BASIC CONCEPTS

CHAPTER-1BASIC CONCEPTS

1.1 IN T R O D U C TIO N

One o f the m ost im portant groups o f advanced m aterials belongs to the groups o f

ceram ic ferroelectrics - a special class o f dielectrics. D ielectrics are the m aterials in

which electrostatic field can persist for a long time. These m aterials offer very high

resistance to the passage o f direct current and therefore, sharply differ from metal,

sem iconductor and superconductors. It is well known that dielectric properties o f

ceram ic m aterials depend on their com position, structure and experim ental

conditions. All crystalline dielectrics in w hich polarization or electric dipole

m om ent can be induced by the application o f external electric field , are divided in

to two classes: -

> Polar (dipole) dielectrics.

a- N on-polar (neutral) dielectrics.

In polar dielectrics, a perm anent polarization (Ps) exists even in the absence ot

applied electric field. In the case o f non-polar dielectrics, there is no such

perm anent polarization [ 1 ],

1.2 D IE L EC TR IC M A TE R IA L S

D ielectrics are a group o f m aterials that possess electric polarization when

applied w ith external electric field and have the capacity o f storing the charges.

M ost o f these m aterials have low electrical conductivity and thus are insulators. A

broad range o f non-m etals are referred to as dielectrics, w hen w e consider their

interaction w ith electric, m agnetic, or electrom agnetic fields. T he various dielectric

properties are the storage and dissipation o f electric and m agnetic energies.

polarization, m agnetization and conduction. Polarization and m agnetization

m easures the electric and m agnetic dipole m om ent per unit volum e. These

m icroscopic m om ents are com posed o f elem entary m olecular moments. Induced

electric dipole m om ents result from the d isplacem ent o f electrons o f nuclei

(electronic and atom ic polarization); the perm anent dipole m om ent o f m olecules

m ay be oriented (orientational polarization). O rientation polarization in liquids and

solids causes relaxation spectra whereas the spontaneous alignm ent o f electric

dipoles by mutual interaction causes (ferroelectricity). The perm anent dipole

m om ents anchored in the structure w ithout a centre o f sym m etry; under m echanical

distortion creating a voltage generates piezoelectric effect. On the basis o f

tem perature dependence o f dielectric constant, and the value o f the Curie constant,

it is observed that ferroelectrics are classified into two groups:-

r C om pounds having the C urie constant in the order o f 103 belong to the order-

d isorder type [2 ] and,

> For those w hich undergo displasive type o f transition, w ith Curie constant in the

order o f 103 [3].

1.2.1 M IC R O SC O PIC DIELEC TR IC P A R A M E T E R S

The electrical properties o f d ielectric m aterials are expressed in term s

o f certain param eters w hich are term ed as m icroscopic dielectric param eters. These

param eters are as follows:-

(1) D IE L E C T R IC CONSTANT: - The dielectric constant (er) o f a m aterial is

defined as the ratio o f the perm ittivity o f the m edium (er) to the perm ittivity o f the

free space £o,

£*r = £ / EO..................................... (1-1)

W here £r is the dielectric constant, w hich is a dim ensionless quantity. The

m easurem ent o f the relative dielectric constant or the relative perm ittivity gives the

properties o f the dielectric m aterial. The dielectric constant o f air is one [4].

(2) D ISPL A C E M E N T VECTOR:- T he displacem ent V ector (D) is defined as the

vector, w hose m agnitude is equal to the surface density o f free charges and w hose

direction is from positive charges to the negative charges unit6 vector ( n). I f charge

Q is given to the parallel plates o f a condenser, and A be the area o f the each plate,

then

D = (Q / A) n ............................................. (1.2)

We know that electric field betw een the plates E = (Q / So A) n, hence

D = So E0 .......................................................(1*3)

(3) POLIRIZATION VECTOR: - Polarization is defined as a vector (P)

whose m agnitude is equal to the surface charge density o f bound charges, (w hose

direction is from negative induced charge) for the plate area A, it can be w ritten as:-

P = (Qd. / A .d ) n .................................(1.4)

"P" is a polarization vector," A " is an area o f the p late,!'Qd"is a charge and “d" is a

distance betw een plates.

1.2.2 DIFFERENT TYPES OF PO L A R IZA T IO N

The application o f an electric field to dielectric m aterials creates or realigns the dipoles

resulting in to polarization. There are four different types o f polarizations.

> Electronic or Induced Polarization (Pe) w hich occurs due to d istortion o f the

electron density.

r- Atom ic or Ionic polarization (P j) w hich is due to elastic deform ation of ionic

charges.

> O rientation Polarization (P()) which is due to the changes in orientation o f

perm anent dipole m om ents.

r- Interfacial or Space charge polarization due to spatial separation o f charges with

in the m aterial.

Different types o f polarizations are schem atically shown in figure 1.1

.......£Z .> tsc tr.^>m c p o * » r i r « i 1 f c O ( r : .

O r t e * n t a f le r polsnrijrati-on

S p a c e c h ^ f p o l a r u c a t i o - n

<£> C = > < S > C=> < £ > < £ > < = > < B > < = ><S> <=> <S> < £> <=>

CJD c -> <*> <3> & CE> <£> CD C3 &< = ) < £ > < = > < £ > & < £ > < £ > O C = > < = >

Figure 1.1 Schematic representations o f different types o f polarizations

1.2.3 D IE L EC TR IC LOSS

W hen an a.c. field is applied to a d ielectric m aterial, som e am ount o f electrical

energy is absorbed by the dielectric m aterial and is dissipated in the form o f heat. This

loss o f energy is know n as dielectric loss.

The dielectric loss is m ajor engineering problem . In an ideal dielectric, the current leads

the voltage by an angle o f 90° as shown in the Figure 1.2 (a). But in the case o f

com m ercial dielectrics, the current does not exactly lead the voltage by 90°. It leads by

som e other angle 0 that is less than 90° .The angle (j) = 90 - 0 is know n as dielectric loss

angle [5] as show n in figure 1.2 (b).

" ” '0 1 I ̂ o

t " " S ' /

1/ > /

([) /

/

/ ,ny0

£.)

90" r" £ 0

(a) (b) (c)

Figure-1.2

The dielectric loss is increased by follow ing factors:

> High frequency o f the applied voltage, the frequency variation s show n in fig. 1.3

> High value o f the applied voltage, as show n in fig. 1.2 ( c)

'r- High tem perature, and

r- Hum idity.

A subgroup o f the dielectric m aterials show s the property o f spontaneous

polarization [6 ], For these m aterials the centre o f positive and negative charges does not

coincide even w ithout an applied electric field. W hen the spontaneous polarization o f a

d ielectric can be reversed by an electric field o f m agnitude less than the dielectric

breakdow n o f the m aterial, it is called a ferroelectric m aterial [7],

Power Audio Radio Infrared Visible

F req u en cy ---------

Figure-1.3 The frequency dependence of dielectric loss

1.2.4 DIELEC TRIC BR EAK DO W N

W hen a voltage is applied to a d ielectric m aterial and thereby the electric field is

increased, it can withstand up to a certain m axim um voltage before it perm its large

current to pass through it. This phenom enon in w hich the dielectric m aterial fails to offer

insulation resistance for large applied voltage is know n as dielectric breakdow n [8 ].

The different types o f dielectric breakdow ns are:-

r- Intrinsic breakdow n

'r Therm al breakdow n

> Electrochem ical breakdown

'r Defect breakdow n, and

r D ischarge breakdow n.

1.3 FE R R O E LE C T R IC M A TERIA LS

Ferroelectric m aterials are those h ighly po lar d ielectric m aterials w hich have a very high

value o f relative perm ittivity or d ielectric constant [9], The characteristics o f

feiToelectrics are represented in term s o f the dynam ics o f the phase transition. T hough a

large num ber o f theories have been proposed, C ochran [10] suggested the m ost general

theory o f ferroelectric phase transitions based on Lyddane-Sachs-Teller (LST) relation

[11]. Ferroelectric crystals have been know n for alm ost a century. The discovery was

preceded by the occurrence o f two related phenom ena viz. piezoelectricity and

pyroelectricity w hich are know n since ancient tim e because o f ability o f such m aterials,

to attract object w hen they are heated. I n i880, Jacques and Pierre C urie discovered the

piezoelectric effect [12], In 1894, Pockets [13] reported the large piezoelectric constants

o f Rochelle salt (N a K C ^ C M H b O ) [14], T he ferroelectricity in this salt was discovered

in 1917 by A.M . N icholson, J. A. A nderson, and W .G. Cady [15]. In 1920, V alasek [16]

observed the ferroelectric hysterersis loop in Rochelle salt crystal [17], later on, Busch

and Scheerer [18] discovered ferroelectricity in K H 2PO 4 and its sister crystals [19] . Now,

it was realized that Ferro electricity was not a property o f som e isolated m aterials, but

rather a m ore com m on phenom enon [20], W ith the discovery o f ferroelectricity in

BaTiC>3, a num ber o f “ firsts" w ere established: first ferroelectric w ithout hydrogen bonds,

first ferroelectric w ith m ore than one ferroelectric phase [21], In addition, the ceram ic

m aterials w ere found very stable and hard w ith a sim ple perovskite crystal structure,

w hich facilitated the theoretical progress at m icroscopic level. By 1960s, m any new

ferroelectric m aterials w ere discovered, and research was focused on the m ost prom ising

m aterials, such as the perovskite and tungsten bronze structure oxides and ferroelectric

polym ers [2 2 ], w ith the im proved thin film deposition techniques, attention w as partly

m oved from ceram ics and single crystals to ferroelectric thin films [23].

The nam e ferroelectricity originates from the sim ilarity o f the fundam ental

concept to those in ferrom agnetic m aterials, such as m agnetization, m agnetic dom ains,

and m agnetic hysterersis loop. H ow ever, the physics behind this phenom enon is

com pletely d ifferent from those in ferroelectric m aterials. W hile m agnetism can be

understood as an intrinsically quantum m echanical phenom enon, ferroelectricity in

general m ay be described by m eans o f classical physics [24],

1.4 BASIC FEA T U R E S OF FE R R O ELEC TRIC S

There are certain dielectric substances called ferroelectrics, having the follow ing typical

properties:-

1. Curie- W eiss law and C urie tem perature.

2. Spontaneous polarization.

3. Hysterersis loop

1. CUR IE W EISS LAW A N D CURIE T E M P E R A T U R E (Tc):- In ferroelectric

m aterials, d ielectric constant changes w ith tem perature according to the follow ing

relation:-

£r = B + C / ( T - T c ) ................................... (1.5)

for , T > Tc w here B and C are tem perature independent constant, This relation is

called C urie - W eiss law [25],C onstant ‘C ! is called C urie constant and T c , the Curie

tem perature. R elation (1.5) is shown by a plot in er vs. T in Fig. 1.4

For T< T(- the above behavior does not hold well.

Tc t ------ ►

Figure 1.4 Dielectric constant vs. temperature curve.

2. SPO N T A N E O U S PO LARIZATION : - In the tem perature below Tc (T<TC), the

m aterials becom e spontaneously polarized, (i.e., an electric polarization develops in it

w ithout the application o f an external field). Thus at Tc , a phase transition occurs.

A bove Tc the substance is in paraelecric phase in w hich elem entary dipoles are

random ly oriented and below T c, the dipoles interact w ith each other. T heir interaction

gives rise to an internal field, w hich lines up the dipoles. Thus the process o f

spontaneous polarization (Ps) arises. This polarization increases gradually as the

tem perature is lowered [26] as show n in figure 1.5.

F igurel.5 Spontaneous polarization (Ps) versus temperature (T) curve.

3. H YSTE R E R SIS LOOP: - C haracteristic o f a ferroelectric substance is that the

polarization is not fixed in a certain definite d irection o f the crystal, w hen a suffic ien tly

strong electric field is applied, the polarization direction can be reversed. Then, crystal

polarization show s hysterersis loop in alternating fields. In Fig. 1.6, a po larization

versus electric field curve is obtained. Ferroelectric hysterersis loop is quite sim ilar to

B-H curve o f the ferrom agnetic m aterials [27].

Figure 1.6 Typical Hysterersis Loop of Ferroelectrics

W hen electric field is zero, the polarization o f the w hole m aterial is zero. W hen electric

field is applied, electric polarization grow s in the field direction. A t a very h igh electric

field, the polarization attains m axim um value and becom es saturated. T his value o f

polarization is called saturated polarization [28]. A t this stage if w e decrease the field,

the polarization curve does not retrace its grow th curve bu t retains larger values. T his

value is rem nant po larization (Pr). w hen d irection o f field is changed, it increased. T hen

polarization decrease and goes to zero at field Ec (coercive field). I f the fie ld is

increased in opposite direction, the po larization becom es saturated in reversed

direction. I f now field is again reversed the po larization follow s the path as show n in

figure get a close curve called hysterersis loop [29], For a ferroelectric m aterial, the

essential feature observed hysterersis curve is below Tc

1.5 FE R R O E LE C T R IC DO M AIN S

In general, uniform alignm ent o f electric dipoles occurs in a certain region of a

ferroelectric crystal. These regions are called the ferroelectric dom ains and the boundary

between tw o dom ains is called the dom ain walls. Dom ain w all are characterized by the

angle betw een the directions o f polarization on either side o f the wall. G enerally dom ains

are formed to reduce the energy o f the wall, w hich changes w ith direction.

W hen applying the weak electric field on the ferroelectric crystal, rotation of

electric dipoles will change in the direction, leading to the rotation of the ferroelectric

dom ains. W hen a strong electric field, is applied the rotation of electric dipole is occurred

in the first step, and the dom ain w hich are aligned in the direction of electric field has the

m axim um area and the dom ain w hich has the direction opposite to the electric field gets

m inim ized. [30],

1.6 P R O PE R T IES OF FER R O ELEC TRIC S

(a) PIE Z O E L E C T R IC IT Y : - T he w ord p iezo is a G reek w ord m eaning pressure;

piezo- electricity m eans pressure electricity [31]. The production o f electric polarization

by the application o f m echanical stresses can take place in som e dielectric m aterials. This

effect is called piezoelectricity. All ferroelectric m aterials are piezoelectric but all

p iezoelectric m aterials are not ferroelectric. The best know n piezoelectric m aterial is

quartz w hich is non-ferroelectric.

(b) P Y R O E L E C T R IC IT Y The production o f electric polarization by the application

o f therm al stresses can take place in som e dielectric m aterials such as quartz, tourm aline

etc. Heating or cooling develop bound charges such that one end becomes positively

charged and other negatively. The pyroelectric property like piezoelectricity is solely

determ ined by the sym m etry properties o f crystals. All pyroelectric crystals are

p iezoelectric but converse is not true [32],

1.7 PHASE TR A N SITIO N

Phase transition is the transform ation o f a m aterial from one therm odynam ic

phase to another, w hich is accom panied by an abrupt/slow change o f certain physical

properties o f the substance on continuous change o f external param eters. The value o f

tem perature, pressure, or som e other physical quantities, at w hich the phase transition

occurs, is referred to as the transition point.

The crystal structure o f m any dielectric m aterials change with tem perature

(i.e., they undergo a phase transition). T he phase transitions in crystals are due to the

change in the forces o f interaction betw een atom s in crystals. This change m ay produce

various new properties in the crystal. The phase transition that produces or alters the

spontaneous polarization is called ferroelectric phase transition. By changing tem perature

or pressure, the atom ic arrangem ents in the crystals m ay be changed w ithout any change

in chem ical com position. The difference in crystal structure on either side 0 + Tc m ay be

large or small. T he higher tem perature phase w ith higher sym m etry generally transform s

to low er tem perature phase with loss o f som e sym m etry elem ents. U sually phase

transition can be classified into two categories, first and second order. In, first order

phase transition, entropy, volum e, polarization and structural param eters o f a crystal (i.e.,

atom ic position, therm al vibration and lattice constants etc.) change discontinuously at

the transition point. In the second order transition, these param eters do not change

continuously at the transition point, whereas the tem peratures derivatives o f the above

param eters show discontinuity. Ehrenfest [33] first defined the kind (order) of transition

(T |) and according to his definition an n lh order transition is a transition where the (n - 1 ) lh

derivative o f G ibbs free energy (G) is continuous w hile the n11' derivative shows

discontinuity at the transition tem perature. Landau explained the ferroelectric phase

transition by m eans o f thrm odynam ical theory. T his theory is known as Landau theory o f

phase transition [34], A therm odynam ical theory explaining the behavior o f a

ferroelectric crystal can be obtained by considering the expansion o f the free energy as a

function o f the polarization P. A ccordingly the Landau free energy F can be written as

F (P, T) = (1/2) a Ps2 + (1/4) PP54 + (1/6) yPs6 + (1.6)

d F/ <rr= a Ps + p Ps3 + y Ps5 + (1.7)

The coefficients a , p, y depend, in general, on the tem perature. The series does not

contain term s in odd powers o f Ps because the free energy o f the crystal will not change

with polarization reversal (Ps-»-Ps). The phenom enological form ulation should be applied

for the w hole tem perature range over which the m aterial is in the paraelecric and

ferroelectric states.

The equilibrium polarization in an electric field E satisfies the condition,

M/cPs = E = u P s + p P s ' + y P / .......................................... (1.8)

To obtain the ferroelecrtric state, the coefficient o f Ps2 term m ust be negative for the

polarized state to be stable, w hile in the paraelecric state it m ust be positive passing

through zero at som e tem perature T 0 (usually called as C urie-W eiss tem perature),leading

to,

a = ( T - T 0) / £ „ C .................................................... (1.9)

W here C is taken as a positive constant called the Curie-W eiss constant. The value o l To

m ay be equal to o r low er than the actual transition tem perature T c (Curie tem perature).

The first or second order phase transition can also be explained with the help o t the order

param eter r|. In first order phase change, r) changes from a finite value to zero abruptly at

the transition tem perature whereas in 2 nd order it changes continuously as shown in figure

1.7(a).Spontaneous polarization (Ps) and dielectric perm ittivity (er) show anom alies at

phase transition. The typical changes are depicted in figure 1.7(b) in 2 nd order phase

change and in Figure 1.7(c) for first order phase transition.

' ■ •" T

Figure 1.7Temperate dependence of order parameter ( i j ),

If r) approaches to zero from some finite value over a small range o f tem perature

around Tc, the transition is o f second order. The schem atic representation o f tem perature

dependence o f order param eter (spontaneous polarization process), physical properties

(Perm ittivity) for the first and second order phase transitions are shown in Fig. 1.7.

D epending on the tem perature variation o f dielectric constant or the C urie constant C,

ferroelectric m aterials are broadly divided into two groups:

'r Soft ferroelectrics (KDP-type).

^ Hard ferroelectrics (BaTiCVtype).

The phase transition in soft (H -bounded) ferroelectrics is o f order-disorder type

w hile for hard ones (i.e., BaTiO^) it is o f displasive type. The ferroelectric phase

transition o f barium titanate was discovered 1946 [35]. In the earlier literatures, the phase

transition was considered to be displasive for m ost o f the ferroelectric m aterials that were

m icroscopically non-polar in the paraelecric phase. However, m aterials in m acroscopic or

therm ally arranged sense as non-polar w ere considered to undergo order-disorder type o f

phase transition [36], This classification is practically equivalent to that based on the

existence o f perm anent or induced dipoles in the non-polar phases o f the crystal. The

nature o f phase change (i.e., order, disorder/displasive can be understood on the basis o f

the structural investigations. In some cases, how ever, this inform ation is already available

from the results o f dielectric investigations [37],On the basis o f tem perature dependence

o f dielectric constant, and the value o f the C urie constant, it is observed that ferroelectrics

are classified into two groups; (i) com pounds having the C urie constant ~10 3 belong to

the order-disorder type and, (ii) those w hich undergo displasive type o f transition, with

Curie constant ~ 1 0 \

The phase transition in soft ferroelectrics involves not only the ordering o f the

disordered hydrogen atoms, but also the deform ation o f the atom ic groups like SO 4'2,

S c 0 4‘ 2 and PO 4"3 [38]. In case o f d isplacive type o f transition, a small atomic

displacem ent o f som e o f the atoms is m ainly responsible for the phase transition, which

has been observed in som e o f the perovskites [39],H ow ever, the difference betw een

displacive and order -d iso rd e r type o f transition becom es uncertain when the separation

o f relevant d isorder becom e com parable to the m ean therm al am plitude o f those atom s

[40],

The characteristics o f ferroelectrics are represented in term s o f the dynam ics o f the phase

transition. Cochran [41] suggested the m ost general theory o f ferroelectric phase

transitions based on Lyddane-Sachs-Teller (LST) relation [42],

w 2i.o/0 )2to = £ ( 0 ) / £ ( x ) ...................................... ( 1 . 1 0 )

W here Wto and (Oi o are the frequencies o f transverse and longitudinal optic m odes

respectively and e(co) and e(0 ) are the high frequency and static dielectric constant

respectively. This LST relation predicts an anom aly in the lattice vibration spectrum o f

ferroelectrics at the transition tem perature [43]. In a ferroelectrics crystal, if the value o f

£(()) is high corresponding to to becom e very low. In case o f second order phase

transition, s(0) follows the Curie-W eiss law (i.e., (o2ro u (T-To)). As the phase transition

tem perature approaches from above or below, e(0) diverges and o)ro becomes zero. The

ferroelectric phase transition could be regarded as instability o f the crystals for a

particular norm al m ode o f vibration, often referred to as soft mode. But in case o f first

order phase transition, copo is not zero at the transition tem perature.

1.8 DIFFUSE PHASE TR A N SITIO N : - T he transition tem perature in m any

m acroscopic hom ogeneous m aterials is not quite sharply defined. The transition is

sm eared over certain tem perature interval know n as C urie range, resulting in the gradual

change o f physical properties. The w idth o f the C urie region depends on com positional

fluctuation and sensitivity o f the Curie tem perature to com position change. This type o f

phase transition is generally know n as" D iffuse Phase Transition" (DPT). T hough this

phenom enon is observed in several types o f m aterials [44] the m ost rem arkable exam ple

o f D PT was found in ferroelectric m aterials [45]. Ferroelectricity with diffuse phase

transitions (D PTT) was first reported [46] and their extensive studies were carried out in

different system s [47]. Some o f the characteristics o f ferroelectric diffuse phase

transitions are:

'r Broadened m axim a in the perm ittivity - tem perature curve.

r- G radual decrease o f spontaneous polarization with rise in tem perature.

> No C urie-W eiss behavior in a certain tem perature interval above the transition

tem perature.

'k R elaxation behavior o f dielectric properties in transition region and,

'r T ransition tem perature obtained by different techniques does not coincide.

The diffuseness o f the phase transition is assum ed to be due to the occurrence o f

fluctuation in a relatively large tem perature interval around the transition. Usually, two

kinds o f fluctuation are considered:-

(a) C om positional fluctuation and, (b) Polarization (structural) fluctuation.

From the therm odynam ic point o f view, it is clear that the com positional fluctuation is

present in ferroelectric solid-solutions, and polarization fluctuation is due to the small

energy difference betw een high and low tem perature phase around the transition. Kanzig

[48] observed from X -ray diffraction that in a narrow tem perature range (around the

transition) B aT iO j single crystal splits up into ferroelectreic (FE) and paraelectric (PE)

m icro-regions. A ccording to Fritsberg [49], substances o f less stability are expected to

have a m ore diffuse phase transition. For relaxer as well as o ther FDPT the w idth o f the

transition region is m ainly im portant for practical applications. Sm olenkii [50] and Rolov

[51] introduced a m odel based on Gaussian distribution to calculate d iffusiv ity o f DPT

(due to com positional and polarization fluctuations). D iffuse phase transition w as also

studied by Sm olenskii- Isupov theory [52] and the results are com pared with those o f

experim ental findings.

1.9 FE R R O E LE C T R IC S WITH O XYG EN O C T A H E D R A L

O ne o f the m ost im portant group o f ferroelectrics is the fam ily o f oxygen octahedral

consisting o f one or m ore com ponent oxides, .A com m on feature o f all these m aterials is

BO(, octahedral building blocks [53] although the m aterials m ay have different crystal

structures, electrical and mechanical properties. The fam ily o f oxygen octahedral

ferroelectrics has four basic structures, nam ely

r Perovskite type ferroelectric

r Tungsten-B ronze type ferroelectrics

r- Layer structure oxides and com plex com pounds

'r- Pyroc hi ore-type ferroelectrics

1.10 A PPL IC A T IO N OF FE R R O ELEC TRIC M A TE R IA L S

1. The dielectric constant o f ferroelectrics is very high and so they are used in

m anufacture o f small size high capacity capacitors.

2. Piezoelectric acoustic transducers and pyroelectric infrared detectors are the devices

based on ferroelectrics.

3. The electrooptic characteristics o f ferroelectrics such as B aT i0 4 and KDP have been

used for m odulating and deflecting laser beam s inside and outside the optical cavity.

4 Ferroelectric films are used in non-volatile m em ories, integrated optics, electro optic

displays, m icro transducers and capacitors fabricated in a film from [54],

5. Ferroelectric crystal exhibit the property o f piezoelectricity, Hence they are used as

transducer (i.e., in devices used to convert electrical energy into m echanical energy).

They are used in the construction o f crystal m icrophones.

6 . Ferroelectric crystals, also exhibit application o f tem perature. Using this property these

are used as IR sensors and detectors.

7. The property o f hysterersis m akes it possible to use them as m em ory devices tor

com puter, actuators m icro transducer and capacitors fabricated in a film form. O ther

applications o f ferroelectrics are exploiting the electrostrictive effect, positive

tem perature coefficient o f resistively, and stress-induced dipoling.

REFEREN C ES

[1] J.C .Burfoot and W. Taylor, M cM illan Press Ltd. (1971)

[2] J.C .B urfolk and W .Taylor POLAR D ielectrics and the A pplications M acm illan Press

Ltd( 1971).

[3] S .A .A m in, R.Guo, A .S.Bhalla, Ceram, Trans 106, 157 (2000).

[4] I.S.Zhludev Physics o f Crystalline D ielectric Plenum, New York (1971).

[5] A .R .V on Hippel D ielectric materials and applications Technology Press, MIT and

W iley, N ew Y ork (1954).

[6 ] H .D .M egaw Ferro electricity in Crystals M ethuen, London (1957).

[7] H .D .M egaw Ferro electricity in Crystals M ethuen and co. London (1957).

[8 ] G .Busch, Ferroelectrics71, 43 (1987).

[9] C .Burfoot, Ferroelectrics Van Nostrand, N ew Y ork (1967).

[10] Cochran A dvances in physics, 9,387, (1960).

[11] R .H .Lyddane, R .C .Sachs and E Teller, Phys R ev.59, 673(1941).

[12] W .G .Cady Piezoelectricity M cG raw Hill N ew Y ork (1946).

[13] T .R .Shrout, H.Chen, L.E.Cross, Ferroelectriucs74, 317 (1987).

[14] K .Sam basiva Rao, N .V .N ath, Ferroelectrics325, 15(2005).

[15] C.Li, R.Guo, A .S.B alia, Ferroelectrics 339,103(2006).

[16] Valasek, Phys.Rev, 15,537(1920).

[17] J.Fousek, Ferroelectrics 113, 3 (1991).

[ 18] G .Busch. ferroelectrics74, 267(1987).

[19] V .A .Isupov. Ferroelectrics 131. 41(1992).

[20] P.H .Fang, Ferroelectrics. 332.213(2006).

[21] B.W ull, L.M .Goldm ann. C .R .A cad.Sci.U SSR.46, 139 (1954).

[22] T .R .Shrout, H .Chen, L.E.Cross, Ferroelectrics74, 317 (1987).

[23] K .Sam basiva Rao, N .V.Nath, Ferroelectrics325, 15 (2005).

[24] C'.Li, R.Guo, A .S.Balia, Ferroelectrics 339,103(2006).

[25] Y .Gagou, D .M ezzane,N .A lioiuane,T .B adeche,M .Elaatm ani..M .H .,Pischedda,P.Saint-

Gregoiire, Ferroelectrics254, 197 (2001).

[26] V .V .N .A charya, A .Bhanum athi, K.V., S .Ram an, Ferroelectric, Lett.Sec.25,

125(1999).

[27] J.H .K o, Do.H.Kim , S.G .LKushnikov, R .S .K atiyar and K.Seiji. Ferroelectrics

286. 61(2003).

[28] K .U m akantham , S.N arayana M uilhy and A .B hanum athi. Ferroelectrics

94,291(1989).

[29] V .V .N .A charya, A .Bhanum athi, Uchinoi, S .N .Prasad, Ferroelectrics

Lctt.Sec.27, 7 (2000).

[30] M .Oualla, A .Zegzouti, M Elaatm ani, M .D aioud, D .M ezzane, Y .Gagou, P.Saini-

G regoire Ferroelectric 291,133(2003).

[31] W .G .Cady Piezoelectricity M cGraw Hill N ew Y ork (1946).

[32] M .E.Lines and A .M .G lass Principles and A pplication o f Ferroelectric and Related

M aterials O xford University Press (1977).

[33] Ehrenfest. Phase Transition in Ferroelectrics (1950).

[34] S.B .Lang Source book o f Pyroelectricity G ordon and Breach N ew York (1974).

[35] W .K anzig Ferroelectrics74, 285 (1987).

[36] A Von Hippel R.G. Breckenridge F.G.C'hesley and L.Tisza. Industr.Engng.Chem .38,

1097(1946).

[37] F.John and G .Shirane, Ferroelectric C rystal.Pergam on Press Ltd (1962).

[38] A .M agneli, Ark, Kem, 1 213(1965).

[39] P .B .Jam ieson,S .C .A braham s,J.L .B ernstein,J.C hem .Phys.48,5048 (1965).

[40] I.S.Zheludev Physics o f Crystalline D ielectrics, Plenum , N ew York (1971).

[41] Cochran A dvances in physics, 9,387(1960).

[42] R.l l.Lyddane, R.C.Sachs and E Teller, Phys Rev.59, 673 (1941).

[43] H.Frohlich, Theory o f Dielectrics C laredon.Press, O xford (1949).

[44] A .J.B urggraaf, Proc 9th Int.Cong.On Sci. o f Ceram ics,

N oordw ijkerhout, Netherlands (1977).

[45] C .G .F .S tm ger and A .J.Burggraaf, J Phys.acta24, 25(1980).

[46] W .Kanzing, H elv.Phys.A cta 24, 25(1951)

[47] A .Fundora,A .V azaquez,J.Portelles,F .C alderan and

J.M .Siqueriros,J.N on.C ryst.Solid ,567,6 235( 1988).

[48] W .K anzing, Ferroelectrics and A ntiferroelectrics, A cadem ic Press, N ew Y ork (1957).

[49] J.Fritsberg, Proc.4th Int.m eeting on Ferroelectricity, Leningrad (1977).

[50] G .H .Sm olenskii P roc.of Second Int.M eet. Ferroelectricity, 1969, 26(1970).

[51] B .N .Rolov. Sov.Phys.Solid-state (E ngl.T ransl.)6 , 1676(1965).

[52] A .Fundora A .V azque J.Portelles, F.Calderon and J.M .Siqueiros. J.N on-

Cryst.Solid.567. 235(1988).

[53] M .H .Francom be. B. lewis. Acta A ctacrystalog 13.131(1960).

[54] J.J.R ubin.L .G .V anU itert.H .JLevinstein. J.cryst. G row th 1 .315(1967).