5 ceramics

Physica B 150 (1988) 168-174 North-Holland, Amsterdam

PHASE TRANSITION STUDY OF PZT 95/5 CERAMICS W A N G Yong Ling, C H E N G Zhi Ming, SUN Yang-Ren* and DAI Xing-Hu Shanghai Institute o f Ceramics, Academia Sinica, P.R. China *Physics Department, East China Institute o f Chemical

Technology, Shanghai, P.R. China In this paper a phenomenological theory of phase transitions of PZT 95/5 ceramics has been developed. The theory deals with the coexistence of antiferroelectric (AFE) and ferroelectric (FE) phases, the hydrostatic pressure induced FE-AFE phase transition, the electric field induced AFE-FE phase transition and the temperature induced FE (LT)-FE (HT) phase transition under dc bias. The equations which describe the properties of phase transitions under various applied fields, and which fit well in semi-quantitative comparisons with experiments, are derived. The physical meaning of the coupling factor n and its variation with temperature and composition have been clarified.

1. Introduction Ferroelectric phase transition ceramics has been studied at the Shanghai Institute of Ceramics for more than seven years. The study of spontaneous polarization of ferroelectrics and its variation with applied field such as electric field, temperature and stress is diagrammed in fig. 1. Two main subjects we studied recently are stress induced ferroelectric (FE)-antiferroelectric ( A F E ) phase transitions, electric field induced A F E - F E phase transitions and temperature induced FE(LT)-FE(HT) phase transitions of P Z T 9 5 / 5 ceramics and some modified compositions. ( L T and H T are low temperature and high temperature designations.) Several main applications we developed are shock wave explosive energy conversion [1], pyroelectric energy conversion [2] and infrared detecting technology. A phenomenological theory dealing with the hydrostatic pressure induced F E - A F E phase trans-

STRESS

~

~

/

~NONLINEAR

PYROELECTRIC SIGNALRESPONSE ~.-'-EI~-GYCONVERSION

TEMPERATURE ELECTRICF,ELD/

LLNEAR PIEZOELECTRIC/

~

"...FIELDEFFECTJ ELECTROOPTICS

~

FERROELECTRIC ,.SEMICONDUCTOR

Fig. 1. Spontaneous polarization variation with stress, temperature and electric field.

tion, electric field induced A F E - F E phase transition and temperature induced FE(LT)-FE(HT) phase transition under dc bias has been developed.

2. Phenomenological theory of phase transitions under applied field For PbZrl~xTixO3 ceramics with 0 < x < 0.37, a general representation of the Gibbs free energy has been developed: 1 2 G = G O+ zf2(Pa + p2) + ~1 f4(Pa4 + p4)

+ ~1 f 6 ( P a6 + p6) 1 2 + lnPaP b + ~g20 + lg404

+ g1 d O 2 ( P a 2 .-b 1

2

1 2 p2) + ~cp 2

+ ~Q(Pa + Pb + 2RP, Pb)P - 1E" (Pa + Pb)"

(1)

All the coefficients in this equation are defined as follows: Pa, Pb: polarization strength of the sublattices of the unit cell, respectively. 0: angle of octahedral tilt. p: hydrostatic pressure. E: strength of applied electric field. fz, gz: functions of temperature, f2 = f p ( T - Tp), g2 : go( T - To).

0378-4363/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

Y.-L. Wang et al. / Phase transition study of PZT 95/5 ceramics f4, f6, g4, d: constants. n: coupling factor between Pa and Pb" It is a function of composition for a vertical A F E - F E phase boundary and equals zero on the phase boundary. For an inclined phase boundary, it is a linear function of temperature. For n < 0, the FE phase is stable; for n > 0, the A F E phase is stable. c: compressibility. (constant) Q: electrostrictive coefficient. R: structure factor which is larger than 1 for perovskite structure materials. The equilibrium condition of the Gibbs free energy is: 0G ~aa = 0 '

OG

= 0,

(2)

OG

-~- =o. The stable condition of the Gibbs free energy is: (a) For the antiferroelectric phase

.O2G "~-~ > 0, oZG Op---~b> 0 ,

(3)

169

Different forms of formula (1) can be chosen according to what kind of problem we deal with. In the following sections, the properties of phase transitions under various applied fields are discussed.

2.1. The F E - A F E phase transition without electric field Without electric field or hydrostatic pressure, the Gibbs free energy for the F E - A F E phase transition can be expressed as: 1 2 G = G O+ af2(Pa + P2b) + g1 f4(Pa4 + p4)

(5)

+ ½neaPb.

From equilibrium and stability conditions (2) and (3), the following relations are obtained [3]: 2f2 + 3 n > 0 , (f2 + n)(fz + 2n) > 0 .

(6)

It can be shown that the restriction for a stable ferroelectric phase is n < - ½f2 and the restriction for a stable antiferroelectric phase is n > 1 f2. f2 is always less than zero at the F E - A F E phase transition. Therefore, the phase regions can be shown in fig. 2. At n = 0, the free energy of the two phases is equal. In the ½f2 < n < - ½f2 region, the two phases can both exist; it means that the phase transition can occur over a wide range of composition and temperature. This analysis is in correspondence with the T E M microstructure study of P Z T 9 5 / 5 ceramics [4].

-

\-~a/\-~b/

Oea O e b

"

(b) For the lower and higher temperature rhombohedral ferroelectric phase FE(LT) and FE(HT) a2G -~>0,

2.2. The A F E - F E phase transition under electric field Under electric field E, the Gibbs free energy is expressed as: 1

L\opZ j \ oO2 / - \ O - - f f ~

2

G = G O+ z f2(Pa + p2) + ~f4(p~ + p4)

02G --~- > 0,

(4)

! >0.

-t- l n P a e b - l e .

( P a "[- e b ) "

(7)

We discuss the case for Pa # Pb" From (2) and (3), the following relations are obtained [3]:

Y.-L. Wang et al. / Phase transition study of P Z T 95/5 ceramics

170 --

FE PHASE

I

COEXISTENCE- - - ~ A F E

PHASE--

I

If2

n 0

-If

2

Fig. 2. Phases expected as the coupling factor n is varied.

PaPb = (f2 - n)/f4 + p 2 ,

(8)

(2n - f z ) P - f4 P3 = E ,

(9)

2n - f2 - 3f4Pz > 0,

place exactly at E where the free energy of the two phases is equal. In order to overcome the potential barrier between the two minimums, a large enough electric field should be applied. This is why the hysteresis loop can be observed in experiments. If we roughly take the average value of the phase transition electric field strength as E = I(IEAI + IEFI), the result of the calculation is very close to the experiment, as shown in fig. 4 [3].

where P = e a + Pb" The analysis of (8) and (9) gives the following results: when n < 0, the A F E phase is metastable, when n > 0 the FE phase is metastable, and

2.3. Temperature induced FE(Lr)-FE(Hr) phase transition under dc bias

I EAI = ~ (2n

1 G = G O + "~g2 0 2 + lg404 +

(10)

- f2)3/2/V~4,

IEFI = (f2 + 2n)~/4( n - f2)/27f4,

(11)

where IEAI is the upper limit of the antiferroelectric state. IEFI is the lower limit of the metastable ferroelectric state. The relation IEAI > lEvi provides that n > 0 and the phase transition observed in the experiment could occur within the E F - E A range. Fig. 3 shows the experimental P - E curve [3] for the material (Pb 0 99Nbo. 02 (( Zro. 6 7 Sn0 3 3 ) 0 . 9 3 Ti0.07)0.9803 . A double hysteresis loop is observed. In fact, the phase transition does not take

When the electric field is in the same direction as the spontaneous polarization, the Gibbs free energy can be expressed as

lfzp2

+ lf4p4

+ ~f6 P6 + 102p2 - E P .

(12)

For the first order FE(LT)-FE(HT) phase transition, f4 < 0, f6 > 0, g4 > 0.

1) E = 0 From

the

equilibrium

condition

(2),

the

P (l.tc/cm z) .---"I

.._ .......-..-- "~

I0 T = 94°C

/

-1500

i ( ! I

I

I

-500 I

~_

--

-10

-"•OO

1500

E (V/ram)

B

y

7.1 ( -7.1

IOBO

E IV/mini -20

tl4.2 14.2

L,,, ~1.3 J Fig. 3. The relationship P - E obtained by experiment.

I Fig. 4. The relationship P - E obtained by calculation. The dashed lines stand for the metastable state, while solid lines stand for the equilibrium state. When E nearly equals 500 V/ mm, the free energies of both phases are the same.

171

Y.-L. Wang et al. / Phase transition study of PZT 95/5 ceramics

following four possible phases have been obtained [5]:

After differentiating eq. (15), the shift of the phase transition temperature is obtained:

a:

P~=0,

0s = 0 .

AT r = kE,

b:

P~#O,

O~=O.

where

c:

P~=O,

Os#O.

k =

d:

P~¢0,

0~%0.

(18)

2dg2f4 - 4g2f 2 6

Xieo

df4go - d2fp - 2gif6go

Ps

f2=fp(Tr0 - T p ) .

g2 =go(Tro - T o ) ,

It is reasonable that solutions b and d correspond to the FE(HT) phase and FE(LT) phase [6]. The stable condition of the FE(HT) phase is

g~f6 + d2f:

-

(13)

dgJ4 < O.

The stable condition of the FE(LT) phase is

(14)

g2f6 + d2f2 - dg2f4 > O.

So the phase transition temperature T,0 between the FE(LT) phase and the FE(HT) phase is determined by: ( g 2 f 6 -Jv d 2 f 2 - d g 2 f 4 ) T =

Tr0 : O .

(15)

'

So (19)

r,(e) = T,o + A T r = Tro + k E .

From the pyroelectric measurement under dc bias, which is shown in fig. 5, the value of k is obtained as 2.67× 10-6°Cm/V. The composition of material we studied is Pb(Zr0.97Ti0.03)O 3 + 1 wt% Nb20 5. 2.4. Hydrostatic p h a s e transition

pressure

induced

FE-AFE

The Gibbs free energy is expressed as G

1

4

4

Go + -~f2(p2a + P~) + ~f4(Pa + Pb)

.~_

½nPaPb

+ l c p 2 + ~1 Q ( e a2 + e b2 + 2 R P a P b ) p

2) E # O

Let the total polarization strength be the sum of spontaneous polarization and electric field induced polarization strength. P= P~+ Xi%E= P~ + tP~

(20) Let PF = l(Pa + Pb) and PA = l(pa _ Pb)- Then eq. (20) becomes

(16) G = G O + ½f2(P 2 + p 2 )

where X i is the polarizability and Ps is the spontaneous polarization. The parameter t, which is defined as the ratio of induced polarization strength to spontaneous polarization strength, is less than 1%. Using a mathematical transformation, the influence of electric field can be put into the coefficients of the Gibbs free energy [5] and the equation which determines the phase transition temperature has the same form as eq. (15) wherein the new coefficients are f ; = (1 - 2t)f4,

f~ = (1 - 4t)f6 •

(17)

1

4

4

2

2

+ a f a ( P v + P A + 6PFPA) 1 2 + ~n(er

e~) + lcp2

+ a ( e ~ + P~ + R(P~ - e ~ ) ) p .

(21)

From the equilibrium condition

I° 0 (22)

172

Y.-L. Wang et al. / Phase transition study of PZT 95/5 ceramics

(a)

A I ii

-

70

l|

b. Antiferroelectric solution p2 = _ f 2 - n + 2 Q ( 1 A L

I. E = O V / m m

2

2. E = I O 0 0 V / m m

11~

3. E= 2000V/mm

60

•

.~

11"I

50

R)p

(24)

The phase transition condition is that the Gibbs free energy of the A F E phase and the FE phase are equal, i.e. GA = GF .

(25)

After substituting (23) and (24) into eq. (25), the least hydrostatic pressure required to induce the F E - A F E phase transition is obtained:

30 20

Po = - n / Q R

IO I0

20

30

40

T

50

(26)

,

n is less than zero for the FE phase. For the PSZT ceramics with vertical phase boundary [7], n is only related to the titanium content. The higher the titanium content, the higher is In I, then the higher is the least hydrostatic pressure that is required to induce the F E - A F E phase transition. This analysis is well verified by the experimental results (this work) shown in fig. 6. The material for experimental study is PSZT ceramic with a vertical phase boundary. If the A F E - F E phase boundary is not vertical, n is closely related to the slope of the phase boundary and is a function of both temperature and composition.

60

(*C)

(b)

B

v0

2.5. Electric f i e l d induced A F E - F E transition

phase

B

The Gibbs free energy is expressed as: 0

I

I

I000

2000

I

.

1

Fig. 5. (a) Pyroelectriccurrent of FE(LT)-FE(HT)phase transition under varied dc bias. (b) Shift of phase transition temperature with dc bias. two solution are obtained [7]:

E

Pv= 2(f2+n) + \ ----Z-~4!

f2 + n + 2Q(1 + R ) p f4

'

4

4

2

2

(23)

(27)

From equilibrium condition (22), neglecting the higher order terms, the following approximate solutions are obtained: a. Ferroelectric solution

a. Ferroelectric solution

PF=

1

2 + ~1 n ( p F _ p2) _ EpF.

E (Wrnm)

2

2

G = G O + ~ f 2 ( e F + p 2 ) + g(PF + P A -t- 6 e v e a )

3000

PA= 0

1/2

(28)

Y.-L, Wang et al. / Phase transition study of P Z T 95/5 ceramics

(o) 30--

x = 0.03~4

0.038 0.042 0.046 0.050

173

After substituting (28) and (29) into eq. (30), the least electric field strength required to induce the A F E - F E phase transition is obtained:

Eo=_f2( --f4 ~1/2

NE 20--

f4 \ f2 + n /

I0-,

I000

n is larger than zero for the AFE phase and is related to the content of titanium in PZT ceramics. The lower the titanium content, the higher is the n, that is, the greater extent that the material is in AFE phase, then the higher is the electric field strength that is required to induce the A F E - F E phase transition. E 0 is also related to temperature as E 0 - ( T p - T) 1/2 for materials with a vertical phase boundary . The higher the temperature, the lower is the least electric field strength E 0. All these analyses are well verified by experiment as shown in fig. 7 and fig. 8 (this work). The material measured is PSZT ceramic with a vertical phase boundary.

I

2000

3000

Kg/cm 2

2800

(b) --

2400 .~. 2000 i 02 ~600

1200 80O

).034

0.042

(31)

'

0.050

x (Ti) Fig. 6. (a) Discharge curve of PSZT ceramics with varied Ti content under hydrostatic pressure, x is the Ti content (T = 17°C). (b) Relationship between least hydrostatic pressure P0 and Ti content (T = 17°C).

Where the first term of PF is the electric field induced polarization and the second term is the spontaneous polarization. b. Antiferroelectric solution E

Pf=

.

X = 0.038

0.042

Eo (V/m m)

0.046 (b)

2400-

9f4 E 3

2 ( f z ~ 2 n ) * 16(f--~_2n)4,

~

(o) m 2)

(29)

f4e +3Le +f2- n = 0 ,

2000 1600 1200

where the two terms of PF are the first and second order of electric field induced polarization. Also the phase transition condition is that the Gibbs free energies of the AFE and FE phases are equal, i.e. GA =

GF.

(30)

8OO 0.038

0.042 0.046" X (Ti)

Fig. 7. (a) Hysteresis loops of PSZT ceramics with vertical phase boundaries and different Ti contents. (b) Relationship between least electric field strength E 0 and Ti content ( T = 17°C).

174

Y.-L. Wang et al. / Phase transition study of P Z T 95/5 ceramics

(a)

'

T = 170C

'

650C

'

wm

,)

8PC (b)

Eo(Wmm)

2000 1500 I 0 0 0 --

s°°0

I

l

20

40

1

I_

6o 8o T (*C)

I

~oo

Fig. 8. (a) Hysteresis loops at different temperatures of PSZT ceramics with vertical phase boundaries, x(Ti) = 0.042. (b) Relationship between least electric field strength E o and temperature.

3. S u m m a r y

(1) T h e condition for a stable ferroelectric phase is n < - ½ f z ; for a stable antiferroelectric phase, n > ½f z .

(2) T h e relation IEAI> IEFI provides that n > 0 and the phase transition o b s e r v e d in the e x p e r i m e n t could occur within the E F - E A range, so a d o u b l e hysteresis loop could be observed. (3) A shift of the phase transition t e m p e r a t u r e of m o r e than 8°C for the FE(LT)-FE(HT) phase transition u n d e r dc bias field has b e e n observed. (4) W h e n the A F E - F E phase b o u n d a r y is vertical, n is only a function of t e m p e r a t u r e ; otherwise, n is closely related to the slope of the phase b o u n d a r y , so the least electric field applied in o r d e r to induce A F E - F E phase transition is a function o f b o t h t e m p e r a t u r e and composition.

References

[1] Y.L. Wang, W.Z. Yuan, C.B. He, S.W. Lin, Y.H. Ling, C.F. Qu and B.G. Wang, Ferroelectrics 49 (1983) 169. [2] J.Y. Lian and Y.L. Wang, Chinese Phys. Lett. 2 (1985). [3] Y.R. Sun and Y.L. Wang, Commun. in Theor. Phys. (Beijing, China) 4 (1985) 291. [4] Y . J . Chang, Appl. Phys. A29 (1982) 237. [5] X.H. Dai and Y.L. Wang, to be published. [6] T.R. Halemane, M.J. Haun and L.E. Cross, Ferroelectrics 62 (1985) 149. [7] Z.M. Cheng and Y.L. Wang, to be published.