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Piezoelectricity in Lead-Zirconate-Titanate Ceramics – Extrinsic and Intrinsic Contributions 19

Frantti, J.; Fujioka, Y. & Nieminen, R. M. (2007). Pressure-Induced Phase Transitions in PbTiO

A Query for the Polarization Rotation Theory. J. Phys. Chem. B, Vol. 111, No. 17,

4287-4290.

Frantti, J.; Fujioka, Y. & Nieminen, R. M. (2008). Evidence against the polarization rotation

model of piezoelectric perovskites at the morphotropic phase boundary. J. Phys.:

Condens. Matter, Vol. 20, No. 47, 472203-472207.

Frantti, J. (2008). Notes of the Recent Structural Studies on Lead Zirconate Titanate. J. Phys.

Chem. B, Vol. 112, No. 21, 6521-6535.

Frantti, J.; Fujioka, Y.; Zhang, J.; Vogel, S. C.; Wang, Y.; Zhao, Y. & Nieminen, R. M. (2009).

The Factors Behind the Morphotropic Phase Boundary in Piezoelectric Perovskites.

J. Phys. Chem. B, Vol. 113, No. 23, 7967-7972.

Fu, H. & Cohen, R. E. (2000). Polarization rotation mechanism for ultrahigh electromechanical

response in single-crystal piezoelectrics. Nature Letters, Vol. 403, 281-283.

Glazer, A. M.; Thomas, P. A.; Baba-Kiski, K. Z.; Pang, G. K. H. & Tai, C. W. (2004). Inﬂuence

of short-range and long-range order on the evolution of the morphotropic phase

boundary in Pb(Zr

1−x

. (2004). Phys. Rev. B, Vol. 70, 184123.

Grigoriev, A.; Sichel, R.; Lee, H. N., Landahl, E. C.; Adams, B.; Dufresne, E. M. & Evans, P. G.

(2008). Nonlinear Piezoelectricity in Epitaxial Ferroelectrics at High Electric Fields.

Phys.Rev.Lett., Vol. 100, 027604.

Grigoriev, A.; Sichel, R. J.; Jo, J. Y.; Choudhury, S.; Chen, L-Q.; Lee, H. N.; Landahl, E. C.;

Adams, B. W.; Dufresne, E. M. & Evans, P. G. (2009). Stability of the unswitched

polarization state of ultrathin epitaxial Pb(Zr, Ti)O

in large ﬁelds. Phys. Rev. B,Vol.

80, 014110.

Hahn, Th. & Klapper, H. (2003). Twinning of Crystals, In: International Tables for Crystallography

D: Physical Properties of Crystals, A. Authier, (Ed.), 393-448, Kluwer Academic

Publishers, ISBN 1-4020-0714-0, Dordrecht.

Hahn, Th. & Klapper, H. (2005). International Tables for Crystallography A: Space-group Symmetry,

Th. Hahn, (Ed.), Kluwer Academic Publishers, ISBN 0-7923-6590-9, Dordrecht.

Hinterstein, M.; Hoelzel, M.; Kungl, H.; Hoffmann, M. J.; Ehrenberg, H. & Fuess, H. (2011).

In situ neutron diffraction study of electric ﬁeld induced structural transitions in

lanthanum doped lead zirconate titanate. Zeitschrift Fur Kristallographie, Vol. 226,

155-162.

Hoffmann, M. J. & Kungl, H. (2004). High strain lead-based perovskite ferroelectrics. Current

Opinion in Solid State and Materials Science, Vol. 8, 51-57.

Hsu, R.; Maslen, E. N.; Du Boulay, D. & Ishizawa, N. (1997). Synchrotron X-ray Studies of

LiNbO

and LiTaO

. Acta Cryst. B, Vol. 53, 420-428.

Jaffe, B.; Cook, W. R. & Jaffe, H. (1971). Piezoelectric Ceramics, Academic Press, ISBN

0123795508, New York.

Janolin, P.-E. (2009). Strain on ferroelectric thin ﬁlms. J. Mater. Sci., Vol., 44, 5025-5048.

Kano, J.; Tsukada, S.; Zhang, F.; Karaki, T.; Adachi, M. & Kojima, S. (2007). Characterization

of Dielectric Property of Nanosized (Pb

0.7

0.3

)TiO

Powders Studied by Raman

Scattering. Jpn. J. Appl. Phys., Vol. 46, No. 10B, 7148-7150.

Kittel, C. (1946). Theory of the Structure of Ferromagnetic Domains in Films and Small

Particles. Phys. Rev., Vol. 70, 965-971.

239

Piezoelectricity in Lead-Zirconate-Titanate Ceramics – Extrinsic and Intrinsic Contributions

20 Will-be-set-by-IN-TECH

Klapper, H & Hahn, Th. (2005). Point-group Symmetry and Physical Properties of Crystals,

In: International Tables for Crystallography A: Space-group Symmetry, Th. Hahn, (Ed.),

804-808, Kluwer Academic Publishers, ISBN 0-7923-6590-9, Dordrecht.

Koch, E. (2004). Twinning, In: International Tables for Crystallography C: Mathematical, Physical

and Chemical Tables, E. Prince, (Ed.), 10-14, Kluwer Academic Publishers, ISBN

1-4020-1900-9, Dordrecht.

Kolasinski, K. W. (2008). Surface Science: Foundations of Catalysis and Nanoscience, John Wiley &

Sons Ltd, ISBN 978-0-470-03308-1, West Sussex, England.

Kozielski, L; Buixaderas, E.; Clemens, F. & Bujakiewicz-Korónska. (2010). PZT Microﬁbre

defect structure studied by Raman spectroscopy. J. Phys. D: Appl. Phys., Vol. 43,

415401.

Jones, J. L.; Hoffman, M.; Daniels, J. E. & Studer, A. J. (2006). Direct measurement of the

domain switching contribution to the dynamic piezoelectric response in ferroelectric

ceramics. Appl. Phys. Lett., Vol. 89, No. 9, 092901.

Landauer, R. (1957). Electrostatic Considerations in BaTiO

Domain Formation During

Polarization Reversal. J. Appl. Phys., Vol. 28, 227-234.

Li, J. Y.; Rogan, R. C.; Üstündag, E. & Bhattacharya, K. (2005). Domain switching in

polycrystalline ferroelectric ceramics. Nature Materials, Vol. 4, 776-781.

Lines, M. E. & Glass, A. M. (2001). Principles and Applications of Ferroelectrics and Related

Materials, Oxford University Press in Oxford Classic Series, ISBN 0-19-850778-X,

Oxford.

Liu, Y. Y.; Zhu, Z. X.; Li, J.-F. & Li, J. Y. (2010). Misﬁt strain modulated phase structures

of epitaxial Pb(Zr

1−x

thin ﬁlms: The effect of substrate and ﬁlm thickness.

Mechanics of Materials, Vol. 42, 816-826.

Lüth, H. (2001). Solid Surfaces, Interfaces and Thin Films, Springer-Verlag, ISBN 3-540-58576-1,

Berlin, Heidelberg.

Mitsui, T. & Furuichi, J. (1953). Domain Structure of Rochelle Salt and KH

. Phys. Rev.,Vol.

90, 193-202.

Newnham, R. E. (2005). Properties of Materials: Anisotropy, Symmetry, Structure,Oxford

University Press, ISBN 0-19-852076-X, New York.

Nishida, K.; Osada, M.; Wada, S.; Okamoto, S.; Ueno, R.; Funakubo, H. & Katoda, T. (2005).

Raman Spectroscopic Characterization of Tetragonal PbZr

1−x

Thin Films: A

Rapid Evaluation Method for c-Domain Volume. Jpn. J. Appl. Phys., Vol. 25, No. 25,

L827-L829.

Noheda, B.; Cox, D. E.; Shirane, G.; Gonzalo, J. A.; Cross, L. E. & Park, S.-E. (1999). A

monoclinic ferroelectric phase in the Pb(Zr

1−x

solid solution. Appl. Phys. Lett.,

Vol. 74, 2059-2061.

Noheda, B.; Gonzalo, J. A.; Cross, L. E.; Guo, R.; Park, S.-E.; Cox, D. E. & Shirane, G. (2000).

Tetragonal-to-monoclinic phase transition in a ferroelectric perovskite: The structure

of PbZr

0.52

0.48

. Phys. Rev. B, Vol. 61, 8687-8695.

Nye, J. F. (1995). Physical Properties of Crystals, Oxford University Press, ISBN 0-19-851165-5,

New York.

Ohno, T.; Matsuda, T.; Ishikawa, K. & Suzuki, H. (2006). Thickness Dependence of

Residual Stress in Alkoxide-DerivedPb(Zr

0.3

0.7

Thin Film by Chemical Solution

Deposition. Jpn. J. Appl. Phys., Vol. 45, No. 9B, 7265-7269.

240

Ferroelectrics – Physical Effects

Piezoelectricity in Lead-Zirconate-Titanate Ceramics – Extrinsic and Intrinsic Contributions 21

Olsen, R. B. & Evans, D. (1983). Pyroelectric energy conversion: Hysteresis loss and

temperature sensitivity of a ferroelectric materials. J. Appl. Phys., Vol. 54, 5941-5944.

Pane, I.; Fleck, N. A.; Huber, J. E. & Chu, D. P. (2008). Effect of geometry upon the performance

of a thin ﬁlm ferroelectric capacitor. International Journal of Solids and Structures,Vol

45, 2024-2041.

Pertsev, N. A. & Zembilgotov, A. G. (1995). Energetics and geometry of 90

◦

domain structures

in epitaxial ferroelectric and ferroelastic ﬁlms. J. Appl. Phys., Vol. 78, 6170-6180.

Phelan, D.; Long, X.; Xie, Y.; Ye, Z.-G.; Glazer, A. M.; Yokota, H.; Thomas, P. A. & Gehring, P.

M. (2010). Single Crystal Study of Competing Rhombohedral and Monoclinic Order

in Lead Zirconate Titanate. Phys.Rev.Lett., Vol. 105, 207601.

Phillips, R. B. (2001). Crystals, Defects and Microstructures: Modeling Across Scales,Cambridge

University Press, ISBN 0-521-79357-2, Cambridge.

Pramanick, A.; Damjanovic, D.; Nino, J. C. & Jones, J. (2009). Subcoercive Cyclic Electrical

Loading of Lead Zirconate Titanate Ceramics I: Nonlinearities and Losses in the

Converse Piezoelectric Effect. J. Am. Ceram. Soc., Vol. 92, No. 10, 2291-2299.

Pramanick, A.; Daniels, J. E. & Jones, J. (2009). Subcoercive Cyclic Electrical Loading of Lead

Zirconate Titanate Ceramics II: Time-resolved X-ray Diffraction. J. Am. Ceram. Soc.,

Vol. 92, No. 10, 2300-2310.

Pruvost, S.; Hajjaji, A.; Lebrun, L.; Guyomar, D. & Boughaleb, Y. (2010). Domain switching

and Energy Harvesting Capabilities in Ferroelectric Materials. J. Phys. Chem. C,Vol.

114, 20629-20635.

Ricote, J.; Corker, D. L.; Whatmore, R. W.; Impey, S. A.; Glazer, A. M.; Dec, J. & Roleder,

K. (1998). A TEM and neutron diffraction study of the local structure in the

rhombohedral phase of lead zirconate titanate. J. Phys.: Condens. Matter, Vol. 10,

1767-1786.

Rogan, R. C.; Üstündag, E.; Clausen, B. & Daymond M. R. (2003). Texture and strain analysis

of the ferroelastic behavior of Pb(Zr,Ti)O

by in situ neutron diffraction. J. Appl. Phys.,

Vol. 93, No. 7, 4104-4111.

Roitburd, A. L. (1976). Equilibrium Structure of Epitaxial Layers. Phys. Status Solidi A,Vol.37,

329-339.

Schilling, A.; Adams, T. B.; Bowman, R. M.; Gregg, J. M.; Catalan, G. & Scott, J. F. (2006).

Scaling of domain periodicity with thickness measured in BaTiO

single crystal

lamellae and comparison with other ferroics. Phys. Rev. B, Vol. 74, 024115.

Sergienko, I. A.; Gufan, Y. M. & Urazhdin, S. (2002). Phys. Rev. B, Vol. 65, 144104.

SouzaFilho,A.G.;Lima,K.C.V.;Ayala,A.P.;Guedes,I.;Freire,P.T.C.;Melo,F.E.A.,

Mendes Filho, J.; Araújo, E. B. & Eiras, J. A. (2002). Raman scattering study of the

PbZr

1−x

system: Rhombohedral-monoclinic-tetragonal phase transitions. Phys.

Rev. B, Vol. 66, 132107.

Streiffer,S.K.;Eastman,J.A.;Fong,D.D.;Thompson,C.;Munkholm,A.;RamanaMurty,M.V.;

Auciello, O.; Bai, G. R. and Stephenson, G. B. (2002). Observation of Nanoscale 180

◦

Stripe Domains in Ferroelectric PbTiO

Thin Films. Phys. Rev. Lett., Vol. 89, 067601.

Strukov, B. A. & Levanyuk, A. P. (1998). Ferroelectric Phenomena in Crystals: Physical

Foundations, Springer-Verlag, ISBN 3-540-63132-1, Berlin.

241

Piezoelectricity in Lead-Zirconate-Titanate Ceramics – Extrinsic and Intrinsic Contributions

22 Will-be-set-by-IN-TECH

Thomas, N. W. & Beitollahi, A. (1994). Inter-Relationship of Octahedral Geometry, Polyhedral

Volume Ratio and Ferroelectric Properties in Rhombohedral Perovskites. Acta Cryst.

B, Vol. 50, 549-560.

Topolov, V. Y. & Turik, A. V. (2001). A new monoclinic phase and features of stress relief in

PbZr

1−x

solid solutions. J. Phys. Condens. Matter, Vol. 13, L771-L775.

Yakunin, S. I.; Shakmanov, V. V.; Spivak, G. V. & Vasiléva, N. V. (1972). Microstructure of

domains and domain boundaries of BaTiO

single crystalline ﬁlms. Fiz. Tverd. Tela,

Vol. 14, 373-377, Sov. Phys. Solid State (English Transl.), Vol. 14, 310.

H. Yokota, N. Zhang, A. E. Taylor, P. Thomas, and A. M. Glazer (2009). Crystal structure of

the rhombohedral phase of PbZr

1−x

ceramics at room temperature Phys. Rev.

B, Vol. 80, 104109.

Wu, X. & Vanderbilt, D. (2006). Theory of hypothetical ferroelectric superlattices incorporating

head-to-head and tail-to-tail 180

◦

domain walls. Phys.Rev.B, Vol. 73, 020103.

Xu, G.; Wen, J.; Stock , C. & Gehring, P. M. (2008). Phase instability induced by polar

nanoregions in a relaxor ferroelectric system. Nature Materials, Vol. 7, 562-566.

242

Ferroelectrics – Physical Effects

B-site Multi-element Doping Effect on Electrical

Property of Bismuth Titanate Ceramics

Jungang Hou

and R. V. Kumar

School of Metallurgical and Ecological Engineering, University of Science and Technology

Department of Materials Science and Metallurgy, University of Cambridge

China

United Kingdom

1. Introduction

This article represents a systematic review of the behaviour of B-site multi-element doping

effect on electrical property of bismuth titanate ceramics. Bismuth titanate, Bi

(BIT) is

a potential candidate for high-temperature device applications due to their high dielectric

constant, Curie temperature (T

), breakdown strength, anisotropy and, low dielectric

dissipation factor, therefore attracting considerable commercial interest in applications such

as high temperature piezoelectric devices, memory storage and optical displays. These

features make bismuth layer-structured ferroelectrics (BLSFs) attractive in the field of

developing lead-free piezoelectric materials. BIT is a well-known member of the BLSFs,

which can be represented by a general formula (Bi

)

m-1

3m+1

)

, where A represents

a mono-, di, or trivalent ion, such as La

, Nd

, Pr

, Sm

, etc., B stands for transition-metal

cations like Ti

, Nb

, Ta

, W

, etc., and m is the number of BO

octahedra in the

perovskite-like layer (m=1-5) (Aurivillius, 1949; Kumar, 2001; Markovec, 2001; Nagata, 1999;

Noguchi, 2000; Sugibuchi, 1975; Shimakawa, 2000; Subbarao, 1961; Shulman, 2000; Shimazu,

1980l; Takenaka, 1981). The layer structure of Bi

(m=3) consists of three perovskite-

like (Bi

)

units with a pseudo-perovskite layer structure, sandwiched between

(Bi

)

layers along its crystallographic c axis. In the (Bi

)

units, Ti ions are enclosed

by oxygen octahedra, and Bi ions occupy the spaces in the framework of octahedral

(Subbarao, 1950).

BIT

is of interest in high-temperature piezoelectric sensors, because it remains ferroelectric

up to 675 °C and offers relatively high piezoelectric property (Subbarao, 1961). However, the

high leakage current and domain pinning due to defects in BIT

have appeared as obstacles

for further applications. The reasons for such problems are suggested due to the instability

in the oxidation state of Ti ions and the volatile property of Bi during the sintering process

(Nagata, 1999). Great efforts have been made to solve the high-leakage current, by

incorporation of W, Nb or Ta dopants, as these can significantly decrease the conductivity in

BIT (Hong, 2000; Markovec, 2001; Shulman, 1999; Takenaka, 1981; Villegas, 1999; Zhang,

2004). Unfortunately, the piezoelectric effect in the high Curie temperature BIT is relatively

low, with coefficient values typically less than 20 pC N

-1

found for both pure and modified

. Thus, it is a challenge to seek a rational pathway to improve the electrical property

of BIT ceramics.

Ferroelectrics – Physical Effects

244

We have reported in our publications, the effects of composition and crystal lattice structure

upon microstructure, dielectric, piezoelectric and electrical properties of BIT, Bi

12+x

+0.2wt%Cr

(BTWC), Bi

3-2x

(BTNT) and Bi

3-2x

x-y

(BTNTS)

ceramics have been widely investigated (Hou et al, 2009, 2010 and 2011). The

processing of as-synthesized BIT were optimized and the main parameters were

determined, and confirmed that the piezoelectric coefficient (d

) of undoped BIT is 8 pC N

-1

As for BTWC, the results have shown the systematic changes in the lattice parameters; the

formation of secondary phase(s) at higher levels of W/Cr doping; and the increase in

dielectric constant and loss at room temperature with increase of doping content. A higher

value of d

, at 22 pC N

-1

, was obtained for the sample with x=0.025, which may result

directly from lowering conductivity. With regard to BTNT and BTNTS, the results have

shown the formation of orthorhombic structure for all the samples within these family of

dopants; the addition of Nb/Ta caused a remarkably suppressed grain growth while there is

not much difference in grain size for BTNTS; as the doping content was increased, the Curie

temperatures of BTNT decreased significantly, to as low as 630

C while the difference is not

very significant for BTNTS. The co-doping at B-site could induce the distortion of oxygen

octahedral and reduce the oxygen vacancy concentration, resulting in the enhancement of

. Especially, the highest values of 26 and 35pC N

-1

, were obtained for

2.98

0.01

and Bi

2.98

0.01

0.002

0.008

, respectively. The activation energy

associated with the electrical relaxation and DC conductivity were determined from the

electric modulus spectra, suggesting the movements of oxygen ions are possible for both

ionic conductivity as well as the relaxation process. To ascertain the electrical conduction

mechanism in the ceramics, various physical models have been proposed, suggesting the

conductivity behavior of the ceramics can be explained using correlated barrier hopping

model. All measurements demonstrated that BTNT ceramics are promising candidates for

high temperature applications.

2. W/Cr modified Bi

ceramics

Bismuth titanate, Bi

(BIT) is a potential candidate for high-temperature device

applications due to their high Curie temperature (T

) and an excellent fatigue endurance

property. However, the piezoelectricity of pure BIT ceramics is relatively very low (d

< 8

pC N

-1

). The piezoelectric properties can be enhanced by grain orientation techniques.

However these methods are not cost effective. So, it is favourable to optimize piezoelectric

properties via structural modification using appropriate doping. In this connection, to

improve the piezoelectric properties of BIT, ions substitution with other cations have been

considered and explored. It has been shown that doping with donor cations such as Nb

or Ta

in the Ti

positions decreases electrical conductivity and improves piezoelectric

properties of BIT ceramics (Du, 2009; Shulman, 1999; Tang, 2007). Cr doping is another one

of the most adopted strategies to tailor the dielectric and piezoelectric properties of

ferroelectrics to practical specifications. It is well known that Cr is effective in decreasing the

aging effect and decreasing dielectric loss thus the effect of doping of Cr

is that of stabilizer

of piezoelectric and dielectric properties (Li, 2008; Yang, 2007). The density of ceramics can

be increased using small amount of Cr

. However, large content of Cr

will inhibit

grain growth because of accumulation of Cr

at the grain boundary, which results in

decrease in the grain size (Hou et al, 2005; Takahashi, 1970).

B-site Multi-element Doping Effect on Electrical Property of Bismuth Titanate Ceramics

245

It is noted that the studies concerning the effect of W

doping on electrical and sintering

behavior have been reported earlier (Jardiel, 2006, 2008; Villegas, 2004). However reports on

W/Cr doped BIT ceramics are scarce. We have made an attempt to optimize the W/Cr

doping to yield enhanced piezoelectric and dielectric properties of BIT ceramics. The

influence of W/Cr doping on the structural, sintering behavior, dielectric, electrical

conductivity and piezoelectric properties of BIT ceramics is reported in this section.

Fig. 1 (A) shows the X-ray diffraction patterns of BITWC ceramics at room temperature.

Diffraction data does not show any evidence of the formation of tungsten and chromium

oxide or associated compounds that contain bismuth or titanium. Therefore, the BITWC

ceramics maintains a layer structure similar to the perovskite BIT even under extensive

modifications by W

/Cr

Fig. 1. (A) XRD patterns of BITWC with different W/Cr content: (a) 0.0, (b) 0.025, (c) 0.05,

(d) 0.075, (e) 0.10 and (f) 0.15. (B)Evolution of XRD patterns associated with the peaks of

(020)/(200) and (220)/(1115) of BITWC powders with different W/Cr content.

Fig. 2. Variation in lattice parameters of BITWC powders calcined at 800 °C for 4 h vs.

different amount of W/Cr doping.

Ferroelectrics – Physical Effects

246

Fig. 3. SEM images of polished and thermal etched surfaces of various samples: (a) 0.025, (b)

0.05, (c) 0.075, (d) 0.10 and (e) 0.15. Scale represented in the figures is 3 μm.

Evolution of XRD patterns associated with the peaks of (020)/(200) and (220)/(1115) of

BITWC with different W/Cr content are shown in Fig. 1 (B). For sample with 0.025W/Cr,

the (020) diffraction pattern at 2θ=33° is clearly split into two (020) and (200) peaks in the

orthorhombic phase thus the lattice constants a ≠ b. With increasing W/Cr content, the

splitting between the (020) and (200) peaks is decreased, indicating the reduction of the

orthorhombicity a/b. When x=0.05, only the reflection (020) can be observed and the (020)

reflections have shifted to higher 2θ values, indicating a decrease in the lattice parameters a

and b in the crystal structure. From Fig. 1 (B) the (220) reflections are observed to shift

upwards in the orthorhombic form and the reflection (1115) is absent at x=0.10. That means

the modification of tungsten and chromium for titanium ions distorts the positions of ions in

the lattice, which may result from the different lattice strain relating to different ionic radius

and outer electronic configuration between W

and Cr

. As typically shown in Fig. 2, the

decrease of the orthorhombic lattice parameters a and b, and lattice volume V of the BIT

phase with an increasing amount of W/Cr doping are obvious, especially for the

composition with W/Cr being less than 0.10. Further an increase in the amount of W/Cr to

0.15 does not cause a change of cell dimensions based on XRD results. However, no

significant drop in lattice parameter, c, is found in BITWC powders calcined at 800 °C for 4

h. It is observed that the almost no volume change could be found for powders with W/Cr

doping more than 0.10, allows us to further study the possibility of the formation of a

second phase like Bi

and Bi

in the samples (Jardiel, 2008), although any

secondary phases were not found by XRD techniques because of the limitation of XRD

intensity below a certain concentration. A careful examination of the XRD patterns in Figs. 1

B-site Multi-element Doping Effect on Electrical Property of Bismuth Titanate Ceramics

247

(B) reveal that apart from the decrease of the lattice parameters and the difference between

the a and b parameters, the peaks have broadened. The (1115) peaks in the patterns of

x=0.10 and 0.15 appear as a weak shoulder on the right of the corresponding (220) peaks.

Although the line-broadening of XRD peaks can have various origins, including grain size

and dislocation structure (Snyder, 1999), it is expected that the observed line-broadening can

be attributed to micro -strain in the material.

Fig. 3 shows the SEM images of the polished and thermally etched surfaces of BITWC

ceramics. It is observed that the average grain size decreased with W/Cr doping ranging

from approximately 10 μm to 1 μm, which suggest that W/Cr control the growth of the

plate-like grains. It is reported that WO

influences the grain growth kinetics due to the

slowing of grain boundary diffusion processes (Jardiel, 2008). The aspect ratio of the grains

decreases with increase of W/Cr doping as shown in Fig. 3. This will lead to a better

arrangement of the particles during the sintering processes and consequently to an

enhanced densification of the ceramics. Table I shows the EDS analysis data of BITWC

ceramics. When x ≤ 0.05, the experimentally observed atomic ratios agreed with the initial

compositions signifies that the BITWC ceramics are single phase. This shows that the

/Cr

cations were incorporated into the layered perovskite structure and presumably

occupied Ti

sites. While for x ≥ 0.075 compositions, EDS results were not in agreement

with the initial theoretical atomic ratios. This indicates the presence of the secondary phases

in the samples.

Element BIT x=0.025 x=0.05 x=0.075 x=0.1 x=0.15

Bi 4.00 3.98 3.97 3.96 3.93 3.87

Ti 2.99 2.98 2.94 2.91 2.86 2.81

W 0 0.025 0.05 0.076 0.11 0.16

Cr 0 0.4 0.4 0.39 0.4 0.37

O 12.00 12.00 12.00 12.08 12.09 12.16

Table 1. Energy-Dispersive Spectra (EDS) Analysis Data for BITWC ceramics

Fig. 4 (a) shows the variation of the real part of impedance (

Z ) with frequency at various

temperatures for x = 0.025 composition. It is observed that the magnitude of

Z decreases

with increase in both frequency as well as temperature, indicating an increase in ac

conductivity with rise in temperature and frequency. The

Z values for all temperatures

merge at high frequencies. Similar trends were observed for the other compositions which

are not depicted in the Fig. 4. Fig. 4 (b) shows the normalized imaginary parts of impedance

max

()ZZ as a function of frequency at the selected temperatures. The values of

max

()ZZ

are observed to shift to higher frequencies with increasing temperature consistent with

temperature dependent electrical relaxation behavior. These observed relaxation processes

for the studied samples could be attributed to the presence of defect/vacancies.

Relaxation processes in many electric, magnetic, mechanical and other systems are governed

by the Kohlrausch-Williams-Watts (KWW) law (Williams, 1970),

()

() exp

⎡

⎤

ϕ= −

⎢

⎥

⎣

⎦

(1)

Ferroelectrics – Physical Effects

248

where τ is the relaxation time and 0 < β ≤ 1 is the parameter which indicates the deviation

from Debye-type relaxation. The dielectric behaviour of the present ceramics is rationalized

by invoking modified KWW function suggested by Bergman (Bergman, 2000). The

imaginary part of the electric modulus (

Z ) can be defined as:

()()

max

max max

(1 ) / .

ffff

⎡

⎤

−β + β +

⎣

⎦

+β

(2)

where

max

Z is the peak value of the

Z and f

max

is the

corresponding frequency. Theoretical

fit of Eq. 2 to the experimental data is shown in Fig. 4 (b) as the solid lines. It is seen that the

experimental data are well fitted to this model except in the low frequency regime which

may be due to electrode effect associated with the samples. From the fitting of

Z versus

frequency plots, the value of

was determined and found to be temperature independent.

The value of

is found to be 0.82±0.02 in the 400-600 °C temperature range. Eq. 2 can be

fitted for other compositions under study which are not shown in Fig. 4.

Fig. 4. (a) Real and (b) imaginary parts of impedance versus frequency plots at various

temperatures and the solid lines are the theoretical fit.

Fig. 5 depicts the variation of relaxation frequency with an inverse of absolute temperature

for the composition of

x=0.025. The activation energy for electrical relaxation can be

calculated using Arrhenius relation as:

(

)

exp

=−

(3)

where

is the pre exponential factor, k is the Boltzmann constant, and T is the absolute

temperature. Activation energy was calculated from the linear fit of the experimental data as

shown in Fig. 5 for

x=0.025 samples. Activation energy was estimated for the other

compositions under study and the plot for activation energy versus composition is shown in

the inset of Fig. 5. The activation energy increases with the W/Cr content, which suggests a

decrease of oxygen vacancy concentration (Coondoo, 2007).

Lallart M. (ed.) Ferroelectrics - Physical Effects

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