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BASIC CONCEPTS
CHAPTER-1
BASIC CONCEPTS
1.1 I N T R O D U C T IO N
O ne 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
w hich electrostatic field can persist for a long tim e. T hese m aterials o ffer very high
resistance to the passage o f direct current and therefore, sharply differ from m etal,
sem ico n d u cto r and superconductors. It is w ell know n 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 p olarization or electric dipole
m om ent can be induced by the application o f external electric field , are divided in
to tw o classes: >
P olar (dipole) dielectrics.
a-
N o n -p o lar (neutral) dielectrics.
In p o lar d ielectrics, a perm anent polarizatio n (P s) exists even in the absence ot
applied electric field. In the case o f n on-polar dielectrics, there is no such
perm an en t p o larizatio n [ 1 ],
1.2 D I E L E C T R I C M A T E R I A L S
D ielectrics are a group o f m aterials that possess electric polarizatio n w hen
applied w ith external electric field and h av e the capacity o f storing the charges.
M ost o f th ese 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 co n sid er their
in teraction w ith electric, m agnetic, or electrom agnetic fields. T h e various dielectric
p ro p erties are the storage and d issipation o f electric and m agnetic energies.
polarization,
m agnetization
and
conduction.
P olarization
and
m agnetization
m easures the electric and m agnetic dipole m om ent p er unit volum e. T hese
m icroscopic m om ents are com posed o f elem entary m o lecu lar m om ents. Induced
electric d ipole m om ents result from the d isp lacem en t 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 w hereas the spontaneous alignm ent o f electric
dipoles by m utual interaction causes (ferroelectricity). T he perm anent dipole
m om ents anchored in the structure w ithout a centre o f sym m etry; under m echanical
d istortion creating a voltage generates piezoelectric effect. On the basis o f
tem p eratu re d ependence o f dielectric constant, and the value o f the C urie constant,
it is observ ed that ferroelectrics are classified into tw o g ro u p s:r
C o m pounds having the C urie constant in the o rd er o f 10 3 belong to the orderd iso rd er type [2 ] and,
>
For those w hich undergo displasive type o f transition, w ith C urie constant in the
o rd er o f 103 [3].
1.2.1 M I C R O S C O P I C D IE L E C T R IC P A R A M E T E R S
T he 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. T hese
p aram eters are as follow s:(1) D IE L E C T R I C C O N S T A N T : - T he dielectric co n stan t (er) o f a m aterial is
defined as th e ratio o f the perm ittivity o f the m ed iu m (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. T he
m easurem ent o f the relative dielectric constant o r the relative perm ittivity gives the
p roperties o f the dielectric m aterial. T he dielectric constant o f air is one [4].
(2) D IS P L A C E M E N T V E C T O R :- T he displacem ent V ector (D ) is defined as the
vector, w h o se m agnitude is equal to the surface density o f free charges and w hose
direction is from positive charges to the negative charges unit 6 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)
W e know that electric field betw een the plates E = (Q / So A) n, hence
D = So E0 .......................................................(1*3)
(3) P O L IR IZ A T IO N
VECTOR:
- P olarization
is defined as a v ecto r (P)
w hose 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 = (Q d. / 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 D IF F E R E N T T Y P E S OF P O L A R IZ A T IO N
The application o f an electric field to dielectric m aterials creates or realigns the dipoles
resulting in to polarization. T here are four different types o f polarizations.
>
E lectronic or Induced P olarization (Pe) w hich occurs due to d isto rtion o f the
electron density.
r-
A tom ic o r Ionic polarization (P j) w hich is due to elastic deform ation of ionic
charges.
>
O rientation P olarization (P()) w hich is due to the changes in orien tatio n o f
p erm anent d ipole m om ents.
r-
Interfacial o r Space charge polarization due to spatial separation o f charges w ith
in the m aterial.
D ifferent types o f polarizations are schem atically show n in figure 1.1
£ Z .> ts c tr.^ > m c p o * » r i r « i 1 f c O ( r : .
O r t e * n t a fle r
S p a c e
ch ^ f
< £> C = > < S > C=>
.......
polsnrijrati-on
p o la r u c a t io - n
<£><£> <=><B><=>
<S > < = > <S> < £ > < = >
C
J
D
c
-><*> <
3
>
&
CE> <
£
>CD C
3&
< = )< £ > < = > < £ > &
<£><£> O
C=><=>
Figure 1.1 Schem atic representations o f different types o f polarizations
1.2.3 D IE L E C T R IC L O SS
W hen an a.c. field is applied to a d ielectric m aterial, som e am ount o f electrical
en erg y is abso rb ed b y the dielectric m aterial and is dissipated in the form o f heat. This
loss o f energy is kn o w n as dielectric loss.
T he dielectric loss is m ajor engineering problem . In an ideal dielectric, the current leads
the vo ltage by an angle o f 90° as show n in the F igure 1.2 (a). B ut in the case o f
com m ercial dielectrics, the current does not exactly lead the voltage by 90°. It leads by
som e o th er 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
1I ^ o
t "
" S ' /
1/>
/
([) /
/
/
90"
,n y0
r"
£ 0
£.)
(a)
(b)
(c)
Figure-1.2
T he dielectric loss is increased b y follow ing factors:
>
H igh freq u en cy o f the applied voltage, the freq u en cy variatio n s show n in fig. 1.3
>
H igh v alu e o f the applied voltage, as show n in fig. 1.2 ( c)
'r-
H igh tem p erature, and
r-
H um idity.
A su b g ro u p o f the dielectric m aterials show s the p ro p erty o f spontaneous
po larizatio n [6 ], F or these m aterials the centre o f po sitiv e and neg ativ e charges does not
co in cid e even w ith o u t an applied electric field. W hen the sp o n tan eo u s p o larizatio n o f a
d ielectric can b e reversed b y an electric field o f m ag n itu d e less than the dielectric
b reak d o w n o f th e m aterial, it is called a ferroelectric m aterial [7],
P ow er
A udio
R adio
F re q u e n c y
Infrared
Visible
---------
Figure-1.3 The frequency depend en ce of dielectric loss
1.2.4 D IE L E C T R IC B R E A K D O W N
W hen a v o ltag e is applied to a d ielectric m aterial and thereby the electric field is
increased, it can w ithstand 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 resistan ce for large applied v o ltag e is know n as dielectric breakdow n [ 8 ].
T he different ty p es o f dielectric breakdow ns are:r-
Intrinsic breakdow n
'r
T herm al breakdow n
>
E lectrochem ical breakdow n
'r
D efect breakdow n, and
r
D ischarge breakdow n.
1.3 F E R R O E L E C T R IC M A T E R IA L S
F erroelectric m aterials are those h ighly p o lar d ielectric m aterials w hich have a v ery high
v alue
o f relativ e
perm ittivity
or
d ielectric
co n stan t
[9],
T he
ch aracteristics
of
feiToelectrics are represented in term s o f the dynam ics o f the phase transition. T hough a
large nu m b er o f theories have been proposed, C ochran [10] suggested the m o st general
theory o f ferroelectric phase transitions based on L yddane-S achs-T eller (LST) relation
[11]. Ferroelectric crystals have been know n for alm ost a century. T he discovery w as
preceded
by the o ccurrence o f tw o related
phenom ena viz. piezoelectricity
and
p y roelectricity 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 i 880, Jacques and Pierre C urie discovered the
piezoelectric effect [12], In 1894, P ockets [13] reported the large piezoelectric constants
o f R ochelle salt ( N a K C ^ C M H b O ) [14], T h e ferroelectricity in this salt w as discovered
in 1917 by A .M . N icholson, J. A. A nderson, and W .G . C ady [15]. In 1920, V alasek [16]
observed the ferroelectric hysterersis loop in R ochelle salt crystal [17], later on, B usch
and S cheerer [18] discovered ferroelectricity in K H 2 PO 4 and its sister crystals [19] . N ow ,
it w as realized that Ferro electricity w as not a property o f som e isolated m aterials, but
rath er a m ore com m on p h enom enon [20], W ith the discovery o f ferro electricity in
BaTiC>3 , a n um 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 v ery stable and hard w ith a sim ple perovskite crystal structure,
w hich facilitated the theoretical progress at m icroscopic level. B y 1960s, m an y new
ferroelectric m aterials w ere discovered, and research w as focused on the m ost p ro m isin g
m aterials, such as the p ero v sk ite and tungsten bronze structure oxides and ferroelectric
p o lym ers [2 2 ], w ith the im proved thin film dep o sitio n techniques, attention w as p artly
m oved from ceram ics and single crystals to ferroelectric thin film s [23].
T he n am e ferro electricity 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 h y sterersis loop. H ow ever, the physics behind this p h en o m en o n 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 BA SIC F E A T U R E S OF F E R R O E L E C T R IC S
T here are certain dielectric substances called ferroelectrics, having the follow ing typical
properties:1. C urie- W eiss law and C urie tem perature.
2. S po n tan eo us polarization.
3. H ysterersis loop
1. C U R IE W E IS S L A W A N D C U R IE T E M P E R A T U R E (T c):- In ferroelectric
m aterials, d ielectric constant changes w ith tem perature according to the follow ing
relation:£r = B +
for , T > Tc
C / ( T - T c ) ................................... (1.5)
w here B and C are tem perature independent
called C urie - W eiss law [25],C onstant ‘C ! is called
constant,
C urie constant and T c , the C urie
tem perature. R elatio n (1.5) is show n b y a plot in er vs. T in Fig. 1.4
For T < T(- th e ab o ve behavior does not hold w ell.
T his relation is
Tc
t
------ ►
Figure 1.4 Dielectric constant vs. tem perature curve.
2 . S P O N T A N E O U S P O L A R IZ A T IO N : - In the tem perature below T c (T < T C), the
m aterials beco m e spontaneously polarized, (i.e., an electric polarization develops in it
w ithout the application o f an external field). T hus at T c , a phase transition occurs.
A bove Tc the substance is in paraelecric phase in w hich elem entary dipoles are
random ly o riented 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. T hus the process o f
sp ontaneous po larization (Ps) arises. This p o larizatio n increases gradually as the
tem p eratu re is low ered [26] as show n in figure 1.5.
F ig u rel.5 Spontaneous polarization (Ps) versus tem peratu re (T) curve.
3. H Y S T E R E R S I S LO O P: - C haracteristic o f a ferroelectric substance is th at the
p o larizatio n is n o t fixed in a certain definite d irectio n o f the crystal, w hen a su ffic ie n tly
strong electric field is applied, the polarizatio n d irection can be reversed. T hen, crystal
p o larizatio n show s hysterersis loop in alternating fields. In Fig. 1.6, a p o lariz atio n
v ersus electric field curve is obtained. F erroelectric hysterersis loop is quite sim ilar to
B -H cu rve o f the ferrom agnetic m aterials [27].
Figure 1.6 Typical Hysterersis L oop o f Ferroelectrics
W h en electric field is zero, the polarizatio n o f the w h o le m aterial is zero. W h e n electric
field is applied, electric polarizatio n grow s in the field direction. A t a very h ig h electric
field, th e p o larizatio n attains m axim um v alu e and becom es saturated. T his v alu e o f
p o larizatio n is called saturated p o larizatio n [28]. A t this stage if w e decrease th e field,
the p o larizatio n cu rv e does not retrace its grow th curve b u t retains larger values. T his
valu e is re m n an t p o larizatio n (Pr). w hen d irectio n o f field is changed, it in creased. T h e n
p o larizatio n d ecrease and goes to zero at field Ec (coercive field). I f th e fie ld is
in creased in o p p o site direction, th e p o lariz atio n becom es
satu rated
in re v e rse d
direction. I f n o w field is again reversed the p o lariz atio n follow s th e p ath as sh o w n in
figure get a clo se curve called hysterersis loop [29],
For a ferroelectric m aterial, the
essential feature observed hysterersis curve is below Tc
1.5 F E R R O E L E C T R IC D O M A IN S
In general, uniform alignm ent o f electric dipoles occurs in a certain region of a
ferroelectric crystal. T hese regions are called the ferroelectric dom ains and the boundary
betw een tw o do m ains is called the dom ain w alls. D om ain w all are characterized by the
angle betw een the directions o f polarization on either side o f the w all. G enerally dom ains
are form ed to reduce the energy o f the w all, w hich changes w ith direction.
W hen app lying the w eak electric field on the ferroelectric crystal, rotation of
electric dipoles w ill 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 o p p o site to the electric field gets
m inim ized. [30],
1.6 P R O P E R T IE S O F F E R R O E L E C T R IC S
(a) P IE Z O E L E C T R I C I T Y : - T h e w ord p iezo is a G reek w ord m eaning pressure;
p iezo- electricity m eans pressure electricity [31]. T he p roduction o f electric polarization
by th e ap p lication o f m echanical stresses can take place in som e dielectric m aterials. This
effect is called p iezoelectricity. A ll ferroelectric m aterials are piezoelectric but all
p iezo electric m aterials are not ferroelectric. T he best know n piezoelectric m aterial is
q u artz w hich is n o n-ferroelectric.
(b) P Y R O E L E C T R I C I T Y
T he p roduction o f electric p o larizatio n b y the application
o f therm al stresses can take place in som e dielectric m aterials such as quartz, tourm aline
etc. H eating or cooling develop bound charges such that one end becom es positively
charged and o th er negatively. T he p yroelectric pro p erty like piezoelectricity is solely
determ ined by the sym m etry properties o f crystals. A ll pyroelectric crystals are
p iezoelectric but converse is not true [32],
1.7 P H A S E T R A N S IT IO N
Phase tran sition 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. T he value o f
tem perature, pressure, or som e other physical quantities, at w hich the phase transition
o ccurs, is referred to as the transition point.
T he crystal structure o f m an y dielectric m aterials change w ith tem perature
(i.e., they undergo a phase transition). T he p h ase transitions in crystals are d u e to the
ch an g e in the forces o f interaction betw een atom s in crystals. T his change m ay produce
various new p ro perties in the crystal. T he phase transition that produces o r alters the
spontaneous p o larization is called ferroelectric ph ase transition. B y changing tem perature
o r pressure, the atom ic arrangem ents in the crystals m ay b e ch an g ed w ithout any change
in chem ical com position. T he difference in crystal structure on either side 0 + T c m ay be
large or sm all. T h e higher tem perature phase w ith higher sy m m etry generally transform s
to low er tem p erature phase w ith loss o f som e sy m m etry elem ents. U sually phase
tran sitio n can be classified into tw o categories, first and second order. In, first order
p h ase transition, entropy, volum e, p olarization and structural p aram eters o f a crystal (i.e.,
atom ic position, therm al vibration and lattice constants etc.) ch ange d iscontinuously at
the transition point. In the second order transition, th ese p aram eters do no t change
continuously at the transition point, w hereas the tem peratures derivatives o f the above
p aram eters show discontinuity. E hrenfest [33] first defined the kind (order) of transition
(T |) and according to his definition an n lh order transition is a transition w here the ( n - 1 ) lh
derivative o f G ibbs free energy (G ) is continuous w hile the n11' derivative show s
disco ntinuity at the transition tem perature. L andau explained the ferroelectric phase
transition by m eans o f thrm odynam ical theory. T h is theory is know n as Landau theory o f
phase
transition
[34],
A
therm odynam ical
theory
explaining
the beh av io r o f a
ferroelectric crystal can be obtained by considering the expansion o f the free energy as a
function o f the p olarization P. A ccordingly the Landau free energy F can be w ritten 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)
T he co efficients a , p, y depend, in general, on the tem perature. T he series does not
contain term s in odd pow ers o f Ps because the free energy o f the crystal will not ch ange
w ith p o larizatio n reversal (Ps-»-Ps). T he phenom enological form ulation should be applied
for the w hole tem perature range o v er w hich the m aterial is in the paraelecric and
ferroelectric states.
T he equilibrium p o larization 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 P s2 term m ust be negative for the
polarized state to be stable, w hile in the paraelecric state it m ust be positive passin g
through zero at som e tem perature T 0 (usually called as C urie-W eiss tem p eratu re),lead in g
to,
a = ( T - T 0) / £ „ C
.................................................... (1.9)
W here C is taken as a positive constant called the C urie-W eiss constant. T he value o l To
m ay be equal to o r low er than the actual transition tem perature T c (C urie tem perature).
T h e first o r second order phase transition can also be explained w ith the help o t the order
p aram eter r|. In first o rder phase change, r) changes from a finite value to zero abruptly at
the transition tem p erature w hereas in 2 nd order it changes continuously as show n in figure
1.7 (a).S pontaneous polarization (Ps) and dielectric p erm ittivity (er) show anom alies at
phase transition. T he 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 o f order p aram eter ( i j ),
If r) ap proaches to zero from som e finite value o v er a sm all range o f tem perature
around T c, the tran sition is o f second order. T he schem atic representation o f tem perature
d ep en d en ce o f o rd er param eter (spontaneous polarization process), physical properties
(P erm ittivity) for the first and second order phase transitions are show n in Fig. 1.7.
D epending on the tem perature variation o f dielectric constant o r the C urie constant C,
ferroelectric m aterials are broadly divided into tw o groups:
'r
Soft ferro electrics (K D P-type).
^
H ard ferro electrics (B aTiC V type).
T he 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. T he ferroelectric phase
transition o f barium titanate was discovered 1946 [35]. In the earlier literatures, the phase
transition w as considered to be displasive for m ost o f the ferroelectric m aterials that w ere
m icro sco p ically no n-polar in the paraelecric phase. H ow ever, m aterials in m acroscopic or
th erm 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
ex isten ce o f p erm anent o r 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 som e 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 tw o groups; (i) com pounds having the C urie constant ~ 1 0 3 belong to
the o rd er-d iso rd er type and, (ii) those w hich undergo d isp lasiv e type o f transition, w ith
C urie constant ~ 1 0 \
T he phase transition in soft ferroelectrics involves not only the ordering o f the
diso rd ered hyd ro g en atom s, but also the d efo rm atio n 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 isp laciv e type o f transition, a sm all atom ic
disp lacem en t o f so m e o f the atom s is m ainly resp o n sib le for the phase transition, w hich
has been observed in som e o f the perovskites [39],H ow ever, the difference betw een
d isp laciv e and o rd e r -d is o rd e r type o f transition becom es un certain w hen the separation
o f relevant d iso rd er becom e com parable to the m ean therm al am plitude o f th o se atom s
[40],
T he characteristics o f ferroelectrics are represented in term s o f the dynam ics o f the phase
transition. C ochran [41] suggested the m ost general th eo ry o f ferroelectric phase
transitions based on L yddane-S achs-T eller (LST) relation [42],
w 2i .o / 0 ) 2t o
= £ ( 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. T his 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) follow s the C urie-W eiss law (i.e., (o2ro u (T-To)). As the phase transition
tem perature approaches from above o r below , e(0) diverges and o)ro becom es zero. T he
ferroelectric ph ase transition could be regarded as in stab ility o f the crystals for a
particu lar norm al m ode o f vibration, often referred to as soft m ode. But in case o f first
order ph ase transition, copo is not zero at the transition tem perature.
1.8
D IF F U S E
PH A SE
T R A N S IT IO N :
- T he
transition
tem perature
in
m an y
m acroscopic h o m ogeneous m aterials is not quite sharply defined. T he transition is
sm eared o v er certain tem perature interval know n as C urie range, resulting in the gradual
change o f physical properties. T he w idth o f the C urie region depends on com positional
fluctuation and sensitivity o f the C urie tem perature to com position change. This type o f
ph ase transition is generally know n as" D iffuse P hase T ransition" (D PT). T hough this
ph en o m en o n is observed in several types o f m aterials [44] th e m ost rem arkable ex am p le
o f D P T w as found in ferroelectric m aterials [45]. F erroelectricity w ith diffuse phase
transitions (D P T T ) w as first reported [46] and th eir ex ten siv e studies w ere carried out in
different system s
[47]. Som e o f the characteristics o f ferroelectric diffuse phase
transitions are:
'r
B roadened m axim a in the perm ittivity - tem perature curve.
r-
G radual decrease o f spontaneous polarization w ith rise in tem perature.
>
No C u rie-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 ran sitio n tem perature obtained by different techniques does not coincide.
The diffuseness o f the phase transition is assum ed to be due to the o ccurrence o f
fluctuation in a relatively large tem perature interval around the transition. U sually, tw o
kinds o f fluctuation are considered:(a) C o m p o sitio n al fluctuation and, (b) P olarization (structural) fluctuation.
From the th erm 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 sm all
energy d ifferen ce betw een high and low tem perature phase around the transition. K anzig
[48] observ ed 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 d iffuse phase transition. For relaxer as w ell as o th er FD PT the w idth o f the
transition region is m ainly im portant for practical applications. Sm olenkii [50] and R olov
[51] in troduced a m odel based on G aussian distribution to calculate d iffu siv ity o f D PT
(due to com p o sitio nal and polarization fluctuations). D iffuse phase transition w as also
studied by S m olenskii- Isupov theory [52] and the results are com pared w ith those o f
experim ental findings.
1.9 F E R R O E L E C T R I C S W ITH O X Y G E N 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 m echanical properties. T he fam ily o f oxygen octahedral
ferroelectrics has four basic structures, nam ely
r
P erovskite type ferroelectric
r
T un g sten -B ronze type ferroelectrics
r-
L ayer structure oxides and com plex com pounds
'r-
Pyroc hi o re-type ferroelectrics
1.10 A P P L IC A T IO N O F F E R R O E L E C T R IC M A T E R IA L S
1. T he dielectric constant o f ferroelectrics is very high and so they are used in
m anufacture o f sm all size high capacity capacitors.
2. P iezoelectric acoustic transducers and pyroelectric infrared detectors are the devices
based on ferroelectrics.
3. T he electrooptic characteristics o f ferroelectrics such as B a T i0 4 and KDP have been
used for m o d u latin g and deflecting laser beam s inside and o u tsid e the optical cavity.
4 F erroelectric film s 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, H ence they are used as
transducer (i.e., in devices used to convert electrical energy into m echanical energy).
T hey are used in the construction o f crystal m icrophones.
6
. Ferroelectric crystals, also exhibit application o f tem perature. U sing this property these
are used as IR sensors and detectors.
7. T he pro p erty 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
of
ferroelectrics
are
exploiting
the
electrostrictive
tem perature coefficient o f resistively, and stress-induced dipoling.
effect,
positive
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