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2)O3 ceramics
Materials Chemistry and Physics 78 (2002) 432–436
Phase transition in Pb(Mn1/4 Cd1/4 W1/2 )O3 ceramics S.K. Sinha a , R.N.P. Choudhary b,∗ , S.N. Choudhary a b
a Department of Physics, T.M. Bhagalpur University, Bhagalpur 812007, India Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur 721302, India
Received 12 November 2001; received in revised form 30 April 2002; accepted 10 May 2002
Abstract The polycrystalline samples of Pb(Mn1/4 Cd1/4 W1/2 )O3 were synthesized by a high-temperature solid-state reaction technique. A preliminary X-ray structural study of the compound at room temperature shows the formation of a single-phase compound with a non-centrosymmetric space group P2221 of orthorhombic structure. Studies of dielectric constant (ε) and loss tangent (tan δ) both as a function of frequency (103 –104 Hz) and temperature (20–350 ◦ C) suggest that the compound undergoes a phase transition at 250 ◦ C and has a very high value of dielectric constant ∼30,000 at transition temperature. Both ac and dc conductivity have been studied over a wide range of temperature. The activation energy (Ea ) of the compound was calculated from both the plot of ac and dc conductivity versus inverse of absolute temperature. Variation of dc resistivity with electric field (0.55–53 kV m−1 ) at room temperature and variation of dc resistivity (106 –103 m) with temperature (26–350 ◦ C) at a constant electric field of 11.2 kV m−1 showed the semiconductor characteristics of the material. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Phase transition; Transition temperature; X-ray diffraction; Orthorhombic; dc Conductivity
1. Introduction
where
Since the discovery of ferroelectricity in BaTiO3 in 1945 [1], much attention has been focussed on the synthesis of oxide ferroelectrics of different structural families such as perovskite, tungsten bronze (TB), etc. during last 10 years. Some ferroelectric oxides of the perovskites family of a general formula ABO3 (A = mono or divalent, B = tri to hexavalent ions) have a great potential for devices [2–4]. Among all the perovskite oxides studied so far, some Pb-based compounds viz. PbTiO3 , PbZrO3 , PbWO3 , PbMoO3 , etc. have been found very important either in pure or complex form for devices [5–8]. It has been found that the desired device parameters can be obtained by suitable substitutions of single or multi-elements at the A and/or B sites of the perovskite compounds [9–11] satisfying the following conditions: (i) charge neutrality and (ii) suitable tolerance factor t [12] as k i=1
xAi nAi +
l
xBi nBi = 6
(i)
i=1
∗ Corresponding author. Tel.: +91-3222-83814; fax: +91-3222-777481. E-mail address: [email protected] (R.N.P. Choudhary).
k
xAi = 1,
0 ≤ xAi ≤ 1;
i=1
1
xBi = 1,
0 ≤ xBi ≤ 1
i=1
where xAi and xBi are the fractions of ions which reach the primitive elementary cell and nAi and nBi are the valence numbers of these ions, and t=√
r¯A + r0 2(¯rB + r0 )
(ii)
where t is the tolerance factor, r¯A and r¯B are the average radii of the ions at the A and B sites, respectively. The r0 = 1.32 Å (Goldschmidt ionic radius of O2− ). For ideal perovskite, t = 1. For normal or usual perovskite t is expected to be within the range 0.80 ≤ t ≤ 1.05. Extensive literature suggests that not much work have been reported on modified lead tungstate and molybdate. This may be due to the higher electrical conductivity of W6+ and Mo6+ ions [13]. The conductivity can be controlled effectively by substituting suitable dopants at B site. Here we propose to substitute isovalent cations Mn2+ and Cd2+ at the W site of lead tungstate. The calculated t of the compound was found to be 0.86. This shows that the compound has distorted structure. In this paper, we report detailed structural, dielectric and electrical propitious of Pb(Mn1/4 Cd1/4 W1/2 )O3 (here after
0254-0584/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 2 ) 0 0 2 2 4 - 9
S.K. Sinha et al. / Materials Chemistry and Physics 78 (2002) 432–436
PMCW) for a better understanding of its phase transition and ferroelectric behaviour.
2. Experimental The polycrystalline samples of PMCW were synthesized from high-purity oxides and carbonates: PbO (99.9%, Aldrich), MnCO3 (AR grade, M/s Loba Chemie Industrial Co., India); CdO (99%, M/s sd Fine Chemical Pvt. Ltd., India) and WO3 (AR grade, M/s BDH Chemical Ltd., UK) using a solid-state reaction technique. These ingredients taken in a suitable stoichiometry were thoroughly mixed in an agate mortar for more than 2 h. The fine mixed powder was then calcined at 765 ◦ C for 18 h in an alumina crucible in air atmosphere. The process of mixing and calcination was repeated until homogeneous fine powder of PMCW was obtained. Finally, the fine calcined powder of PMCW was used to make cylindrical pellets of diameter 10 mm and thickness 1–2 mm under an isostatic pressure of about 6.5 × 107 N m−2 . Polyvinyl alcohol (PVA) was used as a binder to reduce the brittleness of the pellets. The binder was burnt off during the sintering. The pellets were then sintered in an alumina crucible at 775 ◦ C in an air atmosphere. The formation and quality of the compound were checked by an X-ray diffractogram (XRD) technique. The XRD of fine calcined powder was recorded at room temperature using an X-ray powder diffraction (PW 1710) with Cu K␣1 radiation (λ = 1.5418 Å) in a wide range of Bragg angles, 2θ (10◦ ≤ 2θ ≤ 70◦ ) with a scanning rate of 2◦ min−1 . To study the electrical properties both the flat surfaces of the sintered pellets were electroded with air drying silver paint, and then fired on at 200 ◦ C for 2 h to remove the effect of moisture, if any, for all the electrical measurements. The dielectric constant (ε) and loss tangent (tan δ) of PMCW were measured both as a function of frequency (500 Hz–10 kHz) and temperature (26–330 ◦ C) using a GR 1620 AP capacitance measuring assembly with a laboratory-made three-terminal sample holder which compensates all sorts of stray capacitances. The dc electrical resistivity was measured as a function of biasing electric field (0.55–53 kV m−1 ) from room temperature to 350 ◦ C with the help of a Keithley-617 programmable electrometer, laboratory-made sample holder, chromel–alumel thermocouple and PID temperature controller (Indo therm 401D).
3. Results and discussion The sharp and single peaks of the XRD patterns of calcined powder samples, which were different from those of its constituents oxides and carbonates, suggested the formation of a single-phase compound. All the peaks of the XRD pattern were indexed, and cell parameters were determined in various crystal systems with a standard computer program “PowdMult” using observed d-values of strong,
433
Table 1 Comparison of some observed and calculated d-values (Å) of some reflections for PMCW compound at room temperature h
k
l
dobs
dcal
I/I0
0 1 1 1 1 0 0 2 0 1 2 0 0 2 1 0 0 1 1 2 3 1 3 3 1 0 3 2 1 3 2 2 1 0 3 3 1 3 1
2 1 1 0 1 2 4 0 4 0 1 4 1 0 4 0 5 0 1 1 1 6 0 2 0 6 0 4 7 4 3 6 7 7 4 1 8 5 7
0 1 4 4 4 5 0 0 2 6 2 3 7 4 3 8 2 8 8 6 1 0 3 2 10 5 5 7 0 2 9 4 4 6 6 9 3 6 8
6.4165 5.4905 4.7615 3.9887 3.8130 3.4629 3.2489 3.1691 3.0828 3.0096 2.9560 2.9095 2.8586 2.7118 2.6525 2.5609 2.5052 2.3723 2.3367 2.2887 2.0760 2.0413 2.0188 1.9737 1.9504 1.9096 1.8802 1.7927 1.7748 1.7429 1.7004 1.6828 1.6762 1.6238 1.5715 1.5385 1.5265 1.4769 1.4580
6.4151 5.5904 4.7633 3.9871 3.8101 3.4618 3.2326 3.1774 3.0907 3.0153 2.9577 2.9020 2.8555 2.6984 2.6543 2.5618 2.5049 2.3757 2.3366 2.2885 2.0776 2.0384 2.0201 1.9735 1.9517 1.9079 1.8804 1.7914 1.7736 1.7447 1.7002 1.6839 1.6760 1.6248 1.5719 1.5391 1.5267 1.4768 1.4582
1 2 3 4 4 6 5 24 4 9 17 100 9 4 3 7 11 5 4 2 18 9 4 2 3 6 2 6 4 3 14 19 19 2 2 3 6 3 9
medium and low intensity reflections spread over in a wide 2θ range. Finally, a unit cellin orthorhombic system was selected for which d = (dobs − dcal ) was found to be minimum. A good agreement between observed and calculated d-values (Table 1) suggests the correctness of selected crystal system and unit cell parameters. The cell parameters of the unit cell were then refined using a least-squares method, which were found to be: a = 6.3485 (44) Å, b = 12.9303 (44) Å and c = 20.4996 (44) Å. Even with limited number of reflections/peaks of XRD pattern, the space group of the material was found to be P2221 . The average linear crystallite size (Phkl ) was calculated from strong and medium intensity peak profiles using Scherrer’s equation [14] Phkl = 0.89 λ/[β 1/2 cos θ hkl ] (where β1/2 = half peak width) and was found to be 17 nm. As we used powder samples, the XRD peak broadening due to mechanical strain, instrumental and other sources have been ignored in the
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S.K. Sinha et al. / Materials Chemistry and Physics 78 (2002) 432–436
Fig. 1. Variation of dielectric constant (ε) and dielectric loss (tan δ) of PMCW as a function of frequency at room temperature.
calculation of crystallite size. The smaller crystallite size is of great importance, as it offers a higher rate of densification due to both an increase in driving force for sintering and to the smaller distances of mass transport needed to fill the pores. This permits the lowering of sintering temperature and the achievement of fine grain ceramics. Fig. 1 shows the variation of dielectric constant and loss tangent as a function of frequency (500 Hz–10 kHz) at room temperature. A decrease in dielectric constant was observed with increase in frequency. This is because at low frequencies the compound has different types of polarization (i.e. interfacial, atomic, ionic, dipolar, electronic, etc.). As we increase frequency, some of the polarizations were getting ineffective and hence, at higher frequency we have a lower value of ε. The loss tangent first decreases with increasing frequency and then increases with further rise in frequency. This is because the active component (ohmic) of the current increases more rapidly than its reactive component (capacitive). Again at higher frequencies (>10 kHz) tan δ decreases with increasing frequency, because the active component of current is practically independent of the frequency and the reactive component increases proportionally to the frequency (not seen in the Fig. 1). This type of variation was found by us in some of the modified lead tungstate ceramics [15–18]. Fig. 2 shows the variation of ε and tan δ as a function of temperature (26–330 ◦ C) at 10 kHz. From this plot, it is clear that the compound has a weak dielectric anomaly at 250 ◦ C (usually referred as Tc ). At Tc , the value of ε and tan δ was
found to be 30,230 and 0.49, respectively. Above 275 ◦ C, ε increases sharply with further rise in temperature. This is due to the presence of space charge polarization in the bulk material. The dielectric loss varies in a similar way. A small temperature difference between the peaks of dielectric constant and loss tangent is consequently an outcome of Kramers–Kronig relation accounting for the broadening of phase transition in the material [19]. Further, Mn2+ , Cd2+ and W6+ ions occupy octahedral positions. This suggests that in PMCW, the fluctuations in the statistical distribution of Mn2+ , Cd2 and W6+ are too small to be conspicuous for providing a fairly broadened phase transition. The ac electrical conductivity (σ ac ) and activation energy (Ea ) of PMCW were calculated from the measured dielectric data and using the formulae [18] σac = εε0 ω tan δ and σac = σ0 exp (−Ea /kB T) where ε 0 is the vacuum dielectric constant, ω the angular frequency and kB the Boltzmann constant. Fig. 3 shows the variation of ac conductivity (ln σ ac ) with inverse of absolute temperature (103 /T). An anomaly was observed at a temperature near to the transition temperature (Tc ). This type of anomaly was observed in many other ferroelectric ceramics of the perovskite family [20]. The activation energy (Ea ) calculated from the slope of the ln σ ac versus 103 /T was found to be 0.96 eV in the higher temperature region. This value is consistent with the value reported for such isomorphous compounds [21]. In spite of this anomaly in dielectric constant and ac conductivity, proper hysteresis loop could not observed in the compound. This is due to lack of sufficient poling field and time. Attempts are being made again to modify the Sawyer–Tower circuit to obtain a suitable hysteresis loop. Fig. 4 shows the variation of dc resistivity with biasing field at room temperature. The resistivity decreases with increasing bias field. It has been observed that there is a very little variation with biasing field at room temperature. However, at higher field the decrease in resistivity is rather fast. This may be due to the following reasons: (a) ionization occurs in homogenous dielectrics mainly through the mechanism of partial discharge of gases moistures from the pores or cracks present in the ceramics, the electric field results in the generation of local heat which in turn results in the generation of thermal stresses and increase of local conduction, the stresses can generate more pores/cracks leading to further ionization up to a certain field; (b) electrons may be ejected from the electrodes material. These electrons are then accelerated through the sample and collide with ions or atoms in the solid knocking out other electrons and thus ionization takes place. So, resistivity comes down with increasing biasing field [22]. Fig. 5 shows the variation of dc conductivity of PMCW with temperature at a constant biasing field of 11.2 kV m−1 . It is found that conductivity of the compound has a low value ∼10−6 ( m)−1 at room temperature, which increases rapidly to a value of 10−3 ( m)−1 at 350 ◦ C. The increase in conductivity at high temperature may, however, be possibly due to the supply of more and more thermal energy to the
S.K. Sinha et al. / Materials Chemistry and Physics 78 (2002) 432–436
435
Fig. 2. Variation of dielectric constant (ε) and dielectric loss (tan δ) of PMCW as a function of temperature at 10 kHz.
material as the temperature increases. This results in the creation of more and more free electrons that could be set free from O2− ions. When an electron is introduced in the sample it might be associated with cations, which results
in creating an unstable valence state. This type of resistive behavior is found in many ferroelectric materials studied by us [23–25]. The activation energy (Ea ) of PMCW compound calculated from the slope of the ln σ dc versus 103 /T was
Fig. 3. Variation of ac conductivity (ln σ ac ) with inverse of absolute temperature (103 /T) at 10 kHz.
Fig. 4. Variation of dc resistivity (ln σ dc ) of PMCW as a function of biasing field at room temperature.
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S.K. Sinha et al. / Materials Chemistry and Physics 78 (2002) 432–436
structural analysis and observations of double hysteresis loop on poled samples. References
Fig. 5. Variation of dc conductivity of PMCW as a function of temperature at constant biasing field 11.2 kV m−1 .
found to be 0.42 eV in the higher temperature region. From low value of activation energy, it is again confirmed that oxygen may be the main carrier in the electrical conduction.
4. Conclusions Finally, it is concluded that PMCW has orthorhombic structure at room temperature and undergoes dielectric anomaly at 250 ◦ C. The nature of variation of ε with temperature and non-polar space group suggests that PMCW may have antiferroelectric properties. However, conclusions to this may be drawn only by the detailed single crystal
[1] B. Wul, L.M. Goldman, C.R. Acad. Sci. USSR 46 (1945) 123. [2] T. Negas, G. Yeager, S. Bell, N. Coats, Am. Ceram. Soc. Bull. 72 (1993) 80. [3] H. Tamura, T. Konolle, Y. Sakable, K. Wakino, J. Am. Ceram. Soc. 67 (1989) C59. [4] K. Wakino, K. Minai, H. Tamura, J. Am. Ceram. Soc. 67 (1984) 278. [5] K.K. Dev, Ferroelectrics 82 (1988) 45. [6] L.H. Parkar, A.F. Tasch, IEEE Cir. Mag. 1 (1990) 17. [7] A. Mansingh, Ferroelectrics 120 (1990) 69. [8] R.P. Tandon, R. Singh, R.D.P. Singh, Ferroelectrics 120 (1991) 293. [9] D. Vieffland, N. Kim, Z. Xu, D.A. Payne, J. Am. Ceram. Soc. 78 (1995) 2481. [10] S. Bera, R.N.P. Choudhary, Ferroelectrics 220 (1999) 55. [11] T.R. Shrout, A. Hilliyal, Am. Ceram. Soc. Bull. 66 (1987) 704. [12] B. Jaffe, W.R. Cook Jr., H. Jaffe, Piezoelectric Ceramics, Academic Press, New York, 1979. [13] S.N. Bai, T.Y. Tseng, J. Appl. Phys. 74 (1993) 695. [14] P. Scherrer, Gottinger Nachricht 2 (1918) 98. [15] S. Bera, R.N.P. Choudhary, Mater. Lett. 22 (1995) 197. [16] S. Bera, R.N.P. Choudhary, J. Mater. Sci. Lett. 14 (1995) 568–570. [17] S. Bera, R.N.P. Choudhary, J. Mater. Sci. Lett. 15 (1996) 251. [18] R.N.P. Choudhary, R. Palai, S. Sharma, Mater. Sci. Eng. B77 (2000) 235. [19] M.E. Lines, A.M. Glass, Principle and Applications of Ferroelectric and Related Materials, Oxford University Press, Oxford, 1977. [20] W.D. Kingery, Introduction to Ceramics, Wiley, New York, 1960. [21] S.K. Sinha, S.N. Choudhary, R.N.P. Choudhary, Mater. Chem. Phys. 8958 (2000) 1–4. [22] R.C. Buchanan, Ceramic Material for Electronics, Marcel-Dekker, New York, 1986 [23] S.K. Sinha, R.N.P. Choudhary, S.N. Choudhary, T.P. Sinha, J. Phys. Chem. Solids 63 (2002) 323–329. [24] S.K. Sinha, R.N.P. Choudhary, S.N. Choudhary, T.P. Sinha, Mater. Lett. 51 (2001) 336–341. [25] S.K. Sinha, R.N.P. Choudhary, S.N. Choudhary, Ind. J. P. Appl. Phys. 38 (2000) 783.
Phase transition in Pb(Mn1/4 Cd1/4 W1/2 )O3 ceramics S.K. Sinha a , R.N.P. Choudhary b,∗ , S.N. Choudhary a b
a Department of Physics, T.M. Bhagalpur University, Bhagalpur 812007, India Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur 721302, India
Received 12 November 2001; received in revised form 30 April 2002; accepted 10 May 2002
Abstract The polycrystalline samples of Pb(Mn1/4 Cd1/4 W1/2 )O3 were synthesized by a high-temperature solid-state reaction technique. A preliminary X-ray structural study of the compound at room temperature shows the formation of a single-phase compound with a non-centrosymmetric space group P2221 of orthorhombic structure. Studies of dielectric constant (ε) and loss tangent (tan δ) both as a function of frequency (103 –104 Hz) and temperature (20–350 ◦ C) suggest that the compound undergoes a phase transition at 250 ◦ C and has a very high value of dielectric constant ∼30,000 at transition temperature. Both ac and dc conductivity have been studied over a wide range of temperature. The activation energy (Ea ) of the compound was calculated from both the plot of ac and dc conductivity versus inverse of absolute temperature. Variation of dc resistivity with electric field (0.55–53 kV m−1 ) at room temperature and variation of dc resistivity (106 –103 m) with temperature (26–350 ◦ C) at a constant electric field of 11.2 kV m−1 showed the semiconductor characteristics of the material. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Phase transition; Transition temperature; X-ray diffraction; Orthorhombic; dc Conductivity
1. Introduction
where
Since the discovery of ferroelectricity in BaTiO3 in 1945 [1], much attention has been focussed on the synthesis of oxide ferroelectrics of different structural families such as perovskite, tungsten bronze (TB), etc. during last 10 years. Some ferroelectric oxides of the perovskites family of a general formula ABO3 (A = mono or divalent, B = tri to hexavalent ions) have a great potential for devices [2–4]. Among all the perovskite oxides studied so far, some Pb-based compounds viz. PbTiO3 , PbZrO3 , PbWO3 , PbMoO3 , etc. have been found very important either in pure or complex form for devices [5–8]. It has been found that the desired device parameters can be obtained by suitable substitutions of single or multi-elements at the A and/or B sites of the perovskite compounds [9–11] satisfying the following conditions: (i) charge neutrality and (ii) suitable tolerance factor t [12] as k i=1
xAi nAi +
l
xBi nBi = 6
(i)
i=1
∗ Corresponding author. Tel.: +91-3222-83814; fax: +91-3222-777481. E-mail address: [email protected] (R.N.P. Choudhary).
k
xAi = 1,
0 ≤ xAi ≤ 1;
i=1
1
xBi = 1,
0 ≤ xBi ≤ 1
i=1
where xAi and xBi are the fractions of ions which reach the primitive elementary cell and nAi and nBi are the valence numbers of these ions, and t=√
r¯A + r0 2(¯rB + r0 )
(ii)
where t is the tolerance factor, r¯A and r¯B are the average radii of the ions at the A and B sites, respectively. The r0 = 1.32 Å (Goldschmidt ionic radius of O2− ). For ideal perovskite, t = 1. For normal or usual perovskite t is expected to be within the range 0.80 ≤ t ≤ 1.05. Extensive literature suggests that not much work have been reported on modified lead tungstate and molybdate. This may be due to the higher electrical conductivity of W6+ and Mo6+ ions [13]. The conductivity can be controlled effectively by substituting suitable dopants at B site. Here we propose to substitute isovalent cations Mn2+ and Cd2+ at the W site of lead tungstate. The calculated t of the compound was found to be 0.86. This shows that the compound has distorted structure. In this paper, we report detailed structural, dielectric and electrical propitious of Pb(Mn1/4 Cd1/4 W1/2 )O3 (here after
0254-0584/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 2 ) 0 0 2 2 4 - 9
S.K. Sinha et al. / Materials Chemistry and Physics 78 (2002) 432–436
PMCW) for a better understanding of its phase transition and ferroelectric behaviour.
2. Experimental The polycrystalline samples of PMCW were synthesized from high-purity oxides and carbonates: PbO (99.9%, Aldrich), MnCO3 (AR grade, M/s Loba Chemie Industrial Co., India); CdO (99%, M/s sd Fine Chemical Pvt. Ltd., India) and WO3 (AR grade, M/s BDH Chemical Ltd., UK) using a solid-state reaction technique. These ingredients taken in a suitable stoichiometry were thoroughly mixed in an agate mortar for more than 2 h. The fine mixed powder was then calcined at 765 ◦ C for 18 h in an alumina crucible in air atmosphere. The process of mixing and calcination was repeated until homogeneous fine powder of PMCW was obtained. Finally, the fine calcined powder of PMCW was used to make cylindrical pellets of diameter 10 mm and thickness 1–2 mm under an isostatic pressure of about 6.5 × 107 N m−2 . Polyvinyl alcohol (PVA) was used as a binder to reduce the brittleness of the pellets. The binder was burnt off during the sintering. The pellets were then sintered in an alumina crucible at 775 ◦ C in an air atmosphere. The formation and quality of the compound were checked by an X-ray diffractogram (XRD) technique. The XRD of fine calcined powder was recorded at room temperature using an X-ray powder diffraction (PW 1710) with Cu K␣1 radiation (λ = 1.5418 Å) in a wide range of Bragg angles, 2θ (10◦ ≤ 2θ ≤ 70◦ ) with a scanning rate of 2◦ min−1 . To study the electrical properties both the flat surfaces of the sintered pellets were electroded with air drying silver paint, and then fired on at 200 ◦ C for 2 h to remove the effect of moisture, if any, for all the electrical measurements. The dielectric constant (ε) and loss tangent (tan δ) of PMCW were measured both as a function of frequency (500 Hz–10 kHz) and temperature (26–330 ◦ C) using a GR 1620 AP capacitance measuring assembly with a laboratory-made three-terminal sample holder which compensates all sorts of stray capacitances. The dc electrical resistivity was measured as a function of biasing electric field (0.55–53 kV m−1 ) from room temperature to 350 ◦ C with the help of a Keithley-617 programmable electrometer, laboratory-made sample holder, chromel–alumel thermocouple and PID temperature controller (Indo therm 401D).
3. Results and discussion The sharp and single peaks of the XRD patterns of calcined powder samples, which were different from those of its constituents oxides and carbonates, suggested the formation of a single-phase compound. All the peaks of the XRD pattern were indexed, and cell parameters were determined in various crystal systems with a standard computer program “PowdMult” using observed d-values of strong,
433
Table 1 Comparison of some observed and calculated d-values (Å) of some reflections for PMCW compound at room temperature h
k
l
dobs
dcal
I/I0
0 1 1 1 1 0 0 2 0 1 2 0 0 2 1 0 0 1 1 2 3 1 3 3 1 0 3 2 1 3 2 2 1 0 3 3 1 3 1
2 1 1 0 1 2 4 0 4 0 1 4 1 0 4 0 5 0 1 1 1 6 0 2 0 6 0 4 7 4 3 6 7 7 4 1 8 5 7
0 1 4 4 4 5 0 0 2 6 2 3 7 4 3 8 2 8 8 6 1 0 3 2 10 5 5 7 0 2 9 4 4 6 6 9 3 6 8
6.4165 5.4905 4.7615 3.9887 3.8130 3.4629 3.2489 3.1691 3.0828 3.0096 2.9560 2.9095 2.8586 2.7118 2.6525 2.5609 2.5052 2.3723 2.3367 2.2887 2.0760 2.0413 2.0188 1.9737 1.9504 1.9096 1.8802 1.7927 1.7748 1.7429 1.7004 1.6828 1.6762 1.6238 1.5715 1.5385 1.5265 1.4769 1.4580
6.4151 5.5904 4.7633 3.9871 3.8101 3.4618 3.2326 3.1774 3.0907 3.0153 2.9577 2.9020 2.8555 2.6984 2.6543 2.5618 2.5049 2.3757 2.3366 2.2885 2.0776 2.0384 2.0201 1.9735 1.9517 1.9079 1.8804 1.7914 1.7736 1.7447 1.7002 1.6839 1.6760 1.6248 1.5719 1.5391 1.5267 1.4768 1.4582
1 2 3 4 4 6 5 24 4 9 17 100 9 4 3 7 11 5 4 2 18 9 4 2 3 6 2 6 4 3 14 19 19 2 2 3 6 3 9
medium and low intensity reflections spread over in a wide 2θ range. Finally, a unit cellin orthorhombic system was selected for which d = (dobs − dcal ) was found to be minimum. A good agreement between observed and calculated d-values (Table 1) suggests the correctness of selected crystal system and unit cell parameters. The cell parameters of the unit cell were then refined using a least-squares method, which were found to be: a = 6.3485 (44) Å, b = 12.9303 (44) Å and c = 20.4996 (44) Å. Even with limited number of reflections/peaks of XRD pattern, the space group of the material was found to be P2221 . The average linear crystallite size (Phkl ) was calculated from strong and medium intensity peak profiles using Scherrer’s equation [14] Phkl = 0.89 λ/[β 1/2 cos θ hkl ] (where β1/2 = half peak width) and was found to be 17 nm. As we used powder samples, the XRD peak broadening due to mechanical strain, instrumental and other sources have been ignored in the
434
S.K. Sinha et al. / Materials Chemistry and Physics 78 (2002) 432–436
Fig. 1. Variation of dielectric constant (ε) and dielectric loss (tan δ) of PMCW as a function of frequency at room temperature.
calculation of crystallite size. The smaller crystallite size is of great importance, as it offers a higher rate of densification due to both an increase in driving force for sintering and to the smaller distances of mass transport needed to fill the pores. This permits the lowering of sintering temperature and the achievement of fine grain ceramics. Fig. 1 shows the variation of dielectric constant and loss tangent as a function of frequency (500 Hz–10 kHz) at room temperature. A decrease in dielectric constant was observed with increase in frequency. This is because at low frequencies the compound has different types of polarization (i.e. interfacial, atomic, ionic, dipolar, electronic, etc.). As we increase frequency, some of the polarizations were getting ineffective and hence, at higher frequency we have a lower value of ε. The loss tangent first decreases with increasing frequency and then increases with further rise in frequency. This is because the active component (ohmic) of the current increases more rapidly than its reactive component (capacitive). Again at higher frequencies (>10 kHz) tan δ decreases with increasing frequency, because the active component of current is practically independent of the frequency and the reactive component increases proportionally to the frequency (not seen in the Fig. 1). This type of variation was found by us in some of the modified lead tungstate ceramics [15–18]. Fig. 2 shows the variation of ε and tan δ as a function of temperature (26–330 ◦ C) at 10 kHz. From this plot, it is clear that the compound has a weak dielectric anomaly at 250 ◦ C (usually referred as Tc ). At Tc , the value of ε and tan δ was
found to be 30,230 and 0.49, respectively. Above 275 ◦ C, ε increases sharply with further rise in temperature. This is due to the presence of space charge polarization in the bulk material. The dielectric loss varies in a similar way. A small temperature difference between the peaks of dielectric constant and loss tangent is consequently an outcome of Kramers–Kronig relation accounting for the broadening of phase transition in the material [19]. Further, Mn2+ , Cd2+ and W6+ ions occupy octahedral positions. This suggests that in PMCW, the fluctuations in the statistical distribution of Mn2+ , Cd2 and W6+ are too small to be conspicuous for providing a fairly broadened phase transition. The ac electrical conductivity (σ ac ) and activation energy (Ea ) of PMCW were calculated from the measured dielectric data and using the formulae [18] σac = εε0 ω tan δ and σac = σ0 exp (−Ea /kB T) where ε 0 is the vacuum dielectric constant, ω the angular frequency and kB the Boltzmann constant. Fig. 3 shows the variation of ac conductivity (ln σ ac ) with inverse of absolute temperature (103 /T). An anomaly was observed at a temperature near to the transition temperature (Tc ). This type of anomaly was observed in many other ferroelectric ceramics of the perovskite family [20]. The activation energy (Ea ) calculated from the slope of the ln σ ac versus 103 /T was found to be 0.96 eV in the higher temperature region. This value is consistent with the value reported for such isomorphous compounds [21]. In spite of this anomaly in dielectric constant and ac conductivity, proper hysteresis loop could not observed in the compound. This is due to lack of sufficient poling field and time. Attempts are being made again to modify the Sawyer–Tower circuit to obtain a suitable hysteresis loop. Fig. 4 shows the variation of dc resistivity with biasing field at room temperature. The resistivity decreases with increasing bias field. It has been observed that there is a very little variation with biasing field at room temperature. However, at higher field the decrease in resistivity is rather fast. This may be due to the following reasons: (a) ionization occurs in homogenous dielectrics mainly through the mechanism of partial discharge of gases moistures from the pores or cracks present in the ceramics, the electric field results in the generation of local heat which in turn results in the generation of thermal stresses and increase of local conduction, the stresses can generate more pores/cracks leading to further ionization up to a certain field; (b) electrons may be ejected from the electrodes material. These electrons are then accelerated through the sample and collide with ions or atoms in the solid knocking out other electrons and thus ionization takes place. So, resistivity comes down with increasing biasing field [22]. Fig. 5 shows the variation of dc conductivity of PMCW with temperature at a constant biasing field of 11.2 kV m−1 . It is found that conductivity of the compound has a low value ∼10−6 ( m)−1 at room temperature, which increases rapidly to a value of 10−3 ( m)−1 at 350 ◦ C. The increase in conductivity at high temperature may, however, be possibly due to the supply of more and more thermal energy to the
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Fig. 2. Variation of dielectric constant (ε) and dielectric loss (tan δ) of PMCW as a function of temperature at 10 kHz.
material as the temperature increases. This results in the creation of more and more free electrons that could be set free from O2− ions. When an electron is introduced in the sample it might be associated with cations, which results
in creating an unstable valence state. This type of resistive behavior is found in many ferroelectric materials studied by us [23–25]. The activation energy (Ea ) of PMCW compound calculated from the slope of the ln σ dc versus 103 /T was
Fig. 3. Variation of ac conductivity (ln σ ac ) with inverse of absolute temperature (103 /T) at 10 kHz.
Fig. 4. Variation of dc resistivity (ln σ dc ) of PMCW as a function of biasing field at room temperature.
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structural analysis and observations of double hysteresis loop on poled samples. References
Fig. 5. Variation of dc conductivity of PMCW as a function of temperature at constant biasing field 11.2 kV m−1 .
found to be 0.42 eV in the higher temperature region. From low value of activation energy, it is again confirmed that oxygen may be the main carrier in the electrical conduction.
4. Conclusions Finally, it is concluded that PMCW has orthorhombic structure at room temperature and undergoes dielectric anomaly at 250 ◦ C. The nature of variation of ε with temperature and non-polar space group suggests that PMCW may have antiferroelectric properties. However, conclusions to this may be drawn only by the detailed single crystal
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