Open access peer-reviewed chapter

Hydrogen in Ferroelectrics

Written By

Hai-You Huang, Yan-Jing Su and Li-Jie Qiao

Submitted: March 17th, 2011 Reviewed: March 23rd, 2011 Published: August 23rd, 2011

DOI: 10.5772/17882

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1. Introduction

It is well known that the ferroelectric random access memories (FRAM) as one of the most important applications of ferroelectric thin film have attracted much attention. However, the introduction of hydrogen into ferroelectric materials may cause severe degradations in dielectric properties, ferroelectric properties, optical properties and mechanical properties. Ferroelectricity is the most important property of ferroelectrics and the researches on hydrogen in ferroelectrics begin just from the effects on ferroelectric properties. Ferroelectric thin film is often integrated with existing Si technology to fabricate reliable nonvolatile memories. In Si technology, a forming gas (hydrogen containing gas) anneal at about 400 °C needs to carry on tying up dangling bonds at the Si/SiO2 interface and reducing interface-trapped charges(Katz, 1988). Unfortunately, hydrogen could enter into ferroelectric thin film during annealing in forming gas and generates severe issue. For example, both Pb(Zr,Ti)O3 (PZT) and SrBi2Ta2O9 ferroelectric thin-film capacitors lose their polarization hysteresis characteristics as a result of such an anneal (Aggarwal et al., 1998; Shimanoto et al., 1997; Kushida-Abdelghafar et al., 1996; Han & Ma 1997).

Besides the ferroelectricity, ferroelectric materials also have been wildly applied due to other important properties. Because that many ferroelectric ceramics, such as PZT and BaTiO3, are excellent insulator against current, they are used to electric industry as capacitor. Hydrogen can increase leakage current and induce the insulator to a semiconductor (Huang et al., 2007 & Chen et al., 2011). Ferroelectric materials, especially its single crystals, have been widely used in optical devices because of its special optical properties such as photorefractive effect and nonlinear optical effect. Hydrogen can change the optical properties of ferroelectric materials (Wu et al., 2009). The mechanical property is another important property to sure ferroelectric devices could be used reliably. Hydrogen fissure (Peng et al., 2004) and hydrogen-induced delayed fracture (Huang et al., 2005; Zhang et al., 2008; Wang et al., 2003a, 2003b) could occur in some conditions.

This chapter reviews the effects of hydrogen on the properties of ferroelectric materials. This chapter is organized as follows: first of all, some background leading to the research interest of hydrogen in ferroelectric materials are introduced in section 1. In section 2 to 5, the effects of hydrogen on the ferroelectric properties (section 2), on the dielectric properties (section 3), on the optical properties (section 4) and on the mechanical properties (section 5) of ferroelectric materials are discussed in detail, respectively. In the end of this chapter, we conclude in section 6 where the important results of this research area are briefly summarized and outstanding problems and future directions are discussed.


2. Effects of hydrogen on ferroelectricity

2.1. Hydrogen reduces remanent polarization

In a ferroelectric material, there are lots of ferroelectric domains. The electric dipoles create by positive and negative bound charges in each domain are called spontaneous polarization vectors, which point to the positive poles of domains. Ferroelectric domain (polarization vector) can rotate 90 or 180° induced by applied force For electric field E, known as domain switching. When the applied electric field is large enough all polarization vectors of domains have the same direction with the field, resulting in saturation polarization Ps. When the flied is removed, i.e., E=0, the polarization does not back to zero, but equals to remanent polarization Pr, that means a hysteresis effect of polarization. The hysteresis loop can be measured by change the field, as shown in Figure 1 (Aggarwal et al., 1998 & Joo et al., 2002).

Figure 1.

Hydrogen charging causes hysteresis loop narrow and reduce the remanent polarization ((a)Aggarwal et al., 1998& (b)Joo et al., 2002)

Ferroelectric materials have piezoelectricity, which is the generation of polarization charges as a result of applied stress or strain. The electric displacement vector Dis proportional to the stress tensor Twith a coefficient d, piezoelectric constant tensor. For perovskite structure ferroelectric materials, such as BaTiO3 or PZT, piezoelectric constant tensor has only three independent components, d15=d24, d31 = d32, d33. Generally, d33 is used as the piezoelectric constant. Many experimental results have indicated that hydrogen caused a serious degradation of ferroelectric and dielectric properties of ferroelectric materials (Joo et al., 2002 ; Ikarashi, 1998 & Tamura et al., 1999). Charging of hydrogen could make the hysteresis loop narrow or disappear, i.e., make Pr decrease, as shown in Figure 1 (Aggarwal et al., 1998 & Joo et al., 2002). The hysteresis loops of PZT thin film capacitor with Pt electrode continuously narrowed after a annealing at 400 °C in a forming gas with 5% H2 for 3 to 20 min, as shown in Figure 1b (Joo et al., 2002). With the annealing temperature increasing, the hysteresis loops also gradually narrowed and became a straight line at 400 °C (Aggarwal et al., 1998).

Figure 2.

The effects of hydrogen on hysteresis loops (a) PZT & (b) PZNT (Wu et al., 2010)

Our work shows that both for PZT and PZNT (91%PZN+9%PT), when hydrogen concentration in ferroelectric material, Ct, introduced by electrolysis or annealing in hydrogen gas is less than a critical concentration, C* (for PZT, C*=10 ppm and for PZNT, C*=14 ppm), with the increase in hydrogen concentration, the hysteresis loop widens and Pr increases. However, when the hydrogen concentration is more than the critical value of C*, hysteresis loop narrows and Pr falls with the increase in hydrogen concentration, as shown in Figure 2 (Wu et al., 2010). The effects of hydrogen concentration on Pr and d33 are shown in Figure 3 (Wu et al., 2010). When Ct<C*, hydrogen can elevate both Pr and d33. If Ct>C*, Pr and d33 decrease sharply with the raise of Ct.

Figure 3.

The effects of hydrogen onPr andd33 (a) PZT & (b) PZNT (Wu et al., 2010)

2.2. Hydrogen-hindered ferroelectric phase transition

The polarization-voltage hysteresis loop of PZT film disappeared gradually after forming gas annealing above its Curie temperature, as shown in Fig.1. No hysteresis implies that it is a cubic paraelectricity. Therefore, it seems that hydrogen entered above its Curie temperature can hinder the phase transition of the PZT film from cubic paraelectricity to tetragonal ferroelectricity.

X-ray diffraction (XRD) and heating differential scanning calorimetry (DSC) patterns of PZT ceramics in different charging conditions are shown in Figures 4 a and 4b, respectively (Huang, et al., 2006). The appearance of double peaks in curves A, B, C, and E in Figure 4a corresponds to tetragonal phase and no double peaks in curve D corresponds to cubic phase. The ratios of c to a axis calculated based on curves A–E in Figure 4a were 1.0114, 1.0128, 1.0113, 1.0000, and 1.0077, respectively. The calculation of c/a also proves that curve D corresponds to cubic phase and the others correspond to tetragonal phase. Figure 4b indicates that there is an endothermic transition from tetragonal ferroelectricity to cubic paraelectricity at its Curie temperature of 300 °C for the samples uncharged and charged below the Curie temperature, as shown by curves A, B, and C in Figure 4 b. For the sample charged in H2 at 450 °C, however, there is no endothermic peak from 25 to 450 °C, as shown by curve D in Figure 4b. After outgassing at 800 °C, however, the endothermic peak appears again at the Curie temperature of 300 °C, as shown by curve E in Figure 4 b. These results indicate that the lattice parameters and the tetragonal structure of the PZT do not change after charging at the temperature below the Curie temperature. However, if the charging temperature is higher than the Curie temperature, the PZT will be a cubic paraelectricity instead of tetragonal ferroelectricity after cooling to room temperature. After outgassing at 800 °C, the tetragonal ferroelectricity is restored. Therefore, hydrogen charged above its Curie temperature can hinder the phase transition from cubic to tetragonal during cooling to room temperature.

First principles plane-wave pseudopotential density functional theory was applied to calculate the effect of hydrogen on the ferroelectric phase transition in perovskite structure ferroelectricity based on energy calculation method. A hydrogen atom was put into the perovskite-type unit of cubic and tetragonal PbTiO3 and then its possible locations were looked for. Figure 5a is a tetragonal PbTiO3 with one H in the unit cell and A, B, and C are three possible sites H occupied. Calculation showed that the minimum values of total energies corresponding to site A at (0.5, 0.25, 0.05), tetrahedral interstitial site B at (0.25, 0.25, 0.25), and site C between Ti and apical O(1) ion at (0.5, 0.5, 0.25) were -4601.73, -4601.04, and -4600.15 eV, respectively. When hydrogen occupied site A, B, or C, the distances between H and O(1) were 0.1016 nm, 0.1485 nm, and 0.1529 nm, respectively. Hydrogen should occupy site A, the total energy is the lowest and the distance between H and O(1) has a smallest value, compared to sites B and C, which are the possible sites proposed by Aggarwal et al.( Aggarwal et al., 1998) The distance 0.1016 nm means that a strong interaction between H and O(1) exists, which can result in the overlap of the electronic clouds between H and O(1), as shown in Figure 5b. The calculation is consistent with the experimental results (Aggarwal et al., 1998 & Joo et al., 2002), i.e., existing O–H bonds in PZT ceramics. Calculation showed that the electron overlap populations between O–Ti were 0.98 for hydrogen-free PbTiO3 and 0.70 for hydrogenated PbTiO3, respectively. Hydrogen decreases the electron overlap population between O–Ti means that hydrogen weakens the interaction between O–Ti. It has been pointed out that the stronger the hybridization between the two atoms, the larger tendency to form bond or interaction between two atoms. Therefore, hydrogen decreases the overlap population between O–Ti and weakens the hybridization between O–Ti, resulting in the decrease of stability of tetragonal ferroelectric phase.

Figure 4.

XRD (a) and DSC (b) patterns of PZT-5H in different charging conditions A, hydrogen-free; B, charging at 400 mA/cm2 in solution at 20℃; C, charging in H2 at 250℃; D, charging in H2 withPH2=0.4 MPb at 450 ℃; E, outgassing at 800℃ after charging in H2 at 450℃ (Huang, et al., 2006)

Figure 5.

Unit cell of tetragonal PbTiO3 containing one hydrogen atom (a), and electronic clouds of XOY plane (b) (Huang, et al., 2006)

The variation of the total energy with the displacement of Ti along the c axis for hydrogen-free and hydrogenated PbTiO3 is shown in Figure 6. Figure 6a indicates that for hydrogen-free PbTiO3 with the tetragonal structure, there are two lowest energy sites for Ti in the c axis which are ±0.016 nm from the center of the unit cell. The calculation result is consistent with the experimental value of ±0.017 nm. Figure 6b, however, shows that for the hydrogenated tetragonal structure, the double-lowest-energy sites of Ti along the c axis disappear and the lowest energy site located at the center of the cell. Therefore, when hydrogen enters into the cubic PbTiO3 above its Curie temperature, the cubic structure continues to be a stable structure during cooling because for Ti there is no lower energy site than the center of the cell. As a result, ferroelectric tetragonal structure in PbTiO3 charged above the Curie temperature will not appear during cooling to room temperature because of no displacement of Ti along the c axis. The calculation can explain the experiment that hydrogen charged above its Curie temperature will hinder phase transition of PZT from cubic paraelectricity to tetragonal ferroelectricity.

Figure 4, however, also indicates that PZT keeps a tetragonal structure after charging at the temperature below the Curie temperature. The reason is the existence of energy barrier from tetragonal to cubic which composed of elastic energy, depoling energy, and static electric energy. Besides the insufficient thermal energy, hydrogen entered into tetragonal PZT during charging below the Curie temperature cannot provide an additive energy to overcome the energy barrier, and then the tetragonal structure cannot transform to cubic structure during charging below the Curie temperature.

Figure 6.

Total energy vs. displacement of Ti along c axis, the original is the centre of the cell (a) hydrogen-free PbTiO3, (b) hydrogenated PbTiO3 (Huang, et al., 2006)


3. Hydrogen induced semiconductor transformation of ferroelectrics

Ferroelectric or piezoelectric ceramics, such as PZT, is an insulator. However, after annealing in a forming gas containing H2 or electrode plating process, hydrogen can enter into the ceramics and makes its resistivity from 1012-1013 Ω cm down to 106-107Ω cm sharply, resulting in becoming a semiconductor (Han & Ma, 1997). The resistivity and capacitance of multilayer ferroelectric ceramic capacitors degrade to a semiconductor and the dielectric loss increases after hydrogen charging in NaOH (Chen et al., 1998). Figure 7a illustrates the leakage current in PZT ceramics increased sharply after electrolysis or hydrogen gas charging. The semiconductorization of ferroelectric ceramics by hydrogen can be restored by outgassing. For example, after outgassing of hydrogen at a temperature higher than 400 °C, the hydrogenated PZT restores an insulator, as shown in Figure 7b (Huang et al., 2007). A very few hydrogen can lower the resistivity of PZT from 1013 Ω cm to 108 Ω cm. carrier concentration increases rapidly with the raise of hydrogen concentration (Huang et al., 2007). Hall effect measurements show that PZT ceramics change into n-type semiconductor after hydrogen charging (Huang et al., 2007).

Figure 7.

The effects of hydrogen charging (a) and outgassing (b) on the leakage current in PZT (Huang et al., 2007)

The first principles calculation was applied to investigate the effect of hydrogen on the conductivity of ferroelectric materials. The variations of density of states of every atom in PZT with energy difference E-EF (EF is Fermi energy) were calculated (Wu, 2009). If not hydrogen, the total density of states of all atoms in PZT vs E-EF, as shown in Figure 8a, where AB is the valence band, BC is the forbidden band and CD is the empty band. If the hydrogen concentration CH=1536 wppm, the whole curve move to low energy (left) after hydrogen charging, so that the energy of parts of the empty band is less than the Fermi energy and becomes the bottom of conduction band, which was filled by electrons mainly from H 1S (Ti, Pb, Zr also contribute them free electrons). As a result, the forbidden band does no longer exist and the material becomes a conductor, as shown in Figure 8b. When CH reduces to 770 wppm, the energy of parts of the empty band is still below the Fermi energy and it is still a conductor, as shown in Figure 8c. When CH=96 wppm, all empty band higher than the EF, so there is a narrow band gap that means the material becomes a semiconductor, as shown in Figure 8d. For PZT, no matter what method of hydrogen charging was applied, saturation hydrogen concentration is less than 96 wppm. Thus, it is impossible to make PZT to a conductor by hydrogen charging, but hydrogen can make PZT into a semiconductor.

Figure 8.

Density of states for PZT with differentCH (Wu, 2009)

Why hydrogen charging make the PZT into a semiconductor from an insulator. One view is that H can react with O2- to form H2O and oxygen vacancy with two electrons V(2e) (Chen et al., 1998), i.e.,


The two electrons of oxygen vacancy can ionize and induce insulating ferroelectric ceramic to be semiconductor. However, because H2O molecule is too large to locate in the lattice, the reaction (Eq. 1.) can only occur on the surface of ferroelectric ceramic and make the reaction to continue through migration of O2- to the surface. Nevertheless, the diffusion coefficient of O is very small in the ceramics at room temperature (in BaTiO3 at room temperature DO=1.1×10-15 cm2/s) (Huang et al., 2007). Considering hydrogen charging for 45h at room temperature, the maximum diffusion distance is only 0.53 μm. However, the experimental value of transition distance is up to 0.9 mm (see Figure 9), which is 103 times as large as the calculative maximum diffusion distance of O (Huang et al., 2007). Another view is that a part of PbO reduced to Pb by H, i.e., (Han & Ma, 1997)


A small amount of Pb can become the ceramics into the semiconductor. For the same reason, the reaction can’t be achieved kinetically. Figure 8 shows that 1S electron of H can across the band gap and into conduction band, such as if CH>96 ppm, the electrons in the bottom of conduction band (mainly from H 1S) to become a conductor. In fact, the CH<96 ppm, so the hydrogen charging is impossible to make PZT be a conductor. However, the density of states of hydrogenated ferroelectric ceramics moves to left and narrows the band gap to a lever of semiconductor. 1S electron of H can be as free electron and degrade the electrical resistivity drastically.


4. Effects of hydrogen on optical properties

After hydrogen charging, the color of PZT became black (Chen et al., 1998 & Joo et al. 2002). Beside PZT, for BaTiO3 single crystals, the color became darker and is absent transparent after hydrogen charging, as shown in Figure 9. (Huang et al. 2007 & Wu et al. 2009). The darker color means more visible light are absorbed. The experiments show that the absorption coefficient of PZT and BaTiO3 within visible region significantly heighten after hydrogen charging, as shown in Figure 10 (Wu et al. 2009).

The phenomena of hydrogen changing the color of PZT can be used to measure the diffusion coefficient of hydrogen in PZT. 0.9 mm-thick PZT sample was charged of hydrogen from single side for 2.5h, 10h, 20h and 45h. The cross section of hydrogenated sample was shown in Figure 11a, and the average diffusion distance of hydrogen xfor different charging time tcan be measured, as shown in Figure 11b. Based on the linear relationship between xand t1/2, i.e., x=4Dt, the diffusion coefficient of hydrogen in PZT D=4.9×10-8 cm2/s at room temperature can be obtained (Huang et al. 2007 ).

Figure 9.

The color changes of PZT (upper) and BaTiO3 (lower) before and after hydrogen charging (a) before hydrogen charging, (b) electrolytically charged, (c) charged in H2 gas, (d) outgassing after charging (Huang et al. 2007&Wu et al. 2009)

Figure 10.

Hydrogen increases the absorption coefficient within visible region (a)PZT & (b)BaTiO3 (Wu et al. 2009)

Figure 11.

Diffusion of hydrogen in PZT ceramics (a) color change and (b) diffusion distance at different time (Huang et al. 2007)


5. Hydrogen induced cracking

5.1. Hydrogen fissure in PZT ferroelectric ceramics without loading

Three groups of PZT ferroelectric ceramics were used to investigate hydrogen fissure without any loading. The group I samples were polarized by a high electric field (30kV/cm) at room temperature and a large internal stress was induced. The group II samples were polarized at high temperature (400 ˚C, higher than the Curie point) by a small electric field (2kV/cm), and then furnace cooled to room temperature, in which there was little internal stress. The third group of samples was not polarized. We called the three groups of samples as HP, SP and UP samples, respectively. Hydrogen charging was carried out for all samples in a 0.2mol/l NaOH +0.25 g/l As2O3 solution with various current densities i. For the HP samples, appeared four discontinuous microcracks like a, b, c and d appeared on the surface after hydrogen charging with i=5 mA/cm2 for 4h, as shown in Figure 12 (Peng et al., 2004). These microcracks initiated and grew along the grain boundaries. Experiment showed that no hydrogen fissure was found after charging for 48h when i=0.05 mA/cm2, but when i≥0.5mA/cm2, after a certain incubation period, hydrogen fissure can form. However, for SP samples and UP samples, when i≤300 mA/cm2, on hydrogen fissure formed for 48 h. hydrogen fissure appeared until i=400 mA/cm2, as shown in Table 1 (Peng et al., 2004). In order to measure hydrogen concentration CH, some samples were charged for 100 h with various current densities, and then put into a glass tube filled with silicon oil. The CH can be calculated by Eq. 3. based on the saturation volume of hydrogen V(cm3).


where n(g)=PV/RT=V(cm3)/82.06T(K) is the molar number of hydrogen under 1 atm, m(g) is the weight of the sample and T(K) is temperature. The values of CH corresponding to various iwere also listed in Table 1.

Figure 12.

Hydrogen fissure after charging at 5 mA/cm2 for 4 h; a to d are fissures, and A and B are marks for location (Peng et al., 2004)

i, mA/cm20.050.5550300400
CH, wppm0.922.614.87.169.8410.3
HP samplesnoyesyesyesyes--
SP samplesnononononoyes
UP samplesnononononoyes

Table 1.

Hydrogen concentration and fissure appearance corresponding to various charging current densities (Peng et al., 2004)

There are many cavities and microholes in the grain boundary of sintered PZT ceramics. During hydrogen charging H atoms enter into the holes and generate H2, which can induce an internal pressure P. When the hydrogen pressure is large enough, the normal stress on the holes wall P/2 equals to the cohesive strength σth(H) at grain boundary, which has been reduced by atomic hydrogen, hydrogen fissure or microcrack will form. If there is a extra internal stress σi, the critical hydrogen pressure for cracking can be decreased from P=2σth(H) to P*=2σth(H)-σi. Because there is a large internal stress in HP sample, which can promote crack nucleation, so hydrogen fissure appear when i=0.5mA/cm2. The microcracks are found in SP and UP samples only when i=400 mA/cm2 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 KIC according to Eq. 4.


where Pis the load, dis diagonal length of the indentation and lis 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), KIH, by Eq.4. New indentations were carried out on the surface of hydrogenated samples. The fracture toughness for hydrogenated sample KIC(H) can also be obtained. The experiments indicated that both KIH/KIC and KIC(H)/KIC decreased linearly with the increasing CH, as shown in Figure 13 (Zhang et al., 2008).

Figure 13.

Hydrogen concentration dependence of the relative fracture toughness of charged samples,KIH/KIC, and of the normalized threshold stress intensity factor of hydrogen-induced cracking induced by residual stress,KIC(H)/KIC (Zhang et al., 2008)

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, KIC(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.

Figure 14.

The normalized fracture toughnessKIC(H,t)/KIC 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 As2O3 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 CH under different charging current densities is given in Table 2. The curve of KIH/KIC vs ior CH can plot based on Table 2 and one can find a linear relationship between KIH/KIC and the lnCH (Wang et al., 2003b)


where superscript a and b denote polarization vector parallel and perpendicular to the crack plane, respectively. KICa=1.53 MPam1/2 and KICb=1.12 MPam1/2 for PZT ferroelectric

CH( ppm)0.922.614.87.169.84

Table 2.

The threshold stress intensity factors of HIDC corresponding to various hydrogen concentrations (Wang et al., 2003b)

Figure 15.

The normalized stress intensity factor vs time to fracture during dynamically charging with variousi(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)

ceramics. Eq. 5. suggests that the tanisotropy of KIH 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.



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.


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Written By

Hai-You Huang, Yan-Jing Su and Li-Jie Qiao

Submitted: March 17th, 2011 Reviewed: March 23rd, 2011 Published: August 23rd, 2011