Vogel-Fulcher like dielectric response in Pb[(Mg,Zn)
y3Nb2/3]0
3ceramic
S N Choudhary, K Prasad*, A Kumar and R N P*Choudhary
University Department of Physics, T M Bhagaipur University, Bhagafc>ur-812 007, Bihar, India
•Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur-721 302, West Bengal, India
E-mail k prasad65@gmail com
Abstract : Polycrystallme Pb[(Mg2^Znt/3)1/3Nb2/3]03 having tetragonal perovskite type structure was prepared by a high temperature solid state reaction method Dielectric constant and loss tangent were measured over a frequency range 1 kHz to 1 MHz in the temperature region 32°C to 225°C Dielectric studies show the relaxor behaviour with diffuse phase transition The frequency dependence of the temperature of the permittivity maximum (Tm) has been modeled using Vogel-Fulcher relation The dielectric relaxation in Pb[(Mg2^Zn1/3)1/3Nb2^]03 is found analogous to the magnetic relaxation in spm-glass system Cole-Cole analysis indicated that the relaxation is of polydispersive non-Debye type and the relaxation frequency shifts to higher frequencies with the increase in temperature
Keywords : Lead magnesium zinc niobate, diffuse phase transition, transition temperature, dielectric properties, relaxors PACS Nos. : 77 70 +a, 77 80 Bh, 77 84 -s, 77 84 Dy, 81 05 Je
1. Introduction
In recent years, there has been a growing interest in Pb-based relaxor ferroelectrics having perovskite type A(B/B//)03 structure. Among these lead magnesium niobate,
Pb(M9v3Nb2/3)03 (abbreviated PMN) is one of the most interesting and extensively studied system, which has already shown its potential in various electronic devices [ 1 - 3]. Since the discovery of PMN, numerous pure and modified PMN and its isomorphous compounds like : Pb(Zn1/3Nb2/3)03 [4], Pb(Ni1/3Nb2/3)03 [5], Pb(Fe1/2Nb1/2)03 [6], Pb(ln1/2Nb1/2)03 [7], Pb(Mg1 / 4Cd1 / 4Nb1 / 2)03 [8], Pb(Mg1 / 4Cdl / 1 2Nb2 / 3)03 [9], PbfMg^Co^Nb^Oa [10], PbfMg^Zn^Nb^Oa [11], Pb(Mg^Nb^)03 + PbTi03 + BaTi03
[12], Pb(Zn1/3Nb2/3)03 + PbTi03 + BaTi03 [13], Pb(Mg1/3Nb2/3)03 + PbTi03 + Ba(Zn1/3Nb2/3)03 [14], efc. have been investigated. Some of them are technologically important. Promising electrical properties of these materials have given a tremendous boost to carry out the fundamental and applied research on relaxor ferroelectrics.
Further PMN exhibits a high dielectric constant, good temperature stability near Tm with diffuse phase transition (DPT) characterized by frequency dependent dielectric
Corresponding Author © 2007 IACS
110 SNChoudhary, KPrasad, A KumarandRNP Choudhary maximum ( * w ) . As PMN is having highly tolerant AB03-structure, it provides enough scope for modification either at A or B-sites. It has also been observed that the electrical properties and ferro-paraelectric phase transition temperature of PMN can be controlled effectively by proper doping at B-site.
Several explanations (theoretical models) have been proposed to understand the behaviour of the relaxor ferroelectrics. The concept of polar microregions in relaxors was first introduced by Smolenskii within chemical inhomogeneity theory [15] and was later confirmed experimentally [1,16,17]. The deviation from paraelectric Curie-Weiss behaviour of the dielectric permittivity suggested the presence of nano-sized polar clusters.
Randall et al [18] proposed that the scale of the inhomogeneity leads to the relaxor behaviour. The nano-size clusters are dynamical in nature with their dipole moment thermally fluctuating between equivalent directions and in absence of interactions between these regions, this could be analogous to superparamagnetism [1]. Hence, the frequency dependence of the temperature of the dielectric maximum (Tm) should follow a simple Debye relationship [19], A spin-glass state is generally considered as a system of interacting superparamagnetic clusters and is characterized by the existence of a static freezing temperature (Tf) [20,21] and the magnetic relaxation in such system can be described by Vogel [22] and Fulcher [23] relationship. The PMN system is considered to be analogous to the spin-glass system with existence of thermally activated polarization fluctuations above Tf. Based on this analogy, one can consider relaxor ferroelectric as a polar-glassy system [24].
An extensive literature survey suggests that no report, to our knowledge, is available on the polycrystalline P b ^ M g ^ Z n ^ ^ N b ^ O a (abbreviated PMZN). The present work aims at the investigation of dielectric relaxation in PMZN, which has been modeled to spin-glass system using Vogel-Fulcher relation. Also, to understand the relaxation process in PMZN, Cole-Cole analysis has been done and the electrical data have also been analyzed through impedance spectroscopic technique.
2. Experimental
The polycrystalline sample of PMZN was prepared by a high temperature two stage solid-state reaction technique (also known as columbite precursor method) using high- purity AR/GR grade component oxides in a desired stoichiometry. Details of which, are described elsewhere [9-11]. The formation of single-phase compound was checked by X-ray diffraction (XRD) technique using a X-ray diffractometer (Phillips PW1710, Holland) with CuK* radiation X = 1.5443 A over a wide range of Bragg angles (20° < 26 < 80°).
To study the electrical properties, flat surfaces of the pellets were electroded with fine silver paint and were kept at 200°C for 1 h prior to the experiment. Electrical impedance (Z), phase angle {$), capacitance and loss of the sample were measured both as a function of frequency (0.1 kHz-3 MHz) and temperature (32-225°C) using a computer controlled LCR-meter (HIOKI-3532, Japan).
3. Results and discussion
X-Ray diffraction profile (Figure 1) shows that PMZN ceramic was having almost single- phase and a least squares regression fit of the diffradlion data yielded tetragonal structure with lattice parameter, a = 4.059(6) A and c = 4-069(0) A with an estimated error of ±1(T3 A. The unit cell volume is found to be 67.06 A3. The criterion adopted for evaluating the Tightness, reliability of the indexing and|the structure of PMZN was
-!'#*• - dcaid -> minimum. f
!
The temperature dependence of dielectric constant fe) and loss tangent (XanS) at different frequencies are illustrated in Figure 2. The pHMs show a broad maximum
10000
HO 25
H 0 2 0 «£
too
I T 80
1 60
JS 40
&
0 (100)
_ j _ _ _ i ( H
J
1)
( i n )
L. A
. 1 . i , I
(200) <211>
(aoi)
1 . L 1 .
, i J , i 1 caaoy
, 1.
(310) (311)I . I, . I
-4 0 10 0 05
0 00
Bragg angles (20) lenipeniturc (UC ,
Figure 1. X-Ray diffraction pattern of Figure 2. Temperature dependence of PbKMg^Zn^^Nbjj/aJOa at room temperature. dielectric constant of Pb[(Mg2/3Zn1/3)1/3Nb2^]03
at 1 kHz, 10 kHz, 50 kHz, 100 kHz, 500 kHz and 1 MHz. Variation of dielectric permittivity maximum with frequency
(diffuse phase transition, DPT) in the region of 20°C and strong frequency dispersion, which indicate the relaxor behavior of PMZN. It has been observed that the temperature at which the relative permittivity was maximum, 2^ {i.e. phase transition temperature, Tm) shifted to higher temperature (from 60°C at 1 kHz to 78°C at 1 MHz) and £max
decreases (from 9045 at 1 kHz to 7911 at 1 MHz) (inset Figure 2) with the increase in frequency. A sharp decrease in dielectric constant with the increase in frequency can be explained in terms of the interfacial polarization. Contribution from interfacial polarizability comes due to the presence of two layers of materials of different conductivity. Here, the motion of the charge carrier occurs readily in the higher conductivity phase, but is interrupted at the phase boundary due to lower conductivity of the second phase [25]. In case of polycrystalline ceramics, this is commonly observed if the grains are semiconducting and the grain boundaries are insulating. The semiconductive grains in PMZN ceramics is believed to be due to the loss of oxygen during firing at higher temperatures in accordance with the reaction [26] :
00 <=> % Q2 T+ lf"0~+2e~ where all the species are written in accordance with Krdger
112 SNChoudhary, KPrasad, A KumarandRNP Choudhary
Vink notation of defects. These defects affect impedance and capacitance in the formation of barrier layers at the grain-grain boundary interface. During cooling after sintering, the reverse reaction occurs, but due to insufficient time available during cooling, the reoxidation takes place and is restricted only to grain boundaries. This results in difference between resistance of grain boundary and grain, giving rise to barrier [27], The build-up of charges at gram-grain boundary interface causes large polarization resulting in high dielectric constant at lower frequencies.
The diffuse phase transition and relaxor nature of PMZN has been described by the modified Curie-Weiss law [28,29] :
1/r-1/*m a x = C ^ r - T J ' (1)
where C (=2emaxSr) is the modified Curie-Weiss constant, S is the diffusivity parameter, and y is the critical exponent. The value of y can vary from 1, for normal ferroelectrics to 1-2 for relaxor ferroelectrics. The nature of variation of dielectric constant with temperature (Inset Figure 3) follow a quadratic law i.e. y = 2. The linear regression analysis gives the value of C = 1.38 x 108oC. The diffuse phase transition and relaxor behavior in Pb(B'1/3B#3)03-type of compounds are generally due to the B-site
N X
JS 3 02 3 00 2 98 2 96 2 9 4
2 92 290 2 88 286 2.84
- - -
- h
• J
5
Experimental points
>v — Non-linear fit
\ «
\ v £ = 0 0488cV
20
15
10
5
. • Experimental points J\
— Un»#r fit jf WL
0 ft 10 15 20 25 30 ~ ^
(T-TJ* U 1 0 - * ) ( ° C )J
6 7 8 9 10 11 12 13 14
1000/ T (K"1 )
Figure 3. inverse of temperature of the dielectric maximum as a function of measuring frequency. The points
correspond to the expenmental data while the solid line to fitting of Vogel-Fulcher relationship. Inset figure : Dependence of (1/f - 1 / ^ , ) on (T- T J * at 1 kHz.
compositional fluctuation (B7B"ratio) caused by the formation of the 1:1 nonstoichiometric short-range ordered microdomains [1.15,30]. In fact, in PbfB^B'^Oa the bonding preference for 1 : 1 local ordering is incompatible with the global 1 : 2 stoichiometry, leading to a frustrated state with only incomplete and short-range order [30]. Therefore, It is expected that the DPT and relaxor behaviour in PMZN may be due to the B-site compositional fluctuation (Mg/Nb or Zn/Nb).
Figure 3 shows the variation of In f with inverse of temperature Tm where the solid circles represent the experimental data. It can be observed from this figure that the frequency derivative of MTm is smaller at lower frequencies. This illustrates that as f -» 0, a static freezing temperature (Tf) is approached. The frequency dependence of the temperature of the permittivity maximum (Tm) has been modeled using Vogel-Fulcher empirical relationship :
f = f0e-E-'k{T~-T>\ (2)
where f is the operating frequency, f0 is the pre-exponenttal factor (Debye frequency), Ea is the activation energy. The relaxation time (r) i^ distributed over a certain temperature region. As the temperature is lowered, r increases and at a critical value
Tm = Tft r becomes extremely large and consequently the stable polarization is frozen to the glassy state [31]. This phenomenon has been observed in spin-glass system [32]. This relationship was employed by various authors to explain the frequency dispersion of the phase transition temperature in bulk or single crystal relaxor ferroelectrics [6,9-11,24,33,34]. Excellent fitting of Vogel-Fulcher relation with experimental data successfully explains the relaxor behavior in PMZN. The values for Ea, f0 and Tf using nonlinear fit to eq. (2) are found to be 0.0488 eV, 1.014 x 1011 Hz and 28.595°C respectively, which are also consistent with the earlier reports on similar systems [9~
11,24,31,33]. The value of f0 is found to be in the optical frequency range of lattice vibrations.
One of the most convenient ways for checking polydispersive nature of dielectric relaxation is through complex argand plane of e" against e\ usually called Cole-Cole plots [35]. For pure monodispersive Debye process, one expects semicircular plots with the center located on the ^'-axis whereas, for polydispersive relaxation, these argand plane plots are close to circular arcs with end-points on the axis of reals and the center below this axis. The complex dielectric constant in such situations is known to described by the empirical relation
••«->-«--'".«.-
1t(£
r. (3)
where Ae-es-eM is the contribution of the relaxator to static permittivity e^e^ is the contribution of higher frequency polarization mechanism, r is the mean relaxation time of the relaxators. The parameter a characterizes the distribution of relaxation times which increases with increasing internal degrees of freedom of relaxators and gives the magnitude of the departure of the electrical response from an ideal condition. It can however be determined from the location of the center of the Cole-Cole circles. Inset Figure 4 depicts a representative plot for PMZN at 350°C. When a goes to zero {(1-or) -> 1} eq. (3) reduces to classical Debye's formalism. It can be seen from this p\ot that the relaxation process is different from the monodispersive Oebye type (for which a = 0). The parameter a, as determined from the angle subtended by the radius of the circle with the f'-axis passing through the origin of the *"-axis is 0.0611 and
114 SNChoudhary, KPrasad, A KumarandRNPChoudhary 6
5
4 ci
5 3
Nl 2
1
"O.O 0.5 1.0 1.5 2.0 2.5 Z'(co) Mil
Figure 4. Complex impedance plot of PbKMg^Znt^/aNb^lOa at different temperatures. Inset figure : Cole-Cole diagram for at 350°C.
the value of Ae is estimated to be 1233. The non-zero value of a confirms the polydispersive nature of dielectric relaxation of PMZN.
The polydispersive nature of dielectric relaxation in PMZN was also verified by a set of impedance data taken over a wide frequency range (100 Hz-1 MHz) at several temperatures in the form of a Nyquist diagram (Figure 4). The impedance data at room temperature do not assume the shape of a semicircle as in the Nyquist plot rather it depicts a straight line with a large slope, suggesting the insulating behaviour of PMZN at room temperature. It is observed that with the increase in temperature the slope of the lines decreases and they bend towards real (Z') axis, indicating increase in conductivity of the sample. A semicircle could be traced starting form temperature 300°C onwards. All these curves start almost at the origin (R^ ~1Q) and hence there should be no series resistance for the LCR circuit representation of the sample and the high frequency semicircle may be ascribed to the parallel combination of bulk resistance (Rb) and capacitance (Cb) of PMZN. The appropriate equivalent circuit comprising of Rb and Cb has been shown in Figure 4. The value of Rb can be directly obtained from the intercept on the Z'-axis and the value of Cb can be calculated using the relation :
2 * U i « A «1. (4)
where f^ is the frequency at the maxima of the semicircle. It is observed that the peak maxima of the plots decrease and ^ shifts to higher values with the increase in temperature. Further, the values for Rbt cb and tb decrease with increase in temperature (Table 1). It can also be noticed that the complex impedance plots are not represented by full semicircle rather the semicircular arcs are depressed and the center
Table 1 * Parameters obtained from complex impedance plot at different temperatures.
Parameter Rb(W)
Cb(F)
M*>
300°C 1.9813 x l O8
1.3383 x 10"9
2.6515 x 10~3
250°C 9.9439 x 1 0s
8.0914 x tO"10
8.0460 x io-4
400°C 7.5608 x 1 0s
5.2604 x 10"10
3.9773 x 10""4
of the arcs lie below the real (Z') axis similar to the Cojb-Cole plot (inset Figure 4), which confirms the polydispersive nature of dielectric relaxation in PMZN. This may be due to the presence of distributed elements in the material-electrode system [35]. The value of R2 (regression coefficient) for all the fittings, quotdW in this paper, is > 0.9987.
4. Conclusion
Polycrystalline samples of PMZN having cubic structure were prepared by coulombite precursor method, which showed a relaxor behavior with diffuse phase transition.
Modeling of dielectric data using Vogel-Fulcher relationship shows strong evidence for a static freezing temperature of thermally activated polarization fluctuations in PMZN.
Therefore, the dielectric relaxation in PMZN may be considered analogous to magnetic relaxation in spin-glass system with polarization fluctuations above a static freezing temperature [1]. Cole-Cole analysis indicated the relaxation to be of polydispersive non- Debye type and the relaxation frequency shifts to higher side with the increase in temperature.
Acknowledgment
This work has been supported by the Department of Science & Technology (DST), New Delhi (Ref. No.: SP/S2/M-15/97). One of us (KP) wishes to thank Dr. A. A. Bokov, Simon Fraser University, British Columbia, Canada for his useful discussion.
References
[1] L E Cross Ferroelectric* 76 241 (1987)
[2] W Yao, C Feng, H Li, Y Yang and Y Yu Mater. Lett. 57 2834 (2003)
[3] J H Park, J G Park, B K Kinu, H J Je and Y Kim Mater. Res. Bull. 37 305 (2002) [4] Y Yamashita Am. Ceram. Soc. Bull. 73 74 (1994)
[5] E F Alberta and A S Bhalla Mater. Lett. 54 47 (2002)
[6] S A Ivanov, R Tellgren, H Rundlot, N W Thomas and S A Ananta J. Phys.: Cond. Mater. 12 2393 (2000) [7] A A Bokov, M A Leshchenko, M A Malitskaya and I P Raevski J. Phys.: Cond. Mater. 11 4899 (1999) [8] N P Singh and K Prasad J. Korean Phys. Soc. 32 S324 (1998)
[9] A Kumar, K Prasad, S N Choudhary and R N P Choudhary Mater. Lett. 58 3395 (2004) [10] K Prasad, S N Choudhary. A Kumar and R N P Choudhary Solid State Ionics 176 1641 (2005) [11] A Kumar, K Prasad, S N Choudhary and R N P Choudhary Ferroelectrics 326 67 (2005) [12] L Ruan, Y Wang, Z Gui and L Li J. Mater. Set.: Mater. Electron. 8 195 (1997) [13J A Hatliyal, U Kumar, R E Neconham and L E Cross J. Am. Ceram. Soc. 70 119 (1987)
116 SNChoudhary, KPrasad, A KumarandRNPChoudhary
[14] K Uchino, S Nomura and L E Cross Jpn. J. Appl. Phys. 19 L-367 (1980) [15] G A Smolensk J. Phys. Soc. Japan Suppl. 28 26 (1970)
[16] G Burns and F H Dacol Solid State Commun. 48 853 (1983) [17] H Arndt and G Schmidt Ferroelectrics 79 149 (1988)
[18] C Randall, A Bhalla, T Shrout and L E Cross J. Mater. Res. 5 829 (1990) [19] V Kirillov and V Isupov Ferroelectrics 5 3 (1973)
[20] K Binder Z Phys. 26 339 (1977)
[21] A Morgonwnik and J Mydosh Solid State Commun. 47 321 (1983) [22] H Vogel Z Phys, 22 645 (1921)
[23] G Fulcher J. Am. Ceram. Soc. 8 339 (1925)
[24] D Viehland, S J Jang, L E Cross and M Wutting J. Appl. Phys. 68 2916 (1990)
[25] S P Singh, A K Singh, D Pandey, H Sharma and Om Prakash J. Mater. Res. 18 2677 (2003) [26] S B Lee, K H Lee and H Kim Jpn. J. Appl. Phys. 41 5266 (2002)
[27] D R Chen and Y Y Guo Electron. Elemen. Mater. 1 25 (1982) [28] K Uchino and S Nomura Ferroelectrics Lett. 44 55 (1982)
[29] S M Pilgrim, A E Sutherland and S R Winzer J. Am. Ceram. Soc. 73 3122 (1990) [30] l-Wei Chen, P Li and Y Wang J. Phys. Chem. Solids 57 1525 (1996)
[31] A Laha and S B Krupanidhi Mater. Sci. Engg. B98 204 (2003) [32] L P Levy and A T Ogielski Phys. Rev. Lett. 57 3288 (1986)
[33] D Viehland, J F Li, S J Jang L E Cross and M Wutting Phys. Rev. B46 8013 (1992) [34] A K Tagantsev Phys. Rev. Lett. 72 1100 (1994)
[35] J R Macdonald (ed.) Impedance Spectroscopy (New York : Wiely Interscience) (1987)
