shown that the addition of nickel ferrite does not impart any significant change in the DC electrical conductivity as the mol. % of added nickel ferrite is small compared with the mol. % of lithium oxide, which dictates the conductivity.

B. Cole-Cole (Nyquist) analysis
For the analysis of the impedance data using Cole-Cole (Nyquist) plots, we follow the procedure used in Ref. 13. The data were fitted with two simple parallel RC circuits with a resistor (Rp) and a capacitor (Cp). The first Rp and Cp are associated with the layer resistance and geometric capacitance of the layer of glass, respectively, while the second Rp and Cp are associated with the layer resistance and geometric capacitance of the glass/electrode interface. A contact resistance Rs (series resistance) is usually present in all glasses since there is a mismatch between the Fermi levels of the glass/electrode interface and the layer of glass near the electrode. 13 The parameters mentioned above are obtained after convergence of the fitting procedure. In the presence of series resistance (Rs) with Rp and Cp, the impedance of the circuit can be written as 13 We observe either two semicircles or one semicircle and an arc of a circle for all the glass systems under study. The semicircle at higher frequency is due to the impedance of the glass layer, and the semicircle or arc at lower frequency is related to impedance of the glass/electrode interface. These occur due to the different electrical properties and mismatch in the energy level (Fermi energy level) between these regions. For fitting, we used two parallel RC circuits connected in series. R 1 and C 1 in the circuit describe the resistance and capacitance of the bulk glass material, while R 2 and C 2 represent the resistance and capacitance of the depletion layer at the glass/electrode interface, respectively. Cole-Cole plots and the equivalent circuit fit of RC and RQ (described later in the text) for different temperatures are shown in Fig. 5 for undoped VNL glasses and in Fig. 6 for NF doped VNL glasses. The parameters extracted from the fit are listed in various tables in the supplementary material. As can be seen from Figs. 5(a1)-5(c1) for undoped VNL glasses and from Figs. 6(d1)-6(f1) for NF doped VNL glasses, the two parallel RC circuits are inadequate to fit the measured data properly. This may be because a parallel RC circuit simulates an ideal Debye type of relaxation. However, in this case, the relaxation is non-Debye type due to spatial inhomogeneity or local processes like diffusion. These processes will produce a skewed or suppressed Cole-Cole plot. 9,13 A well-established way to account for the non-Debye behavior is to replace C with a phenomenological Constant Phase Element (CPE). 9,13,14 The CPE takes account of the dispersive properties such as frequency dependent dielectric properties and provides a better fitting for the impedance characteristics of disordered materials. 14 The impedance of the CPE is written as ZQ = (iω) − ϕ Q , where Q is a constant and exponent ϕ is the degree of capacitive nature of the component, with values 0 < ϕ < 1. The total impedance of the RQ circuit without a series resistance can be written as 13,14 A proper fitting to the measured data was obtained with introduction of CPEs Q 1 and Q 2 in parallel with resistors R 1 and R 2 . Figures 5(a2)-5(c2) and 6(d2)-6(f2) show the fitting. Thus, the nonideal CPEs were able to correctly model the inhomogeneities and other elements responsible for the non-Debye type of relaxation. As it was mentioned earlier, the combination of R 1 and Q 1 represents the bulk glass behavior whereas the combination R 2 and Q 2 represents the glass/electrode interface. The exponent ϕ in the definition of the CPE reflects the non-ideal nature arising from various reasons in the material. Since Q 1 and hence ϕ 1 stand for bulk glass, it isϕ 1 that represents the elements responsible in relaxation. The range of variations in ϕ 1 , ϕ 2 , R 1 , and R 2 for each glass is summarized and tabulated in Table II. The variations represent values from low temperature to high temperature. The details of the temperature range and the actual values of these parameters at those temperatures are listed in the tables given in the supplementary material.
The lower values of ϕ represent a larger inhomogeneity between relaxing sites. Hence, we may infer that different sites relax with different time scales adding up to a spread in the overall relaxation time of the glass system.

C. Conductivity analysis
The nature of conductivity in alkali containing TMO glasses is expected to be either electronic or ionic or a mixture of both. The electron paramagnetic resonance (EPR) spectra of the present glass samples did not show hyperfine structure, confirming the absence of the V 4+ state of the vanadium ions (see the supplementary material). Thus, we argue that the conductivity in our glass system is purely ionic.

Frequency dependent conductivity
Frequency dependence of conductivity can be analyzed using Jonscher's power law, 15 which, in terms of the real part of frequency dependent conductivity σ ′ ( f ), frequency independent part (DC) conductivity σo , and onset frequency f 0 , is written as The DC conductivity σo can be obtained either by extrapolation of σ ′ ( f ) to low frequencies or by extracting as a parameter from fitting Eq. (4). Figure 7 shows the conductivity spectra of all the glasses at different frequencies. Due to the polarization effect at the sample and electrode interface, the samples show a dent at low frequencies. This effect becomes significant at higher temperatures where the conductivity is high. The DC conductivity value at each temperature was taken as the conductivity σ ′ ( f pol ) at a frequency f pol where polarization effects set in. DC conductivities realized here are slightly higher than values reported earlier. 16 This is probably due to the different thermal history of the samples and the amount of mol. % of V 2 O5 with the lithium ion.
The spectra were fitted to Eq. (4), and the exponent "n" was extracted from the fit and is tabulated in Table III along with temperature and activation energy obtained from the Arrhenius plots [Eq. (6) and Fig. 8].
From Table III, it is observed that n is a decreasing function of temperature. It was suggested that this exponent depends on the dimensionality of the local cation conduction space such that n decreases with decreasing dimensionality. 17

Frequency independent conductivity
Ionic conduction depends on the concentration and mobility of alkali ions. The ionic conductivity, σ 0 , of all alkali conducting glasses is expressed as where Z, n, e, and μ are the valence number of the charge carrier, concentration of charge carriers, charge, and mobility of the charge carriers, respectively. The concentration of charge carriers (i.e., concentration of Li+) is calculated from the knowledge of molar volume. From Eq. (5), the mobility of the lithium ions at 120 ○ C was calculated and is listed in Table IV. In the present glass system, as the concentration of lithium ions increases, the mobility gets lower, as shown in Table IV. Murawski and Barczyński, 18 on the basis of their studies on electronic conductivity in Na 2 O-FeO-P 2 O5 glasses, 19 argue that the alkali ion (Na + in their case) is bound to the Fe-O-P network and has lesser mobility. We consider a similar situation in our glass system and consider This makes Li + harder to separate, and the mobility decreases. The product of σo (DC conductivity) and temperature T follows Arrhenius behavior below glass transition temperature. Equation (6) represents the Arrhenius equation and is used to determine the activation energy, which is tabulated in Table III, where E 0 is the activation energy, k is the Boltzmann constant, and T is the temperature.   As can be seen from Table III, the activation energy for undoped VNL glasses decreases from 0.538 eV to 0.385 eV with an increase in lithium concentration, whereas in NF doped counterparts, the activation energy increases from 0.49 eV to 0.62 eV. This shows that structural changes in the glass have an effect on activation energy. According to the Anderson-Stuart model, 20 the total activation energy for ionic conduction Ea is the sum of two energies given as where ΔEB is the electrostatic binding energy and ΔES is the strain energy. A qualitative explanation is as follows: As mol. % of lithium ions increases, the covalent nature of the V-O-Li bonds changes, and that may affect the binding energy. On the other hand, the strain energy is proportional to the separation between cations. The increase in Li + concentration would effectively reduce the cationic distance and would reduce the strain energy. Thus, the total activation energy decreases as the concentration of lithium ions increases in the case of undoped glasses. For NF doped glasses, the activation energy increases from 0.49 eV to 0.62 eV from 15 mol. % lithium glass to 20 mol. % lithium glass and then remains at 0.62 eV for 25 mol. % glass. This sudden increase may be due to the structure becoming more rigid with NF and 20 mol. % of lithium glass than with the 15 mol. % lithium glass.
The DC conductivity at 120 ○ C vs R (Li-O) and R (Li-Li) is plotted in Fig. 9. The separation between cation and cation-anion was calculated from the density and molar volume.
A perusal of Fig. 9 shows that the conductivity decreases as the cationic separation or the cation-anion separation decreases. We see an appreciable change in conductivity from VNL15 to VNL20 as the separation decreases. However, in the NF doped counterpart, there is not much change in the conductivity. Ionic conductivity depends on alkali concentration and ion mobility, and one may expect electrical conductivity to increase with increasing alkali content. However, in the present glass systems, an adverse effect of increase in lithium concentration on conductivity is observed as it was mentioned earlier that lithium ions in niobo vanadate glasses have less mobility and may be bounded to the V-O-Nb network. Thus, a reduced mobility might be the cause of reduced conductivity.

IV. CONCLUSION
This work investigated the electrical conductivity of lithium substituted niobo vanadate glasses doped with nickel ferrite. Electrical conductivity for all the samples was estimated from impedance measurements. The real and imaginary parts of impedance were represented by Cole-Cole plots. Two different relaxation mechanisms at the glass/electrode interface and in bulk glass materials can be clearly seen from the nature of the Cole-Cole plots. These plots were analyzed using the equivalent circuit method consisting of an ideal resistor and a non-ideal CPE connected in parallel. The extents of inhomogeneity in the glass were determined. The electrical conductivity was analyzed using Jonscher's power law and Arrhenius plots. The power law exponent "n" was found to be a decreasing function of temperature. The variation in electrical activation energy was qualitatively explained using the Anderson-Stuart model. The conductivity is seen to decrease with cationic separation as well with cation-anion separation. This may be due to the reduced mobility of lithium ions.

SUPPLEMENTARY MATERIAL
See the supplementary material for the details of basic characterization of VNL glasses and nickel ferrite as well as tables of various parameters used to fit the Cole-Cole representation of impedance data.