JOURNAL OF APPLIED PHYSICS 109, 093704 (2011)
Metal-semiconductor transition in NiFe2O4 nanoparticles due to reverse cationic distribution by impedance spectroscopy M. Younas,1 M. Nadeem,1,a) M. Atif,2 and R. Grossinger2 1
EMMG, Physics Division, PINSTECH, P.O. Nilore, Islamabad, Pakistan Institute of Solid State Physics, Technical University of Vienna, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria 2
(Received 1 December 2010; accepted 24 March 2011; published online 6 May 2011) We have investigated the magnetic and electrical response of the sol-gel synthesized NiFe2O4 nanoparticles. Changes in the impedance plane plots with temperature have been discussed and correlated to the microstructure of the material. Thermally activated hopping carriers between Fe3þ-Fe2þ and Ni2þ-Ni3þ ions have been determined for a decrease in the resistance of the sample and a change in the conduction mechanism around 318 K. The mixed spinel structure and broken exchange bonds due to small size effects are due to the canted spin structure at the surface of the nanoparticles. The magnetization is found to be influenced by the surface spin canting and anisotropy. We have established the semiconducting to metallic transition (SMT) temperature to be around 358 K in terms of localized and delocalized eg electrons along with a transition from less conductive [Fe3þ–O2"–Fe3þ] and [Ni2þ–O2"–Ni2þ] linkage to more conductive [Fe3þ–Fe2þ] and [Ni2þ–Ni3þ] linkage at the octahedral B site. A decrease in the dielectric constant with temperature has been discussed in terms of the depletion of space charge layers due to the repulsion of delocalized eg electrons from the grain boundary planes. The anomalies in tangent loss and C 2011 American Institute conductivity data around 358 K are discussed in the context of the SMT. V of Physics. [doi:10.1063/1.3582142]
I. INTRODUCTION
Spinel ferrite nanoparticles by virtue of their unique electronic, magnetic, and physical structure may be harnessed for technological applications.1,2 Nano ferrites are an important class of materials because of their high resistivity and low eddy current losses.3 Bulk spinel ferrites are described by the formula (A)[B]2O4, where (A) and [B] represent the tetrahedral and octahedral sites, respectively. Nanocrystalline ferrite systems usually have a mixed spinel structure having the 2þ 3þ 2" 3þ chemical formula, ðM2þ 1"d Fed Þ½Md Fe2"d &O4 . The divalent 2þ metal ion M can occupy the either tetrahedral (A) or octahedral [B] sites or both sites of the spinel structures, depending upon the nature of the system. The inversion parameter, d, is defined as the fraction of the (A) sites occupied by Fe3þ cations and its value depends on the method of preparation.4,5 NiFe2O4 is a well-known inverse spinel structure, with Ni2þ ions occupying only the B sites. Chinnasamy et al.6 have shown that nanocrystalline NiFe2O4 exhibits a mixed spinel structure with Ni2þ ions occupying both (A) and [B] sites. NiFe2O4 nanoparticles with a mixed spinel structure have been shown to exhibit interesting electrical, magnetic, gas, and humidity sensing properties.6,7 The NiFe2O4 sample exhibits paramagnetic, superparamagnetic, or ferrimagnetic behavior depending on the microstructure.8 Scherrer9 observed ferromagnetic and superparamagnetic behavior in NiFe2O4 nanoparticles with grain sizes of 17 and 10 nm, respectively. A reduction in the a)
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saturation magnetization of NiFe2O4 due to a reduction in grain size has been reported to result from the noncollinearity of the magnetic moments at the surface.10 Core-shell morphology is appropriate to explain the magnetic properties of the nanoparticles. Chinnasamy et al.6 reported the high value of magnetocrystalline anisotropy in the mixed spinel NiFe2O4 sample with a canted spin structure at the surface and the core. Several methods have been used for the preparation of ferrite nanoparticles such as ball milling, thermal decomposition, and the sol-gel technique.11,12 The properties of the ferrites are very sensitive to the synthesis techniques. The sol-gel method is a versatile technique to vary the properties of the material by controlling different parameters such as temperature, time of reaction, pH of the medium, and the reagent’s concentration.13 Atif et al.4 observed more reverse cationic distribution in the ZnFe2O4 nanoparticles prepared in urea (i.e., a basic medium) rather than in citric acid (i.e., an acidic medium). In the present study we prepared NiFe2O4 nanoparticles in a basic medium and carried out magnetic and electrical measurements to determine any possible change in the conduction mechanism. To the best of our knowledge, any possible correlation between the electrical parameters and the microstructure for NiFe2O4 nanoparticles above room temperature has not yet been reported. Impedance spectroscopy is a powerful technique in solid states because of its ability to differentiate the transport characteristics in grains and grain boundaries.14 The grains and the grain boundaries are the two main components that comprise the microstructure and the correspondence between the grains and grain boundaries is important in understanding the overall properties of these materials.15 Impedance
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spectroscopy can be used to study the electrical behavior of different microstructures (phases) inside a polycrystalline material. Using the impedance technique, data equivalent to the real and imaginary parts of complex electrical quantities are measured as a function of the frequency of the applied electric field.16 These complex quantities include electrical impedance, dielectric permittivity, and loss tangent, tan d. The electric and dielectric properties of the ferrites are predominantly controlled by the grain boundaries.17 The dielectric properties of the NiFe2O4 nanoparticles will be constructive for extending the range of applications. The electrical properties of ferrites provide supportive information about the behavior of the localized electric charge carriers and an understanding of the dielectric polarization mechanism. Cation–cation interactions are distinguished from cation–anion–cation interactions by affecting the electrical and magnetic properties of oxides containing transition metal elements.18 In this respect, impedance spectroscopy has been successfully employed to explore the possible role of these interactions in changing the electrical and magnetic properties. The temperature did not exceed 373 K to inhibit any possible grain growth during experimentation. II. EXPERIMENTAL
NiFe2O4 nanoparticles were prepared by the sol-gel method. Analytical grade Ni(NO3) . 6H2O, Fe(NO3)3 . 9H2O and urea were used for material preparation. We separately dissolved 0.1 M of Ni(NO3) . 6H2O and Fe(NO3)3 . 9H2O in a minimum amount of distilled water. This solution was then mixed in the aqueous solution of urea in a molar ratio of 1:3. The mixed solution was heated to a temperature of 338–343 K with vigorous stirring until the gel was formed, which was subsequently dried at 393 K for 3 h in an oven. The dried gel was heat treated at 573 K for 3 h to remove volatile species. Then the powder was pressed into a pellet 13 mm in diameter and 1.5 mm in thickness. Finally, the pellet was sintered at 873 K for 4 h. The structural characterization was performed by an x-ray diffractometer (XRD) having Cu Ka radiation ˚ ). The intensities were recorded for 20o ' 2h ' 70o (1.5418 A with a step scan of 0.02o with a time of 1 s/step. The measurements of the hysteresis loops were performed by using a physical property measurement system (PPMS-9 T, Quantum Design) applying a magnetic field of 5 T. Impedance spectroscopy on the sintered pellet of NiFe2O4 was performed in the frequency and temperature range of 1 ' frequency ' 107 Hz and 298 K ' temperature ' 373 K, respectively, using an Alpha-N analyzer (Novocontrol, Germany). The surfaces of both sides of the pellet were properly cleaned and contacts were made by silver paint on opposite sides of the pellet, which were cured at 423 K for 3 h. Before the impedance experiments, the dispersive behavior of the leads were carefully checked to exclude any extraneous inductive and capacitive coupling in the experimental frequency range. The ac signal amplitude used for all of these studies was 0.2 V. WINDETA software was used for data acquisition, which was fully automated by interfacing the analyzer with a computer. ZVIEW software was used for the fitting of the measured results. The sample was arranged inside a homemade
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sample holder and a dc power supply was connected to the sample holder to stabilize the temperature. Measurements were made after stabilizing the temperature for about 10 min prior to each reading. III. RESULTS AND DISCUSSION
Figure 1 shows the XRD pattern of the synthesized nickel ferrite nanopowder. All XRD peaks are indexed well with the standard pattern for NiFe2O4 reported in PCPDF card # 74-2081. The average crystallite size has been calculated from the most intense peak (311) using Scherer’s formula d ¼ kk/b cos h where d is the particle size, b is the full width at half maximum of the peak (311) and k is an instrumental constant.19 The average calculated particle size has been found to ˚ ), computed be 22 6 3 nm. The lattice parameter (8.339 A using respective (hkl) values, is less than that of the bulk material. This reduction in lattice parameter may be attributed to the increased degree of inversion, more surface energy, and surface tension which can lead to the distortion of the lattice constant.4,20 Fig. 2 shows the field dependent magnetization of the NiFe2O4 sample measured at different temperatures in an applied field up to 5 T. From these measurements, it has been found that the magnetization does not saturate at the maximum available field (i.e., 5 T) and the values of magnetization obtained at 300, 350, and 400 K are 15, 14, and 13 emu/g, respectively. The room temperature magnetization value is considerably smaller than the bulk value of 56 emu/g for nickel ferrite.21 This can be explained on the basis of the core-shell morphology of the nanoparticles with a ferrimagnetically aligned core surrounded by the surface shell, which is found to be structurally and magnetically disordered due to the nearly random distribution of cations and the canted spin arrangement. The origin of this surface disorder may be due to broken exchange bonds, high anisotropy on the surface, or a loss of the long-range order in the surface. Furthermore, canted or disordered spins at the surface of the nanoparticles are difficult to align along the field direction causing an unsaturated magnetization in these particles.22–24 As a consequence
FIG. 1. X-ray diffraction pattern of the NiFe2O4 sample recorded at room temperature.
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FIG. 2. (Color online) Magnetization against applied field at different temperatures.
of the frustrated superexchange interactions in the surface shell, our prepared nickel ferrite sample exhibits a reduced unsaturated magnetization which is attributed to the weakening of the AB exchange interactions due to the effect of spin canting that dominates over the effect of site exchange of the cations in the surface shell.25 Figures 3(a) and 3(b) show the complex impedance plane plots of the NiFe2O4 sample at different temperatures and the arrow shows the direction of the increase in frequency. At each temperature, impedance plane plots show two well resolved semicircular arcs, a larger one at low frequency and a smaller one at the higher frequency side. The appearance of two arcs in impedance plane plots at each temperature indicate the presences of two types of relaxation phenomena with sufficiently different relaxation times (s ¼ RC), where R is the resistance and C is the capacitance of the associated phase.16 The size of the semicircular arcs decreases with the increase in temperature and shows its minima around 358 K. A further increase in temperature causes an increase in the diameter of the impedance plane plots as seen in Fig. 3(b). The centers of both of the semicircular arcs have been found to be depressed below the real axis indicating the heterogeneity and deviation from the ideal behavior.16 We define this temperature (358 K) as the semiconducting to metallic transition (SMT) temperature. The
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fitting parameters derived for the equivalent circuit will be discussed in the next paragraph. In order to correlate the electrical properties of the NiFe2O4 sample with the microstructure of the material, an equivalent circuit model (RgQg) (RgbQgb), shown in the inset of Fig. 3(a) has been employed to interpret the impedance plane plots. Here R, Q, g and gb are the resistance, the constant phase element, grain interiors and grain boundaries, respectively. The constant phase element (CPE) is used to accommodate the nonideal behavior of the capacitance which may have its origin in the presence of more than one relaxation process with similar relaxation times.16 The capacitance of the CPE is given by the following relation, C ¼ Q1=n Rð1"nÞ=n , where the parameter n estimates the nonideal behavior having a value of zero for pure resistive behavior and is unity for capacitative behavior.26,27 In these types of ferrites, the grain boundary resistance is generally higher in comparison to the grains.3 Additionally, the arc representing the grain boundaries generally lies on the lower frequency side since the relaxation time of the grain boundaries is much larger than that of the grains.28 Therefore, we assign smaller (high frequency) and larger (low frequency) semicircular arcs to the grains and grain boundaries, respectively.29 The parameters Rg, Rgb, Qg, Qgb, ng, and ngb were obtained for each temperature by fitting the impedance plane plots (within 1% fitting error). Figure 4(a) implies that slight variations in parameters n and C for the grain and grain boundaries in the 298–338 K range is indicative of the inhomogeneous distribution of the energy of the trap centers. With an increase in temperature, there are visible increasing and decreasing trends in the values of ng and ngb, respectively, in the 338–358 K range. These trends signify that the grain capacitance (Cg) is likely to approach ideal behavior and the grain boundary (Cgb) deviates from the ideal behavior as shown in Fig. 4(b). A decrease in the capacitance of the grains may be due to the vanishing of defects such as the release of trapped charges followed by the accumulation of these charges at the grain boundaries, thereby increasing its capacitance. Above 358 K (i.e., the SMT temperature), both Cg and Cgb parameters start saturating. Saturation in the capacitances of the grains and grain boundaries may be due to the combined effect of the delocalized charge carries and spin alignments. Figures 5(a) and 5(b) illustrate the variations in the resistances of the grain and grain boundaries with temperature.
FIG. 3. (Color online) (a) Impedance plane plot of the NiFe2O4 sample at room temperature. Inset shows the equivalent circuit model. Arrow shows the direction of increase in frequency. (b) Impedance plane plot at some selected temperatures. Inset shows the impedance plane plot between 363–373 K.
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FIG. 4. (Color online) (a) Variation of parameters ng and ngb with temperature, and (b) variation of grains and grain boundary capacitances with temperature for the NiFe2O4 sample.
The inset of Fig. 5(b) shows the variations in the total resistance of the sample with temperature. The decrease in the resistance of grains and grain boundaries has been suggested to be due to the thermal activation of the localized charges. Two types of thermal activations, i.e., carrier density in the case of band conduction and carrier mobility in case of hopping, are responsible for the reduction in the resistive properties with temperature.15 With the increase in temperature above 338 K, the grain resistance shows increasing trends while the grain boundary and total resistance (shown in the inset of Fig. 5) still show decreasing trends. The balance between the mobility and density of the thermally activated hopping carriers plays a vital role in determining the change in resistance with temperature. Above 338 K, there is a decrease in the density of thermally activated hopping carriers within the grains but the mobility of the hopping carriers increases with temperature. The increased value of the mobility compensates for the decrease in the density of the hopping carriers and we observe a decrease in the total resistance of the sample with a temperature up to 358 K as shown in the inset of the Fig. 5(b). An increasing trend in the resistance of the grain boundaries beyond 358 K shows its metallic behavior. On the whole, the conduction mechanism can be implicit by considering the potential of the grain boundary and energy of the eg electrons. In ferrites, transport phenomena usually arise by the hopping of localized d electrons between valence distributions of cations that normally occupy the oxygen octahedral site.18 The electrostatic interaction between anion and cation electrons cause a splitting of the cation 3d level into less stable doubly degenerate eg electrons and more stable triply degenerate t2g electrons.30 If Ek is the energy of eg electrons, U is the potential of the grain boundaries, n is the number density of the eg electrons, then mathematically, n ¼ nee/=kTe , where e is the charge on a single electron, U is the potential applied by the grain boundaries, k is the Boltzmann constant, Te is the temperature of eg electrons, and n0 is the number density of electrons at U ) 0.27 If Ek > eU then the electrons will be delocalized and actively participate in the conduction mechanism but when Ek < eU, then eg electrons will be localized. It is inferred here that below 358 K, in the presence of some nonmagnetic disorder (i.e., electronic trap center) and magnetic disorder (i.e., disorientation of the surface and core spins) eg
electrons will be localized, satisfying the condition of Ek < eU and with an increase in temperature up to 358 K, the hopping probability of the eg electrons increases, thereby decreasing the resistance of the sample. However, with a further increase in temperature above 358 K, localized states become delocalized along with alignments of the core/surface spins and effective conducting channels appear. Conducting channels facilitate the movement of charge carriers thereby increasing their mobility and we observe metal-like behavior in this temperature range. Moreover, at the SMT temperature, all of the eg electrons might have multipotential values that give rise to a competition between localized and delocalized charge carriers. The activation energy for the thermally activated charge carriers is obtained by fitting the dc conductivity data using the Arrhenius relation, r ¼ r0 exp½"Ea =kT&, where r0 is the pre-exponential factor, Ea is the activation energy, and k is Boltzmann’s constant. The resistance values of the grains (Rg), grain boundaries (Rgb), and geometrical dimensions have been used to calculate the total dc conductivity by using the relation, r ¼ L=A: R, where r is the conductivity in S cm"1, A is area of the sample in cm2, L is length of the sample in cm, and R is the total resistance of the grains and grain boundaries in X.31 From Fig. 5(c) a change in slope is observed beyond 318 K, showing that a different conduction mechanism is involved. The activation energies 0.71 and 0.41 eV have been calculated from the fitted data below and above 318 K, respectively. A higher value of the activation energy below 318 K suggests dominant hole hopping B-site, and the between Ni2þ $ Niþ3 ions at the ! octahedral " Niþ3 ions ! are"in a low spin state t62g ; e1g as compared to the Feþ3 t32g ; e2g ions. With the increase in temperature above 318 K, the electrons gain enough energy to dominate the overall conduction mechanism that causes a reduction in the activation energy since electron hopping requires a lower value of activation energy compared to that of hole hopping.31 Goodenough32 predicted the simultaneous existence of the both cation–cation and cation–anion–cation interactions in the rock salt type structures such as NiO, MnO, FeO, etc. When strong cation–anion–cation interactions dominate over the weak cation–cation interactions, these materials have semiconducting/insulating behavior. In the case of strong cation–
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FIG. 5. (Color online) (a) Variation of Rg with temperature, (b) variation of Rgb with temperature for the NiFe2O4 sample; inset shows the variation of total resistance with temperature, and (c) total dc conductivity of NiFe2O4 the solid lines are the best fit to the Arrhenius relation.
cation interactions between octahedral B-site, these materials show metallic behavior, and may become semiconducting at low temperatures. Also, the presence of cations of the same elements with different valence states give rise to the metallic character below the Curie temperature. In NiFe2O4 with normal cation distribution (Fe3þ)[Ni2þFe3þ]O42", the cation– cation interaction is dominated by the cation–anion–cation interactions between [Fe3þ–O2"–Fe3þ] and [Ni2þ–O2"– Ni2þ].33,34 In the view of crystal field and ligand field theories, the Ni2þ–O2"–Ni2þ interactions are dominant which rendered this material to be semiconducting. However, Ni2þ ions may distribute randomly on (A) and [B] sites along with Fe3þ ions due to some reverse cationic distributions in the nanocrystalline NiFe2O4 material. The room temperature Mo¨ssbauer spectroscopy (the result will be shown in a forthcoming paper) revealed the sextet and relaxed magnetic structure with a very broad linewidth. The broad linewidth is observed due to the field distribution for small crystallite size which is about 22 nm in this case. The reduced value of the hyperfine field at the B site compared to the bulk counterpart35 is the result of the distribution of the crystallite size. The inversion parameter estimated from the Mo¨ssbauer spectroscopy was 0.64. The reduced value of the tetrahedral isomer shift as compared to the octahedral isomer shift for this material has been attributed to the difference in the coordination of the Fe3þ from the four fold site (A site) to the six fold (B site). Hence, in this material a fraction of Fe3þ and Ni2þ ions migrate to the [B] and (A) sites, respectively. Shifting of the Fe3þ ions causes compressive strains due to the smaller distance between the B-site ions
compared to the A-site ions in nanoparticles.7 These compressive strains may break the surface exchange bonds which results in a canted spin structure. The canted spin structure not only affects the [Ni2þ–O2"–Ni2þ] interactions but also weakens the AB-exchange interactions that cause a lower value of the room temperature magnetization compared to the bulk counterpart previously discussed. An increased number of Fe3þ at [B] enhances the exchange interaction between [Fe3þ–O2"–Fe3þ]. It is presumed here that below 258 K, an increase in temperature causes an increase in hopping of the localized charge carriers between the [Fe3þ–O2"–Fe3þ] and [Ni2þ–O2"–Ni2þ] linkage at the octahedral B site, in this way giving rise to the semiconducting character in the material. However; the affinity of the NiO for the oxidation and creation of defects such as oxygen vacancies during heating in the ferrite lattice leads to the formation of Ni3þ and Fe2þ ions. Above 358 K, diminishing localized states and alignments of the spins give rise to the efficient conductive channels in the form of [Fe3þ–Fe2þ] and [Ni2þ–Ni3þ] links. These channels cause the delocalization of the charge carriers, and in so doing creating a metallic character above 358 K. Figures 6(a) and 6(b) show the variation of tangent loss with frequency at some representative temperatures. Each spectrum possesses two loss peaks with different relaxation times exhibiting the presence of at least two relaxations in the system which is in accordance with the impedance plane plot results previously discussed. The larger peak in the low frequency region 104 Hz is associated with the grains.36 In both relaxation processes, the peak height increases and shifts toward the higher frequency side up to 358 K, as shown in Fig. 6(a). In the NiFe2O4 material,18 the relaxation is attributed to the cation–anion–cation interactions at the octahedral B site. Now the increase in magnitude of the tangent loss peak with temperature is attributed to the increase in the number of thermally activated [Fe3þ–O2"–Fe3þ] and [Ni2þ–O2"–Ni2þ] linkages responsible for the relaxation; whereas the shift in the relaxation frequencies toward higher values is due to the mobility activation of the charge carriers with an increase in temperature. Above 358 K, the magnitude of the loss peak in the low frequency region remains relatively temperature insensitive which supports our discussion of delocalization of the charge carriers with an indiscriminate distribution of the energy. Some of the charge carriers scatter from the grain boundary planes due to the increased lattice vibrations.37 The scattering outcome in the reduced value of the mobility that has been found to be responsible for the shift of the high frequency relaxation peak toward a lower frequency as shown by the arrow in Fig. 6(b). Figure 7(a) shows the frequency dependent real part of the dielectric constant at different temperatures. The trends of the graph show the existence of more than one type of polarization in NiFe2O4 nanoparticles. Typically four types of polarizations, interfacial, dipolar, atomic, and electronic are reported in ferrites.38 Dispersion below 102 Hz is suggested to be due to the interfacial polarization and above 104 Hz, due to rotational displacement of the dipoles. At frequencies higher than 106 Hz, a relatively independent value of the dielectric constant with temperature is attributed to the atomic and electronic polarizations. Figure 7(a) indicates an increase in the dielectric constant with temperature up to 358 K. It is suggested here that thermally activated dipoles cause an increase in the interfacial and rotational polarizations by accumulating at grain boundaries. In the view of the above SMT discussion, an increase in temperature above 358 K alters the overall space charge capability. A decrease in the dielectric constant, as shown in the inset of Fig. 7(a), has been endorsed due to the scattering of the charge carriers which causes a depletion in the space charge layers. At each temperature, a decrease in the dielectric constant with frequency is observed owing to the lower dipolar response to the ac field.39
Different types of conductivities in NiFe2O4 material have been reported in the literature. Baruwati et al.40 attributed the n-type behavior as being due to the presence of Fe3þ in NiFe2O4 nanoparticles. The electron conduction is represented as Fe3þ $ Fe2þ. The hole conduction is represented as Ni2þ $ Ni3þ. Other reports41,42 also support the existence of n-type and p-type conductivities in Ni-Zn ferrites due to the presence of Fe2þ and Ni3þ, respectively. The values of the activation energy (i.e., 0.41 and 0.71 eV) obtained in this study suggest hopping and polaronic conduction between the localized sites.43 In the hopping process, the carrier mobility is temperature dependent, which is usually characterized by activation energy. Figure 7(b) shows the frequency dependent ac conductivity of the NiFe2O4 sample at some representative temperatures. At low frequency, the ac conductivity is found to be weakly frequency dependent due to the nonequilibrium occupancy of the trap charges.27 A further amplification of frequency reduces the occupancy of the trap centers by making them available for conduction. It facilitates the conductive state to become more active by promoting the hopping of electrons and holes. The conductivity increases with increasing frequency and temperature up to 358 K. Above 358 K, the frequency of the hopping ions decreases due to a reduction in the mobility of the charge carriers after reflection from the grain boundary plane and a decrease in conductivity as shown in inset of Fig. 7(b) is observed. Trends in conductivity with temperature supports our results of the dielectric constants as both the conductivity and the dielectric constant runs parallel. In order to obtain a clear understanding of the conduction mechanism, we have divided the conductivity graph over three frequency regions: (I) 1–100 Hz, (II) 3 * 102– 4 * 103 Hz, and (III) 3 * 105–4 * 106 Hz. At each frequency region, the conductivity follows the dynamical ac power law, such that rðx; T Þ ¼ BðT ÞxSðT Þ , where B is the parameter having the unit of conductivity and s is the slope of the frequency dependent region, 0.0 ' s ' 1.18 Fitting of the experimental data yields a value of s whose dependence on temperature is a function of the conduction mechanism. Figure 7(c) shows the variation of the slope parameter, s, with different temperatures. For region (I), there is no change in s with temperature due to a nonequilibrium occupancy of the trap charges. In region (II) there is a linearly decreasing trend of s with temperature suggesting a correlated barrier
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FIG. 7. (Color online) (a) Variation of dielectric constant with log f; the direction of the arrow shows the increase in temperature; inset shows a decrease in the dielectric constant with temperature. (b) Variation of ln(r) with ln(f); inset shows the decrease in conductivity with temperature, and (c) variation of the slope parameter (s) with temperatures at different frequencies.
hopping conduction model in this material. At higher frequencies in region (III), value of s first decreases reaching a minimum value, and then starts increasing again as shown in Fig. 7(c). This behavior of s is in accordance with the overlapping large polaron tunneling model of ac conduction.12 The higher values of activation energy in our case also support this argument.17 The cations surrounded by close packed oxygen anions can be treated as isolated from each other due to little direct overlap of the charge clouds and hence, the localized eg electron model is appropriate. This localization give rise to the formation of the polaron and the charge transport may be considered between the nearest neighbor sites.12,44 The polaronic conduction in this material has been assumed between Fe3þ and Fe2þ due to the presence of defects (i.e., oxygen vacancies, vacancies, agglomerates, and nanovoids) at nanolevels.17 Apparently, the mechanism of ac conduction in the nanostructure NiFe2O4 is different in different frequency ranges. It is expected that the correlated barrier hopping conduction mechanism dominates in this material owing to the presence of the [Fe3þ–O2"–Fe3þ] and [Ni2þ–O2"–Ni2þ] linkage in the lattice. The formation of hopping ion pairs depends upon the occupancy of Ni-ions at the octahedral B-site. However, a clear understanding of the conduction mechanism in this nanostructure NiFe2O4 needs further investigation.
possible correlation to the microstructure of the material. Grain and grain boundary phases are well resolved by impedance plan plots. The parameters Rg, Rgb, Qg, Qgb, ng, and ngb coupled with the grain and grain boundaries are explained using an equivalent circuit model. Thermal activation of trapped charges/dipoles has been found to be responsible for decreasing the resistance of the grain and grain boundaries and an increase in the value of the dielectric constant and tangent loss. The change in slope of the Arrhenius plot around 318 K has been discussed on the basis of hopping between Fe3þ–Fe2þ and Ni2þ–Ni3þ ions and hopping has been suggested as a dominant ac conduction mechanism in this material. As the magnetization study illustrated, surface spin canting of the nanoparticles due to the broken exchange bond and anisotropy is responsible for the weakening of the AB-exchange interaction and hence a lower value of room temperature magnetization. Semiconductor to metallic transition around 358 K has been reported and discussed in terms of the transition from localized charge carrier [Fe3þ–O2"–Fe3þ]/[Ni2þ–O2"–Ni2þ] linkages to delocalized charge carrier [Fe3þ–Fe2þ]/[Ni2þ–Ni3þ] linkages.
ACKNOWLEDGMENTS
One of the authors, M. Atif, acknowledges the Higher Education Commission (HEC), Islamabad Pakistan, for the grant of the PhD scholarship.
IV. CONCLUSIONS 1
It has been shown that impedance spectroscopy is an excellent technique to investigate the electrical transition with the
S. Son, M. Taheri, E. Carpenter, V. G. Harris, and M. E. McHenry, J. Appl. Phys. 91, 7589 (2002). 2 M. Sugimoto, J. Am. Ceram. Soc. 82, 269 (1999).
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