chapter - 4 - shodhgangashodhganga.inflibnet.ac.in/bitstream/10603/88970/15/15...observed that ca-mn...

CHAPTER - 4

Dielectric Properties

CHAPTER 4

Dielectric Properties

4.1 Introduction

The dielectric property of ceramics indicates the quality of the materials for wide range of

applications. The dielectric materials have vast applications in electronic devices such as

transducers, actuators, multilayer capacitors, memory storage devices, etc. Dielectric

properties depend upon the field strength at which it is measured and it is a consequence of

non-linear relation between polarization and electric field. For ferroelectric materials, the

dielectric constant increases up to the transition temperature and after that it obeys the Curie-

Weiss law.

When an external electric field is applied to the ferroelectric materials, the polarized

dipoles reorient in the electric field and exhibit alignment of polar charges accordingly. The

ability of the dielectric material to reorient and neutralize charges on the electrodes can be

measured experimentally; and it is expressed as relative dielectric constant/permittivity (εr)

(the ratio of permittivity (ε) of dielectric material to the permittivity of free space (ε0). The

ferroelectric materials exhibit a large dielectric constant, which is based on collective polar

displacements of the metal ions with respect to the oxygen sublattice; and is a highly

nonlinear and anisotropic phenomenon.

A sample holder has been specially designed for electrical measurement with an

attachment of thermocouple for temperature measurement. The silver electroded samples

were kept in a sample holder such as it works as a capacitor. For temperature variable

electrical measurement, the sample holder containing sample was then kept inside a

laboratory-made furnace and a variac voltage regulator was used to control the current to the

heating coil for uniform and the slow heating environment. The temperature inside the sample

holder was measured by measuring the current of the thermocouple using a milli-voltmeter

and converting that current to temperature by a conversion table. Electrical parameters (i.e.,

the impedance (Z), parallel capacitance (Cp), phase (Ф), and dielectric loss (tan δ)) were

measured as a function of frequency (1 kHz to 3MHz) at steps of 5 0C intervals from room

temperature to 400 0C. The dielectric constant is calculated using an empirical formula: εr =

Cp /Co, where C0 is the air capacitance.

Chapter 4 Dielectric Properties

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The aim of this chapter is to study the dielectric properties of the synthesized

materials as a function of frequency and temperature, which may provide information

regarding the existence of ferroelectricity, the nature of the phase transition in them and the

effect of co-substitution on dielectric properties of the proposed compounds.

4.2 Results and discussion

4.2.1 Composition Dependent Dielectric Study

4.2.1.1 Measurements of εr and tan δ with frequency

The dielectric permittivity of most dielectric materials is frequency dependent, as in the

presence of an applied electric field, the dipole moment inside the material oscillates with the

direction of the electric field [199]. Dielectric constant (εr) is directly related to the electronic,

atomic and dipolar polarizations of the materials. Under the impact of an ac field, the

association of dielectric constant with the polarization of material is prominent. From the

nature of the variation of dielectric constant with frequency, it is possible to find out

contribution of the particular polarizations present in a given frequency range [200].

Typically, in the audible range of frequency, all types of polarizations are present. Space

charge polarization is a purely surface phenomenon and depends upon the purity and

perfection of the materials. At radio frequencies (~106Hz), space charge effect may not have

time to build up in most ionically conducting materials [201]. The dipolar polarization effect

is exhibited in the materials below 1010

Hz. In the low-frequency region, the presence of

dipolar polarization is very much important for applications with suitable capacitive and

insulating properties of the materials. Therefore, the electronic polarization persists above a

frequency of 1013

Hz, atomic polarization above 1010

Hz, while the dispersion for dipolar

polarization may lie anywhere within a wide frequency range (102-10

10Hz), depending on the

materials and its temperature. However, the value of dielectric permittivity depends on other

factors such as voids, grain boundaries and dipolar interactions etc., which are present in the

samples. On the other hand, dielectric loss or tangent loss represents the amount of energy

spent by the applied field in dipolar alignment [202]. The size of grains also affects the

dielectric loss. The dielectric loss in the oxides of perovskite family is caused by oxygen

vacancies and dc conductivity.


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(a) Ba and Mn co-substituted BFO

Fig. 4.1: Variation of dielectric constant (εr) with frequency for (Bi1-xBax) (Fe1-xMnx)O3

(x = 0.0, 0.05, 0.10, 0.15, 0.20) samples at few selected temperatures.

The variation of dielectric constant of (Bi1-xBax)(Fe1-xMnx)O3 (x = 0.0, 0.05, 0.10,

0.15, 0.20) samples is compared in Fig. 4.1. It is found that for all compositions the dielectric

constant decreases rapidly in the low-frequency region, and then became more or less

constant at higher frequencies representing the dielectric dispersion. The dielectric behavior at

lower frequencies can be attributed to the interfacial polarization which is in agreement with

Koop’s phenomenological theory [203]. According to this theory, a dielectric material having

heterogeneous structure is assumed to be made up of well conducting grains separated by

highly resistive thin grain boundaries. The grain boundaries are more effective at lower

frequencies while the grains are found to be more effective at higher frequencies. On

increasing frequency, the decrease in the value of εr is due to the contribution of different

types of polarization at different frequencies. In case of ferrites, the space charges polarization

normally occurs due to defects or oxygen vacancies (VO) created during high-temperature

sintering of samples [195] and the oxygen vacancies will lead to a change in the valence state

of iron (Fe3+

→ Fe2+

ions). At higher frequencies, the small value of εr is may be due to the

electron hopping between Fe3+

and Fe2+

ions (at the octahedral sites), which can not follow up


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the alteration of ac electric field [195]. Therefore electrons have to pass through the well

conducting grains and the poorly conducting grain boundaries. As grain boundaries offer high

resistance, the electrons get crowded there and thus space charge polarization is enhanced.

Therefore εr have larger values for all the samples at lower frequency regions. The direction

of motion of electrons changes rapidly with the increment of frequency, hindering the

movement of electrons inside the material. So, the charge accumulation at the grain

boundaries will be reduced, and thereby space charge polarization is reduced as a result, value

of εr is reduced [204]. It can be noted the modified samples have higher value of εr compared

to that of BFO. This can be correlated to the structural transformation from rhombohedral to

tetragonal. So, the formation of relatively stronger dipoles in tetragonal structure results

enhanced dielectric constant.

Fig. 4.2: Variation of tangent loss (tan δ) with frequency for (Bi1-xBax) (Fe1-xMnx)O3 (x =

0.0, 0.05, 0.10, 0.15, 0.20) samples at few selected temperatures.

Fig. 4.2 shows frequency dependence of tangent loss (tan δ) for (Bi1-xBax)(Fe1-

xMnx)O3 (x = 0.0, 0.05, 0.10, 0.15, 0.20). The dielectric loss arises mainly due to impurities

and imperfections in the crystal lattice, which cause polarization to lag behind with the

applied alternating field. The high dielectric loss in the lower frequency range are due to

space charge polarization losses, which can also be explained in consequence of excitation of


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localized, hardly reoriented polarizations and conduction mechanism [205] The value of tan δ

decreases as the frequency increases because the frequency of charge carriers cannot follow

the frequency of the applied field after certain range of frequency [195]. It is also observed

that the high frequency loss increases with co-substitution; however for higher frequency

region loss is very low and is nearly same. From the micro-structural analysis, it was observed

that the increasing value of x creates certain degree of porosity in the modified systems.

Porosity leads to large number of defects (vacancy, mobile ions or leaky grain boundary, etc.)

[206] in the system and thus tan δ increases.

(b) Ca and Mn co-substituted BFO

Fig. 4.3 shows the frequency dependence of the dielectric constant (εr) for (Bi1-xCax)(Fe1-

xMnx)O3 (x = 0.0, 0.05, 0.10, 0.15, 0.20) at few selected temperatures. It is observed that for

all samples, the value of εr decreases rapidly in the low-frequency region whereas decrease is

quite slow in the high-frequency region (almost approaching to frequency independent

response). In the high-frequency region, the higher value of εr can be described in terms of a

rapid polarization processes with no contribution of ionic motion. At higher frequency, the

ions can only oscillate without reaching the sample–electrode interface. The contribution of

interfaces or grain boundaries to apparent dielectric constant in the ferrites can be explained

by the Maxwell–Wagner theory [207]. As we have performed the measurements with silver

paint electrode, the low-frequency dielectric constants values imply a main non-intrinsic

contribution coming from the electrode/sample interface [196]. Additionally, hopping

conductivity can give a further frequency dependent contribution to apparent dielectric

constant at higher frequencies [207]. Therefore, the decrease in εr with the increase in

frequency is due to the energetic hopping of electrons along the direction of the applied field

between Fe3+

and Fe2+

ions at the octahedral sites as discussed in the previous section [196].

The decrease in εr with rise in frequency is a general trend because of the difference in the

contribution of different types of polarization at different frequencies. Along with this, it is

observed that Ca-Mn co-substitution results decrease in εr value. This may be due to

substitution of Ca-Mn at Bi-Fe sites, the dipole moment decreases, as the atomic radius of Ca-

Mn is slightly smaller as compared that of Bi-Fe. Another reason behind this is decrease in

grain size on increasing the value of x. This leads to the decrease in polarizibility of the atoms

in the structure.


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Fig. 4.3: Variation of dielectric constant (εr) with frequency for (Bi1-xCax) (Fe1-xMnx)O3


Fig. 4.4 shows the frequency dependence of the loss tangent (tan δ) for the (Bi1-

xCax)(Fe1-xMnx)O3 (x = 0.0, 0.05, 0.10, 0.15, 0.20) samples at few selected temperatures. The

value of tan δ is higher in the low-frequency region for the Fe containing compounds, which

decreases drastically with rise in frequency. The dielectric loss initially decreases with

increasing frequency (up to 100 kHz), and then become more or less constant (up to 3 MHz).

The nature of variation of tan δ is very much compositional dependent. In the low-frequency

range, the value of tan δ increases with the increase in value of x, and is nearly same in the

high-frequency region.


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Fig. 4.4: Variation of tangent loss (tan δ) with frequency for (Bi1-xCax) (Fe1-xMnx)O3 (x =

0.0, 0.05, 0.10, 0.15, 0.20) samples at few selected temperatures.

The dielectric loss arises mainly due to impurities and imperfections in the crystal lattice,

which cause polarization to lag behind with the applied alternating field. The density of the

materials also plays an important role in the variation of dielectric constant and dielectric loss,

and thus porous materials have low dielectric constants and high dielectric losses [196].

(c) Sr and Mn co-substituted BFO

Fig. 4.5 shows the frequency dependence of dielectric constant (εr) for (Bi1-xSrx) (Fe1-xMnx)O3

(x = 0.0, 0.05, 0.10, 0.15, 0.20) at few selected temperatures. The pattern shows a sigmoidal

variation as a function of frequency in the low-frequency region followed by a saturation

region in the higher-frequency range. At low frequency, all the different types of polarization

(interfacial, atomic, dipolar and electronic) were present in the dielectric medium.


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Fig. 4.5: Variation of dielectric constant (εr) with frequency for (Bi1-xSrx) (Fe1-xMnx)O3 (x

= 0.0, 0.05, 0.10, 0.15, 0.20) samples at few selected temperatures.

So we got a high dielectric constant at low frequency, in spite of high packing fraction of the

pellet samples. However, with increase in the frequency, it becomes harder for the dipole

moments to catch up with the change of the direction of applied field. This causes the

attenuation in the ability of the material to neutralize charges on the electrodes at high

frequencies, and a usual low value of dielectric constant can be obtained [208]. A great

improvement has been observed in the dielectric properties of BFO on Sr and Mn co-

substitution in BFO. It is observed that dielectric constant increases with the increase with Sr-

Mn co-substitution due to the increase in polarizibility of the atoms in the structure. When a

Sr+2

ions of higher radius replaces lower radius Bi+3

in the structure, dipole moment increases.

The permittivity of modified systems could be increased (in the present study) by increasing

their density and grain size in the sintered samples [209].


87

Fig. 4.6: Variation of tangent loss (tan δ) with frequency for the (Bi1-xSrx) (Fe1-xMnx)O3


Fig. 4.6 shows the variation of tan δ with frequency at few selected temperatures. As

mentioned earlier, the loss arises mainly due to impurities and imperfections in the crystal

lattice, which cause polarization to lag behind with the applied alternating field. In the low-

frequency plot, the tan δ decreases slightly on increasing frequency which looks to be almost

straight line. The dispersion observed in the low-frequency region may arises mainly due to

the onset of dc conduction to satisfy the relation: tan δ α (ω)-1

[210]. One of the reasons behind

the observed high-frequency dispersion is the influence of the contact resistance between the

probe and electrode, presence of barrier layer between the insulating materials and the

electrode surface. The dielectric loss for all the compositions at 125 ˚C has also been shown in

the figure and an increase in tan δ value is observed with the increasing value of x. This may

be due to the inability of some of the polarization processes to respond to the faster polarity

reversals of the field, such that the net contribution of polarization to the dielectric constant is

reduced and the loss is increased [211].


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4.2.1.2 Measurements of εr and tan δ with temperature

(a) Ca and Mn co-substituted BFO

Fig. 4.7: Variation of dielectric constant (εr) with temperature of the (Bi1-xCax) (Fe1-

xMnx)O3 (x = 0.0, 0.05, 0.10, 0.15, 0.20) samples at three different frequencies.

The variation of relative permittivity (εr) with temperature at different frequencies for (Bi1-

xCax) (Fe1-xMnx)O3 (x = 0.0, 0.05, 0.10, 0.15, 0.20) samples is shown in Fig. 4.7. For the

parent compound BFO, two anomalies appear in the reported temperature range of 25–400 ˚C.

The first one in terms of diffused peak that occurs around 180 ˚C at all frequencies which is

consistent earlier report by Plolomska et al [212, 213]. This anomaly is attributed to transient

interaction between oxygen ion vacancy and Fe+3/+2

redox couple [214]. Second one observed

around 370 ˚C for frequencies at and below 100 kHz, which becomes more pronounced in

terms of diffused peaks at slightly higher temperature at higher frequencies. This anomaly

attributed to the anti-ferromagnetic transition [215, 216] is intrinsic, and could not be due to

extrinsic factors like electrode sample interface or grain boundary effect [217]. As the

ferroelectric phase transition temperature (TC) of BFO is very high, the anomaly is not

observed; it might lie outside the studied temperature window.


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A strong temperature dependence of dielectric constant at different temperature may

be due to the charge defects generated by the lattice distortion. For all the samples, an

abnormal dielectric pattern, containing a dielectric constant peak, is observed. An increasing

co-substitution in BFO is leaded by an obviously decreased abnormal intensity and shifting of

the abnormal peak position. With the increasing of Ca-Mn content in BFO, the abnormal peak

position shifts to lower temperatures. As discussed earlier, BFO experiences an anti-

ferromagnetic transition at 643K and a ferroelectric transition at 1103K. The peak

temperatures of the observed abnormal dielectric peaks are much lower than the ferroelectric

transition temperature. They should be related to the anti-ferromagnetic transition. This

dielectric anomaly demonstrates the coupling between the anti-ferromagnetic and dielectric

properties [218]. The sample with x = 0.05 retain the characteristic dielectric anomalies as

parent BFO, but εr value decrease compared to that of BFO. Again with further increment in

the value of x, there is decrease in value of dielectric constant; which concludes Ca-Mn co-

substitution in BFO results in the decrease of εr value [152].

Fig. 4.8: Variation of dielectric loss (tan δ) with temperature for (Bi1-xCax) (Fe1-xMnx)O3

(x = 0.0, 0.05, 0.10, 0.15, 0.20) samples at three different frequencies.


90

Fig. 4.8 shows temperature dependence of dielectric loss (tan δ) at selected frequencies of

(Bi1-xCax) (Fe1-xMnx)O3 (x = 0.0, 0.05, 0.10, 0.15, 0.20). It is clear from the figure that the

change in the value of tan δ shows the similar trend for all the samples. The value of tan δ is

almost constant at low temperature but at higher temperatures this trend changes significantly.

It is found that dielectric loss increases with increase in the value of x, and found to be more

as compared to those of pure BFO. The higher value of loss tangent may be due to presence

of various types of defects including oxygen vacancies in the compound [219].The

observations may also be supported by the appearance of pores and defects in the surface

morphology of the material (discussed in chapter 3). For the sample x = 0.20, the value of

dielectric loss becomes very high, which indicates presence of appreciable conductivity in

these modified samples. So, Ca-Mn substitution in BFO leads to increment in conductivity, as

a result value of tan δ increases.

(b) Ba and Mn co-substituted BFO

Fig. 4.9: Variation of relative dielectric constant (εr) with temperature for (Bi1-xBax) (Fe1-

xMnx)O3 (x = 0.0, 0.05, 0.10, 0.15, 0.20) samples at three different frequencies.


91

Fig. 4.9 shows temperature dependence of relative permittivity (εr) at selected frequencies of

(Bi1-xBax) (Fe1-xMnx)O3 (x = 0.0, 0.05, 0.10, 0.15, 0.20). It is found that єr depends on

temperature, frequency and composition. For all the modified samples, the value of єr

increases drastically with rise in temperature as reported by other on the similar type of

materials [184]. The increase in εr can be attributed to the thermally activated transport of

space charges. During sintering process, due to volatile nature of Bi, space charges like

oxygen vacancies (OVs) are formed [220, 221]. When divalent ion Ba+2

is substituted at

trivalent ions at the Bi-site, oxygen vacancies is created; which is further compensated by

substitution of tetravalent Mn+4

ion at the trivalent Fe-site. However, these OVs lead to the

valence fluctuation of Fe and Mn ions as Fe+3

–Fe +2

and Mn+4

– Mn+3

respectively [222].

Again, the value of εr first increases with increase in the value of x up to 0.10, and then

decreases sharply for x = 0.15 and 0.20. The anti-ferromagnetic peak observed around 370˚C

for parent compound is shifted towards lower temperature side with increasing the value of x

which may be correlated to the structural transformation from rhombohedral to tetragonal

symmetry. Landau–Devonshire theory of phase transition predicted that the dielectric

anomaly observed near Neel temperature (TN) in magneto-electrically ordered system is a

consequence of vanishing magnetic order on electric order. The abnormality in peak position

in the modified samples may be due to disturbance of the magnetic spiral spin structure in

BFO. So, these peaks are ascribed as change from one state of electric dipole ordering to

another because of anti-ferromagnetic transition [145].


(Bi1-xBax) (Fe1-xMnx)O3 (x = 0.0, 0.05, 0.10, 0.15, 0.20). The value of tan δ is almost constant

at low temperatures (< 200 ˚C), after that it increases sharply with further increment in

temperature. However, at higher frequencies, tan δ decreases which may be due to the

presence of interfacial polarization arisen due to the difference in conductivity in the samples.

It is believed that motion of charge carriers gets interrupted at grain boundary due to low

conductivity, which is most commonly observed in ceramics (if the grains are semiconducting

and grain boundaries are insulating) [223].


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Fig. 4.10: Variation of dielectric loss (tan δ) with temperature for (Bi1-xBax) (Fe1-xMnx)O3


At each given frequency, the impression of peaks shows the change from one category of

process to another occurring at a distinct temperature. This phenomenon can be attributed to

some thermal mechanism taking place in the material indicating maximum energy loss. But

the peak is found to be dependent on frequency, and its suppression is noticed for higher value

of x, which may be attributed to the possibility of space charge relaxation. The natures of

variation of tan for all samples are very much substitution dependent. As observed, the value

of tan δ for x = 0.05 exhibits higher loss as compared to that of BFO, but after that decrease

for x = 0.15 and 0.20. This instability in tan δ may be attributed to the structural disorder and

compositional fluctuations in the co-substituted samples.

(c) Sr and Mn co-substituted BFO

Fig. 4.11 shows temperature dependence of relative permittivity (εr) at selected frequencies of

(Bi1-xSrx) (Fe1-xMnx)O3 (x = 0.0, 0.05, 0.10, 0.15, 0.20). A sharp increase in the value of εr

with temperature is observed which suggests the existence of thermally induced hopping


93

conduction in the material. The low dielectric constant at lower temperature is resulted from

the weak contribution of electric dipoles to the polarization, while at higher temperatures the

electric dipoles get thermal energy enough to follow up the changes in the external field, as a

result, we observe enhancement in polarization and dielectric constant. The dielectric constant

becomes more stable at higher temperature and frequency on increasing Sr-Mn content,

thereby, the dielectric properties of the samples are improved. The large value of the dielectric

constant in modified samples can be understood if one considers that the replacement of Bi+3

ions by Sr+2

ions in BFO requires charge compensation, which can be realized by creating

anion vacancies (i.e., OVs) and/or increasing cation valence [224]. The creation of OVs

increases the probability of a hopping conduction mechanism which results a high value of

the dielectric constant for the sample with x = 0.10. The improved dielectric properties at

lower frequencies for co-substituted samples can also be explained by the fact that the

addition of Sr-Mn to BFO requires charge compensation, which can be achieved by one or

Fig. 4.11: Variation of relative dielectric constant (εr) with temperature for (Bi1-xSrx)

(Fe1-xMnx)O3 (x = 0.0, 0.05, 0.10, 0.15, 0.20) samples at three different frequencies.


94

more of the following mechanisms: (i) the filling of oxygen vacancies, (ii) a decrease of the

cation valence (i.e., the formation of Fe+2

), and (iii) the creation of cation vacancies.

Therefore, co-substitution in BFO is expected to decrease the charge defects (oxygen

vacancies) and associated leakage significantly because of the requirement of charge

compensation leading to an increase in the frequency independent region [225].

Fig. 4.12: Variation of dielectric loss (tan δ) with temperature for (Bi1-xSrx) (Fe1-xMnx)O3



(Bi1-xSrx) (Fe1-xMnx)O3 (x = 0.0, 0.05, 0.10, 0.15, 0.20). The value of tan δ is almost constant

at low temperatures (below 250 oC), but it increases drastically with rise in temperature for all

the samples. As observed, the sudden increase of tan δ in the high-temperature region for all

compositions may find its association with free charge carrier conductivity. Since the free

charge carriers are dependent on doping concentration as well as temperature, the rate of

change of tangent loss is also high in the higher composition region. So, high loss takes place

because of domain boundary vibrations or thermal excitation [226]. The loss factor shows an


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inverse relationship to frequency, which may be attributed to the disappearance of space

charges at higher frequencies [227]. So, the conductivity of the materials increases, and thus

increase in tan is prominent.

4.3 Conclusion

Based on dielectric measurement and analysis we conclude that:

As the ferroelectric transition temperature (Tc) of BFO is high, it could not be

recorded due to our experimental limitations.

All the compounds have multiple the dielectric anomalies at around 150-300o C,

which may be attributed to the transient interaction between oxygen ion vacancies and

the Fe3+

/Fe2+

redox couple.

The increase in the value of εr for some compounds is very much consistent with the

observed microstructure.

***

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