Zuo-Guang. Ye Advanced Dielectric Piezoelectric and Ferroelectric Materials: Synthesis, Characterisation and Applications

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Handbook of dielectric, piezoelectric and ferroelectric materials470

Noheda B, Cox D E, Shirane G, Gao J, Ye Z G (2002), ‘Phase diagram of the ferroelectric–

relaxor (1–x)Pb(Mg

1/3

2/3

–xPbTiO

’, Phys. Rev. B, 66, 054104, 1–10.

Nomura S, Uchino K (1982), ‘Electrostrictive effect in Pb(Mg

1/3

2/3

type materials’,

Ferroelectrics, 41, 117–32.

Park J H, Xu F, Trolier-McKinstry (2001), ‘Dielectric and piezoelectric properties of sol-

gel derived lead magnesium niobium titanate films with different textures’, J. Appl.

Phys., 89(1), 568–74.

Park S E, Shrout T R (1997), ‘Ultrahigh strain and piezoelectric behaviour in relaxor

based ferroelectric single crystals’, J. Appl. Phys., 82(4), 1804–11.

Pirc R, Blinc R (1999), ‘Spherical random bond random field model of relaxor ferroelectrics’,

Phys. Rev. B, 60(19), 13470–78.

Pithan C, Hennings D, Waser R (2005), ‘Progress in the synthesis of nanocrystalline

BaTiO

powders for MLCC’, Int. J. Appl. Ceram. Technol., 2(1), 1–14.

Randall C A, Kim N, Kucera J P, Cao W, Shrout T R (1998), ‘Intrinsic and extrinsic size

effects in fine grained morphotropic phase boundary lead zirconate titanate ceramics’,

J. Am. Ceram. Soc., 81(3), 677–88.

Saito Y, Takao H, Tani T, Nonoyama T, Takatori K, Homma T, Nagaya T, Nakamura M

(2004), ‘Lead-free piezoceramics’, Nature, 432, 84–7.

Seol K S, Takeuchi K (2004), ‘Ferroelectricity of single-crystalline, monodispersive lead

zirconate titanate nanoparticles of 9 nm in diameter’, Appl. Phys. Lett., 85 (12), 2325–

Setter N (2002), Piezoelectric Materials in Devices, Lausanne, N. Setter, Ceramics

Laboratory, EPFL Swiss Institute of Technology.

Singh A K, Pandey D (2003), ‘Evidence for M

and M

phases in the morphotropic phase

boundary region of (1–x)Pb(Mg

1/3

2/3

–xPbTiO

: a Rietveld study’, Phys. Rev. B,

67, 064102, 1–12.

Singh A K, Pandey D, Zaharko O (2006), ‘Evolution of short range to long range monoclinic

order of M

type with decreasing temperature in 0.75Pb(Mg

1/3

2/3

–0.25PbTiO

’,

J. Appl. Phys., 99, 076105, 1–3.

Swartz S L, Shrout T R, Schulze W A, Cross L E (1984), ‘Dielectric properties of lead

magnesium niobate ceramics’, J. Am. Ceram. Soc., 67, 311–15.

Takahashi T (1982), ‘Effects of impurity doping in lead zirconate titanate ceramics’,

Ferroelectrics, 41, 143–56.

Trolier-McKinstry S, Muralt P (2004), ‘Thin film piezoelectrics for MEMS’, J. Electroceram.

12(1–2), 7–17.

Uchino K (1998), ‘Materials issues in design and performance of piezoelectric actuators:

an overview’, Acta Mater., 46(11) 3745–53.

Viehland D, Jang S J, Cross L E, Wutting M (1990), ‘Freezing of the polarisation fluctuations

in lead magnesium niobate relaxors’, J. Appl. Phys., 68(6), 2916–21.

Viehland D, WuttiG M, Cross L E (1991), ‘The glassy behaviour of relaxor ferroelectrics’,

Ferroelectrics, 120, 71–77.

Viehland D, Kim M C, Xu Z, Li J F (1995), ‘Long time present tweedlike precursors and

paraelectric clusters in ferroelectrics containing strong quenched randomness’, Appl.

Phys. Lett., 67(17) 2471–3.

Westphal V, Kleemann W, Glinchuk M D (1992), ‘Diffuse phase transition and random

field induced domain states of the relaxor ferroelectric Pb(Mg

1/3

2/3

’, Phys. Rev.

Lett., 68(6), 847–50.

Ye Z G, Schmid H (1993), ‘Optical, dielectric and polarization studies of the electric

field-induced phase transition in Pb(Mg

1/3

2/3

(PMN)’, Ferroelectrics, 145, 83–

106.

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Size effects on the macroscopic properties 471

Ye Z G, Noheda B, Dong M, Cox D, Shirane G (2001), ‘Monoclinic phase in the relaxor-

based piezo-/ferroelectric Pb(Mg

1/3

2/3

–PbTiO

system’, Phys. Rev. B, 64, 184114,

1–5.

Ye Z G, Bing Y, Gao J, Bokov A A, Stephens P, Noheda B, Shirane G (2003), ‘Development

of ferroelectric order in relaxor (1–x)Pb(Mg

1/3

2/3

–xPbTiO

(0 ≤ x ≤ 0.15)’,

Phys. Rev. B, 67, 104104, 1–8.

Zembilgotov A G, Pertsev N A, Waser R (2005), ‘Phase states of nanocrystalline ferroelectric

ceramics and their dielectric properties’, J. Appl. Phys., 97, 114315, 1–9.

Zhang S, Randall C A, Shrout T R (2003), ‘High Curie temperature piezocrystals in the

BiScO

–PbTiO

perovskite system’, Appl. Phys. Lett., 83(15), 3150–52.

Zhao Z, Buscaglia V, Viviani M, Buscaglia M T, Mitoseriu L, Testino A, Nygren M,

Johnson M, Nanni P (2004), ‘Grain size effects on the ferroelectric behaviour of dense

nanocrystalline BaTiO

ceramics’, Phys. Rev. B, 70, 024107, 1–8.

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Part IV

High-power piezoelectric and microwave

dielectric materials

473

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475

16.1 Introduction

Loss or hysteresis in piezoelectrics exhibits both merits and demerits. For

positioning actuator applications, hysteresis in the field-induced strain causes

a serious problem, and for resonance actuation such as ultrasonic motors,

loss generates significant heat in the piezoelectric materials. Further, in

consideration of the resonant strain amplified in proportion to a mechanical

quality factor, low (intensive) mechanical loss materials are preferred for

ultrasonic motors. In contrast, for force sensors and acoustic transducers, a

low mechanical quality factor Q

(which corresponds to high mechanical

loss) is essential to widen a frequency range for receiving signals.

K. H. Haerdtl wrote a review article on electrical and mechanical losses

in ferroelectric ceramics [1]. Losses are considered to consist of four portions:

(1) domain wall motion, (2) fundamental lattice portion, which should also

occur in domain-free monocrystals, (3) microstructure portion, which occurs

typically in polycrystalline samples, and (4) conductivity portion in highly

ohmic samples. However, in the typical piezoelectric ceramic case, the loss

due to the domain wall motion exceeds the other three contributions

significantly. Haerdtl reported interesting experimental results on the

relationship between electrical and mechanical losses in piezoceramics,

0.9

0.1

(Zr

0.5

)

1–x

, where Me represents the dopant ions Mn, Fe

or Al and x varies between 0 and 0.09. However, they measured the mechanical

losses on poled ceramic samples, while the electrical losses on unpoled

samples, i.e. in a different polarization state, which led to big ambiguity in

the discussion.

Few systematic studies of the loss mechanisms in piezoelectrics have

been reported, particularly in high electric field and high power density

ranges. Although some of the formulas in this chapter were described by T.

Ikeda in his textbook [2], the piezoelectric losses, which have been found in

our investigations to play an important role, were totally neglected. In this

chapter, we review the loss mechanisms in piezoelectrics first, followed by

Loss mechanisms and high-power

piezoelectric components

K. UCHINO, Pennsylvania State University and

Micromechatronics Inc., USA, J H ZHENG, Y GAO,

S URAL, S-H PARK and N BHATTACHARYA,

Pennsylvania State University, USA and

S HIROSE, Yamagata University, Japan

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Handbook of dielectric, piezoelectric and ferroelectric materials476

the heat generation processes for various drive conditions. Then, loss anisotropy

is discussed, the importance of which is demonstrated in a finite element

method simulation of a piezoelectric transformer. Second, practical high-

power ‘hard’ PZT materials developed at Penn State are introduced, which

exhibit a vibration velocity higher than 1 m/s, leading to a power density

capability ten times that of the commercially available ‘hard’ PZTs. We

propose an internal bias field model to explain the low loss and high power

origin of these materials, which are suitable to actuator (ultrasonic motor)

applications. We also describe ‘semi-hard’ materials based on PZT–

Pb(Zn,Nb)O

–Pb(Ni,Nb)O

, with reasonable piezoelectric d constants, which

are suitable for piezoelectric transducers. Third, using a low-temperature

sinterable ‘semi-hard’ PZT, we demonstrate high-power multilayer piezoelectric

transformers with Cu or Ag internal electrodes.

The terminologies ‘intensive’ and ‘extensive’ losses are introduced in the

relation with ‘intensive’ and ‘extensive’ parameters in the phenomenology.

These are not directly related with the ‘intrinsic’ and ‘extrinsic’ losses which

were introduced to explain the loss contribution from the mono-domain

single crystal state and from the others [3]. In this chapter, our discussion is

focused on the ‘extrinsic’ losses, in particular, domain-reorientation originated

losses.

16.2 General consideration of loss and hysteresis in

piezoelectrics

16.2.1 Theoretical formulas

Since the detailed mathematics have been described in a previous paper [4],

we only summarize the results in this section. We start from the following

two piezoelectric equations:

x = s

X + d E 16.1

D = d X + ε

E 16.2

where x is strain, X, stress, D, electric displacement, E, electric field. Equations

(16.1) and (16.2) are the expression in terms of intensive (i.e. externally

controllable) physical parameters X and E. The elastic compliance s

, the

dielectric constant ε

and the piezoelectric constant d are temperature-

dependent. Note that, in general, the piezoelectric equations cannot yield a

delay-time related loss, without taking into account irreversible thermodynamic

equations or dissipation functions. However, the latter considerations are

mathematically equivalent to the introduction of complex physical constants

into the phenomenological equations, if the loss is small and can be treated

as a perturbation.

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Loss mechanisms and high-power piezoelectric components 477

Therefore, we will introduce complex parameters ε

, s

and d

in order

to consider the hysteresis losses in dielectric, elastic and piezoelectric coupling

energy:

= ε

–

j tan δ′) 16.3

= s

(1 – j tan φ

′

) 16.4

= d (1 – j tan θ′). 16.5

θ′ is the phase delay of the strain under an applied electric field, or the phase

delay of the electric displacement under an applied stress. Both delay phases

should be exactly the same if we introduce the same complex piezoelectric

constant d

into Eqs. (16.1) and (16.2). δ′ is the phase delay of the electric

displacement to an applied electric field under a constant stress (e.g. zero

stress) condition, and φ′ is the phase delay of the strain to an applied stress

under a constant electric field (e.g. short-circuit) condition. We will consider

these phase delays as ‘intensive’ losses.

Figure 16.1 shows the model hysteresis curves for practical experiments:

D vs. E curve under a stress-free condition, x vs. X under a short-circuit

condition, x vs. E under a stress-free condition and D vs. X under a short-

circuit condition for measuring current, respectively. Note that these

measurements are easily conducted in practice.

The stored energies and hysteresis losses for pure dielectric and elastic

energies can be calculated as:

(a)

(b)

(c)

(d)

16.1

(a)

vs.

(stress-free), (b)

vs.

(short-circuit), (c)

vs.

(stress-free) and (d)

vs.

(short-circuit) curves with a slight

hysteresis in each relation.

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Handbook of dielectric, piezoelectric and ferroelectric materials478

= (1/2) ε

16.6

= π ε

tan δ′ 16.7

= (1/2) s

16.8

= π s

tan φ′ 16.9

The electromechanical hysteresis losses are more complicated, which can be

calculated as follows, depending on the method used for measuring; when

measuring the induced strain under an electric field,

= (1/2) (d

)

16.10

and

= π (d

)

(2 tanθ′ – tanφ′) 16.11

Note that the strain vs. electric field measurement should provide the

combination of piezoelectric loss tanθ′ and elastic loss tanφ′. When we measure

the induced charge under stress, the stored energy U

and the hysteresis loss

during a quarter and a full stress cycle, respectively, are obtained as

= (1/2) (d

/ε

)

16.12

= π (d

/ε

)

(2 tanθ′ – tanδ′) 16.13

Hence, from the measurements of D vs. E and x vs. X, we obtain tanδ’ and

tanφ′, respectively, and either the piezoelectric (D vs. X) or converse

piezoelectric measurement (x vs. E) provides tan θ′ through a numerical

subtraction.

So far, we have discussed the ‘intensive’ dielectric, mechanical and

piezoelectric losses in terms of ‘intensive’ parameters X and E. In order to

consider real physical meanings of the losses in the material, we will introduce

the ‘extensive’ losses [4] in terms of ‘extensive’ parameters x and D. In

practice, intensive losses are easily measurable, but extensive losses are not,

but obtainable from the intensive losses. When we start from the piezoelectric

equations in terms of extensive physical parameters x and D,

X = c

x – h D 16.14

E = –h x + κ

D 16.15

we introduce the extensive dielectric, elastic and piezoelectric losses as

= κ

j tan δ) 16.16

= c

(1 + j tan φ) 16.17

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Loss mechanisms and high-power piezoelectric components 479

= h (1 + j tan θ) 16.18

It is notable that the permittivity under a constant strain (e.g., zero strain or

completely clamped) condition, ε

and the elastic compliance under a constant

electric displacement (e.g. open-circuit) condition, s

can be provided as an

inverse value of κ

and c

, respectively, in this simplest one-dimensional

expression (in the case of a general 3D expression, this part must be translated

as ‘inverse matrix components of κ

and c

tensors’). Thus, using exactly

the same losses in Eqs. (16.16) and (16.17),

= ε

–

j tan δ) 16.19

= s

(1 – j tan φ) 16.20

we will consider these phase delays again as ‘extensive’ losses.

Here, we consider the physical property difference between the boundary

conditions: E constant and D constant, or X constant and x constant in a

simple 1D model. When an electric field is applied to a piezoelectric sample

as illustrated at the top of Fig. 16.2, this state will be equivalent to the

Total input

electrical energy

= (1/2) ε 0 ε

Stored

electrical energy

= (1/2) ε 0 ε

Stored

electrical energy

= (1/2) (

)

Strain

Mechanically

clamped

Electrically

short-circuited

Total input

mechanical energy

= (1/2)

Stored

mechanical energy

= (1/2)

Stored

electrical energy

= (1/2) (

/ε 0ε

)

Current

Electrically

short-circuited

Electrically

open-circuited

Polarization

inverse field

/ε

Inverse

field

16.2

Conceptual figure for explaining the relation between ε

and ε

and s

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