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

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Handbook of dielectric, piezoelectric and ferroelectric materials910

this link. The ferroelectric transition (x < x

f–r

) follows a strong increase of

the interaction (or correlation length) at T

. In the following, this optimal

ferroelectric correlation length will be called ξ

∞

. In the real world, this

correlation length is not infinite as it should theoretically be. The possible

occurrence of limited correlation length for T>>T

, well in the paraelectric

state, is not discussed here. In the soft mode picture of BaTiO

, the infinite

correlation length at T

results from the condensation of a phonon mode

which mainly includes the Ti–O bond oscillations. An alternative model

takes into account the correlated Ti–O chains which are present at all

temperatures [65]. In both cases, the Ti–O bonds are the key origin to

ferroelectricity. These bonds are exactly what is disrupted on substituting

for Ti

, 2Nb

for Ba

+ 2Ti

and Li

–3F

–

for Ti

–3O

2–

. The perturbation

strength ∆P increases in the order of the substitutions. As x increases, the

ferroelectric line T

= f (x) for x < x

f–r

stems from a decrease of the maximal

correlation length ξ

max

(ξ

max

∝ ξ

∝

/x∆P). Formally, this equation means that

there are two ways to decrease the ferroelectric correlation length and thus

to decrease the ferroelectric transition temperature: increase of the number

of substituted defects x and increase of the strength of perturbation of each

defect ∆P. The former parameter leads to the negative slope of T

= f (x) and

the latter increases the slope of this line. This is qualitatively consistent with

the observations in the three studied families.

The next step is to consider that each substituted point defect perturbs a

part of its surrounding host BaTiO

lattice. Because of the anisotropic nature

of this lattice, such polarised clusters are expected to have an ellipsoid shape.

Using the Ornstein Zernicke formalism, it can be thought that this perturbation

is exponentially decreasing along the radii of these ellipsoids as ∝ ∆P exp

(– r/ξ) [66]. It is beyond the scope of the present section to exactly define

this exponential decrease. What can be said is that the maximum size of

these perturbed clusters is reached when ξ = ξ

max

, i.e. at T

. This is the key

point: not only the maximum correlation length ξ

max

drives the host matrix

properties but it also sets the size of the perturbed clusters around each

substituted defect. Since, in this assumption, ξ

max

decreases both with increasing

x and ∆P, the picture which arises is the following (Fig. 30.13):

• For x < x

f–r

, the density of impurity-induced clusters is very small and

the BaTiO

host matrix properties are kept only with a decrease of the

maximal correlation length ξ

max

. At the same time, each cluster can

reach its maximum size (Fig. 30.13, upper row).

• When x~x

f–r

, small clusters start to interact with each other. In this

model, x

f–r

is the right point where all the macroscopic sample is filled

by impurity-induced microscopic clusters. This interaction is the source

for the observed dielectric dispersion.

• When x > x

f–r

, the maximal correlation length cannot be reached and the

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Lead-free relaxors 911

Vogel–Fulcher temperature is the temperature where all clusters stop

relaxing. The clusters can no longer reach their maximum size and,

because of the interaction among clusters, a size distribution sets in (Fig.

30.13, lower row).

Without a quantitative evaluation of ∆P and ξ(x), it is not possible to go

further in the quantitative description of the ferroelectric–relaxor crossover.

It can, however, be explained why the ferroelectric and relaxor phase diagrams

are aligned: this is simply because the BaTiO

ultimate correlation length ξ

∞

appears in all the spatial parameters that were defined. In other words, the

BaTiO

correlation length imprints both the matrix and cluster properties;

the Ti–O bond oscillations are the key mechanisms. This picture is consistent

with the one which was drawn on the basis of high-pressure Raman scattering

experiments and which uses the BaTiO

correlation length [58]. Also, it can

be recalled that the soft-mode related cluster sizes and the Ornstein Zernicke

function were used in the case of lithium-substituted KTaO

[67, 68]. From

these pioneering works, several attempts have been made to transfer the

cluster model to lead-containing relaxors. It seems that the continuous crossover

(f–r)

, ξ<<ξ

max

(f–r)

, ξ~ξ

max

(f–r)

, ξ<<ξ

max

(f–r)

, ξ

average

<ξ

max

30.13

Sketch of the impurity-induced clusters in the BaTiO

host

lattice. On cooling to the transition temperature, the clusters can

reach their maximum extension when their density is low leading to

a ferroelectric state (upper row). When their density is high, this

optimal size cannot be reached and a distribution of cluster size sets

in, leading to a relaxor state (lower row).

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Handbook of dielectric, piezoelectric and ferroelectric materials912

that was evidenced in lead-free compounds is in favour of the cluster model

of relaxors. However, the comparison between lead-containing and lead-free

relaxors is limited since:

• a number of features of lead-containing relaxors do not appear in lead-

free relaxors (diffuse scattering, high-pressure-induced Raman lines,…);

• the electronic lone pair of lead leads to very peculiar Pb dynamics which

is not present in Ba-based compounds;

• a continuous crossover from ferroelectric to relaxor states in Pb-based

compounds is missing. There is perhaps one example of such crossover

which is PbTiO

: La for which x

f–r

is about 0.20. However, this is very

different from the standard relaxors where the substitution has single

discrete values (0.33/0.66 or 0.50/0.50).

30.5 Lead-free relaxors with tetragonal bronze

(TTB) structure

Figure 30.14 shows a schematic representation of the TTB structure projection

along the [001] direction. For a general formulation A

(X = O,

F), large cations (e.g. Na

, K

, Sr

, Ba

, Pb

, La

, Bi

, …) occupy the

15-CN (A) and the 12-CN (B) sites, small cations such as Li

are in the 9-

CN (C) sites and small and highly charged cations (e.g. Nb

, Ta

, …) are

30.14

Schematic projection of the anionic TTB structure along the 4-

fold

-axis (A, B and C correspond to cationic sites with 15, 12 and 9

coordination number).

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Lead-free relaxors 913

in the octahedral (M) site. The present section is devoted to selected lead-

free relaxor compounds of TTB-type structure [69, 70].

The relaxor behaviour was demonstrated in various TTB compositions

including niobates, tantalates, niobo-tantalates and niobo-titanates (Table

30.4) [25, 71, 72]. There was a typical relaxor temperature dependence of

′

and

′′

. In addition, there was a deviation from the Curie–Weiss law and the

shift of T

to lower values for decreasing frequencies obeys the Vogel–

Fulcher law [60, 73].

Table 30.4

Some lead-free TTB relaxor compositions

Relaxor compositions

(± 10K) ∆

(K)

(at 1kHz)

LaNb

165 22

BiNb

220 80

BaLa䊐Nb

203 55

BaBi䊐Nb

295 75

BaLa

2/3

䊐

1/3

NaNb

210 34

BaLaNa(Nb

Ti)O

171 41

BaLaK(Nb

Ti)O

146 13

1.5

La䊐

0.5

(Nb

Ti)O

190 35

1.5

Bi䊐

0.5

(Nb

Ti)O

255 65

La(Nb

185 20

Bi(Nb

270 25

NaTa

120 25

KTa

<80 ∗

NaTa

<80 ∗

KTa

<80 ∗

LiNb

F 210 40

2.25

䊐

0.75

14.5

0.5

175 30

SrK

F 112 16

BaNa

F 140 17

5(1–

)

(0.52 ≤

≤ 0.80) 257 ≥

≥ 251 41 (0.52) to 81 (0.80)

Na(Nb

1–

)

(0.40 ≤

≤ 1) 222 ≥

≥ 120 20 (0.40) to 25 (1)

K(Nb

1–

)

(0.16

≤

≤ 1) 263 ≥

≥ 80 21 (0.16) to ∗ (1)

Na(Nb

1–

)

(0.65 ≤

≤ 1) 260 ≥

≥ 80 6 (0.65) to ∗ (1)

2–

15–

(0.31 ≤

≤ 1) 250 ≥

≥ 140 40 (0.31) to 17 (1)

Na(Nb

5–

15–

(0.31 ≤

≤ 0.50) 265 ≥

≥ 168 15 (0.31) to 30 (0.50)

2–

15–

(0.075

≤

≤ 0.35) 320 ≥

≥ 222 10(0.075) to 20(0.35)

2–

15–

(0.20 ≤

≤ 1) 290 ≥

≥ 112 15 (0.20) to 16 (1)

2.5(1–

)

2.5

䊐

0.5

** ** **

∆

(10

Hz) –

(10

Hz). In the case of solid solutions, the given values of

correspond to the

limit values.

* Unknown values due to the experimental low temperature limitation of our

dielectric measurements.

** A relaxor behaviour was announced by previous authors; due to some

disagreements between them, the values of

and ∆

are not given here. This

is due to the modulated distribution of Sr

and Ba

which can vary versus the

different types of preparation between the various samples.

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Handbook of dielectric, piezoelectric and ferroelectric materials914

Some solid solutions situated between niobate oxide ferroelectric and

relaxor were also studied. Such is the case with A

B(Nb

1–x

)

. The

relaxor behaviour occurs for the highest values of x. Figure 30.15 shows, as

an example, the variations of T

(0 ≤ x < 0.16) and T

(0.16 ≤ x ≤ 1) for

ceramics with composition Sr

K(Nb

1–x

)

. Both values decrease when

the tantalum rate increases.

This is also the case with the Sr

KNb

–SrK

F and Ba

NaNb

–

BaNa

F systems; for the compositions close to the oxide, the behaviour

is ferroelectric while it becomes relaxor when the fluorine rate and thus the

sodium or potassium rate are high enough [74–76]. Figure 30.16 shows as an

example the variations of T

(0 ≤ x ≤ 0.25) and T

(0.20 ≤ x ≤ 1) for the

barium–sodium system. It is interesting to note that both relaxor and

ferroelectric phases coexist for compositions (0.20 ≤ x ≤ 0.25), giving rise to

the transition sequence relaxor–ferroelectric–paraelectric on heating. Here

also both values of T

and T

decrease when x increases. Elsewhere the

frequency dependence of the permittivities of a ceramic with a composition

BaNa

F clearly displays a frequency relaxation at 77K, while it

disappears at 300K, i.e. for T > T

= 140K at 10

Hz) (Fig. 30.17).

Figure 30.18 shows the temperature dependence of the pyroelectric

coefficient p for a ceramic with composition Sr

1.341

1.097

4.875

0.125

(SBNS). It shows a broad maximum around 240K. Above 240K, the

pyroelectric signal decreases to values close to zero at approximately 350K.

The variation of P

of the sample was obtained by integration of p vs.

(K)

500

400

300

200

100

Paraelectric

Ferro.

Relaxor

0 0.2 0.4 0.6 0.8 1

30.15

Variation of transition temperatures with

for ceramics with

composition Sr

K(Nb

1–

)

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Lead-free relaxors 915

temperature (Fig. 30.18). The slow decrease of the spontaneous polarisation

associated to a very noisy pyroelectric signal should be considered as

characteristic of a relaxor ferroelectric: the decrease of the polarisation is

associated to a progressive relaxation of polar microdomains. The switching

(K)

1000

800

600

400

200

Ferroelec.

Paraelectric

Relaxor

0 0.2 0.4 0.6 0.8 1

30.16

Variation of transition temperatures with x for ceramics with

composition Ba

2–

15–

1000

800

600

400

200

0123456

log

(Hz)

′

= 77 K

= 300 K

′

′′

0 1 2 3 log

(Hz) 6

′′

800

600

400

200

30.17

Frequency dependences of

′

and

′′

for a ceramic with

composition BaNa

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Handbook of dielectric, piezoelectric and ferroelectric materials916

of the independent dipoles, isolated in this particular microstructure, occurs

then randomly, giving rise to a very high noise level in the pyroelectric

signal.

Some of these compositions were previously prepared and characterised.

They were announced as ferroelectric, because the measurements had been

performed only at one frequency (1kHz) and not at various frequencies as

required for the studies of relaxor properties. It was the automation of dielectric

measurements performed with impedance analysers which allowed the relaxor

behaviour to be revealed.

As in the perovskites, the relaxor behaviour appears in the TTB-type

compounds when at least two ions occupy the same crystallographic site.

The coexistence of cations seems to be as favourable on the A site as on the

M site. In addition, at least one ferroelectrically active cation (Ti

, Nb

) must be present on the octahedral site.

The relaxor behaviour can be due to a cationic disorder on the A site,

whatever the coupled substitution ensuring the electrical neutrality; this is

the case with BaLaNb

when Ba

and La

occupy only the A site.

NaNb

, in which the same two Ba

cations

occupy the A site and Na

occupies the B sites, is a ferroelectric. On the contrary, BaNa

F is a

relaxor. The crystal structure of this last compound is in good agreement

with the dielectric properties, i.e. the A-site is statistically occupied by equal

quantities of Ba

and Na

, thereby giving rise to a cationic disorder on the

A site while the B site is filled by Na

cations [77, 78]. In addition there is

coexistence of F

–

and O

2–

on the anionic sites.

150 200 250 300 350 400

(K)

(nC/cm

2.5

2.0

1.5

1.0

0.5

(µC/cm

)

30.18

Thermal variations of pyroelectric coefficient

and

spontaneous polarization

in SBNS.

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Lead-free relaxors 917

Concerning the Ta–Nb substitution, the replacement of Nb

, highly

polarisable, by Ta

transforms the macroscopic polarisation into a local one.

This results in a relaxor state as the long-range order is not induced by a

local dipolar cationic order. The higher the associated cationic order in the

A and B sites, the higher the Ta–Nb substitution rate leading to relaxor

behaviour (Table 30.4): e.g. x = 0.16 for Sr

K(Nb

1–x

)

and x = 0.65 for

Na(Nb

1–x

)

. In fact there is no ambiguity regarding the disordered

distribution of the two small Sr

cations and the single large K

one, nor

regarding the ordered distribution of the two large Ba

cations and the

single small Na

ones, since both occur in two large A sites and in one

smaller B one.

For oxyfluorides, the F

–

–O

2–

substitution is coupled with the cationic

one in order to ensure electric neutrality. The origin of relaxor behaviour

comes from cationic or/and anionic substitutions when there are two different

cations on the same crystallographic site, e.g. Ba

2–x

1+x

15–x

, the A

site being filled by both Ba

and Na

and the X site by both O

2–

and F

–

for

x > 0 [79].

However, it seems that the relaxor behaviour can be attributed to the only

anionic F

–

–O

2–

substitution in the lack of different cations on the same site,

e.g. K

LiNb

F: owing to their very different sizes, the 3K

and the Li

cations occupy only the (2A + B) sites and the C site, respectively. The

relaxor behaviour is induced by a dilution of the oxygen network leading to

a local polarisation which breaks the long-range order usually at the origin

of ferroelectric properties.

The influence of the heat treatments of the ceramics was studied with

composition BaNa

F (Table 30.5). The value of ∆T

increased from

9 to 60 when the sintering of the ceramics was followed by either slow

cooling (favouring order) (50K/h), medium cooling (300K/h) or quenching

in liquid nitrogen (favouring disorder). This result is in good agreement

with the relationship between ionic disorder and relaxor behaviour. As a

comparison, similar results were obtained on Pb(Sc

1/2

(PST): the

ceramic was a ferroelectric after a long annealing while it was a relaxor after

quenching [80].

Table 30.5

Values of

and ∆

for ceramics with composition

BaNa

F obtained after different cooling treatments

Slow cooling Medium cooling Quenching

(K) at 0.1 kHz 142 138 101

(K) at 1kHz 143 141 111

(K) at 10 kHz 147 145 122

(K) at 100kHz 151 155 161

∆

(K) 9 17 60

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Handbook of dielectric, piezoelectric and ferroelectric materials918

30.6 Ceramics containing bismuth

The aim of the present section is to discuss the relaxor properties of the

ceramics containing bismuth. The Na

0.5

TiO

-derived compositions are

not considered here, nor is the perovskite-type solid solution between ATiO

(A = Ca, Sr, Ba) and Na

1/2

TiO

[35, 81].

30.6.1 Ceramics of perovskite type

The Ba

1–x

2x/3

䊐

x/3

TiO

(A = La, Bi) ceramics showed ferroelectric properties

for compositions very close to BaTiO

[82]. Relaxor behaviour occurred for

values of x ≥ 0.15. However, both the values of T

or T

were higher for Bi-

than for La- substitution: e.g. T

< 80K in Ba

0.8

0.4/3

TiO

, T

= 165K in

0.8

0.2/3

TiO

and T

= 292K in Ba

0.8

0.4/3

TiO

. This is not related

to a steric effect, since the apparent cationic sizes are very close

( = 1.16Å, = 1.17Å

in 8-CN; these values are given for 8-CN, although

the cations are in the 12-CN site of the perovskite, because no corresponding

value is given for Bi

) [83]. The real cause is undoubtedly related to the

lone pair, which leads to the non-spherical and strongly polarised Bi

cation.

Such an effect is well known, for example, in the case of the influence of

(also possessing a lone pair) on the T

variation of Ba

1–x

TiO

: T

(BaTiO

) = 400K, T

(PbTiO

) = 763K [84–87].

For ceramics with composition Ba

1–x

2x/3

TiO

, for 0 ≤ x < 0.09, i.e. in

the ferroelectric region, the value of T

decreases only very slowly as x

increases (Fig. 30.19). Indeed, two antagonist effects are in competition. The

replacement of the big Ba

cation by the smaller Bi

and the creation of

cationic vacancies should lead to a decrease of T

( = 1.42Å, = 1.17Å

in 8-CN) [83]. In contrast, the introduction of Bi

with its lone pair leads to

an increase of T

. The resultant of these two effects is probably responsible

of the relative stability of T

with x. For compositions 0.09 ≤ x ≤ 0.15, the

nanostructural disorder which characterises the relaxor behaviour is less

sensitive to the local electronic configuration of Bi

, leading thus to a

stronger decrease of T

with x [1]. Figure 30.20 shows the temperature

dependence of

′

and the dissipation factor tan δ =

′′ ′

εε

at 1kHz for a

ceramic with composition corresponding to x = 0.15. The main dielectric

relaxor characteristics ∆T

and ∆

′′

εε

/ increase as the 2/3 Bi

–Ba

substitution rate increases (Table 30.6). This is due of course to the strong

composition heterogeneity that exacerbates the relaxor effect. This was typically

the case in the lead perovskite relaxor PMN where local 1:1 order between

niobium and magnesium atoms generated ordered regions surrounded by

rich niobium polar regions. The heterogeneity thus created induced the relaxor

behaviour commonly correlated with nanoscale spontaneous polarisation

[1]. The present result is of great interest for obtaining relaxor compositions

at temperatures close to 300K for use as lead-free capacitors, dielectrics or

WPNL2204

Lead-free relaxors 919

actuators. The value of T

corresponding to x = 0.15 is 288 K (at 1 kHz),

which can be compared with that of the well-known lead-containing PMN

= 265K).

Another interesting study concerns ceramics with compositions

0.9

0.067

䊐

0.033

(Ti

1–x

, i.e. with substitutions on both 6-CN and 12-

′

4000

3000

2000

1000

tan δ

′

50 100 150 200 250 300 350 400 450

(K)

tan δ

0.12

0.10

0.08

0.06

0.04

0.02

0.00

30.20

Temperature dependences of

′

and tan δ for a ceramic with

composition Ba

0.85

0.10

TiO

, at 1kHz.

Paraelectric

Multi-phase zone

Ferroelectric

Relaxor

0 0.1 0.2 0.3

(K)

500

400

300

200

30.19

Variation of

with

for ceramics of Ba

1–

TiO

composition.

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