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35) ceramic
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Physica B 395 (2007) 1–9 www.elsevier.com/locate/physb
Effect of Nd doping on structural, dielectric and thermodynamic properties of PZT (65/35) ceramic Md Ahamad Mohiddon, Abhishek Kumar, K.L. Yadav Smart Materials Research Laboratory, Department of Physics, Indian Institute of Technology, Roorkee, India Received 27 July 2006; accepted 25 September 2006
Abstract The influence of neodymium (Nd) addition on the phase formation and dielectric properties of Pb(Zr0.65Ti0.35)O3 composition prepared from mixed oxide method was analyzed. Pellets were sintered in air and PbZrO3 (PZ) atmosphere separately. Non-perovskite ZrO2 phase was observed in samples which were sintered in air, also grain size was found to decrease with Nd doping in non-PZ environment samples. Decrease in transition temperature by 80 1C with increasing Nd concentration was observed in both set of samples. Maximum dielectric constant and dielectric losses are found to decrease with Nd doping. Complex impedance analysis revealed that grain boundary resistance increases with Nd doping. Thermodynamic parameters such as change in enthalpy, free energy and change in entropy were studied. r 2006 Elsevier B.V. All rights reserved. Keywords: Ceramics; X-ray diffraction; Dielectric properties; Grain size; Complex impedance analysis; Thermodynamic parameters
1. Introduction Lead-based perovskite ferroelectric ceramics are widely applied in multilayer capacitors, micro-electro mechanical systems (MEMS) and integrated devices such as ferroelectric memories, infrared sensors, micro actuators, etc. [1–5]. Many of these applications demand materials with excellent dielectric and ferroelectric properties. Lead zirconium titanate (PZT) is one of the best lead-based materials that have been studied extensively since late 1940s [6,7]. The dielectric characteristics of PZT ceramic changes with its stoichiometry [8]. PZT is an ABO3 type perovskite structured material with A-site (Pb2+) occupying the cubo-octohedral interstices described by the BO6 site octahedral and has tetragonal, rhombohedral and orthorhombic phases at room temperature, depending on the value of Zr/Ti ratio. It has two morphotropic boundaries (MPB) at 95/5 and 53/47 Zr/Ti ratio, where it undergo phase transition from orthorhombic to low temperature rhombohedral and high temperature rhomboCorresponding author.
E-mail address: [email protected] (K.L. Yadav). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.09.022
hedral to tetragonal phases, respectively. All these compositions show cubic phase above transition temperature. The composition near MPB region normally show an increased capability of polarization and electromechanical response, which make them suitable for non-volatile memories and piezoelectric actuators [9–11]. PZT compositions show significant merit, when they are doped with foreign ions. Its dielectric and piezoelectric properties change, depending on the site occupied by the foreign ion in ABO3 perovskite structure. Dopents are classified as isovalent, acceptors or donors [12]. Donors (trivalent ion at A site and pentavalent ion at B site) reduces the concentration of intrinsic oxygen vacancy created due to PbO evaporation and compensate the hole formed due to lead vacancies, which in tern increases bulk resistance of sample. Acceptors (monovalent at A site and trivalent at B site) introduces oxygen vacancies to maintain charge neutrality, due to this oxygen vacancy domain walls gets pinned and space charges are introduces, which in tern reduces grain resistance and inhibits domain motion [13], also acceptor-doped PZT shows poor hysteresis loop and low dielectric constant. Isovalent (divalent at A site and tetravalent at B site) doping tends to reduce the Curie temperature [9] and
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M.A. Mohiddon et al. / Physica B 395 (2007) 1–9
Table 1 List of common ion substitution in PZT Pb site donors Ti–Zr site donors Pb site acceptors Ti–Zr site acceptors Isovalent substitutions Multivalent ions
La3+, Bi3+, Nd3+, Sb3+, Th4+ Nd5+, Ta5+, Sb5+, W6+ K+, Na+, Rb+ Fe3+, Al3+, Sc3+, In3+, Cr3+, Co3+, Ga3+, Mn3+, Mg2+, Cu2+ Sr2+, Ca2+, Ba2+(for Pb2+) Sn4+ (for Ti4+, Zr4+) Cr, U
increases the density of PZT ceramic, which in tern effect the electrical properties. A list of more commonly used dopands is given in Table 1. In the present work, we have prepared neodymium (Nd3+)-doped PZT (65/35) by mixed oxide method, in a wide composition range (0–10 at%). Structural and electrical characterizations were carried in order to study the effect of doping on the phase formation behavior and electric properties. Complex impedance analysis and thermodynamic characterization were also conducted to understand the variation in grain boundary resistance, free energy, enthalpy and change in entropy. 2. Experimental procedure 2.1. Sample design and preparation Generally interstitial ions do not occur in PZT perovskite structure due to its high packing density. Since Nd3+ has an ionic radius of r12 ¼ 1.27 A˚, which is relatively close to that of Pb2+ (r12 ¼ 1.32 A˚), it seems that Nd3+ occupies mostly on A site in the ABO3 perovskite structure. However B site occupancy is also expected as the ionic radii of Nd3+ (r6 ¼ 0.983 A˚), Zr4+ (r6 ¼ 0.86 A˚) and Ti4+ (r6 ¼ 0.745 A˚) are close to each other. The conventional A and B site vacancy can be formulated as follows: Pb13x=2 Ndx ðZr1y Tiy ÞO3 FA site vacancy; Pb1x Ndx ðZr1y Tiy ÞO3 FB site vacancy. Both types of vacancies were reported in the literature [13,14]. Nd3+-doped PZT specimen studied in this investigation was fabricated according to A-site formula. The compositions Pb13x/2 Ndx (Zr0.65Ti0.35)O3 (here after PNZT), where x ¼ 0.00, 0.01, 0.03, 0.05, 0.07, 0.09 were prepared by traditional mixed oxide solid state reaction method, using analytical grade reagents PbO, ZrO2, TiO2, Nd2O3 as starting materials. The stochiometric amount of individual reagent was homogeneously mixed in acetone media. The well-mixed powder was then calcined at 850 1C for 3 h, in alumina crucible. Calcined powder was pressed into cylindrical pellets of 1–2 mm thick and 7 mm diameter at a pressure of 9 106 Pascal, using uniaxial hydraulic press. These pellets were then sintered at 1100 1C for 2 h in lead zirconate (PZ) and air environment individually.
2.2. Characterization of properties Crystal structure and phase identification of sintered pellets was carried out by X-ray diffractometer (Brueker D8 Advance) using Cu Ka radiation (1.5418 A˚), and grain distribution over the ceramic surface were analyzed by scanning electron microscope (LEO 435 VP). Lattice parameters were also calculated and refined using least square method. Sintered pellets were polished and flat surface were coated with high purity silver paste and then dried at 120 1C for 30 min, before taking electrical measurements. Dielectric measurements were conducted on an automated HIOKI 3532-50 Hi Tester, LCR meter. Dielectric permittivity and dissipation factor were acquired in the frequency range 100 Hz–1 MHz as a function of temperature in a temperature range 40–500 1C, where the sample undergoes the ferroelectric to paraelectric phase transition. 3. Results and discussion 3.1. Structural and microstructural properties Fig. 1(a) and (b) shows the X-ray diffraction (XRD) pattern of PNZT (x ¼ 0.0, 0.01, 0.03, 0.05, 0.07, 0.09) samples, which were sintered in air and PZ environment, respectively. All peaks were indexed and lattice parameters were determined using the least square refinement method using a software package (POWD Mult). The rhombohedral phase is observed in all samples and its unit cell parameters are given in Table 2. Presence of perovskite phase was confirmed in all samples, however close observation of XRD peaks above xX0.07 in Fig. 1(a) reveals that additional non-PZT; ZrO2 orthorhombic peaks were present. This may be because; at higher Nd concentrations excess lead oxide (PbO) evaporates leaving ZrO2 insoluble. This argument is supported by Fig. 1(b) in which no ZrO2 peaks was observed; as the pellets are sintered in presence of PZ environment which may have reduced the PbO evaporation. Densities of the samples were calculated from measured mass and dimensions of the sintered pellets and the data is given in Table 2. It is observed from the results that density of pellets sintered in air is less than that of pellets sintered in PZ environment, also density is found to decrease with Nd concentration, which supports our argument that excess Nd leads to excess evaporation of PbO and creates porosity.
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ZrO2
0.09 Intensity (a u)
0.07 0.05 0.03
0.01
0.00 10
20
30
(A)
40 50 Bragg's angle (2θ)
60
70
Intensity (a u)
0.09 0.07 0.05 0.03 0.01 0.00 10 (B)
20
30
40
50
60
70
Bragg's angle (2θ)
Fig. 1. X-ray diffractogram of Nd-doped PZT (x/65/35) pellets sintered in air (A) and PZ environment (B).
The linear particle size (P) is calculated from the strong reflection XRD peak using Sherrer’s formula [15] P ¼ Kl=b1=2 cos y, where K ¼ 0:89, b1/2 full-width at half-maxima. Variation of particle size as a function of Nd doping is shown in Fig. 2, from the graph it is observed that particle size is found to decrease with Nd doping for pellets sintered in air and no such significant observation was found for PZ environment sintered samples. The decrease in particle size is expected to be due to formation of ZrO2 phase. Similar observations were found from microstructure studies of the samples. Fig. 3(a–c) and (d–f) are the SEM photographs of PNZT (x ¼ 0.01, 0.03, 0.07) pellets sintered in air and PZ atmosphere, respectively. Less compactness and porosity is observed in all photographs. Grain size of PZ environment samples is found larger than air-sintered samples and
porosity is high for air-sintered samples. All these observations suggest that PZ environment reduces the excess PbO evaporation. The average grain size was determined by the linear interception method and data is plotted as function of Nd concentration in Fig. 4. The decrease in grain size by Nd doping may be due to occupation of Nd3+ ion at B site replacing Zr4+/Ti4+ ion, where it act as acceptor. The acceptor dopants in ABO3 perovskite lattice introduces oxygen vacancy to maintain charge neutrality [16], due to this oxygen vacancy domain walls gets pinned and reduces grain size. Also these oxides get precipitated at the grain boundary that subsequently resists the grain growth. 3.2. Dielectric and electric properties Fig. 5 shows the variation of dielectric constant as function of temperature (40–500 1C) at 10 KHz frequency
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Table 2 Structural and dielectric parameters of Nd doped PZT (65/35) ceramic at 10 KHz PNZT (x/65/35)
0.00 0.01 0.03 0.05 0.07 0.09
Rhombohedral lattice parameter a in A˚
4.1085 4.1032 4.0878 4.0924 4.1106 4.0783
Density (gm/cm3) air
PZ
5.489 5.668 5.899 5.818 5.620 5.120
5.752 5.773 6.187 6.118 5.887 5.437
28 26
Particle size (nm)
24 22
sintered in Air sintered in PZ
20 18 16 14 12 -0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 x value in PNZT (x/65/35)
Fig. 2. Particle size variation of PNZT (x/65/35) composition with Nd concentration derived from Sherrer’s equation.
for all different PNZT compositions. The dielectric constant shows phase transition as expected for normal ferroelectrics. Also the region around the dielectric peak is broadened, which is one of the most important characteristics of disordered perovskite structure with diffuse phase transition. The broadening is considered to be due to compositional fluctuation [17] developed at A site by Pb2+, Nd3+ and at B site by Zr4+,Ti4+,Nd3+ ions. The transition temperature (Tm) and maximum dielectric constant (emax) are given in Table 2. Transition temperature was found to shift forward lower temperature by 80 1C with Nd concentration from x ¼ 0.00 to 0.05, with further Nd doping Tm remained at same position. The decrease in Tm with Nd doping may arise from following possible factors. It was established [18] in other Pb-based perovskite and relaxors that the reduction in grain size favors the reduction in Tm, however this may not be the only reason for fall of 80 1C in Tm. In case of undoped PZT film, any particular ion of the lattice experiences the same average field induced by other ion in the lattice. Due to this during ferroelectric phase transition, ion in the lattice shifts in the same way, resulting in macroscopically large region called domain. In contrast, PZT doped with Nd can be
Transition temperature Tm (1C)
Maximum dielectric constant emax
Dissipation factor (tan d)
365 355 305 280 285 285
1758 1772 2687 2363 1247 1092
0.1078 0.0994 0.0597 0.0474 0.0544 0.0821
considered as disordered ferroelectric system where electric dipoles, Nd ion and intrinsic defects such as oxygen and Pb vacancies, acts as source of random electric field distributions which reduces Tm. It was shown earlier in Fig. 4 that the grain size decrease with Nd content, smaller the grain size and hence high density of grain boundary concentration which in tern increases the random field strength and shifts Tm to lower value. The Tm is found to be independent on measured frequency, but maximum dielectric constant is decreasing with increase in frequency. Fig. 6 shows the variation of dielectric constant at 50 1C as function of frequency for all PNZT samples. Dielectric constant shows strong dispersion at lower frequencies. This is attributed to the low frequency space charge accumulation effect. Such strong dispersion in dielectric constant appears to be a common feature in ferroelectrics associated with nonnegligible ionic conductivity and is referred to as the low frequency dielectric dispersion. Dielectric constant appears to increase upto x ¼ 0.03 Nd doping and then decreases. The decrease in dielectric constant at higher Nd doping is due to decrease in grain size and formation of nonperovskite ZrO2 phase. The variation of dielectric loss as a function of temperature (40–500 1C) at 10 KHz frequency is shown in Fig. 7. It was found that dissipation factor (tan d) is very low and is almost constant for all compositions at lower temperatures; however above 400 1C a sharp rise in dielectric loss was observed. This may be because limited number of mobile ion in ionic solid are trapped in relatively stable potential wells during their motion through solids. Owing to a rise in temperature, the donor cations start taking a major part in the conduction process. These donors create a level much near the conduction band, therefore small amount of energy is required to activate them. Also slight change in stoichiometry (i.e. the metal: oxygen ratio) in the multi metal complex oxides cause the creation of a large number of donors and acceptors [19]. Fig. 8 shows the variation of dielectric loss as function of frequency at room temperature, all compositions shows strong lower frequency dispersion. The room temperature dielectric loss (tan d) found to decrease with lower Nd doping (upto x ¼ 0.05) and there after it increases (data given in Table 2), this is consistent with previous literature [20].
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Fig. 3. Microstructure of PNZT samples sintered in air (A) x ¼ 0:01, (B) x ¼ 0:03, (C) x ¼ 0:07 and sintered in PZ environment (D) x ¼ 0:01, (E) x ¼ 0:03, (F) x ¼ 0:07.
The diffuseness in the materials was examined by quadratic relation [21] 1 1 ðT T c Þg ¼ þ , max 2m d2 where emax is maximum value of e at Tm, g and d are diffusivity and diffuseness parameters, respectively. The diffusivity (g) is determined from slope of ln(1/e–1/emax) versus ln(TTC) graph and its value is found to be 2 for all compositions, indicating the pure diffuse phase transition described by Smoeski and Isupov. Fig. 9 shows the dependence of logarithm conductivity on the reciprocal absolute temperature within a broad range of temperature (40–500 1C). The graph consists of two rectilinear portions with different angels of inclination
to the X-axis. At temperature above the point of fracture, the conductivity is mainly determined by intrinsic defects and is physical parameter of compound. On the other hand, below the point of fracture the conductivity is determined by the nature and concentration of impurities. The temperature at which the fracture is observed on the log s vs. 1/T essentially depends on degree of purity and perfection of crystal [22]. From the graph it was found that increasing Nd doping, fracture point shifts towards lower temperature side, which indicates the increase of impurity in the samples. The shift in fracture point temperature with Nd concentration is shown in Fig. 10. The activation energy of the samples was calculated from the slope of log s vs. 1/T curve and the data is given in Table 3.
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1.4
00 01 03 05 07 09
700 Dielectric constant at 50°C (ε)
grain size (μm)
1.2 sintered in Air sintered in PZ
1.0
0.8
0.6
600
500
400
300
0.4 200
0.2 0.00
0.02
0.04
0.06
0.08
0.10
0.0
2.0x105
X value in PNZT (x/65/35)
4.0x105
6.0x105
8.0x105
1.0x106
Frequency (Hz)
Fig. 4. Grain size variation of PNZT (x/65/35) composition with Nd concentration.
Fig. 6. Variation of dielectric constant with frequency for PNZT (x/65/35) ceramics at 50 1C.
3200
2400 2000
00 01 03 05 07 09
8 Dielectric loss (tan δ)
Dielectric constant (ε)
10
00 01 03 05 07 09
2800
1600 1200
6
4
2
800 400
0
0
100
200
300
400
500
Temperature (°C)
0
100
200 300 Temperature (°C)
400
500
Fig. 5. Temperature dependence of the dielectric constant for PNZT (x/65/35) ceramics at 10 KHz frequency.
Fig. 7. The temperature dependence of the dielectric loss at different Nd doping concentration for PZT (65/35) ceramic.
3.3. Complex impedance analysis and thermodynamic properties
impedance plane (also called Nquist plot). The radius of semicircle gives the exact relaxation time of lumped parameters that are associated with the samples. All these curves have their center located away from the real impedance axis indicating the presence of relaxation species with distribution of relaxation times in these samples. Using the numerical method reported by Bishay [23], the interceptions on real axis of all arcs and radius of circles were calculated from which grain boundary resistance and relaxation frequencies were determined. The variation of grain boundary resistance as a function of temperature for all different PNZT compositions is shown in Fig. 12. The grain boundary resistance is found to decrease with increasing temperature and increases with increasing Nd doping. This is because Nd at B site of ABO3 perovskite
Fig. 11 shows a set of impedance data taken over a wide frequency range (100 Hz–1 MHz) at several temperatures as a Nyquist diagram for Nd (x ¼ 0.03)-doped PZT (65/35) ceramic. The shape of the cole–cole plot obtain in the present study is highly depend on temperature. At lower temperature the shape of the plot is straight line with large slope indicating the insulating nature of the sample. Increasing the temperature the slope of line decreases and turn towards real axis. All these curves start at the origin and hence there is no series resistance that can be ascribed to the LCR circuit representation of the sample. This simple RC circuit gives a semicircle in the complex
ARTICLE IN PRESS M.A. Mohiddon et al. / Physica B 395 (2007) 1–9
0.30
0.01 0.03 0.05 0.07 0.09
240 fracture point temperature (°C)
dielectric loss (tan δ)
0.25 0.20 0.15 0.10 0.05
0.0
2.0x105
4.0x105
6.0x105
8.0x105
1.0x106
200
180
0.00
Frequency (Hz)
Fig. 8. Variation of dielectric loss with frequency for PNZT (x/65/35) ceramics.
-12
0.02 0.04 0.06 0.08 X value of Nd in PNZT (x/65/35)
0.10
Fig. 10. Variation of the point of fracture in ln(s) versus 1/T graph with Nd doping in PZT (65/35) ceramic.
Table 3 Thermodynamic parameters and activation energy of PNZT (x/65/35) at different ambient temperatures
-13 -14
00 01 03 05 07 09
-15 ln (σdc)
220
160
0.00
-16 -17
PNZT (x/65/35)
Temperature (K)
Activation energy DE (eV)
DH (Kcal/ mol)
DF (Kcal/ mol)
DS (Kcal/ mol)
0.00
323 373 473
0.1709
24.98
9.82 10.24 13.39
0.0773 0.0395 0.0245
0.01
323 373 473
0.2456
26.04
9.12 10.81 12.76
0.0524 0.0408 0.0281
0.05
323 373 473
0.1027
20.79
8.06 8.85 12.25
0.0394 0.032 0.0181
0.07
323 373 473
0.0602
18.49
8.80 9.98 13.07
0.030 0.023 0.012
-18 Point of fracture -19 -20 0.000
7
0.005
0.010
0.015
0.020
0.025
1/T (/°C) Fig. 9. The variation of the conductivity s with temperature for PZT (65/35) ceramic at different Nd doping.
acts as donor, which reduces the concentration of intrinsic oxygen vacancies, created due to PbO evaporation during sintering of PZT ceramics. Also when the concentration of donor impurity is close to that of the acceptor impurities originating from lead vacancies, most of the holes from acceptor level are compensated by electron from donor level and as a result bulk resistance of PNZT increases. The activation energy of the relaxation DQ for different compositions is calculated from the arrhenius formula [24–26] and is given in Table 3.
relaxation time and ambient temperature can be obtain using following formula [28,29]: h expðDF =RTÞ, t¼ kT where h is plank’s constant, R is universal gas constant and DF is the free energy of activation. The enthalpy of activation (DH) is related to free energy of activation (DF) by the formula
t ¼ t0 expðDQ=kTÞ,
DF ¼ DH TDS,
where k is Boltzmann constant and t0 is pre-exponential factor. According to Eyring [27] the relation between the
where DS is change in entropy. The DH can be calculated from the logarithmic plot of (tT) versus (1/T).
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4. Conclusions 8
B50 C100 D200 E350 F400 G450
Z|| (M ohms)
6
4
2
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
|
Z (M ohms)
Grain boundary resistance Rgb in Megaohms
Fig. 11. Complex impedance plane plots at different temperatures for sintered PNZT (x/65/35), x ¼ 0:03 sample.
In the present work we have reported the Nd3+-doped PZT(65/35) ceramic with composition x ¼ 0.0,0.01,0.03, 0.05,0.07,0.09 prepared by mixed oxide method. X-ray diffraction studies confirmed rhombohedral symmetry for the synthesized compound. Non-perovskite ZrO2 phase was also observed at higher Nd doping for air sintered PZT (65/35) samples, also grain size and particle size was found to decrease with Nd doping in air-sintered samples only. A study of dielectric constant suggests diffuse type of phase transition without any sign of relaxor behaviour in the material. With increasing x, dielectric constant was found to decrease appreciably, whereas Curie temperature (Tm) as determined from dielectric constant vs. temperature plots was found to shift to lower temperature. Dielectric constant and dissipation factor had shown strong lower frequency dispersion. Complex impedance analysis studied by Z00 –Z0 cole–cole plot at different temperature had revealed that grain boundary resistance decreases with temperature and increased with Nd doping. All these properties of prepared sample were may be useful for device applications. Acknowledgements
300 0.00 0.01 0.03 0.05 0.07 0.09
240
180
120
60
0 0
50
100 150 200 250 300 350 400 450 500 Temperature (°C)
Fig. 12. Variation of grain boundary resistance as function of temperature for all different PNZT compositions.
The free energy activation (DF) is deduced according the relation [30] DF ¼ 2:303RT logðkTt=hÞ. The calculated values of free energy DF, enthalpy of activation DH and change in entropy DS for different compositions of PNZT are given in Table 3. It is clear from the results that as ambient temperature increases change in entropy DS is decreases, but free energy is found to be increasing with temperature. However Nd doping decreases the enthalpy change, free energy and change in entropy.
The authors acknowledges to DST, New Delhi (SR/ FTP/PS-05/2003) for financial support for this work. References [1] D.L. Polla, L.F. Francis, MRS Bull. 2 (1996) 59. [2] J.F. Scott, Ferroelectric Memories, Springer, Berlin, 2000. [3] C.T. Lin, B.W. Scanlan, J.D. Mcnell, J.S. Webb, L. Li, J. Matter Res. 7 (1992) 2546. [4] S. Yokayana, Y. Ito, H. Ishihara, K. Hamada, S. Ohnishi, J. Kudo, K. Sakiyama, Jpn. J. Appl. Phys. 34 (1995) 767. [5] N. Neumann, R. Kohler, G. Hofmann, Integrat. Ferro Electric. 6 (1995) 213. [6] G.H. Haertling, J. Am. Ceram. Soc. 82 (1999) 797. [7] B. Jaffe, W.R. Cook, Piezoelectric Ceramics, RAN Publishers, 1971. [8] X. Dai, Z. Xu, D. Viehland, J. Am. Ceram. Soc. 78 (1995) 2815. [9] B. Jaffe, R.C. Williams, H. Jaffe, Piezoelectric Ceramics, Academic Press, London and New York, 1971. [10] Y. Yoshikawa, K. Tsuzuki, J. Am. Ceram. Soc. 75 (1992) 2520. [11] S.E. Park, T.R. Shrout, J. Am. Ceram. Soc. 82 (1997) 1804. [12] L.E. Cross, in: N. Setter, E.L. Colla (Eds.), Ferroelectric Ceramics— Tutorial Review Theory, Processing and Applications, vol. 1, Birkhauser Verlag, Basel, 1993. [13] K. Hardtl, D. Henings, J. Am. Ceram. Soc. 55 (1972) 230. [14] L. Wu, C.C. Lee, T.S. Wu ad, C.C. Wei, Ferroelectrics 41 (1982) 157. [15] B.D. Cullity, Elements of X-ray Diffraction, Addition-Wesley Series Publishing Company, Reading, MA, 1967. [16] S.B. Majumdar, B. Roy, R.S. Katiyar, S.B. Krupanidhi, J. Appl. Phys. 90 (2001) 2975. [17] G.A. Smolenskii, J. Phy. Soc. Japan 28 (1970) 26. [18] M. Tyunina, J. Levoska, A. Sternberg, S. Lepavuori, J. Appl. Phys. 84 (1998) 6800. [19] R.C. Blochanan, Ceramic Materials for Electronics, Oxford University Press, Newyork, 1986.
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Physica B 395 (2007) 1–9 www.elsevier.com/locate/physb
Effect of Nd doping on structural, dielectric and thermodynamic properties of PZT (65/35) ceramic Md Ahamad Mohiddon, Abhishek Kumar, K.L. Yadav Smart Materials Research Laboratory, Department of Physics, Indian Institute of Technology, Roorkee, India Received 27 July 2006; accepted 25 September 2006
Abstract The influence of neodymium (Nd) addition on the phase formation and dielectric properties of Pb(Zr0.65Ti0.35)O3 composition prepared from mixed oxide method was analyzed. Pellets were sintered in air and PbZrO3 (PZ) atmosphere separately. Non-perovskite ZrO2 phase was observed in samples which were sintered in air, also grain size was found to decrease with Nd doping in non-PZ environment samples. Decrease in transition temperature by 80 1C with increasing Nd concentration was observed in both set of samples. Maximum dielectric constant and dielectric losses are found to decrease with Nd doping. Complex impedance analysis revealed that grain boundary resistance increases with Nd doping. Thermodynamic parameters such as change in enthalpy, free energy and change in entropy were studied. r 2006 Elsevier B.V. All rights reserved. Keywords: Ceramics; X-ray diffraction; Dielectric properties; Grain size; Complex impedance analysis; Thermodynamic parameters
1. Introduction Lead-based perovskite ferroelectric ceramics are widely applied in multilayer capacitors, micro-electro mechanical systems (MEMS) and integrated devices such as ferroelectric memories, infrared sensors, micro actuators, etc. [1–5]. Many of these applications demand materials with excellent dielectric and ferroelectric properties. Lead zirconium titanate (PZT) is one of the best lead-based materials that have been studied extensively since late 1940s [6,7]. The dielectric characteristics of PZT ceramic changes with its stoichiometry [8]. PZT is an ABO3 type perovskite structured material with A-site (Pb2+) occupying the cubo-octohedral interstices described by the BO6 site octahedral and has tetragonal, rhombohedral and orthorhombic phases at room temperature, depending on the value of Zr/Ti ratio. It has two morphotropic boundaries (MPB) at 95/5 and 53/47 Zr/Ti ratio, where it undergo phase transition from orthorhombic to low temperature rhombohedral and high temperature rhomboCorresponding author.
E-mail address: [email protected] (K.L. Yadav). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.09.022
hedral to tetragonal phases, respectively. All these compositions show cubic phase above transition temperature. The composition near MPB region normally show an increased capability of polarization and electromechanical response, which make them suitable for non-volatile memories and piezoelectric actuators [9–11]. PZT compositions show significant merit, when they are doped with foreign ions. Its dielectric and piezoelectric properties change, depending on the site occupied by the foreign ion in ABO3 perovskite structure. Dopents are classified as isovalent, acceptors or donors [12]. Donors (trivalent ion at A site and pentavalent ion at B site) reduces the concentration of intrinsic oxygen vacancy created due to PbO evaporation and compensate the hole formed due to lead vacancies, which in tern increases bulk resistance of sample. Acceptors (monovalent at A site and trivalent at B site) introduces oxygen vacancies to maintain charge neutrality, due to this oxygen vacancy domain walls gets pinned and space charges are introduces, which in tern reduces grain resistance and inhibits domain motion [13], also acceptor-doped PZT shows poor hysteresis loop and low dielectric constant. Isovalent (divalent at A site and tetravalent at B site) doping tends to reduce the Curie temperature [9] and
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Table 1 List of common ion substitution in PZT Pb site donors Ti–Zr site donors Pb site acceptors Ti–Zr site acceptors Isovalent substitutions Multivalent ions
La3+, Bi3+, Nd3+, Sb3+, Th4+ Nd5+, Ta5+, Sb5+, W6+ K+, Na+, Rb+ Fe3+, Al3+, Sc3+, In3+, Cr3+, Co3+, Ga3+, Mn3+, Mg2+, Cu2+ Sr2+, Ca2+, Ba2+(for Pb2+) Sn4+ (for Ti4+, Zr4+) Cr, U
increases the density of PZT ceramic, which in tern effect the electrical properties. A list of more commonly used dopands is given in Table 1. In the present work, we have prepared neodymium (Nd3+)-doped PZT (65/35) by mixed oxide method, in a wide composition range (0–10 at%). Structural and electrical characterizations were carried in order to study the effect of doping on the phase formation behavior and electric properties. Complex impedance analysis and thermodynamic characterization were also conducted to understand the variation in grain boundary resistance, free energy, enthalpy and change in entropy. 2. Experimental procedure 2.1. Sample design and preparation Generally interstitial ions do not occur in PZT perovskite structure due to its high packing density. Since Nd3+ has an ionic radius of r12 ¼ 1.27 A˚, which is relatively close to that of Pb2+ (r12 ¼ 1.32 A˚), it seems that Nd3+ occupies mostly on A site in the ABO3 perovskite structure. However B site occupancy is also expected as the ionic radii of Nd3+ (r6 ¼ 0.983 A˚), Zr4+ (r6 ¼ 0.86 A˚) and Ti4+ (r6 ¼ 0.745 A˚) are close to each other. The conventional A and B site vacancy can be formulated as follows: Pb13x=2 Ndx ðZr1y Tiy ÞO3 FA site vacancy; Pb1x Ndx ðZr1y Tiy ÞO3 FB site vacancy. Both types of vacancies were reported in the literature [13,14]. Nd3+-doped PZT specimen studied in this investigation was fabricated according to A-site formula. The compositions Pb13x/2 Ndx (Zr0.65Ti0.35)O3 (here after PNZT), where x ¼ 0.00, 0.01, 0.03, 0.05, 0.07, 0.09 were prepared by traditional mixed oxide solid state reaction method, using analytical grade reagents PbO, ZrO2, TiO2, Nd2O3 as starting materials. The stochiometric amount of individual reagent was homogeneously mixed in acetone media. The well-mixed powder was then calcined at 850 1C for 3 h, in alumina crucible. Calcined powder was pressed into cylindrical pellets of 1–2 mm thick and 7 mm diameter at a pressure of 9 106 Pascal, using uniaxial hydraulic press. These pellets were then sintered at 1100 1C for 2 h in lead zirconate (PZ) and air environment individually.
2.2. Characterization of properties Crystal structure and phase identification of sintered pellets was carried out by X-ray diffractometer (Brueker D8 Advance) using Cu Ka radiation (1.5418 A˚), and grain distribution over the ceramic surface were analyzed by scanning electron microscope (LEO 435 VP). Lattice parameters were also calculated and refined using least square method. Sintered pellets were polished and flat surface were coated with high purity silver paste and then dried at 120 1C for 30 min, before taking electrical measurements. Dielectric measurements were conducted on an automated HIOKI 3532-50 Hi Tester, LCR meter. Dielectric permittivity and dissipation factor were acquired in the frequency range 100 Hz–1 MHz as a function of temperature in a temperature range 40–500 1C, where the sample undergoes the ferroelectric to paraelectric phase transition. 3. Results and discussion 3.1. Structural and microstructural properties Fig. 1(a) and (b) shows the X-ray diffraction (XRD) pattern of PNZT (x ¼ 0.0, 0.01, 0.03, 0.05, 0.07, 0.09) samples, which were sintered in air and PZ environment, respectively. All peaks were indexed and lattice parameters were determined using the least square refinement method using a software package (POWD Mult). The rhombohedral phase is observed in all samples and its unit cell parameters are given in Table 2. Presence of perovskite phase was confirmed in all samples, however close observation of XRD peaks above xX0.07 in Fig. 1(a) reveals that additional non-PZT; ZrO2 orthorhombic peaks were present. This may be because; at higher Nd concentrations excess lead oxide (PbO) evaporates leaving ZrO2 insoluble. This argument is supported by Fig. 1(b) in which no ZrO2 peaks was observed; as the pellets are sintered in presence of PZ environment which may have reduced the PbO evaporation. Densities of the samples were calculated from measured mass and dimensions of the sintered pellets and the data is given in Table 2. It is observed from the results that density of pellets sintered in air is less than that of pellets sintered in PZ environment, also density is found to decrease with Nd concentration, which supports our argument that excess Nd leads to excess evaporation of PbO and creates porosity.
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ZrO2
0.09 Intensity (a u)
0.07 0.05 0.03
0.01
0.00 10
20
30
(A)
40 50 Bragg's angle (2θ)
60
70
Intensity (a u)
0.09 0.07 0.05 0.03 0.01 0.00 10 (B)
20
30
40
50
60
70
Bragg's angle (2θ)
Fig. 1. X-ray diffractogram of Nd-doped PZT (x/65/35) pellets sintered in air (A) and PZ environment (B).
The linear particle size (P) is calculated from the strong reflection XRD peak using Sherrer’s formula [15] P ¼ Kl=b1=2 cos y, where K ¼ 0:89, b1/2 full-width at half-maxima. Variation of particle size as a function of Nd doping is shown in Fig. 2, from the graph it is observed that particle size is found to decrease with Nd doping for pellets sintered in air and no such significant observation was found for PZ environment sintered samples. The decrease in particle size is expected to be due to formation of ZrO2 phase. Similar observations were found from microstructure studies of the samples. Fig. 3(a–c) and (d–f) are the SEM photographs of PNZT (x ¼ 0.01, 0.03, 0.07) pellets sintered in air and PZ atmosphere, respectively. Less compactness and porosity is observed in all photographs. Grain size of PZ environment samples is found larger than air-sintered samples and
porosity is high for air-sintered samples. All these observations suggest that PZ environment reduces the excess PbO evaporation. The average grain size was determined by the linear interception method and data is plotted as function of Nd concentration in Fig. 4. The decrease in grain size by Nd doping may be due to occupation of Nd3+ ion at B site replacing Zr4+/Ti4+ ion, where it act as acceptor. The acceptor dopants in ABO3 perovskite lattice introduces oxygen vacancy to maintain charge neutrality [16], due to this oxygen vacancy domain walls gets pinned and reduces grain size. Also these oxides get precipitated at the grain boundary that subsequently resists the grain growth. 3.2. Dielectric and electric properties Fig. 5 shows the variation of dielectric constant as function of temperature (40–500 1C) at 10 KHz frequency
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Table 2 Structural and dielectric parameters of Nd doped PZT (65/35) ceramic at 10 KHz PNZT (x/65/35)
0.00 0.01 0.03 0.05 0.07 0.09
Rhombohedral lattice parameter a in A˚
4.1085 4.1032 4.0878 4.0924 4.1106 4.0783
Density (gm/cm3) air
PZ
5.489 5.668 5.899 5.818 5.620 5.120
5.752 5.773 6.187 6.118 5.887 5.437
28 26
Particle size (nm)
24 22
sintered in Air sintered in PZ
20 18 16 14 12 -0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 x value in PNZT (x/65/35)
Fig. 2. Particle size variation of PNZT (x/65/35) composition with Nd concentration derived from Sherrer’s equation.
for all different PNZT compositions. The dielectric constant shows phase transition as expected for normal ferroelectrics. Also the region around the dielectric peak is broadened, which is one of the most important characteristics of disordered perovskite structure with diffuse phase transition. The broadening is considered to be due to compositional fluctuation [17] developed at A site by Pb2+, Nd3+ and at B site by Zr4+,Ti4+,Nd3+ ions. The transition temperature (Tm) and maximum dielectric constant (emax) are given in Table 2. Transition temperature was found to shift forward lower temperature by 80 1C with Nd concentration from x ¼ 0.00 to 0.05, with further Nd doping Tm remained at same position. The decrease in Tm with Nd doping may arise from following possible factors. It was established [18] in other Pb-based perovskite and relaxors that the reduction in grain size favors the reduction in Tm, however this may not be the only reason for fall of 80 1C in Tm. In case of undoped PZT film, any particular ion of the lattice experiences the same average field induced by other ion in the lattice. Due to this during ferroelectric phase transition, ion in the lattice shifts in the same way, resulting in macroscopically large region called domain. In contrast, PZT doped with Nd can be
Transition temperature Tm (1C)
Maximum dielectric constant emax
Dissipation factor (tan d)
365 355 305 280 285 285
1758 1772 2687 2363 1247 1092
0.1078 0.0994 0.0597 0.0474 0.0544 0.0821
considered as disordered ferroelectric system where electric dipoles, Nd ion and intrinsic defects such as oxygen and Pb vacancies, acts as source of random electric field distributions which reduces Tm. It was shown earlier in Fig. 4 that the grain size decrease with Nd content, smaller the grain size and hence high density of grain boundary concentration which in tern increases the random field strength and shifts Tm to lower value. The Tm is found to be independent on measured frequency, but maximum dielectric constant is decreasing with increase in frequency. Fig. 6 shows the variation of dielectric constant at 50 1C as function of frequency for all PNZT samples. Dielectric constant shows strong dispersion at lower frequencies. This is attributed to the low frequency space charge accumulation effect. Such strong dispersion in dielectric constant appears to be a common feature in ferroelectrics associated with nonnegligible ionic conductivity and is referred to as the low frequency dielectric dispersion. Dielectric constant appears to increase upto x ¼ 0.03 Nd doping and then decreases. The decrease in dielectric constant at higher Nd doping is due to decrease in grain size and formation of nonperovskite ZrO2 phase. The variation of dielectric loss as a function of temperature (40–500 1C) at 10 KHz frequency is shown in Fig. 7. It was found that dissipation factor (tan d) is very low and is almost constant for all compositions at lower temperatures; however above 400 1C a sharp rise in dielectric loss was observed. This may be because limited number of mobile ion in ionic solid are trapped in relatively stable potential wells during their motion through solids. Owing to a rise in temperature, the donor cations start taking a major part in the conduction process. These donors create a level much near the conduction band, therefore small amount of energy is required to activate them. Also slight change in stoichiometry (i.e. the metal: oxygen ratio) in the multi metal complex oxides cause the creation of a large number of donors and acceptors [19]. Fig. 8 shows the variation of dielectric loss as function of frequency at room temperature, all compositions shows strong lower frequency dispersion. The room temperature dielectric loss (tan d) found to decrease with lower Nd doping (upto x ¼ 0.05) and there after it increases (data given in Table 2), this is consistent with previous literature [20].
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Fig. 3. Microstructure of PNZT samples sintered in air (A) x ¼ 0:01, (B) x ¼ 0:03, (C) x ¼ 0:07 and sintered in PZ environment (D) x ¼ 0:01, (E) x ¼ 0:03, (F) x ¼ 0:07.
The diffuseness in the materials was examined by quadratic relation [21] 1 1 ðT T c Þg ¼ þ , max 2m d2 where emax is maximum value of e at Tm, g and d are diffusivity and diffuseness parameters, respectively. The diffusivity (g) is determined from slope of ln(1/e–1/emax) versus ln(TTC) graph and its value is found to be 2 for all compositions, indicating the pure diffuse phase transition described by Smoeski and Isupov. Fig. 9 shows the dependence of logarithm conductivity on the reciprocal absolute temperature within a broad range of temperature (40–500 1C). The graph consists of two rectilinear portions with different angels of inclination
to the X-axis. At temperature above the point of fracture, the conductivity is mainly determined by intrinsic defects and is physical parameter of compound. On the other hand, below the point of fracture the conductivity is determined by the nature and concentration of impurities. The temperature at which the fracture is observed on the log s vs. 1/T essentially depends on degree of purity and perfection of crystal [22]. From the graph it was found that increasing Nd doping, fracture point shifts towards lower temperature side, which indicates the increase of impurity in the samples. The shift in fracture point temperature with Nd concentration is shown in Fig. 10. The activation energy of the samples was calculated from the slope of log s vs. 1/T curve and the data is given in Table 3.
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1.4
00 01 03 05 07 09
700 Dielectric constant at 50°C (ε)
grain size (μm)
1.2 sintered in Air sintered in PZ
1.0
0.8
0.6
600
500
400
300
0.4 200
0.2 0.00
0.02
0.04
0.06
0.08
0.10
0.0
2.0x105
X value in PNZT (x/65/35)
4.0x105
6.0x105
8.0x105
1.0x106
Frequency (Hz)
Fig. 4. Grain size variation of PNZT (x/65/35) composition with Nd concentration.
Fig. 6. Variation of dielectric constant with frequency for PNZT (x/65/35) ceramics at 50 1C.
3200
2400 2000
00 01 03 05 07 09
8 Dielectric loss (tan δ)
Dielectric constant (ε)
10
00 01 03 05 07 09
2800
1600 1200
6
4
2
800 400
0
0
100
200
300
400
500
Temperature (°C)
0
100
200 300 Temperature (°C)
400
500
Fig. 5. Temperature dependence of the dielectric constant for PNZT (x/65/35) ceramics at 10 KHz frequency.
Fig. 7. The temperature dependence of the dielectric loss at different Nd doping concentration for PZT (65/35) ceramic.
3.3. Complex impedance analysis and thermodynamic properties
impedance plane (also called Nquist plot). The radius of semicircle gives the exact relaxation time of lumped parameters that are associated with the samples. All these curves have their center located away from the real impedance axis indicating the presence of relaxation species with distribution of relaxation times in these samples. Using the numerical method reported by Bishay [23], the interceptions on real axis of all arcs and radius of circles were calculated from which grain boundary resistance and relaxation frequencies were determined. The variation of grain boundary resistance as a function of temperature for all different PNZT compositions is shown in Fig. 12. The grain boundary resistance is found to decrease with increasing temperature and increases with increasing Nd doping. This is because Nd at B site of ABO3 perovskite
Fig. 11 shows a set of impedance data taken over a wide frequency range (100 Hz–1 MHz) at several temperatures as a Nyquist diagram for Nd (x ¼ 0.03)-doped PZT (65/35) ceramic. The shape of the cole–cole plot obtain in the present study is highly depend on temperature. At lower temperature the shape of the plot is straight line with large slope indicating the insulating nature of the sample. Increasing the temperature the slope of line decreases and turn towards real axis. All these curves start at the origin and hence there is no series resistance that can be ascribed to the LCR circuit representation of the sample. This simple RC circuit gives a semicircle in the complex
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0.30
0.01 0.03 0.05 0.07 0.09
240 fracture point temperature (°C)
dielectric loss (tan δ)
0.25 0.20 0.15 0.10 0.05
0.0
2.0x105
4.0x105
6.0x105
8.0x105
1.0x106
200
180
0.00
Frequency (Hz)
Fig. 8. Variation of dielectric loss with frequency for PNZT (x/65/35) ceramics.
-12
0.02 0.04 0.06 0.08 X value of Nd in PNZT (x/65/35)
0.10
Fig. 10. Variation of the point of fracture in ln(s) versus 1/T graph with Nd doping in PZT (65/35) ceramic.
Table 3 Thermodynamic parameters and activation energy of PNZT (x/65/35) at different ambient temperatures
-13 -14
00 01 03 05 07 09
-15 ln (σdc)
220
160
0.00
-16 -17
PNZT (x/65/35)
Temperature (K)
Activation energy DE (eV)
DH (Kcal/ mol)
DF (Kcal/ mol)
DS (Kcal/ mol)
0.00
323 373 473
0.1709
24.98
9.82 10.24 13.39
0.0773 0.0395 0.0245
0.01
323 373 473
0.2456
26.04
9.12 10.81 12.76
0.0524 0.0408 0.0281
0.05
323 373 473
0.1027
20.79
8.06 8.85 12.25
0.0394 0.032 0.0181
0.07
323 373 473
0.0602
18.49
8.80 9.98 13.07
0.030 0.023 0.012
-18 Point of fracture -19 -20 0.000
7
0.005
0.010
0.015
0.020
0.025
1/T (/°C) Fig. 9. The variation of the conductivity s with temperature for PZT (65/35) ceramic at different Nd doping.
acts as donor, which reduces the concentration of intrinsic oxygen vacancies, created due to PbO evaporation during sintering of PZT ceramics. Also when the concentration of donor impurity is close to that of the acceptor impurities originating from lead vacancies, most of the holes from acceptor level are compensated by electron from donor level and as a result bulk resistance of PNZT increases. The activation energy of the relaxation DQ for different compositions is calculated from the arrhenius formula [24–26] and is given in Table 3.
relaxation time and ambient temperature can be obtain using following formula [28,29]: h expðDF =RTÞ, t¼ kT where h is plank’s constant, R is universal gas constant and DF is the free energy of activation. The enthalpy of activation (DH) is related to free energy of activation (DF) by the formula
t ¼ t0 expðDQ=kTÞ,
DF ¼ DH TDS,
where k is Boltzmann constant and t0 is pre-exponential factor. According to Eyring [27] the relation between the
where DS is change in entropy. The DH can be calculated from the logarithmic plot of (tT) versus (1/T).
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4. Conclusions 8
B50 C100 D200 E350 F400 G450
Z|| (M ohms)
6
4
2
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
|
Z (M ohms)
Grain boundary resistance Rgb in Megaohms
Fig. 11. Complex impedance plane plots at different temperatures for sintered PNZT (x/65/35), x ¼ 0:03 sample.
In the present work we have reported the Nd3+-doped PZT(65/35) ceramic with composition x ¼ 0.0,0.01,0.03, 0.05,0.07,0.09 prepared by mixed oxide method. X-ray diffraction studies confirmed rhombohedral symmetry for the synthesized compound. Non-perovskite ZrO2 phase was also observed at higher Nd doping for air sintered PZT (65/35) samples, also grain size and particle size was found to decrease with Nd doping in air-sintered samples only. A study of dielectric constant suggests diffuse type of phase transition without any sign of relaxor behaviour in the material. With increasing x, dielectric constant was found to decrease appreciably, whereas Curie temperature (Tm) as determined from dielectric constant vs. temperature plots was found to shift to lower temperature. Dielectric constant and dissipation factor had shown strong lower frequency dispersion. Complex impedance analysis studied by Z00 –Z0 cole–cole plot at different temperature had revealed that grain boundary resistance decreases with temperature and increased with Nd doping. All these properties of prepared sample were may be useful for device applications. Acknowledgements
300 0.00 0.01 0.03 0.05 0.07 0.09
240
180
120
60
0 0
50
100 150 200 250 300 350 400 450 500 Temperature (°C)
Fig. 12. Variation of grain boundary resistance as function of temperature for all different PNZT compositions.
The free energy activation (DF) is deduced according the relation [30] DF ¼ 2:303RT logðkTt=hÞ. The calculated values of free energy DF, enthalpy of activation DH and change in entropy DS for different compositions of PNZT are given in Table 3. It is clear from the results that as ambient temperature increases change in entropy DS is decreases, but free energy is found to be increasing with temperature. However Nd doping decreases the enthalpy change, free energy and change in entropy.
The authors acknowledges to DST, New Delhi (SR/ FTP/PS-05/2003) for financial support for this work. References [1] D.L. Polla, L.F. Francis, MRS Bull. 2 (1996) 59. [2] J.F. Scott, Ferroelectric Memories, Springer, Berlin, 2000. [3] C.T. Lin, B.W. Scanlan, J.D. Mcnell, J.S. Webb, L. Li, J. Matter Res. 7 (1992) 2546. [4] S. Yokayana, Y. Ito, H. Ishihara, K. Hamada, S. Ohnishi, J. Kudo, K. Sakiyama, Jpn. J. Appl. Phys. 34 (1995) 767. [5] N. Neumann, R. Kohler, G. Hofmann, Integrat. Ferro Electric. 6 (1995) 213. [6] G.H. Haertling, J. Am. Ceram. Soc. 82 (1999) 797. [7] B. Jaffe, W.R. Cook, Piezoelectric Ceramics, RAN Publishers, 1971. [8] X. Dai, Z. Xu, D. Viehland, J. Am. Ceram. Soc. 78 (1995) 2815. [9] B. Jaffe, R.C. Williams, H. Jaffe, Piezoelectric Ceramics, Academic Press, London and New York, 1971. [10] Y. Yoshikawa, K. Tsuzuki, J. Am. Ceram. Soc. 75 (1992) 2520. [11] S.E. Park, T.R. Shrout, J. Am. Ceram. Soc. 82 (1997) 1804. [12] L.E. Cross, in: N. Setter, E.L. Colla (Eds.), Ferroelectric Ceramics— Tutorial Review Theory, Processing and Applications, vol. 1, Birkhauser Verlag, Basel, 1993. [13] K. Hardtl, D. Henings, J. Am. Ceram. Soc. 55 (1972) 230. [14] L. Wu, C.C. Lee, T.S. Wu ad, C.C. Wei, Ferroelectrics 41 (1982) 157. [15] B.D. Cullity, Elements of X-ray Diffraction, Addition-Wesley Series Publishing Company, Reading, MA, 1967. [16] S.B. Majumdar, B. Roy, R.S. Katiyar, S.B. Krupanidhi, J. Appl. Phys. 90 (2001) 2975. [17] G.A. Smolenskii, J. Phy. Soc. Japan 28 (1970) 26. [18] M. Tyunina, J. Levoska, A. Sternberg, S. Lepavuori, J. Appl. Phys. 84 (1998) 6800. [19] R.C. Blochanan, Ceramic Materials for Electronics, Oxford University Press, Newyork, 1986.
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