Investigation of the influences of La substitution and ... 15.pdf · Ni 0.12 Mg 0.18 Cu 0.20 Zn 0.50 Fe 1.925 La 0.075 O 4 sintered at 1250°C among the studied samples. Keyword:

Investigation of the influences of La substitution and sintering temperature

on the structural and complex permeability of Ni-Mg-Cu-Zn ferrites

S. K. Shil1*

, A. K. M. Hossain2, D. K. Shaha

3, S. S. Sikder

1

1Department of Physics, Khulna University of Engineering & Technology, Khulna-9203, Bangladesh.

2Department of Physics, Bangladesh University of Engineering & Technology, Dhaka-1000, Bangladesh.

3Materials Science Division, Atomic Energy Centre, Ramna, Dhaka-1000, Bangladesh.

*Corresponding author: [email protected]

Abstract:

Polycrystalline Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 (with x = 0.00, 0.025, 0.050 and 0.075) were

prepared by conventional solid state reaction technique. Pellet and toroid shaped samples were

prepared from each composition and were sintered at various temperatures (Ts) in air for 5 hours. X-

ray diffraction patterns of the samples show the formation of cubic spinel structure. Lattice parameter

increases with increasing La substitution. Theoretical density (𝝆𝒕𝒉) and bulk density (𝝆𝑩) both

increase with increasing La content. The 𝝆𝑩 increases with increasing Ts up to 1200°C then decreases

for a further increase of Ts up to 1250°C. On the other hand porosity has the opposite trend. It is also

observed that /

i increases with increasing Ts for all ferrites up to 1200°C then decreases for sample

sintered at 1250°C. It is expected that there might have a correlation between 𝝆𝑩 and permeability.

The /

i remains fairly constant in the frequency range up to 10 kHz or greater for parent composition

and 1 MHz or greater for La doped compositions. The imaginary part of initial permeability starts

raising beyond this frequency which is an indication of dispersion or resonance. At high frequency,

the loss factor of all La doped compositions is lower than parent composition and decreases with

increasing La substitution. The relative quality factor is found to be maximum in

Ni0.12Mg0.18Cu0.20Zn0.50Fe1.925La0.075O4 sintered at 1250°C among the studied samples.

Keyword: La substituted Ni-Mg-Cu-Zn ferrite, Complex permeability, Loss factor, Relative quality

factor.

1. INTRODUCTION

Ferrites are ceramic magnetic materials which possess the combined properties of magnetic materials and

insulators. Technological advances in a variety of areas have generated a growing demand for the soft magnetic

materials in devices. The technological applications of ferrites is influenced by the physical and chemical

properties of materials and depends on many factors including the preparation conditions, such as, sintering

temperature, sintering time, rate of heating and cooling. It was known that the metal ions in a ferrite crystal

occupied two different kinds of position called A sites and B sites in AB2O4 crystal structure. Néel made the

basic assumption that the exchange force acting between an ion on A site and an ion on B site, was negative, as

in an antiferromagnetic. There is thus a lattice of A ions spontaneously magnetized in one direction and a lattice

of B ions magnetized in the opposite direction. However, in ferrimagnetic, the magnitudes of the A and B

sublattice magnetization are not equal. The two opposing magnetic moments do not cancel and a net

spontaneous magnetization results. Every magnetic and electric property of ferrites depends on the sublattice

distribution of cations. Among the soft magnetic materials, polycrystalline ferrites have received special

attention due to their good magnetic properties and high electrical resistivity over a wide range of frequencies.

Spinel type ferrites are commonly used in many electronic and magnetic devices due to their high magnetic

permeability and low magnetic losses [1,2] and also used in electrode materials for high temperature

applications because of their high thermodynamic stability, electrical resistivity, electrolytic activity and

resistance to corrosion [3,4]. Spinel ferrites are also used in the fabrication of multilayer chip inductors (MLCIs)

as surface mount devices for miniaturized electronic products such as cellular phones, notebook computers,

video camera recorders, floppy drives etc [5]. Loudspeakers, motors, deflection yokes, electromagnetic

interference suppressors, radar absorbers, antenna rods, proximity sensors, humidity sensors, memory devices,

recording heads, broadband transformers, filters, inductors etc are fabricated based on ferrites. So ferrites are

subject of intense theoretical and experimental investigations [6-13]. The magnetic properties can be changed by

the substitution of various kinds of divalent cations (Co2+

, Mg2+

, Fe2+

, Mn2+

) or by introducing a relatively small

P-ID 15 International Conference on Physics Sustainable Development & Technology (ICPSDT-2015)(August 19-20, 2015)

Department of Physics, CUET.

Page 22

amount of rare-earth ions. Many investigations have been carried out to understand the effect of La substitution

on the properties of Ni-Zn ferrite [14,15], Mn-Zn ferrite [16], Mg-Cu ferrite [17]. Sun et al. [14] reported that

the permeability of Ni-Zn ferrite decreases with La substitution. On the other hand P. K. Roy et al. [18] reported

that permeability of Ni-Cu-Zn ferrite increases with slight substitution of La. So a detailed study is necessary to

ensure the La substitutions. Again Hua Su [19] reported that initial permeability of Ni-Cu-Zn ferrite increases

with substitution of Mg. On the other hand Ch. Sujatha [20] reported that initial permeability decreases with

increasing Mg content. M. A. Gabal [21] also reported improved magnetic properties of Ni-Cu-Zn ferrite with

slight substitution of Mg. It is observed that there is not much publish works on Ni-Mg-Cu-Zn ferrite with La

substitution. So the purpose of our present investigation is to study the effect of La3+

substitutions for Fe3+

on

the structural and magnetic properties of Ni-Mg-Cu-Zn ferrites. For this investigation,

Ni0.12Mg0.18Cu0.20Zn0.50Fe2O4 was taken as the nominal composition.

2. EXPERIMENTAL

The Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 (for x = 0.00, 0.025, 0.050 and 0.075)

samples were prepared by the standard solid-state reaction technique. Powder of NiO (99.9%), MgO (99.9%),

CuO (99.9%), ZnO (99.9%), La2O3 (99.9%) and Fe2O3 (99.9%) were used as raw materials. Proper amounts of

required powders were mixed thoroughly and then calcined at 950°C for 5 h. The calcined powders were then

pressed into disk-shaped and toroid-shaped samples. The samples were sintered at various temperatures 1100,

1150, 1200 and 1250°C in air for 5 h. The temperature rate was 5°C/ min for heating and 10oC/ min for

cooling.X-ray diffraction was carried out with a PHILIPS PW 3040 X’pert PRO X-ray diffractometer using Cu-

K radiation. From the X-ray diffraction pattern lattice parameter was determined by using Nelson-Riley

function. Theoretical density, 𝜌𝑡ℎ , was calculated using the relation 𝜌𝑡ℎ = 𝑍𝑀 𝑁𝐴𝑎03 , where M is the molecular

weight, NA is the Avogadro’s number, 𝑎0 is the lattice parameter and Z is the number of molecules per unit cell,

which is 8 for the spinel structure. The bulk density was calculated by considering the cylindrical shape of the

pellets and using the relation 𝜌𝐵 = 𝑚 𝑉 = 𝑚 𝜋𝑟2ℎ , where m is the mass, r is the radius and h is the thickness

of the pellet. Porosity of the samples was then determined by the relation 𝑃 = (1 − 𝜌𝐵 𝜌𝑡ℎ ). The frequency

characteristics i.e. the initial permeability spectra of the toroid shaped samples were measured using a Wayne

kerr Impedance Analyzer (Model No. 6500B). The complex permeability measurements on toroid shaped

specimens were carried out at room temperature in the frequency range 1 kHz to 100 kHz. The real part of

complex permeability 𝜇𝑖/ was calculated using relation, 𝜇𝑖

/= 𝐿𝑠/𝐿0 , where LS is the self inductance of the

sample and Lo is the inductance of the coil of same geometric shape of vacuum. Lo is determined using the

relation 𝐿0 = 𝜇0𝑁2 𝑑1 − 𝑑2 ℎ/𝜋(𝑑1 + 𝑑2), where 𝜇0 is the permeability of the free space, N is the number of

turns (here N=4), d1 is the outer diameter and d2 is the inner diameter of the sample and h is the thickness of the

sample. The imaginary part of complex permeability 𝜇𝑖//

was determined using the formula 𝜇𝑖//= 𝜇𝑖

/× 𝐷. The

relative quality factor was calculated from the Loss factor, tanδ (𝑡𝑎𝑛𝛿 = 𝜇𝑖//

𝜇𝑖/) using the ratio 𝜇𝑖

//𝑡𝑎𝑛𝛿.

3. RESULTS AND DISCUSSION

3.1 X-ray diffraction analysis

The X-ray diffraction (XRD) was performed to verify the formation of spinel structure of various

Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 ferrites, in which Fe3+

is replaced by La3+

. The XRD patterns of these La

substituted Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 (with x = 0.00, 0.025, 0.050 and 0.075) ferrites sintered at 1200° C

in air for 5h are shown in Fig. 1. The results indicated that there is formation of spinel structure for each

composition. Analyzing the XRD patterns it is observed that the fundamental reflections from the planes (220),

(311), (222), (400), (422), (511) and (440) comply with the reported value [22]. From the XRD patterns, a

secondary phase LaFeO3 was detected in all La doped samples. It has been established that secondary phase

LaFeO3 was formed upon La substitution for Fe in the ferrite. The peak height of LaFeO3 gradually increases

with the substitution of La. This indicates that La did not form solid solution with spinel structure or has limited

solid solubility. A detailed study on this phase formation behaviour has been described by Roy et al. [23].



Page 23

Fig. 1 The X-ray diffraction patterns of polycrystalline various Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 (x=0.00,

0.025, 0.050 and 0.075) sintered at 1200°C.

3.1.1 Lattice parameters

The lattice constant 𝑎0, as a function of La content for various

Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 sintered at 1200°C is presented in Fig. 2. It is noticed from this figure that the

lattice constant increases with increasing La3+

content in the various Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 up to

x=0.050 then decreases. The increase in lattice constant with La content indicates that the present compositions

obey the Vegard’s law [24] up to x=0.050. There exist a correlation between the ionic radius and the lattice

constant, the increase of lattice constant is proportional to the increase of the ionic radius [25]. The lattice

constant increases because the unit cell has expanded when substituted ionic size is larger. The ionic radius of

La3+

(1.061Å) is greater than that of Fe3+

(0.645Å) [26]. When the larger La ions enter the lattice, although the

unit cell expands it preserves the overall cubic symmetry. The decrease of lattice constant at x=0.075 due to

shifting of peaks to the higher angle.

20 30 40 50 60 70

x=0.00

x=0.025

x=0.050

Ts=1200°C

**

(40

0)

(31

1)

(44

0)

(51

1)

(42

2)

(22

2)

Ni0.12

Mg0.18

Cu0.20

Zn0.50

Fe2-x

LaxO

4

Inte

nsi

ty (

a.

u.)

2 (degree)

(22

0)

x=0.075

* =LaFeO3



Page 24

Fig. 2 The variation of Lattice parameter with La content for Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4.

3.2 Density and porosity

Fig. 3 shows the variation of bulk density and theoretical density with La content of the samples sintered at

various temperatures. It is observed that theoretical density and bulk density both increases with increasing La

content. The increase in density with increasing La content can be explained on the basis of the atomic weight.

The atomic weight of Fe (55.845 amu) is less than that of La (138.9055 amu). From our previous study, it is

confirmed that lattice parameter increases with substitution of La. We know density is equal to mass per unit

volume. In this case, with substitution of La atomic weight increases more than volume. Therefore increase in

density is expected. Fig. 4 shows the variation of porosity as a function of La content of the samples sintered at

1100, 1150, 1200 and 1250ºC respectively. It is found that for all samples porosity decreases with La content.

The variation of porosity with La substitution is opposite of variation of density.

0.000 0.025 0.050 0.0758.404

8.408

8.412

8.416

Ts=1200°C

Ni0.12

Mg0.18

Cu0.20

Zn0.50

Fe2-x

LaxO

4

Latt

ice p

ara

mete

r, a

0(Å

)

La content, x



Page 25

Fig. 3 Variation of bulk density and theoretical density with La content of the polycrystalline

Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 sintered at various temperatures.

Fig. 4 Variation of porosity with La content of the polycrystalline Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 sintered at

various temperatures.

0.000 0.025 0.050 0.075

4

6

8

10

12 Ni0.12

Mg0.18

Cu0.20

Zn0.50

Fe2-x

LaxO

4

Por

osit

y, P

(%)

La content, x

1100°C

1150°C

1200°C

1250°C

0.000 0.025 0.050 0.0754.4

4.6

4.8

5.0

5.2

5.4Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

Den

sity

(g

/cm

3)

La content, x

1100°C

1150°C

1200°C

1250°C

Bulk density

Theoretical density



Page 26

Fig. 5 shows the variation of bulk density with sintering temperature of polycrystalline

Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 for x=0.00, 0.025, 0.050 and 0.075. It is observed that bulk density increases

with increasing sintering temperature up to 1200°C then decreases. The increase in density with sintering

temperature is expected. This is because during the sintering process, the thermal energy generates a force that

drives the grain boundaries to grow over pores, thereby decreasing the pore volume and densifying the material.

This decrease in density at higher sintering temperature is attributed to the increased intra-granular porosity

resulting from discontinuous grain growth as proposed by Coble and Burke [27].

Fig. 5 Variation of bulk density with sintering temperature of polycrystalline Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4.

Fig. 6 shows the variation of porosity with sintering temperature of polycrystalline Ni0.12Mg0.18Cu0.20Zn0.50Fe2-

xLaxO4 samples for x=0.00, 0.025, 0.050 and 0.075. It is observed that porosity of all samples decreases with

increasing sintering temperature up to 1200°C then increases. This variation of porosity with sintering

temperature is exactly opposite to the variation of bulk density.

1100 1150 1200 1250

4.6

4.8

5.0

5.2

Ni0.12

Mg0.18

Cu0.20

Zn0.50

Fe2-x

LaxO

4

Sintering temperature (°C)

Bu

lk d

en

sity

(g

/cm

3)

x=0.00

x=0.025

x=0.050

x=0.075

Bu

lk d

en

sity

(g

/cm

3)



Page 27

Fig. 6 Variation of porosity with sintering temperature of the polycrystalline Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4.

It is known that the porosity of ceramic samples results from two sources, intragranular porosity and

intergranular porosity [9]. Thus the total porosity could be written as P=Pintra+Pinter. The intergranular porosity

mainly depends on the grain size [28]. At higher sintering temperatures the density decreases because the

intragranular porosity increases resulting from discontinuous grain growth. When the grain growth rate is very

high, pores may be left behind by rapidly moving grain boundaries, resulting in pores that are trapped inside the

grains. The discontinuous growth of the grain rises with temperature and hence contributes toward the reduction

of bulk density. This result agrees with the result for Ni-Zn ferrites [29].

1100 1150 1200 12502

4

6

8

10

12 Ni0.12

Mg0.18

Cu0.20

Zn0.50

Fe2-x

LaxO

4

Por

osit

y, P

(%)


x=0.00

x=0.025

x=0.050

x=0.075



Page 28

Table 1 The lattice parameter, density, porosity, natural resonance frequency and real part of initial permeability

of the various Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 sintered at various temperatures with fixed dwell time 5h.

3.3 Complex permeability

Figs. 7, 8, 9 and 10 show the complex permeability spectra for Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 sintered at

1100, 1150, 1200 and 1250ºC respectively. It is found that the real (/

i ) and imaginary (//

i ) permeability

decrease with increasing La3+

substitution.

Fig. 7 The variation of (a) /i and (b)

//

i spectra for Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 sintered at 1100˚C in

air.

x a(Å) Ts

(0C)

ρth

(g/cm3)

ρB

(g/cm3)

P

(%)

fr

(MHz)

/i (at 100

kHz)

0.00 8.40496

1100

5.20

4.59 12 15.73 246

1150 4.84 7 11.67 432

1200 4.90 6 8.05 674

1250 4.84 7 2.54 802

0.025 8.40875

1100

5.24

4.69 11 16.00 193

1150 4.90 7 15.18 237

1200 4.96 5 14.60 410

1250 4.89 7 19.07 351

0.050 8.41407

1100

5.28

4.77 10 16.29 167

1150 5.00 5 14.66 257

1200 5.08 4 18.70 343

1250 4.99 5 18.74 338

0.075 8.41078

1100

5.33

4.86 9 17.16 145

1150 5.09 4 19.07 257

1200 5.18 3 17.40 313

1250 5.12 4 13.43 292

105

106

107

108

0

20

40

60

80

100Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

Imag

inary

perm

eab

ilit

y

i

Frequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075

Ts= 1100°C

(b)

102

103

104

105

106

107

108

0

100

200

300

Ni0.12

Mg0.18

Cu0.20

Zn0.50

Fe2-x

LaxO

4

Real

perm

eab

ilit

y

i/

Frequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075

(a)

Ts= 1100°C



Page 29


//


air.


//


air.


//

i spectra for Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 sintered at

1250˚C in air.

105

106

107

108

0

50

100

150

200Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

Imag

inar

y p

erm

eab

ilit

y

i

Frequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075

(b)

Ts= 1250°C

102

103

104

105

106

107

108

0

200

400

600

800Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

Rea

l p

erm

eab

ilit

y

i

Frequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075

Ts= 1250°C

(a)

105

106

107

108

0

50

100

150

Ni0.12

Mg0.18

Cu0.20

Zn0.50

Fe2-x

LaxO

4

Imag

inar

y p

erm

eab

ilit

y

i

Frequency (Hz)

x=0.00

x0.025

x=0.050

x=0.075

Ts= 1200°C

(b)

102

103

104

105

106

107

108

0

200

400

600

800Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

Rea

l p

erm

eab

ilit

y

i/

Frequency (Hz)

x=0.000

x=0.025

x=0.050

x=0.075

Ts= 1200°C

(a)

105

106

107

108

0

50

100

150Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

Imag

inar

y p

erm

eab

ilit

y,

i//

Frequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075

Ts= 1150°C

(b)

102

103

104

105

106

107

108

0

100

200

300

400

500Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

R

eal

per

mea

bil

ity

,

i/

Frequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075Ts= 1150°C

(a)



Page 30

Fig. 11 shows the variation of /i with La content of the samples. It is found that

/i decreases sharply with La

content up to 0.025, with a further increase of La /i decreases slightly except sample sintered at 1150°C.

The initial permeability of ferrite material depends on many factors like reversible domain wall displacement,

domain wall bulging as well as microstructural features viz., average grain size, intra-granular porosity, etc.

[11]. In a demagnetized magnetic material, there are a number of Weiss domains with Bloch walls separating

two domains. These walls are bound to the equilibrium positions. It is well known that the permeability of

polycrystalline ferrite is related to two magnetizing mechanisms: spin rotation and domain wall motion. [30],

which can be described as, spinwi 1 , where w is the domain wall susceptibility; spin is

intrinsic rotational susceptibility. w and spin may be written as: 43 2DM sw and

KM sspin

22 with Ms saturation magnetization, K the total anisotropy, D the average grain diameter, and

the domain wall energy. The /i is a function of grain size. As the grain size decreases with La content, the

/i also decreases. The domain wall motion is affected by the grain size and enhanced with the increase of

grain size thus the /i increases. The magnetization caused by domain wall movement requires less energy than

that required by domain rotation. As the number of domain walls increases with the grain size, the contribution

of wall movement to magnetization increases. Fig. 12 shows the variation of /i

with sintering temperature of

the samples. The /i

of La substituted samples increases with increasing sintering temperature up to 1200°C

then decreases. The /i increases with increasing sintering temperature because porosity decreases with

sintering temperature. The reason behind this is the samples heated at higher temperature contain increasing

number of pores within the grain and pore is a hindrance for the domain wall motion which results in decrease

in permeability.

Fig. 11 The variation of Real part of initial permeability with La content of polycrystalline

Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 sintered at various temperatures in air at frequency 1 kHz.

0.000 0.025 0.050 0.075

200

400

600

800Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

Real

pert

of

init

ial

perm

eab

ilit

y

La content, x

1100°C

1150°C

1200°C

1250°C



Page 31

Fig. 12 The variation of Real part of initial permeability with sintering temperature of polycrystalline

Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 at frequency 1 kHz.

Fig. 13 The variation of bulk density and permeability with sintering temperature of Ni0.12Mg0.18Cu0.20Zn0.50Fe2-

xLaxO4 with (a) x=0.00, (b) x=0.025, (c) x=0.050 and (d) x=0.075.

1100 1150 1200 1250

200

400

600

800 Ni0.12

Mg0.18

Cu0.20

Zn0.50

Fe2-x

LaxO

4

Rea

l par

t of

initi

al p

erm

eabi

lity


x=0.00

x=0.025

x=0.050

x0.075

1100 1150 1200 1250

4.6

4.7

4.8

4.9

5.0

200

400

600

800

Per

mea

bil

ity

,

Bu

lk d

ensi

ty,


Ni0.12

Mg0.18

Cu0.20

Zn0.50

Fe2O

4

(a)

1100 1150 1200 1250

4.7

4.8

4.9

5.0

200

300

400

Per

mea

bil

ity

,

Bu

lk d

ensi

ty,


Ni0.12

Mg0.18

Cu0.20

Zn0.50

Fe1.975

La0.025

O4

(b)

1100 1150 1200 1250

4.8

4.9

5.0

5.1

150

200

250

300

350Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

1.950La

0.050O

4

Per

mea

bil

ity

,

Bu

lk d

ensi

ty,


(C)

1100 1150 1200 1250

4.9

5.0

5.1

5.2

150

200

250

300

350Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

1.925La

0.075O

4

Per

mea

bil

ity

,

Bu

lk d

ensi

ty,


(d)



Page 32

Fig. 13 shows the variation of bulk density and permeability with sintering temperature of the samples. It is

observed that there is a correlation between bulk density and permeability. As the bulk density increases,

permeability also increases. However for sintering temperature > 1200°C of La undoped sample, the bulk

density decreases although /i still increases. On the contrary, for La doped samples, sintered at temperature >

1200°C, bulk density as well as permeability decreases. Therefore it is concluded that the optimum sintering

temperature for La doped samples may be around 1200°C.

Increase in /

i with increase in sintering temperature may be explained as follows. Higher sintering

temperatures result in the increase in the density of the specimen which facilitates the movement of the spins as

the numbers of pores which impede the wall motion are reduced. Increase in the sintering temperature also

results in a decrease in the internal stresses, which reduce the hindrance to the movement of the domain walls

resulting thereby in the increased value of /

i [31].

The /i is observed highest for sample Ni0.12Mg0.18Cu0.20Zn0.50Fe2O4 sintered at 1250ºC and for La substituted

samples sintered at 1200°C, because the microstructure is homogeneous with large grain size and uniform size

distribution. Also it is found that the sintered density is highest for these temperatures. All these values are listed

in Table 1.

The real part of initial permeability value of all the samples remain independent for frequency until resonance

takes place, above which it starts decreasing sharply with simultaneously increase of imaginary part of the

permeability. The resonance frequency fr corresponds to the maximum of the imaginary part of the permeability //

i where magnetic losses can be expressed as the ratio, tan = //

i //

i . It is observed that as the real part of

initial permeability started to decrease, the resonance frequency fr (i.e. the frequency at which //

i show peak)

gets higher. This confirms the Snoek’s relation stated as, /

i r = constant.

It is observed that the /

i is almost independent up to 10 kHz or greater for parent composition and 1MHz or

greater for La doped compositions and after that decreases sharply. The //

i starts raising beyond this frequency

which is an indication of dispersion or resonance. The dispersions of La doped compositions are at higher

frequency compared to parent composition. The dispersion behavior can be explained by Snoek’s law that cut-

off frequency is inversely proportional with magnetic permeability [32]. The values of resonance frequency, fr

are listed in Table 1.

3.4 Loss factor

The variation of loss factor (tanδ) with frequency of the polycrystalline Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4

compositions are shown in Fig. 14 for different sintering temperatures at (a) 1100, (b) 1150, (c) 1200 and (d)

1250°C respectively. At low frequency, tanδ of all the samples is found to decrease with increasing frequency

whereas at high frequency increases. It is also observed that at high frequency, tanδ of all La doped

compositions is lower than parent composition and decreases with increasing La substitution.



Page 33

Fig. 14 The variation of Loss factor with frequency of Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 sintered at (a) 1100˚C,

(b) 1150˚C, (c) 1200˚C and (d) 1250˚C in air.

3.5 Relative quality factor

Figs. 15 show the frequency dependence of relative quality factor (RQ-factor) of the samples sintered at (a)

1100, (b) 1150, (c) 1200 and (d) 1250°C respectively.

104

105

106

107

0.0

0.2

0.4

0.6

Ts= 1100°C

Ni0.12

Mg0.18

Cu0.20

Zn0.50

Fe2-x

LaxO

4

Lo

ss F

acto

r

Frequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075

(a)

104

105

106

107

0.0

0.2

0.4

0.6Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

Lo

ss F

acto

rFrequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075

Ts= 1150°C

(b)

104

105

106

107

0.0

0.2

0.4

0.6Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

Lo

ss F

acto

r

Frequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075

Ts= 1200°C

(c)

104

105

106

107

0.0

0.2

0.4

0.6Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

Lo

ss F

acto

r

Frequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075

Ts= 1250°C

(d)



Page 34

Fig. 15 The variation of relative quality factor with frequency of Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 sintered at

(a) 1100, (b) 1150, (c) 1200 and (d) 1250˚C in air.

102

103

104

105

106

107

108

0

2000

4000

6000

8000Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

Rela

tiv

e Q

uali

ty F

acto

r

Frequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075

Ts= 1250°C

(d)

102

103

104

105

106

107

108

0

1000

2000

3000

4000

5000Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

Rela

tiv

e Q

uali

ty F

acto

r

Frequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075

Ts= 1200°C

(c)

102

103

104

105

106

107

108

0

1000

2000

3000

4000

5000Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

Rela

tiv

e Q

uali

ty F

acto

rFrequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075

Ts= 1150°C

(b)

103

104

105

106

107

108

0

1000

2000

3000

4000

5000

6000Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

R

ela

tiv

e Q

uali

ty F

acto

r

Frequency (Hz)

x=0.00

x=0.025

x=0.050

x=0.075

Ts= 1100°C

(a)



Page 35

Fig. 16 The variation of RQ-factor with La content of Ni0.12Mg0.18Cu0.20Zn0.50Fe2-xLaxO4 sintered at 1250°C in

air.

The variation of the RQ-factor with frequency showed a similar trend for all the samples. RQ-factor increases

with an increase of frequency, showing a peak and then decreases with frequency. This happens at the frequency

where the permeability begins to drop. This phenomenon is associated with the ferrimagnetic resonance within

the domains [33] and at the resonance maximum energy is transferred from the applied magnetic field to the

lattice resulting in the rapid decrease in RQ-factor. In the samples sintered at 1150 and 1200°C, the RQ-factor is

found to decrease with La substitution. On the other hand in the samples sintered at 1100 and 1250°C, the RQ-

factor shows an irregular variation with La substitution. The highest value of the RQ-factor is found in

Ni0.12Mg0.18Cu0.20Zn0.50Fe1.925La0.075O4 sintered at 1250°C. It is also observed that the highest value of the RQ-

factor of all La doped samples shifted at the higher frequency. At the higher frequency the RQ-factor of all

samples increases with increasing La content. Fig. 16 shows the variation of RQ-factor at 1MHz with La

content. It is observed from those RQ-factor increases with increasing La content.

4. CONCLUSION

Ferrites are very important materials for the advancement and development of technology. They possess the

combined properties of magnetic materials and insulators which are used in almost every item of electronic

equipment produced today. The following conclusions have been drawn from this study:

X-ray diffraction patterns of the samples show the formation of spinel crystal structure. From the XRD

patterns a secondary phase LaFeO3 was also detected of all La doped samples. The peak height of LaFeO3

gradually increases with the substitution of La. This indicates that La did not form solid solution with spinel

structure or has limited solid solubility.

Lattice parameter increases with increasing La substitution. This increase in lattice constant with La

indicates that the compositions obey the Vegard’s law. This result is explained with the help of ionic radii

of substituted cations.

Theoretical density and bulk density both increases with increasing La content. Bulk density increases with

increasing sintering temperature up to 1200°C then decreases. On the other hand porosity has the opposite

trend.

The real part of initial permeability (/i ) value decreases with increasing La substitution. It is also

observed that real part of initial permeability increases with increasing sintering temperature for all

compositions up to 1200°C then decreases. The real part of the initial permeability remains fairly constant

in the frequency range up to 10 kHz or greater for parent composition and 1 MHz or greater for La doped

compositions after that decreases. The imaginary part of initial permeability value starts raising beyond this

frequency which is an indication of dispersion or resonance. This confirms the Snoek’s relation. The

dispersions of La doped compositions are at higher frequency compared to La undoped composition.

0.000 0.025 0.050 0.075

2000

4000

6000Ni

0.12Mg

0.18Cu

0.20Zn

0.50Fe

2-xLa

xO

4

RQ

-facto

r at

1M

Hz

La content, x

Ts=1250°C



Page 36

At low frequency, Loss factor of all the samples is found to decrease with increasing frequency whereas at

higher frequency increases. It is also observed that at higher frequency, Loss factor of all La doped

compositions is lower than parent composition and decreases with increasing La substitution.

The highest value of the relative quality factor (RQ-factor) of all La doped compositions shifted at the

higher frequency and at the higher frequency RQ-factor increases with increasing La content. This property

describes the application of La doped samples. The RQ-factor is found to maximum in

Ni0.12Mg0.18Cu0.20Zn0.50Fe1.925La0.075O4 sintered at 1250°C.

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Investigation of the influences of La substitution and ... 15.pdf · Ni 0.12 Mg 0.18 Cu 0.20 Zn 0.50 Fe 1.925 La 0.075 O 4 sintered at 1250°C among the studied samples. Keyword: