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Microstructure characterization and cation distribution of nanocrystalline cobalt ferrite
Journal of Magnetism and Magnetic Materials 323 (2011) 2748–2756
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Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Microstructure characterization and cation distribution of nanocrystalline cobalt ferrite Y.M. Abbas, S.A. Mansour, M.H. Ibrahim, Shehab E. Ali n Suez Canal University, Faculty of Science, Physics Department, Ismailia, Egypt
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 October 2010 Received in revised form 19 May 2011 Available online 14 June 2011
Nanocrystalline cobalt ferrite has been synthesized using two different methods: ceramic and co-precipitation techniques. The nanocrystalline ferrite phase has been formed after 3 h of sintering at 1000 1C. The structural and microstructural evolutions of the nanophase have been studied using X-ray powder diffraction and the Rietveld method. The refinement result showed that the type of the cationic distribution over the tetrahedral and octahedral sites in the nanocrystalline lattice is partially an inverse spinel. The transmission electronic microscope analysis confirmed the X-ray results. The magnetic properties of the samples were characterized using a vibrating sample magnetometer. & 2011 Elsevier B.V. All rights reserved.
Keywords: Cobalt ferrite Microstructural Rietveld Cationic distribution
1. Introduction Nanocrystalline spinel ferrites have been investigated intensively in recent years due to their potential applications in nonresonant devices, radio frequency circuits, high quality filters, rod antennas, transformer cores, read/write heads for high-speed digital tapes and operating devices [1–6]. Cobalt ferrite, CoFe2O4, is a hard magnetic material [7], which finds a number of applications in heterogeneous catalysis, adsorption, sensors and in magnetic technologies. Solid-state processing technique is very suitable for the preparation of nanocrystalline ferrite powders exhibiting many of the useful properties listed above [8–11]. Ferrites have the general formula (M1 xFex) [MxFe2 x]O4. The divalent metal element M (Mg, Zn, Mn, Fe, Co, Ni or mixture of them) can occupy either tetrahedral (A) or octahedral [B] sites in the cubic, spinel-type structure. The structural formula of Co-ferrite is usually written as (Co1 xFex)[CoxFe2 x]O4, where x represents the degree of inversion (defined as the fraction of (A) sites occupied by Fe3 þ cations). The magnetic properties of a spinel ferrite are strongly dependent on the distribution of different cations among (A) and [B] sites. It has been also experimentally verified that the distribution of cations among the lattice sites depends on material’s preparation. This often leads to a variation in the unit cell dimensions. Both variations are seen as broadening and/or shift of the diffraction lines. As the ionic radii of Co2 þ and Fe3 þ are quite different, different
n
Corresponding author. E-mail addresses: [email protected] (Y.M. Abbas), [email protected] (S.E. Ali). 0304-8853/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2011.05.038
distributions of cations will also lead to different lattice strain. All these effects may be accounted for the analysis of the profiles of the peaks in the powder diffraction pattern. Physical properties of materials depend upon their microstructure and, therefore, its knowledge is an important prerequisite to controlling material’s performance. Rietveld analysis [12–14] has been adopted in the present study to determine the microstructural parameters of nanocrystalline CoFe2O4. The analysis aims to (i) characterizing the prepared materials in terms of microstructural parameters such as crystallite size and lattice strain and (ii) estimating the distribution of cations among (A) and [B] sites in the spinel lattice.
2. Experimental techniques Ferrite materials are commonly prepared by two techniques: ceramic technique and co-precipitation technique, in order to make a comparison between the estimated structure parameters, which affect the particle size and magnetic properties of cobalt ferrite. 2.1. Preparation techniques 2.1.1. Ceramic technique The nanocrystalline CoFe2O4 was prepared by the ceramic technique. Accurately weighed powders of CoO (99.9% purity) and Fe2O3 (99.9% purity) were mixed together using Triple distilled water as mixing medium in mortar, then dried at 200 1C for 2 h, and then milled for 4 min in a Blender (18,000 rpm). The milled powder was presintered to 500 1C for 3 h, followed by rapid cooling to room temperature, then remilled again for another 4 min. The pre-firing
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mixture was sintered at 1000 1C for 3 h, after that remilled again for 2 min. All sintering processes are carried in open air. 2.1.2. Chemical co-precipitation method The nanocrystalline CoFe2O4 was prepared by the co-precipitation method. Stochiometric quantities of analytical grade CoSO4 7H2O, NH4Fe(SO4)2 12H2O and SnCl4 5H2O. 0.5 M solutions of the material were mixed to each other. The NH4OH solution was continuously added to increase the pH value to 9. After the reaction, the precipitated particles are washed by Triple distilled water and filtered several times by Gush (filter crucible) G5, then dried. The co-precipitated ferrite particles were presintered at 500 1C for 3 h and then milled for 4 min in a Blender (18,000 rpm). The presintered powder was sintered to 1000 1C for 3 h, then remilled again for another 2 min. All sintering processes are carried out in open air. 2.2. Characterization techniques The X-ray powder diffraction patterns of the samples were collected on a Brucker Axs-D8 Advance powder diffractometer with a goniometer using Cu K-Alpha radiation. The diffracted intensities were collected in step-scan mode (step size 2y ¼0.021; counting time 2 s) in the angular range 2y ¼10–801. To correct instrumental broadening a Si standard [15] was used. Microstructure characterization of the powder has also been done using TEM (Model JEM 1230, JEOL, Japan). LDJ (Model 9600) vibrating sample magnetometer (VSM) is used for the magnetic measurement.
Fig. 1. X-ray diffraction pattern for CoFe2O4 prepared by ceramic technique and co-precipitation technique sintering at1000 1C for 3 h.
3. Rietveld analysis of the experimental data 3.1. Method of analysis In the Rietveld analysis, we employed the program FULLPROF; it is designed to refine simultaneously both the structural (lattice cell constants and atomic positions and occupancies) and microstructural parameters (crystallite size and lattice strain). The shape of the peaks in the experimental diffraction patterns was well described by an asymmetric pseudo-Voigt (pV) function. To simulate the theoretical X-ray powder diffraction patterns of Co-ferrite (inverse spinel) the following considerations for the different phases were made: 1- Identification of the phases by computer search-match to compare experimental pattern with the International Centre for Diffraction Data (ICDD) database of known compounds. 2- Index the diffraction pattern to determine the crystal system, unit cell dimensions and space group. Cobalt ferrite (face centered cubic, space group: Fd-3m(227), a ¼0.83919 nm (ICDD PDF 22–1086))
3.2. Crystal structure refinement A detailed account of the mathematical procedures implemented in the Rietveld analysis has been reported elsewhere [16–22]. Here, we give a brief, step-by-step description of the analysis of experimental powder diffraction patterns done by us. First, the positions of the peaks were corrected for zero-shift error by successive refinements. Considering the integrated intensity of the peaks to be a function of the refined structural parameters, the Marquardt least-squares procedure was adopted to minimize the difference between the observed and simulated powder diffraction patterns. The progress of the minimization was monitored through the usual reliability parameters, Rwp (weighted residual factor) and Rexp
Fig. 2. (h2 þ K2 þ l2)1/2 vs (1/d) for the CoFe2O4 prepared by (a) ceramic technique and (b) co-precipitation technique.
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(expected residual factor), defined as "P
2 i wi ðIo Ic Þ P 2 i wi ðIo Þ
Rwp ¼ "
Rexp ¼ P
concentration (weight fraction) in the mixture. We used it to obtain the weight fraction (wi) for each phase as follows: S ðZMVÞi wi ¼ P i j Sj ðZMVÞj
#1=2
NP
i wi ðIo Þ
#1=2
where Sj is the refined scale factor of phase i, Z is the number of formula units per unit cell, M is the atomic weight of the formula unit and V is the volume of the unit cell.
2
where Io and Ic are the experimental and calculated intensities, respectively, wi ¼1/Io are weight factors, N is the number of experimental observations and P is the number of refined parameters. Also, we used the so-called goodness of fit (GoF) factor [18–22] Rwp GoF ¼ Rexp Refinements were carried out until convergence was reached and the value of the GoF factor became close to 1 (usually, the final GoF varies from 1.1 to 1.3). There is a simple relationship [19–22] between the individual scale factor determined of a crystalline phase in a multiphase material, and the phase
3.3. Size-strain analysis It has been well established that the observed broadening of the diffraction peaks is mainly due to the small crystallite size and the presence of root mean square (r.m.s.) strain inside the crystallites. The crystallite size and strain broadening can be approximated with Cauchy and Gaussian type functions, respectively [15,19–22]. Thus, the basic consideration of the method employed in the Rietveld analysis by us is the modeling of the diffraction profiles with an analytical function, which is a combination of Cauchy and Gauss as well as a function taking into account the asymmetry in the
Fig. 3. Profile fitting for CoFe2O4 prepared by (a) ceramic technique and (b) co-precipitation technique.
Y.M. Abbas et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 2748–2756
diffraction profile. Again, the process of successive profile refinements was adopted to refine the crystallite size and strain in the studied materials. The refinement was continued until convergence was reached and the value of the quality factor (GoF) approached 1.
4. Results and discussion 4.1. XRD analysis The X-ray diffraction patterns of polycrystalline CoFe2O4 prepared by the ceramic technique and the co-precipitation technique at 1000 1C for 3 h are shown in Fig. 1. The figure shows that the peak corresponding to the planes (3 1 1), (4 4 0) and (2 2 0) confirms the phase formation of pure CoFe2O4 with a well defined spinel structure without any impure phase and coinciding with the (ICDD PDF: 22-1086). Graphical representation of the variation of the (h2 þK2 þ l2)1/2 vs (1/d) is shown in Fig. 2.
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4.2. Refinement of XRD data FULLPROF Rietveld software program has been used for Rietveld XRD data analysis for CoFe2O4. It is designed to refine simultaneously both the structural (lattice cell constants and atomic positions and occupancies) and microstructural parameters (crystallite size and lattice strain). All refinements were performed in space group: Fd-3m. Atomic scattering factor for fully ionized atoms Co2 þ , Fe3 þ and O2- were taken from the international table for crystallography volume C (1992). Starting cell parameter was taken from the results of the precedent section and the oxygen parameter starting values were taken as the ideal atomic position of the ion O2 ¼0.25. In each refinement, a total of more than twenty parameters were refined: zero shift, scale factor, back ground coefficients, three lattice constants, asymmetry parameter, three oxygen parameters for isotropic temperature factor and parameter for the full width at half maximum.
Fig. 4. Zoom out of a part of the pattern for the profile fitting of CoFe2O4 sintered at 1000 1C, prepared by (a) ceramic technique and (b) co-precipitation technique.
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The Rietveld plots of the refinements for the ceramic and co-precipitation prepared systems are given in Fig. 3. In the figure the observed intensity data, y, is plotted in the upper field as points. The calculated patterns are shown in the same field as a solid-line curve. The difference, observed minus calculated, is shown in the lower field. The short vertical bars in the middle field indicate the positions of possible Bragg reflections. Fig. 4 zooms out a part of the pattern of the profile fitting for the CoFe2O4 ceramic and co-precipitation prepared systems to indicate the agreement between the observed and calculated data. Tables 1 and 2 depict the refinement, fitting parameters, lattice ˚ and oxygen parameter for CoFe2O4. parameter a (A) 4.2.1. Cations distribution It is well known that the magnetic properties of spinel ferrites depend on the summation of the magnetic moments at (A) and [B] sites [23]. It has also been experimentally verified that the distribution of cations among the lattice sites depends on the material preparation. This often leads to a variation in the unit cell dimensions. Both variations are seen as broadening and/or shift of the diffraction lines. Various techniques have been applied to characterize the spinel ferrites in order to understand their intrinsic magnetic properties. Profile fitting by Rietevld analysis is the most general method to determine the site occupation factors. All these effects may be accounted for the analysis of the peak profiles in the powder diffraction pattern. Cation distributions on (A) and [B] sites for cobalt ferrite are shown in Table 3. The refinement result showed that the nanocrystalline ferrite phase is partially an inverse spinel. The information of mixed spinel instead of inverse spinel may result due to the decrease in the occupancy of Fe3 þ cation on (A) site during the formation of spinel ferrite. At the same time, the occupancy of Co2 þ cation on [B] site decreases and then increases on (A) site. This occurs when there is a random distribution of cations among the (A) and [B] sites inside the spinel matrix.
4.2.2. Inter-atomic distance and the inter bond angles The value of inter-atomic distance between the cations for the tetragonal (A) and octahedral [B] sites can be characterized with the help of the following relations [24]: pffiffiffi! 3 MA MA ¼ a 4 MA MB ¼
MB MB ¼
pffiffiffiffi
p
4
a
pffiffiffi! 2 a 4
pffiffiffi 1 MA OA ¼ a 3 d þ 8 1=2 pffiffiffi 1 d 2 þ3d MB OB ¼ a 3 16 2 where d is the deviation from oxygen parameter (U), d ¼U–Uideal, and R0 ¼radius of oxygen ion¼1.35 A˚ [25]. The determination of inter-atomic distance and the inter bond angles are amenable method to give a full description of the crystallographic structure and the magnetic properties, where MA and MB refer to the cations at the center of the tetrahedral (A) and octahedral [B] sites, respectively, while OA and OB refer to the Table 3 Cation distribution on A-site and B-site for CoFe2O4. Method
Composition
Cation distribution (A site)
Cation distribution [B site]
Ceramic Co-precipitation
CoFe2O4 CoFe2O4
(Co0.19895Fe0.80105) (Co0.17899Fe0.82101)
[Co0.80105Fe1.19895] [Co0.82101Fe1.17899]
Table 1 Refinement result for CoFe2O4. Miller Indices
Ceramic technique
Co-precipitation technique
h
k
l
2h
Iobs
Icalc
9Iobs Icalc9
2h
Iobs
Icalc
9Iobs Icalc9
1 2 3 2 4 3 4 3 5 4 5 4 6 5 6 4
1 2 1 2 0 3 2 3 1 4 3 4 2 3 2 4
1 0 1 2 0 1 2 3 1 0 1 2 0 3 2 4
18.326 30.145 35.508 37.143 43.155 47.251 53.54 57.075 57.075 62.677 65.902 66.959 71.109 74.154 75.159 79.134
11.4 28.2 106.2 9.70 24.3 0.90 11.2 7.3 27.5 48.8 0.7 0.0 3.1 10.3 5.0 4.1
8.30 30.3 108.5 9.10 22.3 0.80 10.5 7.20 27.1 45.9 1.0 0.0 4.0 9.9 4.9 2.8
3.1 2.1 2.3 0.7 2.1 0.1 0.7 0.1 0.4 3.0 0.3 0.0 0.9 0.4 0.1 1.3
18.324 30.141 35.503 37.138 43.149 47.244 53.533 57.067 57.067 62.667 65.892 66.949 71.098 74.143 75.147 79.121
10.1 28.7 133.3 7.6 23.7 0.9 10.8 6.8 30 48.7 0.6 0 3.7 9.2 5.1 3.6
5.8 28.5 141 6.8 24.9 0.7 12.2 6.7 29.8 41.2 0.5 0 4.9 9.2 3.7 2.2
4.3 0.2 7.7 0.8 1.3 0.1 1.4 0.1 0.3 7.5 0.2 0 1.1 0 1.4 1.4
Table 2 ˚ and oxygen parameter for CoFe2O4. Fitting parameters, lattice parameter a (A) Method
Composition
GoF
Bragg R-factor
RF factor
˚ a (A)
U
Ceramic Co-precipitation
CoFe2O4 CoFe2O4
1.140 1.281
5.838 8.592
4.604 6.509
8.378315 8.379406
0.25501 0.25413
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Table 4 Calculated values of inter-atomic distances for nanocrystalline CoFe2O4. Method
Composition
MA MA
MA MB
MB MB
MA OA
MB OB
Ceramic Co-precipitation
CoFe2O4 CoFe2O4
3.6279168 3.6283892
3.7132912 3.7137748
2.9621817 2.9625674
1.8866619 1.8741356
2.0534616 2.0608258
Table 5 Calculated values of magnetic moment for nanocrystalline CoFe2O4. Method
Composition
MA (mB)
MB (mB)
m (molecule)
Ceramic Co-precipitation
CoFe2O4 CoFe2O4
4.6021 4.64202
8.3979 8.35798
3.7958 3.71596
Table 6 Average crystallite size and lattice strain for nanocrystalline CoFe2O4. Method
Composition
Average crystallite size (nm)
Lattice strain (%)
Ceramic Co-precipitation
CoFe2O4 CoFe2O4
34.026151 50.18498
0.2742 0.1877
center of oxygen anions related to the tetrahedral (A) and octahedral [B] configurations, respectively. The calculated values of these distances for nanocrystalline CoFe2O4 are listed in Table 4. 4.2.3. Magnetic structure model One of the most important results obtained from the cation distribution in ferrites is the evaluation of the magnetic structure model for these materials. If the magnetic moment of (A) and [B] sites are MA and MB, respectively, then the net magnetic moment in ferromagnetic material will be 9MB MA9. In our study, the magnetic ions and their magnetic moment, respectively, are Co2 þ ¼3 mB and Fe3 þ ¼5 mB [26]. The calculated magnetic moment is shown in Table 5. 4.2.4. Microstructure analysis The characterization of the prepared materials in terms of microstructural parameters, such as crystallite size and root mean square (r.m.s.) lattice strain, is estimated in Table 6. 4.3. SEM and TEM analysis The microstructure and surface morphology were observed with a scanning electron microscopy (SEM). SEM representative micrograph for the nanocrystalline Co ferrite is shown in Fig. 5. The surface morphology of all the samples as seen from the SEM consists of well-crystallized grains, with relatively homogeneous grain distribution and an average grain size smaller than 100 nm. Transmission electron microscopy (TEM) is considered the main method for characterizing the microstructure of nanocrystalline materials (the particle size and shape of the particles) [27]. TEM micrograph for CoFe2O4 samples are shown in Fig. 6. TEM micrograph revealed that the particles of the sample are spherical in shape and the average size of the particles ( E52.8 nm) for co-precipitation and ( E34.88 nm) for ceramic, which are quite closer to the X-ray crystallite size. The shape of the precipitated CoFe2O4 particles becomes regular and the distribution of particle size is uniform. The non-uniform particles size distribution should attribute to a non-uniform ingredient mixture and a non-uniform grain distribution of powder. 4.4. Magnetic measurements (vibrating sample magnetometer) (VSM) The hysteresis loops were identified and characterized to determine parameters, such as the saturation magnetization (Bs), remnant magnetization (Br) and coercivity (Hc). The magnetic properties of powders have been determined at room temperature using a vibrating sample magnetometer in the maximum
Fig. 5. SEM for CoFe2O4 prepared by (a) ceramic technique and (b) co-precipitation technique.
external field of 16 kOe. The hysteresis loops for the nanocrystalline CoFe2O4 prepared by ceramic and co-precipitation methods are shown in Fig. 7. Magnetic parameter for the system prepared by ceramic and co-precipitation methods are listed in Table 7. The site occupancies of magnetic ions at the tetrahedral and octahedral sites define the saturation magnetization. Magnetic cation distribution reflects the saturation magnetization of the sample. According to the anti-parallel magnetic spin in the tetrahedral and octahedral sites in the spinel lattice, the following
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Fig. 6. TEM for CoFe2O4 prepared by (a) ceramic method and (b) co-precipitation method.
magnetic spin configuration can be estimated as shown in Fig. 8. The magnetic moment m would be expressed as (3þ4x) mB as a function of composition x. Ceramic and co-precipitation techniques show saturation magnetization values to be 64.63 and 56.22 emu/g, respectively. The difference in the saturation magnetization is due to the difference in cation distribution at the tetrahedral and octahedral sites [28]. Table 7 shows that saturation magnetization of the Co ferrite prepared by co-precipitation was found to be 56.22 emu/g, which is lower than CoFe2O4 bulk (65 emu/g) [29]. This behavior is attributed to the nature of disordered surface effects of the small
particles [30,31], which appear as a result of the finite size of nanocrystallites and which lead to a non-collinearity of the magnetic moments at the nanocrystallites surface. These effects are getting more intense when the mean size of the nanocrystallites is getting smaller and the surface/volume ratio is increasing. The decrease in saturation magnetization with decreasing particle size has been reported by Morrish and Haneda [32]. The decrease in the saturation magnetization in the case of nanoparticles systems was also observed by other authors [33,34]; one can also note that the coercivity is the largest for the co-precipitation prepared samples. This can be attributed to the
Y.M. Abbas et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 2748–2756
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Fig. 7. Plots of magnetization vs applied field for the nanocrystalline CoFe2O4.
Table 7 Magnetic parameters obtained from magnetization curves for CoFe2O4. Method
Composition
Hc (Oe)
Bs (emu/g)
Br (emu/g)
R ¼ Br/Bs
Average crystalline size (nm)
Ceramic Co-precipitation
CoFe2O4 CoFe2O4
432.5 797.4
64.62723 56.22
14.231 20.19
0.220201 0.359125
34.88 52.80
the co-precipitation method, while the coercive force (Hc) for the prepared sample by the co-precipitation method is larger than the one prepared by the ceramic method. The distribution of cations among the lattice sites depends on methods of preparation.
Fig. 8.. Magnetic model for CoFe2O4.
smallest size of the co-precipitation prepared particles compared to ceramic prepared particles. This represents that magnetic properties depend on the preparation technique and magnetic behavior is related to the variation of the particle size.
5. Conclusion The refinement of X-ray results for the obtained samples by ceramic and co-precipitation methods showed a nanocrystalline ferrite phase with average values of particle size 34 and 50.18 nm, respectively. The prepared nanocrystalline ferrite phase is partially an inverse spinel due to the random distribution of cations among the (A) and [B] sites inside the spinel matrix. The SEM micrographs for all samples show well crystallized grains, with relatively homogeneous grain distribution. Micrographs of TEM show spherical grains with average particles size 34.88 and 52.80 nm, which are quite closer to the X-ray crystallite size for samples prepared by the ceramic and co-precipitation methods, respectively. The magnetic properties of the samples, clearly, depend on the size of the nanocrystallites, the distribution of the different cations among (A) and [B] sites and the methods of preparation. The ceramic method gives sample with value of saturation magnetization (Bs) larger than the one prepared by
Acknowledgment The authors would deeply like to thank Prof. Dr. Aisha M. Moustafa (Physics Division, Solid State Department, X-ray Crystallography Lab, National Research Center, Dokki, Cairo, Egypt), Dr. Salah A. Shata (Geophysics Department, Science Faculty, Suez Canal University) and Dr. Ahmed M. Nawar (Physics Department, Science Faculty, Suez Canal University) for good discussions.
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Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Microstructure characterization and cation distribution of nanocrystalline cobalt ferrite Y.M. Abbas, S.A. Mansour, M.H. Ibrahim, Shehab E. Ali n Suez Canal University, Faculty of Science, Physics Department, Ismailia, Egypt
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 October 2010 Received in revised form 19 May 2011 Available online 14 June 2011
Nanocrystalline cobalt ferrite has been synthesized using two different methods: ceramic and co-precipitation techniques. The nanocrystalline ferrite phase has been formed after 3 h of sintering at 1000 1C. The structural and microstructural evolutions of the nanophase have been studied using X-ray powder diffraction and the Rietveld method. The refinement result showed that the type of the cationic distribution over the tetrahedral and octahedral sites in the nanocrystalline lattice is partially an inverse spinel. The transmission electronic microscope analysis confirmed the X-ray results. The magnetic properties of the samples were characterized using a vibrating sample magnetometer. & 2011 Elsevier B.V. All rights reserved.
Keywords: Cobalt ferrite Microstructural Rietveld Cationic distribution
1. Introduction Nanocrystalline spinel ferrites have been investigated intensively in recent years due to their potential applications in nonresonant devices, radio frequency circuits, high quality filters, rod antennas, transformer cores, read/write heads for high-speed digital tapes and operating devices [1–6]. Cobalt ferrite, CoFe2O4, is a hard magnetic material [7], which finds a number of applications in heterogeneous catalysis, adsorption, sensors and in magnetic technologies. Solid-state processing technique is very suitable for the preparation of nanocrystalline ferrite powders exhibiting many of the useful properties listed above [8–11]. Ferrites have the general formula (M1 xFex) [MxFe2 x]O4. The divalent metal element M (Mg, Zn, Mn, Fe, Co, Ni or mixture of them) can occupy either tetrahedral (A) or octahedral [B] sites in the cubic, spinel-type structure. The structural formula of Co-ferrite is usually written as (Co1 xFex)[CoxFe2 x]O4, where x represents the degree of inversion (defined as the fraction of (A) sites occupied by Fe3 þ cations). The magnetic properties of a spinel ferrite are strongly dependent on the distribution of different cations among (A) and [B] sites. It has been also experimentally verified that the distribution of cations among the lattice sites depends on material’s preparation. This often leads to a variation in the unit cell dimensions. Both variations are seen as broadening and/or shift of the diffraction lines. As the ionic radii of Co2 þ and Fe3 þ are quite different, different
n
Corresponding author. E-mail addresses: [email protected] (Y.M. Abbas), [email protected] (S.E. Ali). 0304-8853/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2011.05.038
distributions of cations will also lead to different lattice strain. All these effects may be accounted for the analysis of the profiles of the peaks in the powder diffraction pattern. Physical properties of materials depend upon their microstructure and, therefore, its knowledge is an important prerequisite to controlling material’s performance. Rietveld analysis [12–14] has been adopted in the present study to determine the microstructural parameters of nanocrystalline CoFe2O4. The analysis aims to (i) characterizing the prepared materials in terms of microstructural parameters such as crystallite size and lattice strain and (ii) estimating the distribution of cations among (A) and [B] sites in the spinel lattice.
2. Experimental techniques Ferrite materials are commonly prepared by two techniques: ceramic technique and co-precipitation technique, in order to make a comparison between the estimated structure parameters, which affect the particle size and magnetic properties of cobalt ferrite. 2.1. Preparation techniques 2.1.1. Ceramic technique The nanocrystalline CoFe2O4 was prepared by the ceramic technique. Accurately weighed powders of CoO (99.9% purity) and Fe2O3 (99.9% purity) were mixed together using Triple distilled water as mixing medium in mortar, then dried at 200 1C for 2 h, and then milled for 4 min in a Blender (18,000 rpm). The milled powder was presintered to 500 1C for 3 h, followed by rapid cooling to room temperature, then remilled again for another 4 min. The pre-firing
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mixture was sintered at 1000 1C for 3 h, after that remilled again for 2 min. All sintering processes are carried in open air. 2.1.2. Chemical co-precipitation method The nanocrystalline CoFe2O4 was prepared by the co-precipitation method. Stochiometric quantities of analytical grade CoSO4 7H2O, NH4Fe(SO4)2 12H2O and SnCl4 5H2O. 0.5 M solutions of the material were mixed to each other. The NH4OH solution was continuously added to increase the pH value to 9. After the reaction, the precipitated particles are washed by Triple distilled water and filtered several times by Gush (filter crucible) G5, then dried. The co-precipitated ferrite particles were presintered at 500 1C for 3 h and then milled for 4 min in a Blender (18,000 rpm). The presintered powder was sintered to 1000 1C for 3 h, then remilled again for another 2 min. All sintering processes are carried out in open air. 2.2. Characterization techniques The X-ray powder diffraction patterns of the samples were collected on a Brucker Axs-D8 Advance powder diffractometer with a goniometer using Cu K-Alpha radiation. The diffracted intensities were collected in step-scan mode (step size 2y ¼0.021; counting time 2 s) in the angular range 2y ¼10–801. To correct instrumental broadening a Si standard [15] was used. Microstructure characterization of the powder has also been done using TEM (Model JEM 1230, JEOL, Japan). LDJ (Model 9600) vibrating sample magnetometer (VSM) is used for the magnetic measurement.
Fig. 1. X-ray diffraction pattern for CoFe2O4 prepared by ceramic technique and co-precipitation technique sintering at1000 1C for 3 h.
3. Rietveld analysis of the experimental data 3.1. Method of analysis In the Rietveld analysis, we employed the program FULLPROF; it is designed to refine simultaneously both the structural (lattice cell constants and atomic positions and occupancies) and microstructural parameters (crystallite size and lattice strain). The shape of the peaks in the experimental diffraction patterns was well described by an asymmetric pseudo-Voigt (pV) function. To simulate the theoretical X-ray powder diffraction patterns of Co-ferrite (inverse spinel) the following considerations for the different phases were made: 1- Identification of the phases by computer search-match to compare experimental pattern with the International Centre for Diffraction Data (ICDD) database of known compounds. 2- Index the diffraction pattern to determine the crystal system, unit cell dimensions and space group. Cobalt ferrite (face centered cubic, space group: Fd-3m(227), a ¼0.83919 nm (ICDD PDF 22–1086))
3.2. Crystal structure refinement A detailed account of the mathematical procedures implemented in the Rietveld analysis has been reported elsewhere [16–22]. Here, we give a brief, step-by-step description of the analysis of experimental powder diffraction patterns done by us. First, the positions of the peaks were corrected for zero-shift error by successive refinements. Considering the integrated intensity of the peaks to be a function of the refined structural parameters, the Marquardt least-squares procedure was adopted to minimize the difference between the observed and simulated powder diffraction patterns. The progress of the minimization was monitored through the usual reliability parameters, Rwp (weighted residual factor) and Rexp
Fig. 2. (h2 þ K2 þ l2)1/2 vs (1/d) for the CoFe2O4 prepared by (a) ceramic technique and (b) co-precipitation technique.
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(expected residual factor), defined as "P
2 i wi ðIo Ic Þ P 2 i wi ðIo Þ
Rwp ¼ "
Rexp ¼ P
concentration (weight fraction) in the mixture. We used it to obtain the weight fraction (wi) for each phase as follows: S ðZMVÞi wi ¼ P i j Sj ðZMVÞj
#1=2
NP
i wi ðIo Þ
#1=2
where Sj is the refined scale factor of phase i, Z is the number of formula units per unit cell, M is the atomic weight of the formula unit and V is the volume of the unit cell.
2
where Io and Ic are the experimental and calculated intensities, respectively, wi ¼1/Io are weight factors, N is the number of experimental observations and P is the number of refined parameters. Also, we used the so-called goodness of fit (GoF) factor [18–22] Rwp GoF ¼ Rexp Refinements were carried out until convergence was reached and the value of the GoF factor became close to 1 (usually, the final GoF varies from 1.1 to 1.3). There is a simple relationship [19–22] between the individual scale factor determined of a crystalline phase in a multiphase material, and the phase
3.3. Size-strain analysis It has been well established that the observed broadening of the diffraction peaks is mainly due to the small crystallite size and the presence of root mean square (r.m.s.) strain inside the crystallites. The crystallite size and strain broadening can be approximated with Cauchy and Gaussian type functions, respectively [15,19–22]. Thus, the basic consideration of the method employed in the Rietveld analysis by us is the modeling of the diffraction profiles with an analytical function, which is a combination of Cauchy and Gauss as well as a function taking into account the asymmetry in the
Fig. 3. Profile fitting for CoFe2O4 prepared by (a) ceramic technique and (b) co-precipitation technique.
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diffraction profile. Again, the process of successive profile refinements was adopted to refine the crystallite size and strain in the studied materials. The refinement was continued until convergence was reached and the value of the quality factor (GoF) approached 1.
4. Results and discussion 4.1. XRD analysis The X-ray diffraction patterns of polycrystalline CoFe2O4 prepared by the ceramic technique and the co-precipitation technique at 1000 1C for 3 h are shown in Fig. 1. The figure shows that the peak corresponding to the planes (3 1 1), (4 4 0) and (2 2 0) confirms the phase formation of pure CoFe2O4 with a well defined spinel structure without any impure phase and coinciding with the (ICDD PDF: 22-1086). Graphical representation of the variation of the (h2 þK2 þ l2)1/2 vs (1/d) is shown in Fig. 2.
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4.2. Refinement of XRD data FULLPROF Rietveld software program has been used for Rietveld XRD data analysis for CoFe2O4. It is designed to refine simultaneously both the structural (lattice cell constants and atomic positions and occupancies) and microstructural parameters (crystallite size and lattice strain). All refinements were performed in space group: Fd-3m. Atomic scattering factor for fully ionized atoms Co2 þ , Fe3 þ and O2- were taken from the international table for crystallography volume C (1992). Starting cell parameter was taken from the results of the precedent section and the oxygen parameter starting values were taken as the ideal atomic position of the ion O2 ¼0.25. In each refinement, a total of more than twenty parameters were refined: zero shift, scale factor, back ground coefficients, three lattice constants, asymmetry parameter, three oxygen parameters for isotropic temperature factor and parameter for the full width at half maximum.
Fig. 4. Zoom out of a part of the pattern for the profile fitting of CoFe2O4 sintered at 1000 1C, prepared by (a) ceramic technique and (b) co-precipitation technique.
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The Rietveld plots of the refinements for the ceramic and co-precipitation prepared systems are given in Fig. 3. In the figure the observed intensity data, y, is plotted in the upper field as points. The calculated patterns are shown in the same field as a solid-line curve. The difference, observed minus calculated, is shown in the lower field. The short vertical bars in the middle field indicate the positions of possible Bragg reflections. Fig. 4 zooms out a part of the pattern of the profile fitting for the CoFe2O4 ceramic and co-precipitation prepared systems to indicate the agreement between the observed and calculated data. Tables 1 and 2 depict the refinement, fitting parameters, lattice ˚ and oxygen parameter for CoFe2O4. parameter a (A) 4.2.1. Cations distribution It is well known that the magnetic properties of spinel ferrites depend on the summation of the magnetic moments at (A) and [B] sites [23]. It has also been experimentally verified that the distribution of cations among the lattice sites depends on the material preparation. This often leads to a variation in the unit cell dimensions. Both variations are seen as broadening and/or shift of the diffraction lines. Various techniques have been applied to characterize the spinel ferrites in order to understand their intrinsic magnetic properties. Profile fitting by Rietevld analysis is the most general method to determine the site occupation factors. All these effects may be accounted for the analysis of the peak profiles in the powder diffraction pattern. Cation distributions on (A) and [B] sites for cobalt ferrite are shown in Table 3. The refinement result showed that the nanocrystalline ferrite phase is partially an inverse spinel. The information of mixed spinel instead of inverse spinel may result due to the decrease in the occupancy of Fe3 þ cation on (A) site during the formation of spinel ferrite. At the same time, the occupancy of Co2 þ cation on [B] site decreases and then increases on (A) site. This occurs when there is a random distribution of cations among the (A) and [B] sites inside the spinel matrix.
4.2.2. Inter-atomic distance and the inter bond angles The value of inter-atomic distance between the cations for the tetragonal (A) and octahedral [B] sites can be characterized with the help of the following relations [24]: pffiffiffi! 3 MA MA ¼ a 4 MA MB ¼
MB MB ¼
pffiffiffiffi
p
4
a
pffiffiffi! 2 a 4
pffiffiffi 1 MA OA ¼ a 3 d þ 8 1=2 pffiffiffi 1 d 2 þ3d MB OB ¼ a 3 16 2 where d is the deviation from oxygen parameter (U), d ¼U–Uideal, and R0 ¼radius of oxygen ion¼1.35 A˚ [25]. The determination of inter-atomic distance and the inter bond angles are amenable method to give a full description of the crystallographic structure and the magnetic properties, where MA and MB refer to the cations at the center of the tetrahedral (A) and octahedral [B] sites, respectively, while OA and OB refer to the Table 3 Cation distribution on A-site and B-site for CoFe2O4. Method
Composition
Cation distribution (A site)
Cation distribution [B site]
Ceramic Co-precipitation
CoFe2O4 CoFe2O4
(Co0.19895Fe0.80105) (Co0.17899Fe0.82101)
[Co0.80105Fe1.19895] [Co0.82101Fe1.17899]
Table 1 Refinement result for CoFe2O4. Miller Indices
Ceramic technique
Co-precipitation technique
h
k
l
2h
Iobs
Icalc
9Iobs Icalc9
2h
Iobs
Icalc
9Iobs Icalc9
1 2 3 2 4 3 4 3 5 4 5 4 6 5 6 4
1 2 1 2 0 3 2 3 1 4 3 4 2 3 2 4
1 0 1 2 0 1 2 3 1 0 1 2 0 3 2 4
18.326 30.145 35.508 37.143 43.155 47.251 53.54 57.075 57.075 62.677 65.902 66.959 71.109 74.154 75.159 79.134
11.4 28.2 106.2 9.70 24.3 0.90 11.2 7.3 27.5 48.8 0.7 0.0 3.1 10.3 5.0 4.1
8.30 30.3 108.5 9.10 22.3 0.80 10.5 7.20 27.1 45.9 1.0 0.0 4.0 9.9 4.9 2.8
3.1 2.1 2.3 0.7 2.1 0.1 0.7 0.1 0.4 3.0 0.3 0.0 0.9 0.4 0.1 1.3
18.324 30.141 35.503 37.138 43.149 47.244 53.533 57.067 57.067 62.667 65.892 66.949 71.098 74.143 75.147 79.121
10.1 28.7 133.3 7.6 23.7 0.9 10.8 6.8 30 48.7 0.6 0 3.7 9.2 5.1 3.6
5.8 28.5 141 6.8 24.9 0.7 12.2 6.7 29.8 41.2 0.5 0 4.9 9.2 3.7 2.2
4.3 0.2 7.7 0.8 1.3 0.1 1.4 0.1 0.3 7.5 0.2 0 1.1 0 1.4 1.4
Table 2 ˚ and oxygen parameter for CoFe2O4. Fitting parameters, lattice parameter a (A) Method
Composition
GoF
Bragg R-factor
RF factor
˚ a (A)
U
Ceramic Co-precipitation
CoFe2O4 CoFe2O4
1.140 1.281
5.838 8.592
4.604 6.509
8.378315 8.379406
0.25501 0.25413
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Table 4 Calculated values of inter-atomic distances for nanocrystalline CoFe2O4. Method
Composition
MA MA
MA MB
MB MB
MA OA
MB OB
Ceramic Co-precipitation
CoFe2O4 CoFe2O4
3.6279168 3.6283892
3.7132912 3.7137748
2.9621817 2.9625674
1.8866619 1.8741356
2.0534616 2.0608258
Table 5 Calculated values of magnetic moment for nanocrystalline CoFe2O4. Method
Composition
MA (mB)
MB (mB)
m (molecule)
Ceramic Co-precipitation
CoFe2O4 CoFe2O4
4.6021 4.64202
8.3979 8.35798
3.7958 3.71596
Table 6 Average crystallite size and lattice strain for nanocrystalline CoFe2O4. Method
Composition
Average crystallite size (nm)
Lattice strain (%)
Ceramic Co-precipitation
CoFe2O4 CoFe2O4
34.026151 50.18498
0.2742 0.1877
center of oxygen anions related to the tetrahedral (A) and octahedral [B] configurations, respectively. The calculated values of these distances for nanocrystalline CoFe2O4 are listed in Table 4. 4.2.3. Magnetic structure model One of the most important results obtained from the cation distribution in ferrites is the evaluation of the magnetic structure model for these materials. If the magnetic moment of (A) and [B] sites are MA and MB, respectively, then the net magnetic moment in ferromagnetic material will be 9MB MA9. In our study, the magnetic ions and their magnetic moment, respectively, are Co2 þ ¼3 mB and Fe3 þ ¼5 mB [26]. The calculated magnetic moment is shown in Table 5. 4.2.4. Microstructure analysis The characterization of the prepared materials in terms of microstructural parameters, such as crystallite size and root mean square (r.m.s.) lattice strain, is estimated in Table 6. 4.3. SEM and TEM analysis The microstructure and surface morphology were observed with a scanning electron microscopy (SEM). SEM representative micrograph for the nanocrystalline Co ferrite is shown in Fig. 5. The surface morphology of all the samples as seen from the SEM consists of well-crystallized grains, with relatively homogeneous grain distribution and an average grain size smaller than 100 nm. Transmission electron microscopy (TEM) is considered the main method for characterizing the microstructure of nanocrystalline materials (the particle size and shape of the particles) [27]. TEM micrograph for CoFe2O4 samples are shown in Fig. 6. TEM micrograph revealed that the particles of the sample are spherical in shape and the average size of the particles ( E52.8 nm) for co-precipitation and ( E34.88 nm) for ceramic, which are quite closer to the X-ray crystallite size. The shape of the precipitated CoFe2O4 particles becomes regular and the distribution of particle size is uniform. The non-uniform particles size distribution should attribute to a non-uniform ingredient mixture and a non-uniform grain distribution of powder. 4.4. Magnetic measurements (vibrating sample magnetometer) (VSM) The hysteresis loops were identified and characterized to determine parameters, such as the saturation magnetization (Bs), remnant magnetization (Br) and coercivity (Hc). The magnetic properties of powders have been determined at room temperature using a vibrating sample magnetometer in the maximum
Fig. 5. SEM for CoFe2O4 prepared by (a) ceramic technique and (b) co-precipitation technique.
external field of 16 kOe. The hysteresis loops for the nanocrystalline CoFe2O4 prepared by ceramic and co-precipitation methods are shown in Fig. 7. Magnetic parameter for the system prepared by ceramic and co-precipitation methods are listed in Table 7. The site occupancies of magnetic ions at the tetrahedral and octahedral sites define the saturation magnetization. Magnetic cation distribution reflects the saturation magnetization of the sample. According to the anti-parallel magnetic spin in the tetrahedral and octahedral sites in the spinel lattice, the following
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Fig. 6. TEM for CoFe2O4 prepared by (a) ceramic method and (b) co-precipitation method.
magnetic spin configuration can be estimated as shown in Fig. 8. The magnetic moment m would be expressed as (3þ4x) mB as a function of composition x. Ceramic and co-precipitation techniques show saturation magnetization values to be 64.63 and 56.22 emu/g, respectively. The difference in the saturation magnetization is due to the difference in cation distribution at the tetrahedral and octahedral sites [28]. Table 7 shows that saturation magnetization of the Co ferrite prepared by co-precipitation was found to be 56.22 emu/g, which is lower than CoFe2O4 bulk (65 emu/g) [29]. This behavior is attributed to the nature of disordered surface effects of the small
particles [30,31], which appear as a result of the finite size of nanocrystallites and which lead to a non-collinearity of the magnetic moments at the nanocrystallites surface. These effects are getting more intense when the mean size of the nanocrystallites is getting smaller and the surface/volume ratio is increasing. The decrease in saturation magnetization with decreasing particle size has been reported by Morrish and Haneda [32]. The decrease in the saturation magnetization in the case of nanoparticles systems was also observed by other authors [33,34]; one can also note that the coercivity is the largest for the co-precipitation prepared samples. This can be attributed to the
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Fig. 7. Plots of magnetization vs applied field for the nanocrystalline CoFe2O4.
Table 7 Magnetic parameters obtained from magnetization curves for CoFe2O4. Method
Composition
Hc (Oe)
Bs (emu/g)
Br (emu/g)
R ¼ Br/Bs
Average crystalline size (nm)
Ceramic Co-precipitation
CoFe2O4 CoFe2O4
432.5 797.4
64.62723 56.22
14.231 20.19
0.220201 0.359125
34.88 52.80
the co-precipitation method, while the coercive force (Hc) for the prepared sample by the co-precipitation method is larger than the one prepared by the ceramic method. The distribution of cations among the lattice sites depends on methods of preparation.
Fig. 8.. Magnetic model for CoFe2O4.
smallest size of the co-precipitation prepared particles compared to ceramic prepared particles. This represents that magnetic properties depend on the preparation technique and magnetic behavior is related to the variation of the particle size.
5. Conclusion The refinement of X-ray results for the obtained samples by ceramic and co-precipitation methods showed a nanocrystalline ferrite phase with average values of particle size 34 and 50.18 nm, respectively. The prepared nanocrystalline ferrite phase is partially an inverse spinel due to the random distribution of cations among the (A) and [B] sites inside the spinel matrix. The SEM micrographs for all samples show well crystallized grains, with relatively homogeneous grain distribution. Micrographs of TEM show spherical grains with average particles size 34.88 and 52.80 nm, which are quite closer to the X-ray crystallite size for samples prepared by the ceramic and co-precipitation methods, respectively. The magnetic properties of the samples, clearly, depend on the size of the nanocrystallites, the distribution of the different cations among (A) and [B] sites and the methods of preparation. The ceramic method gives sample with value of saturation magnetization (Bs) larger than the one prepared by
Acknowledgment The authors would deeply like to thank Prof. Dr. Aisha M. Moustafa (Physics Division, Solid State Department, X-ray Crystallography Lab, National Research Center, Dokki, Cairo, Egypt), Dr. Salah A. Shata (Geophysics Department, Science Faculty, Suez Canal University) and Dr. Ahmed M. Nawar (Physics Department, Science Faculty, Suez Canal University) for good discussions.
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