# Microstructure and Superparamagnetic Properties of Mg-Ni-Cd Ferrites Nanoparticles

Authors: M. M. Eltabey; A. M. Massoud; Cosmin Radu
Journal: Journal of Nanomaterials
 (2014)

---

## Abstract

Magnesium substituted nickel cadmium ferrite nanoparticles MgxNi0.6−xCd0.4Fe2O4 (from x = 0 to 0.6 with step 0.1) have been synthesized by the chemical coprecipitation route. X-ray diffraction (XRD) and infrared spectroscopy (FTIR) revealed that the obtained powders have a single phase of cubic spinel structure. The crystallite sizes calculated from XRD data have been confirmed using transmission electron microscopy (TEM) showing that the powders are consisting of nanosized grains with an average size range 5–1.5 nm. Magnetic hysteresis loops were traced at 6.5 K as well as at room temperature using VSM. It was found that, due to the Mg2+-ions substitution, the values of saturation magnetization M
s for the investigated samples were decreased, whereas the coercive field H
c increased. Both zero field cooling (ZFC) and field cooling (FC) curves are measured in the temperature range (6.5–350 K) and the values of blocking temperature T
B were determined. No considerable variation in the values of T
B was observed with increasing Mg-content, whereas the values of the effective anisotropy constant K
e
f
f were increased.


---

## Body

## 1. Introduction

Ferrites have drawn the attention for decades for their wide range of applications. Technological and industrial applications of ferrites depend mostly on their distinguishable magnetic and electric properties. Microwave devices, ferrofluids, and storage media of computers are the most important applications that make use of ferrites properties [1–3]. Structural and magnetic properties of ferrites are varying with the preparation methods as well as with the kind of substituting ions. Nanoferrites show special magnetic and electric properties which are quite different from the bulk ferrites [4]. Nickel substituted ferrites are considered to be the most versatile and found wide spread application in the electronics and microwave devices due to their high electrical resistivity, low eddy current, and dielectric loss [5]. Nickel cadmium (Ni-Cd) ferrite has many microwave applications for its high value of coercivity, remanence, and saturation magnetization [3]. CdxNi1−xFe2O4 was investigated by Shelar et al. [6] and the saturation magnetization showed an increase with the Cd-content. Magnesium ferrite is a soft magnetic material that is utilized in transformer cores and catalysts [7, 8]. In addition, Liu reported that magnesium containing ferrites is preferred to obtain high resistivity and avoid the tendency of discontinuous grain growth to have dense ferrite [9]. The influence of the nonmagnetic Mg2+-ions as a substitutant for magnetic Ni2+-ions on the different ferrite systems has been investigated by studying structural and magnetic properties of these ferrite samples [10, 11]. A significant increase in the initial permeability was determined at Ni-content of 0.3 (Mg-content = 0.2) in NixMg0.5−xCu0.1Zn0.4Fe2O4 ferrite system [10]. Therefore, it is expected that the structural and magnetic properties of Ni-Cd ferrites could show a remarkable variation by Mg2+ substitution. In the current work, Mg2+-ions are substituted in the nanoferrite system Ni0.6Cd0.4Fe2O4 which was reported to give reasonable high magnetic values [6]. Nanoparticle samples of the ferrite system MgxNi0.6−xCd0.4Fe2O4 (x = 0–0.6 with step 0.2) were synthesized and studied in a wide range of temperatures.


## 2. Materials and Methods

Magnesium nickel cadmium nanoferrites (MgxNi0.6-xCd0.4Fe2O4, x = 0,0.1,0.2,0.3,0.4,0.5,0.6) were synthesized via the chemical coprecipitation method using NiSO4·6H2O, MgSO4·7H2O, CdCl2·H2O, FeCl3, and NaOH. Salts were mixed in the required stoichiometric ratios in deionized water. Sodium hydroxide (NaOH) solution was then added dropwise, while stirring, until the measured pH value was 12. The mixture was continually stirred at 700 rpm for two hours while being heated at 353 K. A dark color was observed due to the formation of the ferrite particles. Particles were allowed to settle and the mixture was washed several times until the measured pH value was about 7. The powder sample was then allowed to dry at room temperature. X-ray diffraction (XRD) patterns were performed using the diffractometer of type Philips and they were identified by CuKα radiation (λ
=
1.5418 Å). The (311) reflection line in XRD pattern was used to calculate the average crystallite size D using the Debye-Scherrer equation, D
=
(
0.9
λ
)
/
(
β
cos
⁡
θ
) [12], where β is the full width at half-maximum FWHM of the diffraction line and θ is the corresponding diffraction angle. The grain micrograph was obtained by low vacuum TEM JEOL (JEM-1400 TEM). FTIR spectra were carried out (using Perkin Elmer spectrophotometer) in the wavenumbers range 150–650 cm−1. Hysteresis loops were obtained at low temperature (6.5 K) as well as at room temperature using a Model 7410 Lake Shore Cryotronics Vibrating Sample Magnetometer (VSM). The results are normalized and displayed as saturation magnetization M
s (emu/g) versus field H (Oe).


## 3. Results and Discussion

### 3.1. X-Ray and TEM Analysis

XRD patterns in Figure1 indicate that all samples are formed in single phase of cubic spinel structure. The values of d-spacing are calculated according to Bragg’s law and hence the average lattice parameter a (Å) is determined. Variation of lattice parameter with the concentration of Mg2+-ions is plotted in Figure 2. It is clear that as the Mg-concentration increases the lattice parameter increases. Such a behavior was previously observed in Mg-substituted Ni-Cu-Zn ferrites [13]. The increase in lattice parameter could be explained on the basis of the ionic radii due to the replacement of ions with smaller ionic radius of Ni2+ (0.69 Å) by the larger ones of Mg2+ (0.72 Å). The composition dependence of crystallite size D is shown in Figure 2. It is obvious that D decreases slightly with increasing the Mg-content. The decrease of crystallite size due to Mg-substitution in Mg-Cd-Zn ferrites was reported in a previous work [14]. Such a behavior could be explained in the light of crystal growth process in a solution. It was reported that the crystal growth in a solution depends on various factors; the most important two are the following:(i)
the molecular concentration of the material approaching the surface of the tiny crystal during the growth process,
(ii)
the site preferences of the cations in the ferrite system.Figure 1
X-ray diffraction pattern of the system MgxNi0.6−xCd0.4Fe2O4.Figure 2
Changeof the lattice parametera (Å) and the crystallite size D (nm) with Mg-content of the system MgxNi0.6−xCd0.4Fe2O4.For the first factor (i), the local temperature is normally higher than the solution temperature due to the liberation of latent heat at the surface. The surface temperature affects the molecular concentration at the surface of the crystal and, hence, the crystal growth rate [15]. For the second one (ii), the grain growth is obstructed when the cationic preferences are not fully satisfied [16]. In view of these factors and the obtained behavior of D, one can conclude that as the Mg-content increases more heat may be liberated. This leads to a decrease in the molecular concentration at the crystal surface and hence obstructing the grain growth. Furthermore, according to the assumed cation distribution (Section 3.3), the tendency of both Mg2+- and Ni2+-ions to occupy B-sites leads to the migration of some Ni2+-ions from B- to A-sites although its high preference for B-sites occupation. This shows that the presence of Mg2+- and Ni2+-ions together makes the cationic preference not satisfied fully leading to the decrease of the rate of crystal growth.Transmission electron micrograph TEM was performed for the unsubstituted sample withx
=
0, as an example, and it is represented in Figure 3(a). The micrograph reveals that the obtained particles are spherical in shape and have a dominant value of diameter of about 5 nm. The particle size distribution that is obtained from TEM micrograph is represented by a histogram as shown in Figure 3(b).TEM micrograph for sample withx
=
0 (a) and its particle size distribution (b).
(a)
(b)


### 3.2. FTIR Spectra Analysis

The study of far-infrared spectrum is an important tool to get information about the position of ions in the crystal through the vibrational modes [17]. According to the group theory, the normal and inverse cubic spinel should have individual bands for the tetrahedral and octahedral complexes and another one for lattice vibrations [17, 18]. Figure 4 shows the FTIR spectra for the investigated samples in the wave number ranging from 150 to 650 cm−1. The given absorption bands from the spectrophotometer showed that there exist three fundamental bands {
ν
1
,
ν
2
,
ν
3
} confirming that the present system is formed in a cubic inverse spinel structure as was discussed in Section 3.1 [19]. It has been reported that the first two IR fundamental bands are due to tetrahedral and octahedral complexes, while the third one is due to the lattice vibrations [17]. IR spectra show no sharp peaks due to the extremely small particle size and therefore the limitation of the crystallinity in the current investigated samples. The high frequency band ν
1 (616–548 cm−1) is attributed to the vibration of iron ions in the tetrahedral positions. The second band ν
2 (363–494 cm−1) is associated with the iron ions with divalent octahedral metal ions and oxygen complexes. Finally, the third vibrational band (less than 300 cm−1) is attributed to the lattice vibrational frequency [20]. Figure 5(a) shows the variation of ν
1 and the values of A-sites radii r
A with the increase of the Mg-content. An increasing trend in values of ν
1 is noticed. This behavior could be attributed to the decrease in r
A which was calculated according to the assumed cation distribution taking into consideration that the values of the ionic radii are depending on the coordination number [21]. The cation distribution will be discussed in detail later. The decrease of r
A with Mg-content could be explained in the light of that distribution given in (1). Whereas the Mg-concentration increases in B-sites, the amount of Fe3+-ions (r
Fe
3
+
=
0.49 Å) increases in A-sites on the expense of Ni2+-ions (r
Ni
2
+
=
0.55 Å). That decrease of r
A leads to making the bond shorter/stronger, leading to an increase in the values of ν
1. On the other hand, Figure 5(b) shows the variation of ν
2 and the values of B-sites radii r
B with Mg-content. It is obvious that ν
2 dramatically decreases whereas r
B linearly increases with increasing the Mg-content. That decrease of ν
2 could be understood and explained by the increase of r
B. According to the assumed cation distribution, as the Mg-concentration increases in B-site (r
Mg
2
+
=
0.72 Å), both the amount of Fe3+-ions (r
Fe
3
+
=
0.65 Å) and amount of Ni2+-ions (r
Ni
2
+
=
0.69 Å) are decreasing. The decrease of r
A leads to making the bond longer/weaker, leading to a decrease in the values of ν
2.Figure 4
FTIR spectra of the system MgxNi0.6−xCd0.4Fe2O4.(a) Composition dependence of A-sites radii with the variation of the tetrahedral and (b) composition dependence of B-sites radii with the variation of the octahedral band in the system MgxNi0.6−xCd0.4Fe2O4.
(a)
(b)


### 3.3. Magnetic Properties

Hysteresis loops at room temperature (300 K) and at low temperature (6.5 K) for samples withx = 0, 0.2, 0.4, and 0.6 are shown in Figures 6(a) and 6(b). It is clear from Figure 6(a) that the loops for the samples that are measured at room temperature are closed ones, showing almost no coercivity, which is considered to be a typical superparamagnetic behavior. There is no full saturation behavior observed even near the high values of magnetic field for all the investigated samples which could be attributed to the canted surface spins in nanoparticles [22]. The values of the slopes of the M
-
H curves increase as the Mg-content increases. This behavior could be referred to the decreasing of particle size with the Mg-content leading to an increase in the area to volume ratio. On the other hand, Figure 6(b) in which the loops are measured at 6.5 K shows open hysteresis loops indicating the presence of an ordered magnetic structure. Variations of the values of saturation magnetization M
s (emu/g) which are measured at 300 and 6.5 K with Mg-concentration are represented in Figure 7. It is clear that at 6.5 K the values of M
s are higher than those measured at 300 K with an average percentage of 77.4%. This behavior is mainly due to the thermal disorder of magnetic moments. It is obvious that, at both temperatures, as Mg-content increases, the values of M
s linearly decrease. This trend could be explained in the light of the following proposed cation distribution:
(1)
(
Cd
0.4
2
+
Ni
(
0.04
-
0.06
x
)
2
+
Fe
(
0.56
+
0.06
x
)
3
+
)
A
[
Mg
x
2
+
N
i
(
0.56
-
0.94
x
)
2
+
Fe
(
1.44
-
0.06
x
)
3
+
]
B
.
That distribution is assumed according to the following bases.(1)
Cadmium ions prefer to occupy the tetrahedral sites (A-sites) [5, 23].
(2)
Magnesium preferential sites are the octahedral ones (B-sites) [11, 24].
(3)
It was reported that Ni2+-ions are distributed between the tetrahedral and octahedral sites such that the majority of these ions (about 94%) are located into the B-sites [11, 24].Hysteresis loops of the system MgxNi0.6−xCd0.4Fe2O4 (x = 0, 0.2, 0.4, and 0.6) at (a) room temperature and (b) 6.5 k.
(a)
(b)Figure 7
Composition dependence of saturation magnetization at low and room temperature of the system MgxNi0.6−xCd0.4Fe2O4. Inset shows the composition dependence of the coercive field at low temperature.According to the above cation distribution, the net magnetization (M) could be calculated as follows: M
=
M
B
-
M
A, where M
B and M
A are the magnetic moments of the octahedral and tetrahedral sites, respectively. Using the values of the magnetic moments of Fe3+, Ni2+, Mg2+, and Cd2+ as 5, 2, 0, and 0 μ
B, respectively, the total magnetic moment could be written as
(2)
M
=
5.44
-
2.36
x
.
Equation (2) represents a linear relationship between the Mg2+-ions concentration (x) and the magnetization value (M) which is in agreement with the obtained experimental behavior (cf. Figure 7). This agreement supports the validity of the assumed cation distribution.The coercivityH
c is automatically determined for the measured loops at 6.5 K and it is plotted as an inset in Figure 7. It is obvious that, in average, H
c is increasing with the increase of the Mg-concentration with an acceptable anomaly at x = 0.2. This behavior could be explained according to Brown’s relation [25]:
(3)
H
c
≥
(
2
K
eff
)
(
μ
o
M
s
)
,
where K
eff is the effective anisotropy constant, μ
o is the magnetic permeability, and M
s is the saturation magnetization. The increase in the values of H
c with Mg-content could be attributed to the decrease of M
s as the magnesium concentration increases, in addition to the increase of the values of the effective anisotropy constant K
eff with the increasing of Mg-content as will be discussed hereafter.The temperature dependence of ZFC- and FC-magnetization at 1 kOe for the current investigated samples is shown in Figure8. The peaks in ZFC-curves determine the values of the blocking temperature T
B. This phenomenon is called superparamagnetism and it is often observed in the nanoparticles in which each nanoscaled particle is considered to be a single magnetic domain [26]. The thermal energy at T
>
T
B is sufficient to induce fluctuations in the magnetization. The observed magnetization would depend on the measurement time t
m relative to the relaxation time τ of thermal fluctuations. This relaxation time τ for a single particle is given by [26]
(4)
τ
=
τ
o
exp
⁡
(
K
eff
V
k
B
T
)
,
where a characteristic time τ
o is typically 10−9 s, and k
B
T, K
eff, and V are, respectively, the thermal energy, the effective magnetic anisotropy constant, and the particle volume. The blocking temperature is then
(5)
T
B
=
K
eff
V
[
k
B
ln
⁡
(
t
m
/
τ
o
)
]
,
with the measuring time t
m
=
τ.Figure 8
ZFC- and FC-magnetization curves of the system MgxNi0.6−xCd0.4Fe2O4. The blocking temperature values are listed in the legend box.By assumingt
m
/
τ
o
=
10
11 in a typical magnetization measurement, one arrives at the commonly cited equation:
(6)
T
B
=
K
eff
V
25
k
B
.The values of blocking temperatureT
B are determined from the peak of ZFC-curve for each sample and they are listed inside Figure 8. It is clear that the blocking temperature shows no considerable variation with the Mg-content. This could be explained according to (6) as follows.As the Mg-content increases, the particle volume (V
=
(
π
/
6
)
D
3) decreases (cf. Figure 2) leading to decreasing the values of T
B. On the other hand, it was reported that the values of the effective anisotropy constant for Mg-Zn and Ni-Zn ferrites are 105 and 1.7 × 104 J/m3, respectively [27, 28]. This means that the presence of magnesium in such ferrites enhances the values of K
eff. Thus, the increase of Mg-content leads to an increase in T
B. In other words, the almost constancy of T
B could be attributed to the competition between the increase of anisotropy constant and the decrease in the particle size with increasing Mg-content. The increase of the calculated values of the anisotropy constant with Mg-content for the present samples is illustrated in Figure 9.Figure 9
Composition dependence of the anisotropy constant and the splitting range of the system MgxNi0.6−xCd0.4Fe2O4.Figure8 shows also that, for all investigated samples, there is a coincidence between the values of ZFC- and FC-magnetization down to a certain temperature (referred to as T
S) at which the splitting between the two curves begins to take place. According to (6), each particle size (V) meets a certain value of blocking temperature (T
B). This means that when all the particles in the sample have the same size (maximum homogeneity) there will be a coincidence between the values of T
B and T
S with a sharp peak in ZFC-curve. The above discussion reveals that, as the homogeneity is destroyed, the difference between T
S and T
B (Δ
T
S
B
=
T
S
-
T
B) will increase. The composition dependence of Δ
T
S
B for the current investigated samples is illustrated in Figure 9. It is clear that as Mg-content increases, Δ
T
S
B increases, indicating that magnesium destroys homogeneity.


## 3.1. X-Ray and TEM Analysis

XRD patterns in Figure1 indicate that all samples are formed in single phase of cubic spinel structure. The values of d-spacing are calculated according to Bragg’s law and hence the average lattice parameter a (Å) is determined. Variation of lattice parameter with the concentration of Mg2+-ions is plotted in Figure 2. It is clear that as the Mg-concentration increases the lattice parameter increases. Such a behavior was previously observed in Mg-substituted Ni-Cu-Zn ferrites [13]. The increase in lattice parameter could be explained on the basis of the ionic radii due to the replacement of ions with smaller ionic radius of Ni2+ (0.69 Å) by the larger ones of Mg2+ (0.72 Å). The composition dependence of crystallite size D is shown in Figure 2. It is obvious that D decreases slightly with increasing the Mg-content. The decrease of crystallite size due to Mg-substitution in Mg-Cd-Zn ferrites was reported in a previous work [14]. Such a behavior could be explained in the light of crystal growth process in a solution. It was reported that the crystal growth in a solution depends on various factors; the most important two are the following:(i)
the molecular concentration of the material approaching the surface of the tiny crystal during the growth process,
(ii)
the site preferences of the cations in the ferrite system.Figure 1
X-ray diffraction pattern of the system MgxNi0.6−xCd0.4Fe2O4.Figure 2
Changeof the lattice parametera (Å) and the crystallite size D (nm) with Mg-content of the system MgxNi0.6−xCd0.4Fe2O4.For the first factor (i), the local temperature is normally higher than the solution temperature due to the liberation of latent heat at the surface. The surface temperature affects the molecular concentration at the surface of the crystal and, hence, the crystal growth rate [15]. For the second one (ii), the grain growth is obstructed when the cationic preferences are not fully satisfied [16]. In view of these factors and the obtained behavior of D, one can conclude that as the Mg-content increases more heat may be liberated. This leads to a decrease in the molecular concentration at the crystal surface and hence obstructing the grain growth. Furthermore, according to the assumed cation distribution (Section 3.3), the tendency of both Mg2+- and Ni2+-ions to occupy B-sites leads to the migration of some Ni2+-ions from B- to A-sites although its high preference for B-sites occupation. This shows that the presence of Mg2+- and Ni2+-ions together makes the cationic preference not satisfied fully leading to the decrease of the rate of crystal growth.Transmission electron micrograph TEM was performed for the unsubstituted sample withx
=
0, as an example, and it is represented in Figure 3(a). The micrograph reveals that the obtained particles are spherical in shape and have a dominant value of diameter of about 5 nm. The particle size distribution that is obtained from TEM micrograph is represented by a histogram as shown in Figure 3(b).TEM micrograph for sample withx
=
0 (a) and its particle size distribution (b).
(a)
(b)


## 3.2. FTIR Spectra Analysis

The study of far-infrared spectrum is an important tool to get information about the position of ions in the crystal through the vibrational modes [17]. According to the group theory, the normal and inverse cubic spinel should have individual bands for the tetrahedral and octahedral complexes and another one for lattice vibrations [17, 18]. Figure 4 shows the FTIR spectra for the investigated samples in the wave number ranging from 150 to 650 cm−1. The given absorption bands from the spectrophotometer showed that there exist three fundamental bands {
ν
1
,
ν
2
,
ν
3
} confirming that the present system is formed in a cubic inverse spinel structure as was discussed in Section 3.1 [19]. It has been reported that the first two IR fundamental bands are due to tetrahedral and octahedral complexes, while the third one is due to the lattice vibrations [17]. IR spectra show no sharp peaks due to the extremely small particle size and therefore the limitation of the crystallinity in the current investigated samples. The high frequency band ν
1 (616–548 cm−1) is attributed to the vibration of iron ions in the tetrahedral positions. The second band ν
2 (363–494 cm−1) is associated with the iron ions with divalent octahedral metal ions and oxygen complexes. Finally, the third vibrational band (less than 300 cm−1) is attributed to the lattice vibrational frequency [20]. Figure 5(a) shows the variation of ν
1 and the values of A-sites radii r
A with the increase of the Mg-content. An increasing trend in values of ν
1 is noticed. This behavior could be attributed to the decrease in r
A which was calculated according to the assumed cation distribution taking into consideration that the values of the ionic radii are depending on the coordination number [21]. The cation distribution will be discussed in detail later. The decrease of r
A with Mg-content could be explained in the light of that distribution given in (1). Whereas the Mg-concentration increases in B-sites, the amount of Fe3+-ions (r
Fe
3
+
=
0.49 Å) increases in A-sites on the expense of Ni2+-ions (r
Ni
2
+
=
0.55 Å). That decrease of r
A leads to making the bond shorter/stronger, leading to an increase in the values of ν
1. On the other hand, Figure 5(b) shows the variation of ν
2 and the values of B-sites radii r
B with Mg-content. It is obvious that ν
2 dramatically decreases whereas r
B linearly increases with increasing the Mg-content. That decrease of ν
2 could be understood and explained by the increase of r
B. According to the assumed cation distribution, as the Mg-concentration increases in B-site (r
Mg
2
+
=
0.72 Å), both the amount of Fe3+-ions (r
Fe
3
+
=
0.65 Å) and amount of Ni2+-ions (r
Ni
2
+
=
0.69 Å) are decreasing. The decrease of r
A leads to making the bond longer/weaker, leading to a decrease in the values of ν
2.Figure 4
FTIR spectra of the system MgxNi0.6−xCd0.4Fe2O4.(a) Composition dependence of A-sites radii with the variation of the tetrahedral and (b) composition dependence of B-sites radii with the variation of the octahedral band in the system MgxNi0.6−xCd0.4Fe2O4.
(a)
(b)


## 3.3. Magnetic Properties

Hysteresis loops at room temperature (300 K) and at low temperature (6.5 K) for samples withx = 0, 0.2, 0.4, and 0.6 are shown in Figures 6(a) and 6(b). It is clear from Figure 6(a) that the loops for the samples that are measured at room temperature are closed ones, showing almost no coercivity, which is considered to be a typical superparamagnetic behavior. There is no full saturation behavior observed even near the high values of magnetic field for all the investigated samples which could be attributed to the canted surface spins in nanoparticles [22]. The values of the slopes of the M
-
H curves increase as the Mg-content increases. This behavior could be referred to the decreasing of particle size with the Mg-content leading to an increase in the area to volume ratio. On the other hand, Figure 6(b) in which the loops are measured at 6.5 K shows open hysteresis loops indicating the presence of an ordered magnetic structure. Variations of the values of saturation magnetization M
s (emu/g) which are measured at 300 and 6.5 K with Mg-concentration are represented in Figure 7. It is clear that at 6.5 K the values of M
s are higher than those measured at 300 K with an average percentage of 77.4%. This behavior is mainly due to the thermal disorder of magnetic moments. It is obvious that, at both temperatures, as Mg-content increases, the values of M
s linearly decrease. This trend could be explained in the light of the following proposed cation distribution:
(1)
(
Cd
0.4
2
+
Ni
(
0.04
-
0.06
x
)
2
+
Fe
(
0.56
+
0.06
x
)
3
+
)
A
[
Mg
x
2
+
N
i
(
0.56
-
0.94
x
)
2
+
Fe
(
1.44
-
0.06
x
)
3
+
]
B
.
That distribution is assumed according to the following bases.(1)
Cadmium ions prefer to occupy the tetrahedral sites (A-sites) [5, 23].
(2)
Magnesium preferential sites are the octahedral ones (B-sites) [11, 24].
(3)
It was reported that Ni2+-ions are distributed between the tetrahedral and octahedral sites such that the majority of these ions (about 94%) are located into the B-sites [11, 24].Hysteresis loops of the system MgxNi0.6−xCd0.4Fe2O4 (x = 0, 0.2, 0.4, and 0.6) at (a) room temperature and (b) 6.5 k.
(a)
(b)Figure 7
Composition dependence of saturation magnetization at low and room temperature of the system MgxNi0.6−xCd0.4Fe2O4. Inset shows the composition dependence of the coercive field at low temperature.According to the above cation distribution, the net magnetization (M) could be calculated as follows: M
=
M
B
-
M
A, where M
B and M
A are the magnetic moments of the octahedral and tetrahedral sites, respectively. Using the values of the magnetic moments of Fe3+, Ni2+, Mg2+, and Cd2+ as 5, 2, 0, and 0 μ
B, respectively, the total magnetic moment could be written as
(2)
M
=
5.44
-
2.36
x
.
Equation (2) represents a linear relationship between the Mg2+-ions concentration (x) and the magnetization value (M) which is in agreement with the obtained experimental behavior (cf. Figure 7). This agreement supports the validity of the assumed cation distribution.The coercivityH
c is automatically determined for the measured loops at 6.5 K and it is plotted as an inset in Figure 7. It is obvious that, in average, H
c is increasing with the increase of the Mg-concentration with an acceptable anomaly at x = 0.2. This behavior could be explained according to Brown’s relation [25]:
(3)
H
c
≥
(
2
K
eff
)
(
μ
o
M
s
)
,
where K
eff is the effective anisotropy constant, μ
o is the magnetic permeability, and M
s is the saturation magnetization. The increase in the values of H
c with Mg-content could be attributed to the decrease of M
s as the magnesium concentration increases, in addition to the increase of the values of the effective anisotropy constant K
eff with the increasing of Mg-content as will be discussed hereafter.The temperature dependence of ZFC- and FC-magnetization at 1 kOe for the current investigated samples is shown in Figure8. The peaks in ZFC-curves determine the values of the blocking temperature T
B. This phenomenon is called superparamagnetism and it is often observed in the nanoparticles in which each nanoscaled particle is considered to be a single magnetic domain [26]. The thermal energy at T
>
T
B is sufficient to induce fluctuations in the magnetization. The observed magnetization would depend on the measurement time t
m relative to the relaxation time τ of thermal fluctuations. This relaxation time τ for a single particle is given by [26]
(4)
τ
=
τ
o
exp
⁡
(
K
eff
V
k
B
T
)
,
where a characteristic time τ
o is typically 10−9 s, and k
B
T, K
eff, and V are, respectively, the thermal energy, the effective magnetic anisotropy constant, and the particle volume. The blocking temperature is then
(5)
T
B
=
K
eff
V
[
k
B
ln
⁡
(
t
m
/
τ
o
)
]
,
with the measuring time t
m
=
τ.Figure 8
ZFC- and FC-magnetization curves of the system MgxNi0.6−xCd0.4Fe2O4. The blocking temperature values are listed in the legend box.By assumingt
m
/
τ
o
=
10
11 in a typical magnetization measurement, one arrives at the commonly cited equation:
(6)
T
B
=
K
eff
V
25
k
B
.The values of blocking temperatureT
B are determined from the peak of ZFC-curve for each sample and they are listed inside Figure 8. It is clear that the blocking temperature shows no considerable variation with the Mg-content. This could be explained according to (6) as follows.As the Mg-content increases, the particle volume (V
=
(
π
/
6
)
D
3) decreases (cf. Figure 2) leading to decreasing the values of T
B. On the other hand, it was reported that the values of the effective anisotropy constant for Mg-Zn and Ni-Zn ferrites are 105 and 1.7 × 104 J/m3, respectively [27, 28]. This means that the presence of magnesium in such ferrites enhances the values of K
eff. Thus, the increase of Mg-content leads to an increase in T
B. In other words, the almost constancy of T
B could be attributed to the competition between the increase of anisotropy constant and the decrease in the particle size with increasing Mg-content. The increase of the calculated values of the anisotropy constant with Mg-content for the present samples is illustrated in Figure 9.Figure 9
Composition dependence of the anisotropy constant and the splitting range of the system MgxNi0.6−xCd0.4Fe2O4.Figure8 shows also that, for all investigated samples, there is a coincidence between the values of ZFC- and FC-magnetization down to a certain temperature (referred to as T
S) at which the splitting between the two curves begins to take place. According to (6), each particle size (V) meets a certain value of blocking temperature (T
B). This means that when all the particles in the sample have the same size (maximum homogeneity) there will be a coincidence between the values of T
B and T
S with a sharp peak in ZFC-curve. The above discussion reveals that, as the homogeneity is destroyed, the difference between T
S and T
B (Δ
T
S
B
=
T
S
-
T
B) will increase. The composition dependence of Δ
T
S
B for the current investigated samples is illustrated in Figure 9. It is clear that as Mg-content increases, Δ
T
S
B increases, indicating that magnesium destroys homogeneity.


## 4. Conclusion

Taken together, we provide the following conclusions.(i)
The chemical coprecipitation technique has been used for the synthesis of a single spinel cubic phase of MgxNi0.6−xCd0.4Fe2O4 ferrite nanoparticles with Mg-concentration up to 0.6.
(ii)
The values of lattice parameter were increased due to the Mg-substitution whereas the calculated crystallite size decreased slightly.
(iii)
Mg-substitution in Ni-Cd ferrites leads to a decrease in the values of the saturation magnetization and an increase in the values of coercive field.
(iv)
No considerable variation was observed in the values of the blocking temperature with increasing Mg-content, whereas the values of the effective anisotropy constant were increased.



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*Source: 492832-2014-05-26.xml*