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Size control and magnetic property trends in cobalt ferrite

nanoparticles synthesized using an aqueous chemical route
Praveena Kuruva, Shidaling Matteppanavar, Srinath. S, and Tiju Thomas, Member,
IEEE

Abstract

Cobalt ferrite (CoFe2O4) is an engineering material which is used for

applications such as magnetic cores, magnetic switches, hyperthermia based
tumor treatment, and as contrast agents for magnetic resonance imaging. Utility
of ferrites nanoparticles hinges on its size, dispersibility in solutions, and
synthetic control over its coercivity. In this work, we establish correlations
between room temperature co-precipitation conditions, and these crucial
materials parameters. Furthermore post-synthesis annealing conditions are
correlated with morphology, changes in crystal structure and magnetic
properties. We disclose the synthesis and process conditions helpful in obtaining
easily sinterable CoFe2O4 nanoparticles with coercive magnetic flux density (Hc)
in the range 5.5-31.9 kA/m and Ms in the range 47.9-84.9 A.m2Kg-1. At a grain
size of ~54±2 nm (corresponding to 1073 K sintering temperature), multi-domain
behavior sets in, which is indicated by a decrease in Hc. In addition, we observe
an increase in lattice constant with respect to grain size, which is the inverse of
what is expected of in ferrites. Our results suggest that oxygen deficiency plays a
crucial role in explaining this inverse trend. We expect the method disclosed here
to be a viable and scalable alternative to thermal decomposition based CoFe2O4
synthesis. The magnetic trends reported will aid in the optimization of functional
CoFe2O4 nanoparticles.

Index terms – Ferrites, Ferrimagnetic materials, Cobalt compounds, Magnetic

materials.

Praveena Kuruva is with the Materials Research Centre, Indian Institute of Science,
Bangalore (e-mail: praveenauofhyd@gmail.com).
Shidaling Matteppanavar is with the Department of Physics, Bangalore
University,Karnataka, India (e-mail: shipurn@gmail.com).
S. Srinath is with the School of Physics, University of Hyderabad, Andhra Pradesh,
India (e-mail: sssp@uohyd.ernet.in).
Tiju Thomas works at the Materials Research Centre, Indian Institute of Science,
Bangalore, Karnataka, India (email: tt332@cornell.edu)

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Introduction

Ferrite systems continue to be of abiding interest due to their relevance to engineering

and technology. This material system finds application in the magnetic core of coils in

microwave frequency devices, and in computer memory core elements. Due to

relatively low permeability and flux density, ferrites are useful in low field, low

power applications. Ferrites also find use in low frequency applications such as

timers, magnetic switches in refrigerators, air conditioners etc. Magnetic head

transducers in recorders also employ ferrites [1]. In all these technologies, utility of

ferrites is aided by particle size control, and synthetic control over coercivity.

More recently, nano-ferrites such as cobalt ferrite (CoFe2O4) nanoparticles

have found use in biomedical applications [2]. Currently these nanoparticles are being

employed for a variety of applications such as hyperthermia based tumor treatment,

and contrast agents for magnetic resonance imaging (MRI) or computer tomography

[2, 3]. Apart from CoFe2O4, Fe3O4 [3, 4] and polymer coated hybrid nanoparticles [5]

have also been explored for use as contrast agents. In fact, there is significant effort

being put into developing one-pot, synthetic approaches to such hybrids [6]. Low

coercivity, easy surface functionalization, and biocompatibility are the primary factors

that decide whether or not these nanomaterials are useful as contrast agents.

CoFe2O4 has also garnered the attention of researchers who hope to further

improve or miniaturize magnetic memory devices. There are several on-going efforts

in this direction to enhance device functionality of this nanomaterial by improving its

coercivity and saturation magnetization [7, 8]. Considering all the applications of

ferrites, it is clear that the practical use of its nanoparticles hinges on our ability to

engineer its (i) particle size, (ii) dispersibility, (iii) coercivity, and (iv) remnant

magnetization [9].

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Besides its obvious technological importance, ferrites continue to be of tremendous

scientific interest. For example, inter-particle interactions [10], behavior of ferrite

nanomaterials in host lattice [11], impact of doping [12], ferrite based bi-magnetics

[13] and magneto-optical properties [14] of this material are currently being pursued

by several groups. Hence it is evident that “green routes” that allow particle size

control of dispersible CoFe2O4 nanoparticles, while maintaining desirable magnetic

properties (such as optimum coercivity and saturation magnetization) is important

from the point of view of contemporary science and electrical engineering.

Currently thermal decomposition is considered better than co-precipitation for

making uniformly sized ferrites [4], since thermal decomposition usually gives better

size control. In applications such as contrast agents, size control is crucial to

biocompatibility, since cytotoxicity is a function of both chemical composition and

particle size [15]. These technical considerations raise a fundamental question: would

it be possible to determine soft chemical co-precipitation conditions using which (i)

size, and (ii) magnetic property optimization is possible? This is a relevant question

since co-precipitation tends to be a much “greener” and easily scalable method for

ferrite synthesis (when compared to thermal decomposition).

Green routes such as aqueous, low cost co-precipitation method usually result

in materials with low crystallinity and poor monodispersity. However we demonstrate

that with careful choice of co-precipitation conditions one can significantly minimize

polydispersity. The scalable co-precipitation CoFe2O4 synthesis technique studied

here is simple, quick, energy efficient, solvent free, and cost-effective. The method

reported is an adaptation of the Yang et. al‟s method[16] which is helpful in

synthesizing high specific surface area CoFe2O4. The reported method is a green, and

viable alternative to other synthesis techniques currently used which (among others)

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include sol-gel [17], forced hydrolysis [18], combustion [19], micro-emulsion [20],

mechano-chemical [21], and redox methods [22].

In this work we show that pH of the co-precipitation reaction mixture can be used to

ensure significant reduction in polydispersity, and easy dispersibility of CoFe2O4

nanoparticles. Furthermore post-synthesis annealing can enable optimization of the

magnetic properties of these materials. The aqueous synthesis method presented here

results in particles that have high sinterability making it attractive for devices such as

magnetostrictive sensors and actuators [23]. We quantify the role that thermal

treatment plays in enhancing the magnetization and coercivity of these nanoparticles.

Furthermore, we observe an increase in lattice constant with respect to grain size,

which is the inverse of what is expected of in ferrites. Our results suggest that oxygen

deficiency plays a crucial role in explaining this inverse trend. Synthesis-property

correlations elaborated here will be useful in optimizing CoFe2O4 nanoparticles for a

wide variety of engineering and bio-medical applications.

2. Experimental

1 mM of Cobalt nitrate (Co(NO3)2.6H2O) and 2 mM of ferric nitrate (Fe(NO3)2.9H2O)

are dissolved in 50 ml of deionized (DI) water. pH of this solution is varied between

8.5 to 13 by careful, dropwise addition of 2M NaOH. This pH range is chosen based

on known regions of formation of Co(OH)2, and iron(III) oxy-hydroxides [24, 25].

The mixture is stirred constantly, as the base is being added. The addition of base is

accompanied by darkening of the reaction mixture. The temperature of the solution is

maintained at about 333 K. The process is continued for 2 hours, after which the

particles formed are allowed to precipitate out. The supernatant water is poured out,

and fresh DI water is used to wash the particles. This process of washing is repeated

eight times to wash away the water soluble by-products. Thermogravimetric analysis

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(TGA), and Fourier transform infrared (FTIR) spectroscopy is performed on as-

prepared samples. Bruker Tensor 27 is used to perform FTIR, while Sieko

TGA/DTA6200 Standard is used to perform TGA.

Pellets are prepared by sintering as-prepared powders at 673, 773, 873, 973, 1073, and

1173 K for 2 hours. To characterize both as-prepared and sintered samples, a Phillips

PANalytical X‟pert powder X-ray diffractometer (XRD) is used, with Cu Kα (1.54Å)

radiation. The morphology of these powders are examined using a Carl Zeiss field

emission scanning electron microscope (FE-SEM). Room temperature magnetic

measurements are made using a vibrating sample magnetometer (VSM Lakeshore

7500, USA). The VSM chosen has a high field stability of ±0.05%/day, and hence

provides coercive field strength (Hc) with very high precision and reproducibility.

Transmission electron microscope (TEM) is performed using JEM-2010 from JEOL

Inc. (Tokyo, Japan).

3. Results and Discussions

X-ray diffraction (XRD) patterns of as-synthesized powders at different pH confirms

the formation of CoFe2O4 (Figure 1.a). CoFe2O4 is found in inverse spinel structure,

which has the general formula AB2O4 (where A: divalent metal ion, B: trivalent metal

ion). In the normal spinel (MgAl2O4) the oxygen atoms form a cubic close packed

(ABCABC) array, and the Mg2+ and Al3+ sits in tetrahedral (one-eighth occupied) and

octahedral (half-occupied) sites in the lattice. An inverse spinel is an arrangement

where the divalent ions („A‟ in the formula AB2O4) swap with half of the trivalent

(„B‟ in the formula AB2O4) ions so that the A-atoms now occupy octahedral sites.

Given the pH range chosen for CoFe2O4 synthesis, the precipitate phases

expected are Co(OH)2, and hydroxylated anionic complexes such as Fe(OH)-13 ,

Fe(OH)2-4 , and Fe(OH)-14 [24, 25]. However, XRD clearly reveals CoFe2O4

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formation showing that the Co(OH)2 and hydroxylated iron complexes co-precipitate

out of the reaction mixture to form single phase CoFe2O4. XRD shows no peaks

corresponding to Co(OH)2 or any of the oxides or hydroxides of Fe, confirming that

the only crystalline phase obtained is CoFe2O4. All peaks could be indexed using

JCPDS card number 22-1086. The (3 1 1) reflection which is characteristic of ferrite

particles [21, 26] is seen in every sample synthesized.

The Scherrer formula is used to determine the crystallite size of as-synthesized

powders. The crystallite size of the as-synthesized CoFe2O4 samples are estimated

from X-ray peak broadening of the (3 1 1) peak using. In order to ensure that the

crystallite size determined is correct, lattice strain is evaluated using Rietveld

refinement. Even when lattice strain is taken into account the crystallite size obtained

is in good agreement with the value obtained using the Scherrer formula. Peak

broadening and TEM images confirm that the particles formed are indeed in the nano-

regime (Figure 1.b). With increase in pH, the (3 1 1) peak broadening decreases,

indicating an increase in crystallite size. Increase in crystallite size with pH is likely

due to the faster particle growth kinetics favored by high pH. It is also observed that

with increasing pH, there is an increase in the lattice constant and average crystallite

size (Figure 1.c).

Lattice constants of materials synthesized are always close to the values of the

CoFe2O4 synthesized by other methods [27, 28]. The concomitant increase in lattice

constant with the particle size is akin to the report by D. Thapa et. al [28]. She showed

that this trend is the inverse of what usually occurs (in ferrites usually a decrease in

particle size is accompanied by increase in lattice constant) [29]. She shows that in

ferrite systems (CuFe2O4 in her case), the usual trend can be reversed due to the

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conversion of a small fraction of Fe3+ to Fe2+ [28]. This is most likely the cause for

our observation as well, wherein we see an increase in lattice constant with particle

size increase. This is reasonable since in the synthesis conditions (temperature: 333K,

pH>8.5), Fe prefers to be divalent [25].

The mechanism of formation of CoFe2O4 most likely involves the co-

precipitation of mixed amorphous hydroxides of Co and Fe. An indication of this

mechanism comes from the TGA performed on as-prepared samples (Figure 1.d). As

synthesized powders show multi-step weight loss, indicating that the as-prepared

material is a complex mixture with several amorphous phases, in addition to

crystalline CoFe2O4. Weight loss at and below 373 K (region I) is due to loss of water

molecules. The weight loss seen just above 400K (region II) is attributed to

decomposition of Fe-rich mixed nitrates, since decomposition temperature of pure

Fe(NO3)3 is about 430 K [30]. Weight loss occurring beyond 520 K (region III) is

attributed to Co-rich mixed hydroxides [31]. Beyond 620 K (region IV), the weight

loss observed is likely due to the decomposition of both Fe-rich mixed hydroxides,

and Co(NO3)3 [31, 32]. No evidence of crystalline Co(OH)3 and Fe(OH)3 exists,

hence it is very likely that mixed amorphous hydroxides (indicated by TGA

measurements) act as precursors for the co-precipitation of CoFe2O4 nanoparticles.

Presence and role of mixed hydroxides is also indicated by FTIR

measurements performed on as-prepared samples (Figure 1.e). The assigned peak

positions are tabulated in Table 1. For example, an IR band around 1600 cm-1

observed in as-prepared samples could be due to OH-1 or molecular H2O. Presence of

residual nitrates is confirmed by the 1379 cm-1 IR peak, which is associated with the

asymmetric stretching of NO3-1. The FTIR spectra obtained is quite broad for all the

samples. Such broadening is commonly observed for inverse spinel ferrites (MFe2O4).

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Two main broad peaks are seen around 400-300 cm-1 and 600-500 cm-1. 600-500 cm-1

stretches corresponds to intrinsic stretching vibrations of the metal-oxygen bonds,

where the metal is at the tetrahedral site. 400-300 cm-1 (more accurately 430-385 cm-
1
) band is because of metal-oxygen stretching where metal is in the octahedral site.

The band at 975cm-1 is due to the stretching vibration of Fe-Co bonds [33]. The

broadening in this peak could be due to the statistical distribution of Fe at A and B

sites in the inverse spinel structure. From the figure, it seems likely that this statistical

distribution of Fe in A and B sites becomes more pronounced, when nanoparticles are

synthesized at high pH (say≥ 8). This could very well be associated with the faster co-

precipitation kinetics, which takes place at higher pH. It may be noted that it is this

faster growth kinetics which is also responsible for larger crystallites at higher pH.

Polydispersity in the annealed samples is measured using an index of

dispersion called Fano factor. In this case, it is the ratio of the variance (σ2) to the

mean size (d). Samples with relatively low Fano factor are less polydisperse when

compared to those with larger Fano factors. Both the variance and the mean size is

obtained using image analysis (performed using ImageJ software) on SEM images.

The particle size distribution is obtained by analyzing 6 SEM images for each sample.

We notice that the particle size distribution follows a log-normal distribution

regardless of synthesis pH.

Particles synthesized at pH 13 show the best dispersability (Table 2). These

particles (i.e those synthesized at pH 13) are annealed at 673, 773, 873, 973, 1073,

and 1173 K. XRD on annealed samples reveal improvement in crystallinity as a result

of heat treatment (Figure 2 a, b). Rietveld refinement of CoFe2O4 annealed at 1073 K

is shown in Figure 2 c. Widths of IR bands (Figure 2 d) in the range 500-1000 cm-1

are found to reduce with sintering temperature. In fact the 975 cm-1 peak, the width of

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which is a measure of statistical distribution of Fe in A and B sites [33], also reduces

with sintering. This is an indication of better crystallinity and order in sintered

samples. IR bands corresponding to residual nitrates (1379 cm-1) and water (1600 cm-
1
) are not seen in sintered samples.

SEM images (Figure 3 a) show that the CoFe2O4 annealed nanocrystals

possess spherical shape. The average particle size observed is close to the values

obtained using the Scherrer equation. Hence it is very likely that each of the observed

particles is a single crystallite. The physical size of the CoFe2O4 crystals increases

with the annealing temperature since, at high temperatures the solid-vapour interfaces

tend to be replaced by solid-solid interface via solid-state diffusion. This phenomenon

has been observed in several systems (including ferrites), and is attributed to the

crystal‟s tendency to reduce the overall surface energy [34].

Increase in annealing temperature results in particle size distributions with

lower Fano factors, which implies that annealing promotes monodispersity (Table 3).

Also, increase in annealing temperatures result in larger particle and crystallite sizes,

and is accompanied by marginal increase in the lattice parameter (Figure 3 b, Table

4). However in all the sintered samples, the particle size distribution is found to be

log-normal (Figure 3 c).

In samples sintered at higher temperatures, increase in grain size is accompanied by

an increase in lattice constant. This trend is the opposite of what is usually expected in

ferrites, wherein lattice constant increases with decreasing particle size [29]. Earlier in

this paper, we mentioned that the “inverse trend” is also observed when CoFe2O4 is

precipitated out at different pH values. Hence in CoFe2O4 synthesized by the method

presented here, an inverse particle size-lattice constant relationship is observed.

Recently D. Thapa et al. showed that the “inverse trend” (i.e increase in lattice

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constant with increase in particle size) occurs in ferrites when a fraction of Fe3+

converts to Fe2+. Hence process conditions that aid in the conversion of Fe3+ to Fe2+

would cause an increase in magnetization. She also observes that calcination aids in

the conversion of Fe3+ to Fe2+ (in case of CuFe2O4) [28]. Using energy dispersive x-

ray analysis, we find that sintering results in change in O:Fe ratio. In fact the O:Fe

ratio changes from 2.00 when sintering temperature is 673 K, to 1.99 when sintering

temperature is >1073 K. We also find that increasing synthesis pH results in oxygen

deficiency. Hence we infer that the Fe3+→Fe2+ reduction process is aided by (i) high

pH in the co-precipitation chamber, and (ii) increase in annealing temperature. Due to

the higher magnetic moment associated with Fe2+, the observed increase in

magnetization with increasing calcination temperatures is expected. Given that Fe2+

rich (i.e oxygen deficient) ferrites are expected to have the “inverse” lattice constant-

size relationship [28], the inverse trend we observe in our samples is reasonable.

The main aim of synthesizing the CoFe2O4 nanocrystallites by chemical co-

precipitation is to obtain a magnetic material with good magnetization (Ms). In

addition knowledge of correlation between coercive field (Hc), synthesis and process

conditions is useful from the point of view of manufacturing technology. The

maximum magnetic field applied is 1.5 T. All magnetic measurements (see Table 5)

are carried out at room temperature. Hysteresis loops of samples annealed at different

temperatures are provided (Figure 4 a, b). Ms and remnant magnetization (Mr)

monotonically increases with respect to temperature (Figure 4 (c, d)). This is

consistent with the fact that higher annealing temperatures aids in the conversion of a

certain fraction of Fe3+ to Fe2+ in ferrites. This atomistic process tends to not only

increase the unit cell volume, but also results in increased magnetization [28].

10

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The coercive field Hc reaches a maximum of 31.9 kA/m for sample calcined at 1073

K (Figure 4 e); which corresponds to an average crystallite size of ~54 nm. This

maximum coercive field is lesser than the highest value reported for CoFe2O4. In

general, micron-sized particles tend to have much higher coercivity (~114.9 kA/m)

[35]. This suggests that the method presented here results in softer ferrite particles.

Results presented here also show how synthesis and calcination conditions can be

used to control Hc and Ms of CoFe2O4 nanoparticles.

In CoFe2O4 nanoparticles that fall within the size regime reported here (~50 nm),

fairly high room temperature coercivities have been reported (as much as 96.6 kA/m)

[36, 37]. Even in super-paramagnetic CoFe2O4 particles, which are otherwise very

small (typically <10 nm), coalescence and aging results in agglomerates that are ~50

nm, which show comparable room temperature coercivities (i.e ~96 kA/m) [36]. In

comparison, particles reported here have Hc in the range 5.5-31.9 kA/m. Even the

sample with the highest Ms (84.9 A.m2.Kg-1), has a Hc of only about 5.5 kA/m (Fig 4

(c, e)). This makes materials reported here desirable from the point of view of

practical applications. It must be noted that the best Ms reported here is an

improvement over previous reports on CoFe2O4 nanoparticles (in the ≤50 nm size

regime). The Ms of CoFe2O4 nanoparticles are usually ~69 A.m2.Kg-1 [36-38], while

we obtain ~84.9 A.m2.Kg-1. The Fe3+ to Fe2+ conversion in these samples, which is

discussed above, is most likely responsible for the observed enhancement of Ms in our

samples.

Beyond a certain calcination temperature (~1073 K), the crystallite size

continues to increase with sintering temperature; however the Hc decreases (Figure 4

e). This is most likely due to a change in behavior from single domain to multi-

domain [26]. The squareness factor (Mr/Ms) also monotonically increases with

11

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calcination temperatures, suggesting an increase in magnetocrystalline anisotropy

(Table 5). We believe this increase in magnetocrystalline anisotropy is most likely

due to improvement in crystal order and structure, expected in samples calcined at

high temperatures.

4. Conclusions

Synthesis and process conditions are explored to obtain fairly monodisperse, easily

sinterable CoFe2O4 nanoparticles with Ms in the range (47.9-87.9 A.m2.Kg-1) and Hc

in the range 5.5-31.9 kA/m. The technique presented here is a viable alternative to

thermal decomposition for obtaining functional ferrite nanoparticles, since size

control is indeed possible using this approach. The method presented in green and

easily scalable.

Dispersity is found to be best for particles synthesized at pH~13. Both increase in pH

(during co-precipitation) and calcination temperature result in simultaneous increase

in lattice constant and average particle size. This trend is the inverse of the usual trend

for ferrites, wherein lattice constant increases with decreasing particle size. The

observed “inverse trend” is likely due to the fact that both high pH of synthesis and

high calcination temperatures promote Fe3+→Fe2+ conversion. Increase in pH and

calcination temperature is helpful in minimizing the polydispersity in co-precipitation

synthesized CoFe2O4.

Increasing calcination temperature results in particles with better Ms and improved

squareness factor. Beyond a domain size of ~54 nm, a single domain to multi-domain

transition results in lowering of Hc. The simplicity, cost-effectiveness, high yield

(~96%) and scalability of the method ensures its viability for commercial applications

(eg. magnetic storage, ferrofluids, contrast agents in MRI etc). The easy adaptability

12

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of the technique makes it promising for obtaining related doped and undoped ferrite

systems.

Acknowledgments

K. Praveena thanks University Grants Commission (UGC), New Delhi for providing

the D. S. Kothari Postdoctoral Fellowship. She also thanks Prof. S. Srinath

(University of Hyderabad) for helpful discussions. Tiju Thomas acknowledges the

financial support received from the “Department of Science and Technology,

Government of India”, in the form of grant no. DST01117.

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15

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FIGURE CAPTIONS

Figure 1: (a) XRD patterns of CoFe2O4 samples synthesized at two different pH values (8.5,

and 13.0). (b) TEM of CoFe2O4 nanoparticles synthesized at pH 13. (c) Average crystallite

size and lattice parameters (extracted from XRD) increase with respect to pH. (d)

Thermogravimetry is used to obtain normalized weight loss (as a function of temperature) of

samples prepared. Region I represents loss of water, II is due to decomposition of Fe-rich

mixed nitrates, region III is likely due to Co-rich mixed hydroxides, and region IV is

attributed to the decomposition of Fe-rich mixed hydroxides, and Co(NO3)3. (e) Shows FTIR

spectra of samples prepared at various pH values.

Figure 2: (a) XRD patterns of CoFe2O4 nanoparticles (prepared at pH 13), annealed at

different temperatures (b) Shows change in the characteristic (311) peak when the sample is

annealed at different temperatures. FIGURE 2: (c) Shows the Rietveld refined XRD pattern of

CoFe2O4 annealed at 1173K. The fitting is very close to the experimental XRD, since the

error (blue line) in Rietveld fitting is found to be minimal. (d) FTIR of sintered CoFe 2O4 at

different temperatures.

Figure 3: (a) Shows scanning electron micrographs of samples annealed at 773, 873,

973, 1073, 1173 and 1273K respectively. Increasing annealing temperature promotes

agglomeration of particles, and leads to larger particle sizes. (b) Both the average

crystallite size and lattice constant increases with respect to the annealing

temperature. (c) Shows the log-normal particle size distribution in CoFe2O4 sample

which was co-precipitated at pH 13 and annealed at 1173 K. Distribution obtained

using image analysis (using ImageJ software) is used to determine mean particle size

and variance. All samples studied show log-normal particle size distribution.

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Figure 4: (a) M-H hysteresis curves for particles prepared at pH 13, and annealed at

different temperatures. (b) Shows how Mr and Hc is extracted using M-H curves. The

M-H loop provided is that which is obtained using CoFe2O4 co-precipitated at pH 13,

and annealed at 1073 K. (c, d) Show variation of saturation magnetization (Ms) and

remnant magnetization (Mr) with respect to annealing temperature. Both these

magnetic quantities increase monotonically with respect to calcination temperature.

(e, f) Coercive field (Hc) of CoFe2O4 increases with respect to annealing temperature.

However the Hc reaches a maximum value when the grain size reaches 54±2 nm. The

decrease in Hc beyond this grain size is most likely due to a single domain to multi-

domain transition.

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(b)

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(a) (b)

(c) (d)

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(a)

(b) (c)

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(a) (b)

(c) (d)

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(e)

(f)

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Table 1. List of peak positions form FTIR analysis of CoFe2O4.

Peak Assignments
positions
1600 OH-1or H2O molecule
1379 NO3-1
975 Fe-Co bonds
600-500 Intrinsic stretching vibrations of the metal oxygen bonds
400-385 Metal tetrahedral

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Table 2. Average crystallite size (mean (d) and variance (σ) using SEM based image analysis.
The Fano factor (σ2/d) is used as the index of dispersion. Increasing pH of the synthesis bath
results in monotonic reduction in polydispersity.

pH σ (nm) d(nm) σ2/d

8.5 13.7 18 10.4
9.4 13.8 22 8.6
10 14.1 27 7.4
11 14.5 31 6.7
12 15.2 38 6.1
12.5 15.5 43 5.5
13 15.7 48 5.1

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Table 3. Variation of dispersity (measured in the form of Fano factor (σ2/d) with respect to
calcination temperature. Calcination reduces the polydispersity of CoFe2O4 particles, synthesized
at pH 13.

Temperature D σ (nm) (σ2/d)

(K) (nm)
673 23 13.9 8.3
773 27 13.9 7.1
873 35 14 5.6
973 46 14.5 4.5
1073 53 15.3 4.3
1173 69 15.5 3.4
1273 88 15.8 2.8

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Table 4. Rietveld refinement of CoFe2O4 and comparison of lattice constants. a0 is the reported
lattice constant, as in JCPDS 22-1086.

Temperature (K) Lattice Lattice Strain

constant (a) (Å) Constant (Å) XRD a  a0
XRD refinement a
673 8.36 8.37 0.004
773 8.39 8.38 0.000
873 8.40 8.39 0.000
973 8.43 8.41 0.005
1073 8.43 8.42 0.005
1173 8.45 8.44 0.007
1273 8.50 8.49 0.013

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Table 5. Grains size, lattice constant, remnant magnetization (Mr), saturation magnetization (Ms)
and Hc (coercive field) of CoFe2O4 sintered at different temperatures. Beyond 1073 K
(corresponding to grains of size ~54 nm), Hc reduces, which is most likely due to a single to
multi-domain transition.

Temperature Lattice Ms Mr Mr/Ms Hc

(K) constant (A.m2/Kg) (A.m2/Kg) (kA/m)
(Å)
673 8.36 47.9 2.2 0.05 10.4
773 8.39 52.2 3.4 0.07 17.5
873 8.40 61.8 11.2 0.18 21.5
973 8.43 67.1 13.5 0.20 28.7
1073 8.43 70.9 14.2 0.20 31.9
1173 8.45 81.7 14.8 0.18 11.9
1273 8.50 84.9 15.3 0.18 5.6

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