# Optical, X-Ray Diffraction, and Magnetic Properties  of the Cobalt-Substituted Nickel Chromium Ferrites

Authors: Sonal  Singhal; Santosh Bhukal; Jagdish Singh; Kailash Chandra; S. Bansal
Journal: Journal of Nanotechnology
 (2011)

---

## Abstract

Cobalt-substituted nickel chromium ferrites (CrCoxNi1−xFeO4, x=0, 0.2, 0.4, 0.6, 0.8, 1.0) have been synthesized using sol-gel autocombustion method and annealed at 400 ∘C, 600 ∘C, 800 ∘C, and 1000 ∘C. All the ferrite samples have been characterized using UV-VIS spectrophotometery, FT-IR spectroscopy, Transmission Electron Microscopy, powder X-Ray Diffraction, and magnetic measurements.  Typical FT-IR spectra of the samples annealed at 400∘C, 600∘C, 800∘C, and 1000∘C exhibit two frequency bands in the range of ~480 cm−1 and ~590 cm−1 corresponding to the formation of octahedral and tetrahedral clusters of metal oxide, respectively. TEM images reveal that crystallite size increases from ~10 nm to ~45 nm as the annealing temperature is increased from 400∘C to 1000∘C. The unit cell parameter “a” is found to increase on increasing the cobalt concentration due to larger ionic radius of cobalt. Also, as the cobalt concentration increases, the saturation magnetization increases from 4.32 to 19.85 emu/g. This is due to the fact that cobalt ion replaces the less magnetic nickel ions. However, the coercivity decreases with increase in cobalt concentration due to the decrease in anisotropy field. The band gap has been calculated using UV-VIS spectrophotometry and has been found to decrease with the increase of particle size.


---

## Body

## 1. Introduction

Magnetic nanoferrite particles have generated diverse technological interests because of their potential applications in magnetic fluids, high frequency magnets, magnetic bulk cores, microwave absorbers, and high-density data storage [1, 2]. Among the various ferrites, nickel ferrites and cobalt ferrites have been extensively used in electronic devices because of their large permeability at high frequency, remarkably high electrical resistivity, mechanical hardness, chemical stability, and cost-effectiveness [3, 4]. Substituted nickel ferrites are widely used as magnetic materials due to their high electrical resistivity, low eddy current, and dielectric losses [5, 6].The magnetic properties of materials are strongly affected when the particle size approaches a critical diameter, below which each particle is a single domain. As a result the influence of thermal energy over the magnetic moment ordering leads to super paramagnetic relaxation [7, 8]. Cobalt and nickel, both the ferrites, belong to the category of inverse spinel ferrites. Therefore, by substituting the Co2+, Ni2+, and/or Fe3+ ions by suitable cations, their structures undergo a change from inverse spinel to mixed spinel, leading to a corresponding change in the magnetic properties. Thus, by the choice of the cations as well as their distribution in tetrahedral and octahedral sites of the lattice, interesting and useful magnetic properties can be obtained [9].The effect of substitution of Fe3+ by Cr3+ in NiFe2O4 has been studied by various workers [10–12], and it has been reported that Cr3+ always seeks to the octahedral sites. Lee et al. [10] suggested that Ni2+ moves to tetrahedral site within the range 0.2<x<0.6 and the magnetic moment and Curie temperature decrease with the chromium substitution. Fayek and Ata Allah [11] reported that Cr3+ occupies the octahedral sites for a maximum of x=0.6 and the excess Cr3+ replaces the Fe3+ at the tetrahedral site. Gismelseed and Yousif [12] studied the Cr3+ substituted NiCrxFe1-xO4   (0<x<1.4) prepared through conventional double sintering ceramic technique and suggested that as the Cr3+ substitution increases, the system is slowly converted into a normal spinel structure.Chae et al. [13] reported the magnetic properties of chromium substituted cobalt ferrites prepared using sol-gel method and suggested that the coercivity decreases fast but saturation magnetization decreases slowly with the chromium content. Gabal and Al Angari [14] reported the effect of chromium ion substitution on the electromagnetic properties of nickel ferrite and observed that coercivity increases, whereas the saturation magnetization decreases linearly with the Cr content. They also reported that the Neel’s magnetic moments calculated from expected cation distribution are in confirmation with those obtained from the hysteresis loops for ferrites up to x=0.8.The present work deals with the synthesis of nanoparticles of cobalt-substituted nickel chromium ferrites (CrCoxNi1-xFeO4, where x=0,0.2,0.4,0.6,0.8&1.0) via sol-gel autocombustion method and investigation of their optical, X-ray diffraction, and magnetic properties by means of FT-IR, UV-Vis spectrophotometry, Powder X-ray diffraction, and magnetic measurements.


## 2. Experimental

### 2.1. Preparation ofCrCoxNi1-xFeO4 Nanoparticles

Nanoparticles ofCrCoxNi1-xFeO4 (x=0,0.2,0.4,0.6,0.8&1.0) have been synthesized by sol-gel autocombustion method [15–17]. AR Grade Fe(NO3)3·9H2O, Co(NO3)2·6H2O, Cr(NO3)3·9H2O, Ni(NO3)2·6H2O and citric acid have been used for the synthesis of these ferrites. The nitrates and citric acid were weighed in desired stoichiometric proportions and dissolved separately in minimum amount of distilled water. The individual solutions were then mixed together and the pH value of the solution was adjusted to about 6 by adding 1 M NH4OH solution. The solution was then slowly heated and stirred using a hot plate magnetic stirrer till gels were formed, which were ignited and burnt in a self-propagating combustion manner to obtain lose powder. The powders were annealed at 400°C, 600°C, 800°C, and 1000°C in a muffle furnace for 2 hours.


### 2.2. Physical Measurements

Fourier Transform infrared (FT-IR) spectra have been recorded using Perkin Elmer RX-1 FT-IR spectrophotometer with KBr pellets in the range 4000–400 cm−1. Powder X-ray diffraction studies have been carried out using a Bruker AXS, D8 Advance spectrophotometer with Cu-Kα radiation. Hitachi (H-7500) TEM, operated at 120 kV was used to record the micrographs of the samples. The magnetic properties have been measured at room temperature by a vibrating sample magnetometer (VSM) (155, PAR) up to a magnetic field of ±10 kOe. UV-Visible spectrum was recorded using a Hitachi 330 UV-VIS-NIR spectrophotometer.


## 2.1. Preparation ofCrCoxNi1-xFeO4 Nanoparticles

Nanoparticles ofCrCoxNi1-xFeO4 (x=0,0.2,0.4,0.6,0.8&1.0) have been synthesized by sol-gel autocombustion method [15–17]. AR Grade Fe(NO3)3·9H2O, Co(NO3)2·6H2O, Cr(NO3)3·9H2O, Ni(NO3)2·6H2O and citric acid have been used for the synthesis of these ferrites. The nitrates and citric acid were weighed in desired stoichiometric proportions and dissolved separately in minimum amount of distilled water. The individual solutions were then mixed together and the pH value of the solution was adjusted to about 6 by adding 1 M NH4OH solution. The solution was then slowly heated and stirred using a hot plate magnetic stirrer till gels were formed, which were ignited and burnt in a self-propagating combustion manner to obtain lose powder. The powders were annealed at 400°C, 600°C, 800°C, and 1000°C in a muffle furnace for 2 hours.


## 2.2. Physical Measurements

Fourier Transform infrared (FT-IR) spectra have been recorded using Perkin Elmer RX-1 FT-IR spectrophotometer with KBr pellets in the range 4000–400 cm−1. Powder X-ray diffraction studies have been carried out using a Bruker AXS, D8 Advance spectrophotometer with Cu-Kα radiation. Hitachi (H-7500) TEM, operated at 120 kV was used to record the micrographs of the samples. The magnetic properties have been measured at room temperature by a vibrating sample magnetometer (VSM) (155, PAR) up to a magnetic field of ±10 kOe. UV-Visible spectrum was recorded using a Hitachi 330 UV-VIS-NIR spectrophotometer.


## 3. Results and Discussion

### 3.1. FT-IR Characterization

The FT-IR spectra for all the samples annealed at 400°C, 600°C, 800°C, and 1000°C exhibit two main absorption bands below 1000 cm−1, corresponding to the vibrational modes of the metal oxides of ferrites. The band in the range of ~590 cm−1 is attributed to the stretching mode of the tetrahedral clusters, whereas that in the range of ~470 cm−1 is attributed to the stretching mode of the octahedral clusters [18, 19].  The vibrational mode of the tetrahedral cluster is higher than that of octahedral mode due to shorter edge length of the tetrahedral clusters.


### 3.2. TEM Characterization

The TEM micrographs of all the samples exhibit highly agglomerated particles because of the interfacial surface tension as reported in our earlier studies [20–22]. As the annealing temperature increases from 400°C to 1000°C, the particle size increases from ~10 nm to ~45 nm. Such an increase in grain size has also been reported earlier [23, 24]. It is widely believed that the net decrease in the solid-solid and solid-vapour interface free energy provides the driving force for grain growth during annealing process.


### 3.3. X-Ray Diffraction Studies

The typical X-ray diffraction patterns of the as-obtained CrCo0.6Ni0.4FeO4  and those annealed at 400°C, 600°C, 800°C, and 1000°C for 2 hours are shown in Figure 1. The absence of any peak in the X-ray diffractograph of the as-obtained sample indicates the amorphous nature of the samples. However, the annealed samples exhibit characteristic diffraction peaks of the ferrite. The broad peaks at 400°C signify lower crystallite size of the synthesized sample and as the annealing temperature is increased, the peaks become sharp due to increase in the grain size.Figure 1
X-ray diffraction patterns of CrCo0.6Ni0.4FeO4 (a) as obtained and annealed at (b) 400, (c) 600, (d) 800, and (e) 1000°C.The average crystallite size for all the samples has been calculated from the line broadening of the most intense peak corresponding to (311) plane of the spinel structure using the classical Scherrer equation [25]. It is observed that the particle size increases as the annealing temperature is raised from 400°C to 1000°C, which is also confirmed by the TEM studies.Typical X-ray diffraction patterns for all the ferrites annealed at 1000°C for 2 hours are shown in Figure2. All the samples have been found to be face centred cubic (fcc) with Fd-3m space group. The lattice parameters, calculated using Powley as well as Le-Bail refinement methods (built in TOPAS V2.1 of BRUKER AXS), are listed in Table 1. The lattice parameter “a” has been found to increase with cobalt concentration; this may be due to smaller ionic radius of nickel.Table 1
Lattice parameters, saturation magnetization, coercivity, and energy band gap of the ferrites after annealing at 1000°C.
Ferrites compositionLattice parameter,a(Å)Volume(Å)Saturation magnetization,Ms(emu/ g)CoercivitHc (Oe)Energy band gap,Eg (eV)CrNiFeO48.2974571.244.3215002.30CrNi0.8Co0.2FeO48.3026572.329.752902.27CrNi0.6Co0.4FeO48.3143574.7514.862402.73CrNi0.4Co0.6FeO48.3321578.4517.701902.82CrNi0.2Co0.8FeO48.3567583.5919.851302.62CrCoFeO48.3736587.1313.28382.50Table 2
Cation distribution forCrCoxNi1-xFeO4 annealed at 1000°C.
Ferrites CompositionObserved magnetic moment, (nB)Cation distributionCalculated magnetic momentCrNiFeO40.18(Fe0.8Cr0.2)A[NiCr0.8Fe0.2]BO40.20CrNi0.8Co0.2FeO40.40(Fe0.95Co0.05)A[CrNi0.8Co0.15Fe0.05]BO40.40CrNi0.6Co0.4FeO40.62(Fe0.95Co0.05)A[CrNi0.6Co0.35Fe0.05]BO40.60CrNi0.4Co0.6FeO40.73(Fe0.97Co0.03)A[CrNi0.4Co0.57Fe0.03]BO40.72CrNi0.2Co0.8FeO40.82(Fe0.99Co0.01)A[CrNi0.2Co0.79Fe0.01]BO40.84CrCoFeO40.58(Fe)A[CoCr]BO41.00Figure 2
X-ray diffraction patterns of  (a) CrNi0.2Co0.8FeO4, (b) CrNi0.4Co0.6FeO4, (c) CrNi0.6Co0.4FeO4, (d) CrNi0.8Co0.2FeO4, (e) CrNiFeO4, and (f) CrCrFeO4 annealed at 1000°C.


### 3.4. Magnetic Measurements

Hysteresis loops for all the samples annealed at 600°C and 1000°C are shown in Figures3 and 4, respectively.  It is observed that the saturation magnetization (Ms) increases with the annealing temperature due to increase in particle size [26]. From Table 1, it can be seen that the saturation magnetization, Ms, increases from 4.32 emu/g to 19.85 emu/g on increasing the cobalt concentration from 0 to 0.8. This increase can be understood because of the less magnetic behavior of nickel. However, the saturation magnetisation decreases to 13.28 emu/g, with further increase of cobalt concentration to x=1.0.Figure 3
B-H loops of some typicalCrCoxNi1-xFeO4 ferrites annealed at 600°C.Figure 4
B-H loops of some typicalCrCoxNi1-xFeO4 ferrites annealed at 1000°C.This behaviour can be explained on the basis of the super exchange interaction mechanism. In a cubic system of ferromagnetic spinels, the magnetic order is mainly due to super exchange interactions occurring between the metal ions in theA  and B sublattices. Therefore, it is possible to vary magnetic properties of the samples by varying the cations. According to Neel’s two sublattice model of ferrimagnetism, the magnetic moment per formula unit (in μB), nBN(x) is expressed as [27](1)nBN(x)=MB(x)-MA(x),
where MB and MA are the B- and A-sublattice magnetic moments in μB, respectively. Cation distribution of the ferrites has been estimated using this model and is listed in Table 1, which suggests that cobalt and chromium ions predominantly occupy the octahedral sites, which is consistent with their preference for large octahedral site energy. This causes an increase in the saturation magnetization of the substituted ferrites up to x=0.8.  However, in the case of CoCrFeO4 saturation magnetization decreases because all the iron enters in to the A site. This may be due to the fact that the exchange interaction between A and B sites gets lowered resulting in strengthening of B-B interaction and weakening of A-B interaction, which leads to decrease of saturation magnetization. Therefore in CoCrFeO4 Neel’s magnetic moments calculated from expected cation distribution in comparison with that from the hysteresis loop do not  give the satisfactory result.The variation of the coercivity with average grain size has also been studied. It is observed that as the grain size increases, the value of coercivity (Hc), reaches a maximum value and then decreases. This variation of  Hc  with grain size can be explained on the basis of domain structure, critical diameter, and the anisotropy of the crystal [28, 29]. From Table 1, it is clear that the coercivity decreases with the decrease of nickel concentration. This may be attributed to the decrease in anisotropy field, which in turn decreases the domain wall energy [30, 31]. In the case of CrNiFeO4, the coercivity value is very high 1500 G. This behaviour in coercivity may be understood as described by the Banerjee and O’Reilly [32] on the basis of a new model for cation distribution. This may be due to the fact that the chromium ions enter into the tetrahedral site when x>0.8. According to the cation distribution model [32] when Cr3+ ions occupy tetrahedral sites, they cause a negative trigonal field to be superimposed on the octahedral Cr3+ ions. Due to this a twofold degeneracy of the orbital ground state results in an unquenched orbital angular momentum and a large anisotropy.


### 3.5. Optical Studies

The energy band gaps of all the ferrites have been calculated with the help of optical absorption and percentage transmission data. The absorption and transmission spectra of CrCo0.6Ni0.4FeO4 annealed at 1000°C are shown in Figure 5. The absorption coefficient, α of the nanoparticles has been calculated using the fundamental relationships [33](2)I=Ioe-αt,A=log⁡(I0I),α=2.303(A/t),Figure 5
Plot of absorbance and transmittance as a function of wavelengthλ (nm) for CrCo0.6Ni0.4FeO4 annealed at 1000°C.whereA is the absorbance and  t  is the thickness of the sample. To estimate the energy band gap for all the samples, the graph of  (αhυ)2 versus hυ has been plotted. The intercept of the line at α=0 gives the value of energy band gap. The values of energy band gap for all the samples annealed at 1000°C has been found to be in the range of 2.3–2.8 eV listed in Table 1. It is observed that as the particle size decreases, the energy band gap increases. This may be explained on the basis of Bras’ effective mass model [34, 35] according to which the measured band gap, Eg can be expressed as a function of particle size as(3)Eg*≅Egbulk+ℏ2π22er2(1me+1mh)-1.8e24πεε0r′,
where Egbulk is the bulk energy gap, r is the particle size, me is the effective mass of electrons, mh is the effective mass of holes,  ε  is the relative permittivity, εo is the permittivity of free space, ℏ is the planck’s constant divided by  2π,  and e is the charge on electron.


## 3.1. FT-IR Characterization

The FT-IR spectra for all the samples annealed at 400°C, 600°C, 800°C, and 1000°C exhibit two main absorption bands below 1000 cm−1, corresponding to the vibrational modes of the metal oxides of ferrites. The band in the range of ~590 cm−1 is attributed to the stretching mode of the tetrahedral clusters, whereas that in the range of ~470 cm−1 is attributed to the stretching mode of the octahedral clusters [18, 19].  The vibrational mode of the tetrahedral cluster is higher than that of octahedral mode due to shorter edge length of the tetrahedral clusters.


## 3.2. TEM Characterization

The TEM micrographs of all the samples exhibit highly agglomerated particles because of the interfacial surface tension as reported in our earlier studies [20–22]. As the annealing temperature increases from 400°C to 1000°C, the particle size increases from ~10 nm to ~45 nm. Such an increase in grain size has also been reported earlier [23, 24]. It is widely believed that the net decrease in the solid-solid and solid-vapour interface free energy provides the driving force for grain growth during annealing process.


## 3.3. X-Ray Diffraction Studies

The typical X-ray diffraction patterns of the as-obtained CrCo0.6Ni0.4FeO4  and those annealed at 400°C, 600°C, 800°C, and 1000°C for 2 hours are shown in Figure 1. The absence of any peak in the X-ray diffractograph of the as-obtained sample indicates the amorphous nature of the samples. However, the annealed samples exhibit characteristic diffraction peaks of the ferrite. The broad peaks at 400°C signify lower crystallite size of the synthesized sample and as the annealing temperature is increased, the peaks become sharp due to increase in the grain size.Figure 1
X-ray diffraction patterns of CrCo0.6Ni0.4FeO4 (a) as obtained and annealed at (b) 400, (c) 600, (d) 800, and (e) 1000°C.The average crystallite size for all the samples has been calculated from the line broadening of the most intense peak corresponding to (311) plane of the spinel structure using the classical Scherrer equation [25]. It is observed that the particle size increases as the annealing temperature is raised from 400°C to 1000°C, which is also confirmed by the TEM studies.Typical X-ray diffraction patterns for all the ferrites annealed at 1000°C for 2 hours are shown in Figure2. All the samples have been found to be face centred cubic (fcc) with Fd-3m space group. The lattice parameters, calculated using Powley as well as Le-Bail refinement methods (built in TOPAS V2.1 of BRUKER AXS), are listed in Table 1. The lattice parameter “a” has been found to increase with cobalt concentration; this may be due to smaller ionic radius of nickel.Table 1
Lattice parameters, saturation magnetization, coercivity, and energy band gap of the ferrites after annealing at 1000°C.
Ferrites compositionLattice parameter,a(Å)Volume(Å)Saturation magnetization,Ms(emu/ g)CoercivitHc (Oe)Energy band gap,Eg (eV)CrNiFeO48.2974571.244.3215002.30CrNi0.8Co0.2FeO48.3026572.329.752902.27CrNi0.6Co0.4FeO48.3143574.7514.862402.73CrNi0.4Co0.6FeO48.3321578.4517.701902.82CrNi0.2Co0.8FeO48.3567583.5919.851302.62CrCoFeO48.3736587.1313.28382.50Table 2
Cation distribution forCrCoxNi1-xFeO4 annealed at 1000°C.
Ferrites CompositionObserved magnetic moment, (nB)Cation distributionCalculated magnetic momentCrNiFeO40.18(Fe0.8Cr0.2)A[NiCr0.8Fe0.2]BO40.20CrNi0.8Co0.2FeO40.40(Fe0.95Co0.05)A[CrNi0.8Co0.15Fe0.05]BO40.40CrNi0.6Co0.4FeO40.62(Fe0.95Co0.05)A[CrNi0.6Co0.35Fe0.05]BO40.60CrNi0.4Co0.6FeO40.73(Fe0.97Co0.03)A[CrNi0.4Co0.57Fe0.03]BO40.72CrNi0.2Co0.8FeO40.82(Fe0.99Co0.01)A[CrNi0.2Co0.79Fe0.01]BO40.84CrCoFeO40.58(Fe)A[CoCr]BO41.00Figure 2
X-ray diffraction patterns of  (a) CrNi0.2Co0.8FeO4, (b) CrNi0.4Co0.6FeO4, (c) CrNi0.6Co0.4FeO4, (d) CrNi0.8Co0.2FeO4, (e) CrNiFeO4, and (f) CrCrFeO4 annealed at 1000°C.


## 3.4. Magnetic Measurements

Hysteresis loops for all the samples annealed at 600°C and 1000°C are shown in Figures3 and 4, respectively.  It is observed that the saturation magnetization (Ms) increases with the annealing temperature due to increase in particle size [26]. From Table 1, it can be seen that the saturation magnetization, Ms, increases from 4.32 emu/g to 19.85 emu/g on increasing the cobalt concentration from 0 to 0.8. This increase can be understood because of the less magnetic behavior of nickel. However, the saturation magnetisation decreases to 13.28 emu/g, with further increase of cobalt concentration to x=1.0.Figure 3
B-H loops of some typicalCrCoxNi1-xFeO4 ferrites annealed at 600°C.Figure 4
B-H loops of some typicalCrCoxNi1-xFeO4 ferrites annealed at 1000°C.This behaviour can be explained on the basis of the super exchange interaction mechanism. In a cubic system of ferromagnetic spinels, the magnetic order is mainly due to super exchange interactions occurring between the metal ions in theA  and B sublattices. Therefore, it is possible to vary magnetic properties of the samples by varying the cations. According to Neel’s two sublattice model of ferrimagnetism, the magnetic moment per formula unit (in μB), nBN(x) is expressed as [27](1)nBN(x)=MB(x)-MA(x),
where MB and MA are the B- and A-sublattice magnetic moments in μB, respectively. Cation distribution of the ferrites has been estimated using this model and is listed in Table 1, which suggests that cobalt and chromium ions predominantly occupy the octahedral sites, which is consistent with their preference for large octahedral site energy. This causes an increase in the saturation magnetization of the substituted ferrites up to x=0.8.  However, in the case of CoCrFeO4 saturation magnetization decreases because all the iron enters in to the A site. This may be due to the fact that the exchange interaction between A and B sites gets lowered resulting in strengthening of B-B interaction and weakening of A-B interaction, which leads to decrease of saturation magnetization. Therefore in CoCrFeO4 Neel’s magnetic moments calculated from expected cation distribution in comparison with that from the hysteresis loop do not  give the satisfactory result.The variation of the coercivity with average grain size has also been studied. It is observed that as the grain size increases, the value of coercivity (Hc), reaches a maximum value and then decreases. This variation of  Hc  with grain size can be explained on the basis of domain structure, critical diameter, and the anisotropy of the crystal [28, 29]. From Table 1, it is clear that the coercivity decreases with the decrease of nickel concentration. This may be attributed to the decrease in anisotropy field, which in turn decreases the domain wall energy [30, 31]. In the case of CrNiFeO4, the coercivity value is very high 1500 G. This behaviour in coercivity may be understood as described by the Banerjee and O’Reilly [32] on the basis of a new model for cation distribution. This may be due to the fact that the chromium ions enter into the tetrahedral site when x>0.8. According to the cation distribution model [32] when Cr3+ ions occupy tetrahedral sites, they cause a negative trigonal field to be superimposed on the octahedral Cr3+ ions. Due to this a twofold degeneracy of the orbital ground state results in an unquenched orbital angular momentum and a large anisotropy.


## 3.5. Optical Studies

The energy band gaps of all the ferrites have been calculated with the help of optical absorption and percentage transmission data. The absorption and transmission spectra of CrCo0.6Ni0.4FeO4 annealed at 1000°C are shown in Figure 5. The absorption coefficient, α of the nanoparticles has been calculated using the fundamental relationships [33](2)I=Ioe-αt,A=log⁡(I0I),α=2.303(A/t),Figure 5
Plot of absorbance and transmittance as a function of wavelengthλ (nm) for CrCo0.6Ni0.4FeO4 annealed at 1000°C.whereA is the absorbance and  t  is the thickness of the sample. To estimate the energy band gap for all the samples, the graph of  (αhυ)2 versus hυ has been plotted. The intercept of the line at α=0 gives the value of energy band gap. The values of energy band gap for all the samples annealed at 1000°C has been found to be in the range of 2.3–2.8 eV listed in Table 1. It is observed that as the particle size decreases, the energy band gap increases. This may be explained on the basis of Bras’ effective mass model [34, 35] according to which the measured band gap, Eg can be expressed as a function of particle size as(3)Eg*≅Egbulk+ℏ2π22er2(1me+1mh)-1.8e24πεε0r′,
where Egbulk is the bulk energy gap, r is the particle size, me is the effective mass of electrons, mh is the effective mass of holes,  ε  is the relative permittivity, εo is the permittivity of free space, ℏ is the planck’s constant divided by  2π,  and e is the charge on electron.


## 4. Conclusion

CrCoxNi1-xFeO4, x=0,0.2,0.4,0.6,0.8&1.0 have been synthesized using the sol-gel autocombustion method. The formation of the ferrite powders has been confirmed by FT-IR and XRD studies. The TEM studies confirm that as the annealing temperature increases particle size increases up to 45 nm. The values of saturation magnetization increases and coercivity decreases with increasing Co3+ content. The values of energy band gap have been found to range ~2.5 eV. However, the band gap increases up to ~3.0 eV with the decrease of the particle size from ~45 nm to ~10 nm.



---

*Source: 930243-2011-05-22.xml*