Electrical and Elastic Behavior of In and Al Substituted Mg-Mn Ferrites

September 23, 1998 11:31 WSPC/140-IJMPB 0024

International Journal of Modern Physics B, Vol. 12, No. 22 (1998) 2247–2262c© World Scientific Publishing Company

ELECTRICAL AND ELASTIC BEHAVIOR OF In

AND Al SUBSTITUTED Mg-Mn FERRITES

Y. PURUSHOTHAM, MAHAVIR SINGH†, S. P. SUD† and P. VENUGOPAL REDDY∗

Department of Physics, Osmania University, Hyderabad 500 007, India†Department of Physics, H. P. University, Shimla 171 005, India

Received 23 June 1998

Thermopower and electrical conductivity studies of polycrytslline In3+ and Al3+ sub-stituted Mg-Mn ferrites having different compositions were undertaken in the temper-ature range 300–700 K, using differential and two-probe methods respectively. It hasbeen observed that all the ferrites are found to exhibit clear and well-defined transtionsnear their respective Curie temperatures in both Seebeck coefficient and electrical con-

ductivity versus temperature behavior. The elastic behavior of these ferrites has alsobeen studied as a function of composition at room temperature using ultrasonic pulsetransmission technique and it has been found that the elastic moduli decrease continu-ously with increasing Indium concentration and increase with increasing Aluminiumdopants. Suitable explanation for the observed phenomena are given.

1. Introduction

Spinel ferrites in general and magnesium and manganese-magnesium ferrites in par-

ticular have extensive applications in the construction of non-reciprocal devices at

microwave frequencies such as circulators, gyrators, phase shifters, isolators etc.

In fact, magnesium ferrite is often used as a component in commercial soft ferrite

formulations such as memory and switching circuits of digital computers, phase

shifters and other applications mainly due to their rectangular hysteresis loop

characteristics.1,2 Therefore, a study of these ferrites is technologically significant

and important. Further, it has been reported earlier by Kirichok and Antoschuk3

that when small amounts of diamagnetic In3+ are substituted in Mg ferrites, they

are known to have preference to the tetrahedral sites replacing Fe3+ ions which

results in improving their magnetic properties. This observation corroborates the

earlier report that various physical properties of ferrites can be upgraded by in-

corporating suitable diamagnetic impurities.4,5 Similarly, when another trivalent

non-magnetic ion such as Al3+ is introduced at the Fe3+ sites, the saturation mag-

netisation, expected to reduce continuously. In fact Puri et al.6 investigated the in-

fluence of In3+ on various physical properties such as lattice parameters, dielectric

∗To whom all the correspondence should be addressed.

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2248 Y. Purushotham et al.

constant, initial permeability, Mossbauer studies etc. Thus, although the influence

of both divalent and trivalent dopants of magnesium ferrites on its various physical

properties were reported by a number of researchers, no systematic investigation

was undertaken to understand the influence on electrical transport properties such

as thermopower, electrical conductivity and elasticity properties as well. As such,

a systematic investigation of these parameters has been undertaken and the results

of such a study are presented in this paper.

2. Experimental

2.1. Materials

Two sets of ferrite materials having the compositional formula

Mg0.9Mn0.1InxFe2−xO4

Mg0.9Mn0.1AlyFe2−yO4

where x = 0 to 0.7 and y = 0.1 to 0.5 in steps of 0.1, were prepared by the

conventional double-sintering process, using analytical grade chemicals taken in

stochiometric proportions. The samples after calcination at 1000◦C for 3 hrs. in air

were sintered at 1350◦C for 4 hrs. followed by slow cooling upto room tempera-

ture. The other details of preparation and characterisation of the samples are given

elsewhere.6

2.2. Methods

The bulk densities of all the materials under investigation were determined by

an immersion method, while the X-ray densities were computed by using lattice

parameter values. Determination of magnetic transition temperature is essential to

characterise the ferrite materials, and as such these values were also determined by

the gravity method.7 In order to understand the conduction mechanism of these

materials, the electrical conductivity and thermopower measurements were carried

out by two-probe and differential methods8 respectively over a temperature range

300–700 K. Finally, the compressional (Vl) and shear (Vs) wave velocities of all

the materials were determined by the pulse transmission technique,9 using PZT

transducers having a fundamental frequency of 1 Mhz. For this purpose, the surface

of the samples were polished to form parallel faces. In this technique, the transit

time of ultrasonic wave was measured upto an accuracy of 1 ms using a 100 Mhz

digital storage oscilloscope (Tektronix Model No. 2221). The overall error in the

measurement of velocity is ±10 m/sec.

3. Results and Discussion

3.1. Lattice parameter versus composition

It has been observed from the X-ray diffractograms that all the samples of present

investigation are having single-phase and spinel structure. Later, using these

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Electrical and Elastic Behavior . . . 2249

diffractograms the d-spacings and hence the lattice parameters have been calcu-

lated and are given in Table 1. As can be seen from the table, the cell parameters

for MIF-series are found to increase continuously from 0.839 to 0.859 nm, while

those in the case of MAF-series are found to decrease from 0.839 to 0.835 nm. In

fact this result is expected because, in MLF-series, In3+ ions with larger ionic radii

(0.091 nm) are replacing Fe3+ ions having relatively smaller ionic radii (0.067 nm)

resulting in continuous increase of lattice parameter, while in MAF-series, Al3+ ions

with smaller ionic radii (0.051 nm) are replacing Fe3+ ions with larger ionic radii

(0.067 nm) resulting in a continuous shrinkage of the lattice. In fact in both the

cases the variation of lattice parameters with increasing dopant’s concentration is

found to be almost linear.

3.2. Curie temperature (Tc)

The magnetic transition temperature values of both the series as determined by

gravity method are found to decrease continuously with increasing dopant’s con-

centration (Fig. 1) and the observed variation can be explained on the basis of their

cation distribution as follows:

The cation distribution of a slowly-cooled magnesium ferrite was reported by

Blasse10 as

(Mg2+0.1Fe3+

0.9)[Mg2+0.9Fe3+

1.1]O2−4 (1)

Table 1. Experimental data on In and Al substituted Mg-Mn ferrites.

Lattice Bulk X-ray

Ferrite parameter density density

code Composition (A0) (103 kg/m3)

Group-I

MIF-1 Mg0.9Mn0.1Fe2O4 8.39 3.79 4.56

MIF-2 Mg0.9Mn0.1In0.1Fe1.9O4 8.42 3.80 4.65

MIF-3 Mg0.9Mn0.1In0.2Fe1.8O4 8.44 3.89 4.72

MIF-4 Mg0.9Mn0.1In0.3Fe1.7O4 8.53 4.02 4.75

MIF-5 Mg0.9Mn0.1In0.4Fe1.6O4 8.56 4.06 4.80

MIF-6 Mg0.9Mn0.1In0.5Fe1.5O4 8.57 4.26 4.91

MIF-7 Mg0.9Mn0.1In0.6Fe1.4O4 8.58 4.27 5.01

MIF-8 Mg0.9Mn0.1In0.7Fe1.3O4 8.59 4.57 5.12

Group-II

MAF-1 Mg0.9Mn0.1Al0.1Fe1.9O4 8.39 4.11 4.52

MAF-2 Mg0.9Mn0.1Al0.2Fe1.8O4 8.38 4.03 4.46

MAF-3 Mg0.9Mn0.1Al0.3Fe1.7O4 8.37 3.88 4.43

MAF-4 Mg0.9Mn0.1Al0.4Fe1.6O4 8.35 3.85 4.40

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Fig. 1. Variation of curie temperature with dopant’s concentration.

where 〈〉 indicates tetrahedral (A) sites and [ ] indicates cathedral (B) sites. As

mentioned earlier, the substituted trivalent In3+ and Al3+ are expected to occupy

cathedral sites thereby reducing the number of Fe3+ ions on B-sites decrease con-

tinuously with increasing dopant’s concentration, while those (Fe3+) on A sites

remain almost constant. Therefore, the exchange interaction, known as A–B in-

teraction, obviously between the reduced Fe3+ ions on octahderal sites and those

on tetrahedral sites which are supposed to be constant, thereby indicating that

the exchange interaction decreases continuously. As such, since the A–B exchange

weakens continuously, a continuous decrease in Tc values is expected.

4. Part A Electrical Transport Properties

4.1. Temperature variation of Seebeck coefficient

The Seebeck coefficient (S) of both the types of materials were determined over

a temperature range of 300–700 K and their variation with temperature is shown

in Figs. 2(a)–(c) and 3(a)–(b). As can be seen from the figures, S values of all

the samples, with the exception of MIF-7 and MIF-8, are found to decrease with

increasing temperature, exhibiting a maximum value at a particular temperature,

hereafter designated as Ts. In the case of MIF-7 and MIF-8 however, thermopower

values after showing a continuous decrease attains a minimum value and is also

designated as Ts. In contrast to the earlier behavior S values in both the cases

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(a)

(b)

Fig. 2. Seebeck coefficient as a function of temperature for MIF-series.

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(c)

Fig. 2. (Continued)

(a)

Fig. 3. Variation of Seebeck coefficient with temperature for MAF-series.

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are found to increase continuously on further increase of temperature. In order to

understand Physics behind the occurence of such maxima/minima, the values of

Ts for all the samples are compared with those of Curie temperatures in Table 2.

It can be seen that the values of Ts and Tc are in agreement within the limits of

experimental errors thereby indicating that the occurrence of a hump at Ts may be

due to ferri to para magnetic transition.

4.2. Variation of electrical conductivity with temperature

The electrical conductivity values of all the samples, as can be seen from log(sT )

versus 103/T plots [Figs. 4(a)–(d) and 5(a)–(b)] increase monotonously with in-

creasing temperature, exhibiting a change of slope around Tc thereby indicating

that, it could be due to ferri to para magnetic transition. The variation of electrical

conductivity with temperature for all the samples studied can be expressed by the

equation

σ =

(A

T

)exp

(− E

kT

), (2)

where A is a constant over a substantial range of temperature, T is temperature of

the material, E is the activation energy and k is Boltzmann constant. The activation

energies of all the materials under investigation have been obtained using the slopes

of linear portion of log(σT ) versus 103/T and are given in Table 2. It is interesting

to note that the activation energy values in the paramagnetic region are higher

than those in the ferrimagnetic region and the behavior is in conformity with the

theory developed by Irkhin and Turov11 earlier.

(b)

Fig. 3. (Continued)

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(a)

(b)

Fig. 4. Electrical conductivity as a function of temperature for MIF-series.

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(c)

(d)

Fig. 4 (Continued)

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(a)

(b)

Fig. 5. A plot log(σT ) versus 103/T for MAF-series.

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Table 2. Experimental data on In and Al substituted Mg-Mn ferrites.

Activation energy (eV)

Ferrite Tc Ts Tσ Ferri- Para-

code (Degree Kelvin) magnetic region

Group-I

MIF-1 673 670 671 0.21 0.33

MIF-2 616 620 621 0.16 0.31

MIF-3 568 565 561 0.14 0.21

MIF-4 516 520 521 0.15 0.29

MIF-5 456 454 461 0.19 0.28

MIF-6 381 380 386 0.24 0.25

MIF-7 346 335 341 0.22 0.28

MIF-8 290 285 292 0.17 0.22

Group-II

MAF-1 636 631 631 0.10 0.14

MAF-2 598 600 601 0.18 0.23

MAF-3 533 535 533 0.13 0.21

MAF-4 503 505 502 0.12 0.19

4.3. Charge carrier mobility

The charge carrier mobility at each temperature for all the materials have been

calculated using the relationship

σ = neµe + peµh (3)

It has been observed from charge carrier mobility (µ) versus temperature (T ) plots

that me is found to increase continuously with increasing temperature for all the

materials.

4.3.1. Conduction mechanism

On the basis of experimental observations it has been concluded that:

(1) The conduction in these ferrites is due to the hopping of charge carriers between

Fe2+ to Fe3+ rather than due to the band mechanism.

(2) The observed activation energy values suggest that the charge carriers respon-

sible for electrical conductivity may be due to small polarons rather than due to

electrons.12 This may be due to the fact that in solids with large coupling con-

stant and narrow conduction band, small polaron formation is more probable.13

Further, in oxides of iron group metals, especially in ferrites, the overlap of 3d

wave function between neighboring metal ions is relatively small.14 In such a

case, there is a strong experimental proof for the existence of small polaronsand

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hopping process.15,16 As such, it may be speculated that the conduction mech-

anism in the samples of the present investigation may be due to hopping of

polarons.

(3) On the basis of the experimental observations and theoretical considerations, it

has been concluded that the conduction in these ferrites at high temperatures

(T > θD/2) may proceed via thermally activated hopping motion of strongly

correlated small polarons form site to site. On the contrary, at low temper-

atures (T < θD/2) the weakly activated hopping motion of polarons might

degenerate into Brownian-like motion resulting in tunneling instead of hopping

of polarons. Thus this type of motion may be responsible for the conduction at

low temperatures.

5. Part-B Elastic Behavior

The experimental values of compressional (Vl) and shear (Vs) wave velocities along

with those of Young’s (E), rigidity (n) and bulk (k) moduli obtained for all the

sample under investigation are given in Table 3.

Table 3. Experimental elastic (Uncorrected) data.

Ferrite Vl Vs E n k

code (m/sec) (GPa)

Group-I

MIF-1 6368 3770 132.8 53.9 82.0

MIF-2 6106 3571 120.3 48.5 77.1

MIF-3 5744 3271 105.1 41.7 73.0

MIF-4 5396 3072 95.7 37.9 66.5

MIF-5 5278 2962 90.4 35.6 65.5

MIF-6 5002 2807 85.4 33.6 61.9

MIF-7 4846 2720 80.3 31.6 58.2

MIF-8 4615 2590 77.9 30.7 56.5

Group-II

MAF-1 6038 3658 133.1 54.9 76.5

MAF-2 6205 3717 135.8 55.6 80.8

MAF-3 6566 3888 144.5 58.7 89.2

MAF-4 6702 3968 138.6 56.4 85.6

5.1. Porosity correction

The elastic moduli of a solid material in general and ceramics in particular depend

on the density of a material. As ferrites under study are found to be porous, the

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measured elastic moduli will be less than those of non-porous ones and are of little

significance unless they are corrected to zero porosity. The effect of porosity on

the elastic moduli has been investigated both theoretically and experimentally by

a number of investigators.17–19 In the present investigation the void free elastic

moduli have been arrived at using Ledbetter and Datta’s formula20 and are given

in Table 4.

Table 4. Corrected elastic data.

Ferrite E0 n0 k0 σ0 Vm θDcode (Gpa) (m/sec) (K)

Group-I

MIF-1 186.6 75.4 118.1 0.23 4650 564

MIF-2 173.9 69.6 115.6 0.25 4425 530

MIF-3 149.7 58.8 110.2 0.27 4035 485

MIF-4 130.1 51.1 95.1 0.27 3755 456

MIF-5 123.6 48.1 95.4 0.28 3622 437

MIF-6 111.1 42.2 84.9 0.28 3399 418

MIF-7 108.2 42.2 83.2 0.28 3317 402

MIF-8 96.6 37.7 72.9 0.28 3105 388

Group-II

MAF-1 159.5 65.8 92.1 0.21 4567 565

MAF-2 165.6 67.7 99.5 0.22 4734 573

MAF-3 185.4 75.1 116.4 0.23 4865 586

MAF-4 202.3 81.8 128.3 0.24 4930 594

5.2. Average sound velocity (Vm) and Debye temperature (θD)

The average sound velocity (Vm) values of all the samples have been calculated

using Anderson’s21 formula

Vm =

{1

3

(2

V 3s

+1

V 3l

)}−1/3

, (4)

where Vl and Vs are the longitudinal and shear wave velocities corrected to zero

porosity and are obtained from the corresponding non-porous moduli using the

relations

Vl =

{2V 2

s

1− 2σ+ V 2

s

},

(5)

Vs =

{n0

ρ

}1/2

,

and are included in Table 4.

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Acoustic Debye temperature (θD) provides useful information for thermal prop-

erties in general and elastic properties in particular. As such, the Debye tempera-

tures have also been calculated for all the samples using the Ledbetter’s22 relation

and are given in Table 4.

θD =1.122h

k

[3

4πνa

]1/3 [n

ρ

]1/2

(6)

where νa is the atomic volume, n is modulus of rigidity and ρ is mass density. The

acoustic Debye temperature values are found to decrease in the case of MIF-series

and increase for MAF-series continuously.

With a view to arrive at a relationship between the average sound velocity (Vm),

an acoustic parameter and Debye temperature (θD) a thermodynamic function, a

plot between them is drawn and is shown in Fig. 6. It is interesting to note from

the figure that the Debye temperature is found to vary linearly with average sound

velocity. A similar result was reported by Narayana and Swamy23,24 in the case of

rare earth and noble metals and by Reddy et al.,25 Reddy et al.,26 in the case of

some mixed ferrites.

Fig. 6. A plot of Debye temperature versus average sound velocity.

5.3. Relationship between mean atomic weight Vl/ρ and Vs/ρ

Birch27 has shown that the longitudinal velocity (Vl) is approximately a linear

function of density (ρ) in the case of silicates and oxides having same mean atomic

weight (M/q), where M is the molecular weight and q is number of atoms in a chem-

ical formula unit. Subsequently, Simmons28,29 confirmed this result and extended

the applicability of such a linear representation to shear wave velocities also. In

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view of this, an attempt has been made to establish if possible a similar relation-

ship between Vl/ρ, Vs/ρ and mean atomic weight for these materials also. For this

purpose, the corrected values of Vl and Vs and those of M/q, have been used and

the calculated values of Vl/ρ, Vs/ρ and M/q are given in Table 5. It is interesting to

note that the values of Vl/ρ, Vs/ρ are found to decrease for MIF-series and increase

for MAF-series with increasing mean atomic weight values, thereby giving an indi-

cation that these ferrites also behave like other ceramic oxide materials mentioned

above.

Table 5. Elastic data of MIF and MAF ferrites.

Ferrite M/q Vl/ρ Vs/ρ

code (m4/kg s)

Group-I

MIF-1 25.37 1676.67 992.62

MIF-2 26.11 1605.57 938.99

MIF-3 26.85 1473.57 839.14

MIF-4 27.58 1340.95 763.41

MIF-5 28.32 1301.60 730.45

MIF-6 29.06 1172.80 658.14

MIF-7 29.80 1134.62 636.85

MIF-8 30.53 1008.74 566.12

Group-II

MAF-1 25.01 1469.74 890.24

MAF-2 24.65 1540.84 923.01

MAF-3 24.29 1689.65 1000.51

MAF-4 23.93 1872.59 1108.68

Acknowledgments

The authors are grateful to Dr. Pran Kishan, Scientist “G”, Associate Director,

Solid State Physics Laboratory, Delhi for his encouragement. One of the authors

(Y.P.) would like to thank the Council of Scientific and Industrial Research (CSIR),

New Delhi for awarding Research Associateship.

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Electrical and Elastic Behavior of In and Al Substituted Mg-Mn Ferrites

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Transcript of Electrical and Elastic Behavior of In and Al Substituted Mg-Mn Ferrites