Lallart M. (ed.) Ferroelectrics

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Hydrogen in Ferroelectrics

149

which has been reduced by atomic hydrogen, hydrogen fissure or microcrack will form. If

there is a extra internal stress σ

, the critical hydrogen pressure for cracking can be

decreased from P=2σ

(H) to P*=2σ

(H)-σ

. Because there is a large internal stress in HP

sample, which can promote crack nucleation, so hydrogen fissure appear when

i=0.5mA/cm

. The microcracks are found in SP and UP samples only when i=400

mA/cm

for absence of internal stress.

5.2 Hydrogen reduce fracture toughness of ferroelectric material

Vickers indentation was carried out on the surfaces of three ferroelectric ceramic samples to

obtain indentation fracture toughness K

according to Eq.4.

0.0638 /KPdl (4)

where P is the load, d is diagonal length of the indentation and l is the crack length. Then,

the samples with indentation cracks were charged into 4.1 ppm, 8.1 ppm and 12.1 ppm

hydrogen, respectively. Unloaded indentation cracks can grow induced by the indentation

residual stress during charging. The indentation crack length after hydrogen charging was

measured to calculate the threshold stress intensity factor of hydrogen-induced delayed

cracking (HIDC), K

, by Eq.4. New indentations were carried out on the surface of

hydrogenated samples. The fracture toughness for hydrogenated sample K

(H) can also be

obtained. The experiments indicated that both K

and K

(H)/K

decreased linearly

with the increasing C

, as shown in Figure 13 (Zhang et al., 2008).

Fig. 13. Hydrogen concentration dependence of the relative fracture toughness of charged

samples, K

and of the normalized threshold stress intensity factor of hydrogen-

induced cracking induced by residual stress, K

(H)/K

(Zhang et al., 2008)

Ferroelectrics – Physical Effects

150

The crack length increased with increasing hydrogen concentration in the samples. Therefore,

the cracks can also grow with the prolongation of dwell time during indentation test in a pre-

charged sample since the hydrogen concentration will increase at the indentation crack tips by

stress-induced diffusion. The experimental results indicate that the longer the indentation load

hold, the larger the indentation crack length is, and the smaller fracture toughness, K

(H,t)

measures, as shown in Figure 14 (Zhang et al., 2008). Under a constant load, the HIDC can

occur by the stress-induced hydrogen diffusion and enrichment.

Fig. 14. The normalized fracture toughness K

(H,t)/K

versus the logarithm of the dwell

time during the indentation test for the charged sample (Zhang et al., 2008)

5.3 Hydrogen-induced delayed cracking in ferroelectric ceramics

During single-edge-notched-tensile sample of PZT ferroelectric ceramics hydrogen charging

dynamically in 0.2mol/l NaOH+0.25 g/l As

solution, hydrogen-induced delayed

cracking (HIDC) can occur (Wang et al., 2003a) and depends on the relative orientation

between notch plane and the polarization vector, i.e., the HIDC also shows anisotropy in

ferroelectric ceramics, as shown in Figure 15 (Wang et al., 2003b). Hydrogen concentration

under different charging current densities is given in Table 2. The curve of K

vs i or

can plot based on Table 2 and one can find a linear relationship between K

and the

lnC

(Wang et al., 2003b)

aabb

IH IC IH IC

//KKKK =0.4-0.15lnC

(5)

where superscript a and b denote polarization vector parallel and perpendicular to the crack

plane, respectively.

K =1.53 MPam

1/2

and

K =1.12 MPam

1/2

for PZT ferroelectric

Hydrogen in Ferroelectrics

151

i (mA/cm

) 0.05 0.5 5 50 300

(

ppm) 0.92 2.61 4.8 7.16 9.84

K (MPam

1/2

)

0.54 0.34 0.28 0.13 0.01

K (MPam

1/2

)

0.36 0.26 0.17 0.08 -

IH IC

/KK

0.40 0.25 0.21 0.10 0.01

IH IC

/KK

0.40 0.28 0.19 0.09 -

Table 2. The threshold stress intensity factors of HIDC corresponding to various hydrogen

concentrations

(Wang et al., 2003b)

0 20406080100

0.0

0.2

0.4

0.6

0.8

1.0

Parallel

0.05 mA/cm

0.5 mA/cm

5 mA/cm

50 mA/cm

300 mA/cm

Time to fracture, h

(a)

0 20406080100

0.0

0.2

0.4

0.6

0.8

1.0

0.05 mA/cm

0.5 mA/cm

5 mA/cm

50 mA/cm

Time to fracture, h

Perpendicular

(b)

Fig. 15. The normalized stress intensity factor vs time to fracture during dynamically

charging with various i (the arrows mean no fracture within 100 h). (a) Polarization

direction parallel to the crack plane; (b) Polarization direction perpendicular to the crack

plane (Wang et al., 2003b)

Ferroelectrics – Physical Effects

152

ceramics. Eq.5 suggests that the t anisotropy of K

is entirely caused by the anisotropy of

fracture toughness.

6. Conclusion

In this chapter, the effects of hydrogen on main properties of ferroelectric materials are

reviewed. Even if a little amount of hydrogen enters a ferroelectric material, the

ferroelectricity and dielectric properties would be degraded, such as hydrogen causes

hysteresis loop narrower, reduces remnant polarization, increases leakage current, etc. If

great amount hydrogen is charged into ferroelectrics, hydrogen fissure and hydrogen-

induced delayed cracking can occur. Fortunately, hydrogen can escape from the

hydrogenated ferroelectric materials and properties can restore after a heat treatment.

Therefore, outgassing treatment is an effectual method to prevent hydrogen damage.

Although most of reports about hydrogen in ferroelectrics proved that hydrogen has

negative influence, hydrogen can’t be consider completely harmful to the ferroelectric

materials. For example, a very small amount of hydrogen can enhance the ferroelectricity.

Now, the mechanism of enhancement effect is not clear yet, but this phenomenon enough

to absorb more interests to develop the potential role of hydrogen in ferroelectric

materials.

7. Acknowledgment

Authors acknowledge support from the National Nature Science Foundation of China under

grants 51072021 and 50632010 and from Beijing Municipal Commission of Education under

YB20091000801 grant.

8. References

Aggarwal, S.; Perusse, S. R.; Tipton, C. W.; Ramesh, R.; Drew, H. D.; Venkatesan, T.;

Romero, D. B.; Podobedov, V. B. & Weber, A. (1998). Effect of hydrogen on

Pb(Zr,Ti)O

-based ferroelectric capacitors. Applied Physics Letters, Vol.73, No.14, pp.

1973-1975, ISSN 0003-6951

Chen, F.; Chen, W. P.; Wang, Y.; Hu, Y. M.; Shen, Z. J. & Chan, H. L. W. (2011). Effects of

forming gas annealing on LiNbO3 single crystals. Physica B: Condensed Matter, Vol.

406, No.3, pp. 683-686, ISSN 0921-4526

Chen, W. P.; Li, L. T.; Qi, J Q. & Gui Z. L. (1998). Effect of electrochemical hydrogen charging

on Ba1-xPbxTiO3-Based semiconducting ceramics. Journal of Materials Science

Letters, Vol.17, No.11, pp.899-900, ISSN 0261-8028

Joo, H. J.; Lee, S. H.; Kim, J. P.; Ryu, M. K. & Jang, M. S. (2002). Effect of hydrogen on the

electrical and optical properties in ferroelectric Pb(Zr,Ti)O

thin films. Ferroelectrics,

Vol.272, No.1, pp.149-154, ISSN 1563-5112

Han, J. P. & Ma, T. P. (1997). Electrode dependence of hydrogen-induced degradation in

ferroelectric Pb(Zr,Ti)O

and SrBi

thin films. Applied Physics Letters, Vol.71,

No.9, pp. 1267-1269, ISSN 0003-6951

Huang, H. Y.; Chu, W. Y.; Su, Y. J.; Qiao, L. J. & Gao, K. W. (2005). Combined effect of

electric field and residual stress on propagation of indentation cracks in a PZT-5H

Hydrogen in Ferroelectrics

153

ferroelectric ceramic. Materials Science and Engineering B, Vol. 122, No.1, pp. 1-6,

ISSN 0921-5107

Huang, H. Y.; Chu, W. Y.; Su, Y. J.; Li, J. X.; Qiao, L. J. & Shi, S. Q. (2006). Experiment and

first principles investigation on the hydrogen-hindered phase transition of

ferroelectric ceramics. Applied Physics Letters, Vol.89, No.142904, ISSN 0003-6951

Huang, H. Y.; Chu, W. Y.; Su, Y. J.; Gao, K. W.; Li, J. X. & Qiao, L. J. (2007). Hydrogen-

induced semiconductor transformation of PZT ferroelectric ceramics. Journal of the

American Ceramics Society, Vol. 90, No.7, pp. 2062

–2066, ISSN 0002-7820

Ikarashi, N. (1998) Analytical transmission electron microscopy of hydrogen-induced

degradation in ferroelectric Pb(Zr,Ti)O

on a Pt Electrode. Applied Physics Letters,

Vol.73, No.14, pp.1955-1957, ISSN 0003-6951

Katz, L. E. (1988). In: VLSI Technology (2nd ed), S. M. Sze (Ed), pp. 127,

McGraw-Hill, ISBN

978-007-0627-35-2, New York

Kushida-Abdelghafar, K.; Miki, H.; Torii, K. & Fujisaki, Y. (1996). Electrode-induced

degradation of Pb(Zr

1−x

(PZT) polarization hysteresis characteristics in

Pt/PZT/Pt ferroelectric thin-film capacitors. Applied Physics Letters, Vol.69, No.21,

pp. 3188-3190, ISSN 0003-6951

Pen, X.; Su, Y. J.; Gao, K. W.; Qiao, L. J. & Chu, W. Y. (2004). Hydrogen fissure in

PZT ferroelectric ceramic, Materials Letters, Vol.58, No.15, pp. 2073-2075, ISSN 0167-

577x

Shimamoto, Y.; Kushida-Abdelghafar, K.; Miki, H. & Fujisaki, Y. (1997). H

damage of

ferroelectric Pb(Zr,Ti)O

thin-film capacitors-The role of catalytic and adsorptive

activity of the top electrode. Applied Physics Letters, Vol.70, No.23, pp. 3096-3097,

ISSN 0003-6951

Tamura, T.; Matsuura, K.; Ashida, H.; Kondo, K. & Otani, S. (1999). Hysteresis variations of

(Pb,La)(Zr,Ti)O3 capacitors baked in a hydrogen atmosphere. Applied Physics

Letters, Vol.74, No. 22, pp.3395-3397, ISSN 0003-6951

Wang, Y.; Chu, W. Y.; Qiao, L. J. & Su, Y. J. (2003a). Hydrogen-induced delayed fracture of

PZT ceramics during dynamic charging under constant load

，Materials Science and

Engineering B, Vol. 98, No.1, pp. 1-5, ISSN 0921-5107

Wang, Y.; Chu, W. Y.; Su, Y. J.; Qiao, L. J. & Gao, K. W. (2003b)

，Hydrogen-induced

cracking and its anisotropy of a PZT ferroelectric ceramics

，Science in China E,

Vol.46, No.3, pp.318-325, ISSN 1674-7321

Wu, M.; Huang, H. Y.; Jiang, B.; Chu, W. Y.; Su, Y. J.; Li, J. X & Qiao, L. J. (2009). Experiments

and first principles calculations on the effects of hydrogen on the optical properties

of ferroelectric materials. Journal of Materials Science, Vol. 44, No.21, pp. 5768-5772,

ISSN 0022-2461

Wu, M. (2009). Study of effect of hydrogen on the properties of ferroelectric

ceramics. Doctoral dissertation, University of Science and Technology Beijing.

Wu, M.; Huang, H. Y.; Chu, W. Y.; Guo, L. Q.; Qiao, L. J.; Xu, J. Y. & Zhang, T. Y. (2010).

Tuning the ferroelectric and piezoelectric properties of 0.91Pb(Zn

1/3

2/3

0.09PbTiO

single crystals and lead zirconate titanate ceramics by doping

hydrogen. Journal of Physical Chemistry C, Vol.114, No.21, pp. 9955-9960, ISSN

1932-7447

Ferroelectrics – Physical Effects

154

Zhang, H.; Su, Y. J.; Qiao, L. J. & Chu, W. Y. (2008). The Effect of Hydrogen on the Fracture

Properties of 0.8(Na

1/2

)TiO

-0.2(K

1/2

)TiO

Ferroelectric Ceramics. Journal of

Electronic Materials, Vol.37, No. 3, pp.368-372, ISSN 0361-5235

Thermal Conduction Across Ferroelectric Phase

Transitions: Results on Selected Systems

Jacob Philip

Department of Instrumentation and STIC, Cochin University of Science and Technology

India

1. Introduction

A ferroelectric phase transition represents a special class of structural phase transition

characterized by the appearance of a spontaneous polarization in the material. Above the

Curie temperature the transition often follows a diverging differential dielectric response or

permittivity



, which varies with temperature in an approximate Curie-Weiss manner



C/(T-T

), where T

is the Curie-Weiss temperature, which is equal to the Curie temperature T

for a continuous transition. The crystalline phase which undergoes transformation to the

ferroelectric form at T

is the paraelectric one. Below T

, in the absence of an applied field, there

are at least two directions along which a spontaneous polarization can develop. To minimize

the depolarizing fields different regions of the crystal polarize in each of these directions, each

volume of uniform polarization being called a domain. The resulting domain structure usually

results in a near complete compensation of polarization and the crystals consequently exhibit

very small pyroelectric effects until they are poled by the application of a field.

A ferroelectric transition is usually associated with the condensation of a soft (or low-

frequency) mode of lattice motion at the Brillouin-zone centre. Structural transitions

triggered by zone-centre soft modes are generally termed ferrodistortive, and in this sense

ferroelectrics constitute a subgroup of the class of ferrodistortive transitions. This subgroup

involves the condensation of a polar or optically active mode whose condensation causes

the appearance of a long rage polar order. If the transition is strongly first order then mode

softening may not occur to a significant degree, and in this situation, there is also a

possibility that the large polarization which sets in discontinuously at T

may not be

reversible, or the low temperature phase may be pyroelectric only. Ferroelectric transitions

are categorized as being either displacive or order-disorder in character. This distinction is

generally made in terms of whether the paraelectric phase is microscopically nonpolar

(displacive) or only nonpolar in a macroscopic or thermally averaged sense (order-disorder).

The displacive or order-disorder character is often defined in terms of the dynamics of the

phase transition, as to whether the soft mode is a propagating or diffusive type respectively.

The displacive or propagating soft mode is a damped optic phonon, representing small

quasi-harmonic motion about the mean position, while the diffusive soft mode represents

large amplitude thermal hopping motion between the domain wells.

Although most ferroelectrics are ferrodistortive (common examples being barium titanate,

sodium nitrite, and triglycine sulphate) some are not. To understand this it is necessary to

recognize that, because of the existence of coupling between modes, it is not a necessary

Ferroelectrics – Physical Effects

156

condition for ferroelectricity that a zone centre polar mode should be driving the instability.

Sometimes a driving antidistortive mode can couple directly or indirectly to a zone centre

polar mode and upon condensation induce a small spontaneous polarization in an indirect

fashion. In this case the primary order parameter is antidistortive in character while the

spontaneous polarization is said to be a secondary order parameter of the transition. There

can of course be only one primary order parameter (at least for a continuous or near

continuous transition), but there may be many induced or secondary order parameters

resulting from couplings to the primary order parameter. All the known antiferroelectrics

(examples: lead zirconate, ammonium dihydrogen phosphate etc.) are intrinsically

antidistortive, although one can conceive of a ferrodistortive antiferroelectric as one having

an antiparallel arrangement of electric dipoles occurring within a primitive cell of the

higher-symmetry phase. Such a phase is characterized by the condensation of an antipolar

zone-centre soft mode.

Once the importance of coupling between polar modes and other modes has been

recognized it is clear that, via the piezoelectric interaction (or coupling to acoustic modes), a

spontaneous strain will be virtually a universal characteristic of ferroelectrics since all

ferroelectrics are piezoelectric. If this strain can be switched by application of stress then an

obvious parallel in elastic terms exists with ferroelectricity. This property is termed

ferroelasticity, and a crystal is said to be ferroelastic when it has two or more orientation

states in the absence of mechanical stress (and electric field) and can be shifted from one to

another of these states by mechanical stress. Intrinsic ferroelastic transitions are associated

with the condensation of long-wavelength acoustic phonons and many are known.

The optical and acoustic phonon modes involved in ferroelectric and ferroelastic phase

transitions can be probed with Brillouin light scattering and ultrasonic techniques. When

phonon modes soften, the involved elastic constants undergo anomalous variations which

get reflected in ultrasound velocity and attenuation. Elaborate reviews on these subjects

have appeared in literature (Luthi & Rehwald, 1980; Cummins, 1990). Other popular

techniques used to probe modes in ferroelectrics are dielectric spectroscopy (Grigas, 1996)

and neutron scattering (Dorner, 1981). A number of books and reviews on these subjects

have appeared in literature (Lines & Glass, 1977). Though technique like measurement of

thermal conductivity across phase transition can reveal information about the coupling

between ferroelectric soft modes and thermal phonons, not many measurements have

appeared in literature on this. The few measurements that have appeared in literature have

used the well established steady-state methods of measuring thermal conductivity (Dettmer

et al., 1989).

There are several ferroelectrics that undergo successive phase transitions with

incommensurate phases (I-phase) from a symmetrical paraelectric to an incommensurate phase

at Ti and then from the incommensurate phase to a commensurate polar phase at T

(Cummins, 1990, Blinc & Levanyuk, 1986). This phase transition sequence can be

qualitatively described in terms of the phenomenological Landau theory of phase transitions

(Toledano & Toledano, 1987). The appearance of an I-modulated structure can be observed

experimentally as satellite peaks in X-ray or neutron diffraction patterns. In the I-phase, at

temperatures close to Ti, the I-modulation wave is harmonic, but as the temperature

approaches Tc, the ideal crystal can be considered as a system of equally spaced

commensurate constant-phase domains separated by narrow phase varying regions, i.e.,

phase solitons. The presence of these modulation waves can influence heat conduction in

ferroelectric crystals in two distinctive ways. As has been shown earlier, an interaction

Thermal Conduction Across Ferroelectric Phase Transitions: Results on Selected Systems

157

manifested in sound attenuation exists between the acoustical waves and the I-modulation

waves in the I-phase (Levanyuk et al., 1992; Lebedev et al., 1992). The usual expression for

the thermal conductivity in an insulating crystal is given by

Cvl





(1)

where C,

v and l denote the specific heat, group velocity, and mean free path for phonons,

respectively (Ashcroft & Mermin, 1976). The incommensurate modulation waves can affect

the mean free path and, consequently, can cause an anomalous variation of thermal

conductivity in the I-phase. Another possibility is that the modulation waves may

participate directly in heat conduction as carriers. In this case, one would expect the

modulation waves to enhance the thermal conductivity by the sliding motion in addition to

causing the usual phonon scattering effect. The effect of sliding modulation waves on

thermal conductivity has been investigated earlier within a phenomenological approach

(Levanyuk et al., 1992). In spite of the fact that measurement of thermal properties across

transition points is highly relevant to understand the coupling between modes, only limited

experimental work has appeared on this in literature.

2. Overview of thermal properties across ferroelectric phase transitions

In the few measurements of the variations of thermal conductivity near ferroelectric phase

transitions reported in literature, steady state methods have been employed. One of the first

measurements was on BaTiO

by Mante & Volger (1967). Their results show dips in thermal

conductivity at temperatures corresponding to phase transition points. The results are

explained in terms of mode conversion near the transition points. The low lying temperature

dependant optical phonon branches can get zero energy at zero wave-vector, which causes

permanent polarization of the crystal. Near the transition temperature the optical branches

have energies comparable to those of the acoustic branches which usually transport the heat.

This influences the number of scattering processes in which optical phonons participate,

resulting in a reduction of the conductivity due to acoustic branches. In case transverse

optical phonon branch shows enough dispersion and is not scattered too much, one can

expect additional conductivity which might compensate for the effect of decreased

conduction by the acoustic phonons.

Thermal conductivities and specific heat capacities of a wide spectrum of ferroelectrics,

BaTiO

, PbTiO

, KNbO

, KTaO

, NaNbO

and Pb(Mg

1/3

2/3

(PMN) single crystals have

been measured from 2 to 390 K (Tachibana et al., 2008). Pronounced jumps are found at

structural transitions in BaTiO

and KNbO

. A low-temperature anomaly from soft optical

phonons is observed in KTaO

. For PMN and NaNbO

, glass-like behaviour is observed in

both thermal conductivity and heat capacity measurements. The glass-like behaviour in

NaNbO

is associated with the phase separation phenomena which have been reported in

earlier studies. Thermal analysis techniques such as differential scanning calorimetry (DSC)

have been employed by several researchers to probe ferroelectric phase transitions (Setter &

Cross, 1980,

Podlojenov et al., 2006).

Belov & Jeong (1998) have reported thermal conductivity measurements for two ferroelectric

crystals, (NH4)

BeF

and Rb

ZnCl

, with incommensurate phases. It is found that anomalies

exist in the thermal conductivities of these crystals in the I-phases. I-modulation waves

cause anomalies in the heat transport processes by scattering of heat carrying phonons

Ferroelectrics – Physical Effects

158

rather than by their direct participation as heat carriers. They have employed the steady-

state technique for their measurements. Comparatively large samples, of size typically

greater than 5 mm

, are needed for these techniques in order to avoid boundary effects.

Moreover, comparatively large rises in temperature are often necessary to obtain a

reasonably high signal to-noise ratio, which lead to considerable temperature gradients

being set up in the sample. These drawbacks make these techniques unsuitable for studying

critical thermal conductivity behaviour near phase transitions.

Thermal wave measurements based on a photothermal effect, such as the photothermal

deflection technique, photoacoustic method and photopyroelectric measurement do not

disturb the thermal equilibrium of the sample during transitions. In these techniques one

measures the thermal diffusivity, rather than thermal conductivity. Thermal diffusivity

measurements do not suffer from heat losses from the sample during measurements and

hence are more accurate than a direct measurement of thermal conductivity by the steady

state method. With a proper choice of boundary conditions, photothermal techniques make

a simultaneous measurement of thermal diffusivity and thermal effusivity possible, from

which the thermal conductivity and specific heat capacity can be extracted. The

photopyroelectric technique has been used earlier to measure the variations of thermal

conductivity and heat capacity of a few crystalline solids as they undergo phase transitions

with temperature (Marinelli et al., 1990; Zammit et al., 1988; Mandelis et al., 1985).

3. The photopyroelectric technique

Complete characterization of the thermal properties of a material requires the determination

of the thermal transport properties such as the thermal conductivity as well as the specific

heat capacity. Techniques for high resolution measurement of specific heat capacity are well

established (Kasting et al., 1980; Thoen et al., 1982). It has been shown that photothermal

techniques allow simultaneous measurement of specific heat capacity c

and thermal

conductivity λ

(Marinelli et al., 1990). The photoacoustic technique has been used for the

simultaneous determination of the thermal diffusivity, thermal conductivity and heat

capacity of liquid-crystalline compounds (Zammit et al., 1988). A somewhat similar

technique has been used for measuring the thermal diffusivity and heat capacity of solids at

room temperature using a photopyroelectric (PPE) detector (Mandelis et al., 1985; John et al.,

1986). This technique enables simultaneous determination of thermal diffusivity, thermal

effusivity, thermal conductivity and heat capacity as a function of temperature. Moreover,

this technique allows studies of critical behaviours of thermal parameters when the material

undergoes a transition. Marinelli et al. (1990) developed a technique to determine thermal

diffusivity, thermal conductivity and heat capacity simultaneously at low temperatures with

a pyroelectric detector kept in vacuum. At temperatures above room temperature, the

boundary conditions involved in the theory of this method are not easy to satisfy, so that

application of the method can lead to errors in measurement.

A photothermal technique for the simultaneous determination of the thermal conductivity

and specific heat capacity near solid state phase transitions using a pyroelectric detector

kept in contact with a thermally thick backing medium has been developed by Menon &

Philip (2000). The PPE technique has some distinct advantages, such as its simplicity, good

sensitivity and ability to perform nondestructive probing, over other photothermal

methods. In this measurement the sample is heated by a modulated light source on one side

and the temperature oscillations on the opposite side of the sample are detected with a

Lallart M. (ed.) Ferroelectrics - Physical Effects

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