Lallart M. (ed.) Ferroelectrics

Подождите немного. Документ загружается.

The Induced Antiferroelectric Phase - Structural Correlations

189

)

SmC*

SmA

0.0 0.2 0.4 0.6 0.8 1.0

T [ C]

100

120

140

160

180

200

SmC*

SmA

0.0 0.2 0.4 0.6 0.8 1.0

T [ C]

100

120

140

160

180

200

Fig. 16. Phase diagrams of bicomponent mixtures of compounds with fluoroalkyl group

with additive miscibility of SmC* phase - system 1-3 (a), and with additive miscibility of

SmC*

phase – system 10-11 (b)

)c)

SmC*

SmA

0.0 0.2 0.4 0.6 0.8 1.0

T [ C]

100

120

140

160

180

200

SmC*

SmA

0.0 0.2 0.4 0.6 0.8 1.0

T [ C]

100

120

140

160

180

200

SmC*

SmA

SmC*

0.0 0.2 0.4 0.6 0.8 1.0

T [ C]

100

120

140

160

180

200

Izo+

SmA

Fig. 17. Phase diagrams of bicomponent mixtures of compound 1 with compounds 11 (a), 10

(b) and 12 (c) giving the small enhancement of SmC*

phase

SmA

0.0 0.2 0.4 0.6 0.8 1.0

100

120

140

160

180

200

SmC*

I+SmA

SmC*

Fig. 18. Phase diagrams of bicomponent mixtures of compounds 1-13 with fluoroalkyl group

giving the induction of SmC*

phase

Ferroelectrics – Physical Effects

190

composed only of compounds with fluoroalkyl group, giving the induction of SmC*

phase.

Compound 1 was dopped with compound 13, having terphenyl rigid core lateraly

substituted by four fluorine atoms, Fig. 18. This examples is an exeption from the rule that

induction of SmC*

phase can appear in mixtures of compounds differing in the polarity.

The steric factors play also crucial role in this behaviour, because the induction of SmC*

phase was not found in mixtures of both nonchiral compounds. For the last system, it

cannot be also excluded that the appearance of SmC*

phase could be a result of interactions

between nonfluorinated and fluorinated rigid core.

4. Conclusion

There are many systems in which the induced antiferroelectric phase can be observed.

Compounds with polar group (1, 3-5) have virtual SmC*

phase. They have similar

structure to compounds forming SmC*

phase by themselvs; e.g. the structure of compound

1 and 4 is similar to the structure of the first antiferroelectric compound MHPOBC; they

have the same rigid core and chiral terminal chain. The placement of molecules of

compounds with virtual SmC*

phase, which have a tendency to form the antiferroelectric

phase but cannot fulfil all conditions, in a suitable matrix of less polar compounds causes

the appearance of an antiferroelectric phase.

The ability of more polar compounds with virtual SmC*

phase for induction of this phase

decreases in the following order: compounds 1, 3, 4 and 5. Compounds with cyano group in

terminal chain have smaller ability than compounds with fluoroalkyl group. Compounds

with biphenylate core have bigger ability than compounds with benzoate core. The same is

observed in group of less polar compounds with alkyl group in the terminal chain, i.e. the

biphenylate core is more preferable, as well as the increase of the terminal chain causes the

inrease of tendency to induce SmC*

phase.

In systems of similar polarity nonadditive behaviuor can be observed when fluorinated part

of the non-branched chain is short.

The appearance of liquid crystalline phases is possible due to intermolecular interactions.

Interactions between permanent dipoles play a crucial role but interactions between induced

dipoles cannot be neglectible. The steric interactions are also important.

The possibility of obtaining antiferroelectric phase from compounds forming SmC* phase or

only SmA phase broadens the range of compounds useful for preparation of

antiferroelectric mixtures for display application.

5. References

Chandani, A.D.L., Górecka, E., Ouchi, Y., Takezoe, H. & Fukuda, A. (1989). Antiferroelectric

Chiral Smectic Phases Responsible for the Trislable Switching in MHPOBC,

Jpn.J.Appl.Phys., Vol.28, No.7, (July 1989), pp. L1265-L1268, ISSN 0021-4922

Czupryński, K., Skrzypek, K., Tykarska, M. & Piecek, W. (2007). Properties of induced

antiferroelectric phase, Phase Transitions, Vol.80, No.6-7, (June 2007), pp. 735-744,

ISSN 0141-1594

Dąbrowski, R. (2000). Liquid crystals with fluorinated terminal chains and antiferroelectric

properties, Ferroelectrics, Vol.243, No.1, (May 2000), pp. 1-18, ISSN 0015-0193

The Induced Antiferroelectric Phase - Structural Correlations

191

Dąbrowski, R., Czupryński, K., Gąsowska, J., Otón, J., Quintana, X., Castillo, P. & Bennis, N.

(2004). Broad temperature range antiferroelectric regular mixtures, Proceedings of

SPIE, Vol.5565, (2004), pp. 66-71, ISSN 0277-786X

Drzewiński, W., Czupryński, K., Dąbrowski, R. & Neubert, M. (1999). New antiferroelectric

compounds containing partially fluorinated terminal chains. Synthesis and

mesomorphic properties, Mol.Cryst.Liq.Cryst., Vol.328, (August 1999), pp. 401-410,

ISSN 1058-725X

Drzewiński, W., Dąbrowski, R. & Czupryński, K. (2002). Synthesis and mesomorphic

properties of optically active (S)-(+)-4-(1-methylheptyloxycarbonyl)phenyl 4’-

(fluoroalkanoyloxyalkoxy)biphenyl-4-carboxylates and 4’-(alkanoyloxyalkoxy)

biphenyl-4-carboxylates, Polish J.Chem., Vol.76, No.2-3, (February 2002), 273-284,

ISSN 0137-5083

Dziaduszek, J., Dąbrowski, R., Czupryński, K. & Bennis, N. (2006). , Ferroelectrics, Vol.343,

No.1, (November 2006), pp. 3-9, ISSN 0015-0193

Fukuda, A., Takanishi, Y., Isozaki, T., Ishikawa, K. & Takezoe, H. (1994). Antiferroelectric

chiral smectic liquid crystals, J.Mater.Chem., Vol.4, No.7, (January 1994), pp. 997-

1016, ISSN 0959-9428

Gauza, S., Czupryński, K., Dąbrowski, R., Kenig, K., Kuczyński, W. & Goc, F. (2000).

Bicomponent systems with induced or enhanced antiferroelectric SmC

* phase,

Mol.Cryst.Liq.Cryst., Vol.351, (November 2000), 287-296, ISSN 1058-725X

Gauza, S., Dąbrowski, R., Czypryński, K., Drzewiński, W. & Kenig, K. (2002). Induced

antiferroelectric smectic C

* phase. Structural correlations, Ferroelectrics, Vol.276,

(January 2002), pp. 207-217, ISSN 0015-0193

Gąsowska, J. (2004). PhD thesis, WAT, Warsaw.

Gąsowska, J., Dąbrowski, R., Drzewiński, W., Filipowicz, M., Przedmojski, J. & Kenig, K.

(2004). Comparison of mesomorphic properties in chiral and achiral homologous

series of high tilted ferroelectrics and antiferroelectrics, Ferroelectrics, Vol.309, No.1,

(2004), pp. 83-93, ISSN 0015-0193

Kobayashi, I., Hashimoto, S., Suzuki, Y., Yajima, T., Kawauchi, S., Imase, T., Terada, M. &

Mikami, K. (1999). Effects of Conformation of Diastereomer Liquid Crystals on the

Preference of Antiferroelectricity, Mol.Cryst.Liq.Cryst.A, Vol.328, (August 1999), pp.

131-137, ISSN 1058-725X

Kula, P. (2008). PhD thesis, WAT, Warsaw.

Mandal, P.K., Jaishi, B.R., Haase, W., Dąbrowski, R., Tykarska, M. & Kula, P. (2006). Optical

and dielectric studies on ferroelectric liquid crystal MHPO(13F)BC: Evidence of

SmC*



phase presence, Phase Transitions, Vol.79, No.3, (March 2006), pp. 223-235,

ISSN 0141-1594

Matsumoto, T., Fukuda, A., Johno, M., Motoyama, Y., Yuki, T., Seomun, S.S. & Yamashita

M. (1999). A novel property caused by frustration between ferroelectricity and

antiferroelectricity and its application to liquid crystal displays-frustoelectricity and

V-shaped swiching, J.Mater.Chem., Vol.9, No.9, (1999), pp. 2051-2080 ISSN 0959-

9428

Skrzypek, K. & Tykarska, M. (2006). The induction of antiferroelectric phase in the

bicomponent system comprising cyano compound, Ferroelectrics, Vol.343, No.1,

(November 2006), pp. 177-180, ISSN 0015-0193

Ferroelectrics – Physical Effects

192

Skrzypek, K., Czupryński, K., Perkowski, P. & Tykarska, M. (2009). Dielectric and DSC

Studies of the Bicomponent Systems with Induced Antiferroelectric Phase

Comprising Cyano Terminated Compounds, Mol.Cryst.Liq.Cryst., Vol.502, (2009),

154-163, ISSN 1542-1406

Tykarska, M. & Skrzypek, K. (2006). The enhancement and induction of antiferroelectric

phase, Ferroelectrics, Vol.343, No.1, (November 2006), pp. 193-200, ISSN 0015-0193

Tykarska, M., Dąbrowski, R., Przedmojski, J., Piecek, W., Skrzypek, K., Donnio, B. &

Guillon, D. (2008). Physical properties of two systems with induced antiferroelectric

phase, Liq.Cryst., Vol.35, No.9, (September 2008), pp. 1053-1059, ISSN 0267-8292

Tykarska, M., Skrzypek, K., Ścibior, E. & Samsel, A. (2006). Helical pitch in bicomponent

mixtures with induced antiferroelectric phase, Mol.Cryst.Liq.Cryst., Vol.449, No.1,

(July 2006), pp. 71-77, ISSN 1542-1406

Tykarska, M., Garbat, K. & Rejmer, W. (2011). The influence of the concentration of fluoro-

and cyanoterminated compounds on the induction of antiferroelectric phase and on

helical pitch, Mol.Cryst.Liq.Cryst., accepted for publication 2011.

Part 2

Piezoelectrics

Andriy Andrusyk

Institute for Condensed Matter Physics

Ukraine

1. Introduction

For the last several years there has been signiﬁcant progress in the development of new

piezoelectric materials (relaxor ferroelectric single crystals (Park & Shrout, 1997), solid

solutions with high transition temperature (Zhang et al., 2003), lead-free materials (Saito

et al., 2004)) and in understanding of mechanisms of the piezoelectric coupling in ferroelectric

piezoelectrics (Fu & Cohen, 2000; Guo et al., 2000). This progress was triggered in particular by

the wide use of piezoelectric effect in a variety of devices (resonators, tactile sensors, bandpass

ﬁlters, ceramic discriminators, SAW ﬁlters, piezoresponse force microscopes and others).

What concerns theoretical study of the piezoelectric effect, signiﬁcant efforts were made

in ﬁrst-principles calculations. Such calculations are possible for the ferroelectrics with

a relatively simple structure, in particular for simple and complex perovskites (Bellaiche

et al., 2000; Garcia & Vanderbilt, 1998). For compounds with a complex structure often

only the research within the Landau theory is possible. The structure complexity justiﬁes

the application of semimicroscopic models considering only that characteristic feature of

the microscopic structure which is crucial in explaining the ferroelectric transition or the

piezoelectric effect. Such models are adequate for the crystal under study if they are able

to explain the wide range of physical properties.

In this chapter sodium potassium tartrate tetrahydrate NaKC

·4H

O (Rochelle salt or

RS) is studied on the base of the semimicroscopic Mitsui model.

The microscopic mechanism of ferroelectric phase transitions in RS was the subject of

numerous investigations. Studies based on x-ray diffraction data (Shiozaki et al., 1998) argued

that these were the order-disordermotions of O9 and O10 groups, coupled with the displacive

vibrations of O8 groups, which were responsible for the phase transitions in Rochelle salt as

well as for the spontaneous polarization. Later it was conﬁrmed by the inelastic neutron

scattering data (Hlinka et al., 2001). Respective static displacements initiate the emergence

of dipole moments in local structure units in ferroelectric phase. Such displacements can

be interpreted also as changes in the population ratio of two equilibrium positions of sites

in the paraelectric structure (revealed in the structure studies (Noda et al., 2000; Shiozaki

et al., 2001)). The order-disorder pattern of phase transitions in RS forms the basis of the

semimicroscopic Mitsui model (Mitsui, 1958). In this model the asymmetry of occupancy

of double local atomic positions and compensation of electric dipole moments occurring in

paraelectric phases were taken into account.

Piezoelectric Effect in Rochelle Salt

2 Will-be-set-by-IN-TECH

Recently (Levitskii et al., 2003) Mitsui model as applied to RS was extended by accounting

of the piezoelectric coupling between the order parameter and strain ε

. Later this model

was extended to the four sublattice type (Levitskii et al., 2009; Stasyuk & Velychko, 2005)

that gives more thorough consideration of real RS structure. We performed our research of

piezoelectric effect in Rochelle salt on the basis of the Mitsui-type model containing additional

term of transverse ﬁeld type responsible for dynamic ﬂipping of structural elements (Levitskii,

Andrusyk & Zachek, 2010; Levitskii, Zachek & Andrusyk, 2010). Originally, this term was

added with the aim to describe resonant dielectric response which takes place in RS in

submillimeter region. First, we provide characteristics of ferroelectric phase transitions in

RS and experimental data for constants of physical properties of RS. Then, we present our

study results (thermodynamic and dynamic characteristics) obtained within Mitsui model for

RS. Speciﬁcally, we calculate permittivity of free and clamped crystals, calculate piezoelectric

stress coefﬁcient e

, elastic constant c

. The key attention is given to investigation of the

phenomenon of piezoelectric resonance.

2. Physical properties of Rochelle salt

Rochelle salt (RS), NaKC

·4H

O is the oldest and has been for a long time the only

known ferroelectrics. RS has been the subject of numerous studies over the past 60 years.

It is known for its remarkable ferroelectric state between two Curie points T

= 255 K and

= 297 K (Jona & Shirane, 1965). Second order phase transitions occur at both Curie points.

The crystalline structure of RS proved to be complex. It is orthorhombic (space group

—P2

2) in the paraelectric phases and monoclinic (space group C

—P2

)inthe

ferroelectric phase (Solans et al., 1997). Spontaneous polarization is directed along the a crystal

axis; it is accompanied by a spontaneous shear strain ε

. There are four formula units (Z = 4;

112 atoms) in the unit cell of Rochelle salt in both ferroelectric and paraelectric phase. In

recent study (Görbitz & Sagstuen, 2008) the complete Rochelle salt structure in paraelectric

phase was described.

Due to the symmetry of RS crystal structure some elements of material tensors are zeroes. In

RS case material tensors in Voigt index notations are of the form presented below (Shuvalov,

1988).

Elastic stiffnesses or elastic constants (c

=(∂σ

/∂ε

)

⎛

⎜

⎝

0000c

⎞

⎟

⎠

(1)

Coefﬁcients of piezoelectric stress (e

=(∂P

/∂ε

)

= −(∂σ

/∂E

)

(e)=

⎛

⎝

0000e

⎞

⎠

(2)

196

Ferroelectrics – Physical Effects

Piezoelectric Effect in Rochelle salt 3

Dielectric permittivity (χ

=(∂P

/∂E

)

,whereα is σ or ε):

(χ

σ,ε

⎛

⎝

0 χ

⎞

⎠

(3)

It is necessary to make some comments about the notations. Superscripts to the matrices of

physical properties indicate that a physical characteristic denoted by a superscript is constant

or zero (for instance

electric ﬁeld:

)). We omitted superscripts E and σ, ε for components of tensors (c

) and

(χ

σ,ε

) respectively but keep them in mind. Notation (χ

σ,ε

) denotes two different tensors:

(χ

) and (χ

) which we will call tensors of dielectric permittivity at constant stress and strain

respectively. We will also call them tensor of free crystal dielectric permittivity (zero stress is

assumed) and of clamped crystal dielectric permittivity. Hereinafter coefﬁcients equal to zero

in paraelectric phases are presented in bold.

Experimental data for physical constants are presented in Figs. 1, 2, and 3.

240 260 280 300

-0,2

-0,1

0,0

0,1

+ c

T (K)

(10

-2

)

200 225 250 275 300

1,0

1,5

2,0

2,5

3,0

3,5

4,0

4,5

(10

-2

)

T (K)

250 275 300

0,0

0,2

0,4

0,6

0,8

(10

-2

)

T (K)

Fig. 1. Rochelle salt elastic constants. Solid lines for c

(i, j = 1, 2, 3) are experimental data

(Mason, 1950),

∗ correspond to c

(Yu. Serdobolskaya, 1996), ◦ correspond to c

+ c

(Shiozaki et al., 2006). Lines for c

, c

are the results of theoretical calculations (Levitskii

et al., 2005).

260 280 300 320

240 260 280 300

-0,4

-0,2

0,0

0,2

0,4

0,6

(Cm

-2

)

T (K)

(Cm

-2

)

T (K)

Fig. 2. Rochelle salt coefﬁcients of piezoelectric stress. Points  are experimental data (Beige

& Kühnel, 1984) for e

. Solid lines correspond to the results of theoretical calculations e

(j = 1, 2, 3) (Levitskii et al., 2005).

197

Piezoelectric Effect in Rochelle Salt

4 Will-be-set-by-IN-TECH

240 260 280 300

0,00

0,04

0,08

0,12

0,16

0,20

240 260 280 300

0,00

0,04

0,08

0,12

0,16

0,20

1/χ

T (K)

1/χ

T (K)

Fig. 3. Experimental data for clamped and free crystal inverse dielectric permittivity of

Rochelle salt. 1/χ

:  (Sandy & Jones, 1968), ♦ (Mueller, 1935). 1/χ

: + (Yurin, 1965), •

(Mason, 1939),  (Taylor et al., 1984).

As Fig. 1 shows elastic constants c

(i, j = 1, 2, 3) do not change their behaviour in phase

transition points, whereas constant c

becomes zero at the transition point. Besides, c

strongly dependent on T as c

(i, j = 1, 2, 3) are almost independent of T. Constants c

, c

, as it is expected on symmetry grounds, are equal to zero in paraelectric phases. There are

no experiments for c

and there are no experiments for c

, c

measured separately. There

is only the experiment for c

+ c

(Shiozaki et al., 2006). However, c

, c

,andc

were

estimated theoretically (Levitskii et al., 2005) and the result of estimation is presented in Fig. 1.

Correspondent result for c

+ c

is compared to experimental data where good agreement

was derived.

Fig. 2 presents temperature dependencies of piezoelectric stress coefﬁcients. As one can see

coefﬁcients e

, e

differ from zero only inside ferroelectric phase. Coefﬁcient e

has

sharp (but ﬁnite) peak in the transition point, whereas coefﬁcients e

, e

do not have it.

Free and clamped crystal longitudinal susceptibilities are presented in Fig. 3. Free crystal

susceptibility has singularities in transition point, whereas clamped susceptibility remains

ﬁnite.

3. Thermodynamic characteristics of Rochelle salt

3.1 Theoretical study of the Mitsui model

We give consideration to a two-sublattice order-disorder type system with an asymmetric

double-well potential. Hamiltonian of such system is referred to as the Mitsui Hamiltonian.

We assume this system has essential piezoelectric coupling of the order parameter with

component of strain tensor ε

which should be accounted. We suppose the polarization is

directed along x-axes and arises due to the structural units ordering in the one of two possible

equilibrium positions. Precisely this case occurs in RS and such modiﬁed Mitsui model was

considered earlier (Levitskii et al., 2003). We complement this model with transverse ﬁeld to

take into account the possibility of dynamic ordering units ﬂipping between two equilibrium

198

Ferroelectrics – Physical Effects

Lallart M. (ed.) Ferroelectrics - Physical Effects

Подождите немного. Документ загружается.