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Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore
Journal of Alloys and Compounds xxx (xxxx) xxx
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Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore P.Y. Tan a, K.B. Tan a, *, C.C. Khaw b, Z. Zainal a, S.K. Chen c, O.J. Lee d, M.P. Chon a a
Department of Chemistry, Faculty of Science, Universiti Putra Malaysia, 43400, UPM Serdang, Selangor, Malaysia Department of Mechanical and Material Engineering, Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, 53300, Kuala Lumpur, Malaysia c Department of Physics, Faculty of Science, Universiti Putra Malaysia, 43400, UPM Serdang, Selangor, Malaysia d School of Fundamental Science, Universiti Malaysia Terengganu, 21300, Kuala Terengganu, Terengganu, Malaysia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 June 2019 Received in revised form 30 September 2019 Accepted 4 October 2019 Available online xxx
Phase-pure Bi3.55Mg1.78Nb2.67O13.78, BMN pyrochlore was prepared by conventional solid-state reaction at 1025 C for 2e3 days. Electrical properties measured by impedance spectroscopy over the range 10 e1073 K showed relaxor behaviour with a maximum dielectric constant, ε0 max of 209 at its temperature maximum, Tmax of 204 K. Impedance data were analysed by fixed-frequency sweeps of dielectric constant and tan d and variable frequency scans at fixed temperature. Low temperature data were modelled using the classic dielectric relaxation circuit that consists of a resistance in combination with series and parallel capacitances, but modified to include a constant phase element that introduced variable resistances and capacitances into the equivalent circuit. There was no evidence of ferroelectric behaviour, either from extrapolation of high temperature Curie-Weiss plots or the temperature-dependence of low temperature capacitance data. At intermediate temperatures, ~240e623 K, BMN is an insulator with resistivity >10 MU cm. Above ~623 K, it is a modest electrical conductor, activation energy 1.07 eV; the charge carriers are probably oxide ions. © 2019 Elsevier B.V. All rights reserved.
Keywords: Pyrochlore Dielectric Relaxor Equivalent circuit modelling
1. Introduction Much attention has been given to ferroelectrics with diffuse phase transition, DPT and/or relaxor characteristics. One feature of relaxors is a broad peak of dielectric constant as a function of temperature, unlike first order ferroelectrics which exhibit a sharp dielectric constant maximum, ε0 max at the Curie temperature, Tc. A second feature is frequency-dependent dielectric constant over a wide temperature range that includes the peak maximum. Consequently, ε0 max is both temperature- and frequency-dependent and a single Tmax cannot be identified for relaxors. By contrast, Tmax coincides with Tc for first order ferroelectrics and a symmetry change occurs at the ferroelectric-paraelectric phase transition. It is not clear from the literature whether relaxor materials are also ferroelectric; undoubtedly, some are but not necessarily in all cases. Relaxors are used in multilayer ceramic capacitors as they have high dielectric constant which varies little over a wide range of temperatures [1,2]. Relaxors with complex perovskite structure are
* Corresponding author. E-mail address: [email protected] (K.B. Tan).
usually lead-based, e.g. PbMg1/3Nb2/3O3 (PMN), PbZn1/3Nb2/3O3 (PZN), PbSc1/2Nb1/2O3 (PSN) and PbSc1/2Ta1/2O3 (PST) [3e5]. Class II dielectrics have dielectric constants, ε0 in the range 2000e20000, whereas class I dielectrics have lower ε’, typically in the range 5e500. Recently, Bi-based pyrochlore relaxors have been explored as possible class I dielectrics. Examples include: (Bi1.5Zn0.5) (Zn0.5Ta1.5)O7, BZT; (Bi1.5Zn0.5) (Zn0.5Nb1.5)O7, BZN; (Bi1.5Zn0.5). (Nb0.5Ti1.5)O7, BZNT. Their ε0 max and Tm values are in the range ~76e~160 and ~150e~190 K, respectively [1,6e8]. Replacement of Zn by other divalent cations, e.g. Mg and Ni yielded Bi1.667Mg0.70Nb1.52O7, BMN and Bi1.667Ni0.75Nb1.5O7, BNN with ε0 max values of ~172 at ~190 K and ~118 at ~220 K, respectively [9]. Pyrochlores in the BMN system have high ε’ and low dielectric loss, tan d which lead to possible microwave dielectric applications [9e12]. Previous studies indicated relaxor behaviour at low temperature [9] but the composition studied may have been a mixture of the cubic pyrochlore, Bi5Nb3O15 and BiNbO4 according to our unpublished phase diagram results [13]: it was found that BMN pyrochlore form a quadrilateral-shaped solid solution area in the Bi2O3eMgO e Nb2O5 phase diagram which could be described best using the general formula, Bi3.36þxMg1.92-yNb2.72-xþyO13.76-xþ(3/2) y: 0.01 x 0.20; 0.00 y 0.16. Assuming full occupancy of the
https://doi.org/10.1016/j.jallcom.2019.152576 0925-8388/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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cation sites, x and y quantify the cation composition, with creation of either oxygen vacancies or interstitials for charge compensation, through two possible mechanisms: (i) x Bi3þ 4 x Nb5þ þ x O2 and (ii) y Mg2þ 4 y Nb5þ þ 3y/2 O2 [12,13]. The objectives of the present study are to (i) characterise phasepure, relaxor-like BMN, (ii) study its low temperature electrical properties, (iii) determine the most appropriate equivalent circuit to satisfactorily model the impedance data, (iv) provide a physical interpretation of the relaxor behaviour and (v) determine whether BMN is ferroelectric or non-ferroelectric. The composition chosen was x ¼ 0.19, y ¼ 0.14. 2. Experimental Bi3.55Mg1.78Nb2.67O13.78 was prepared by conventional solidstate reaction. The starting materials were reagent-grade powders, Bi2O3 (Alfa Aesar, 99.99%), MgO (Aldrich, 99%) and Nb2O5 (Alfa Aesar, 99.9%). All oxides were dried before use: Bi2O3 at 300 C and the others at 600 C. The reagents were weighed, mixed with acetone in an agate mortar, dried, transferred to a Pt boat and heated in air at 300 C for 1 h, followed by 600 C for 1 h to ensure the Bi2O3 reacted to form less-volatile intermediates. This allowed subsequent firing at higher temperatures without significant loss of Bi. The powders were heated at 800 C overnight followed by 1025 C for 2e3 days with intermediate regrinding. The BMN product, Bi3.55Mg1.78Nb2.67O13.78, was confirmed to be single phase by X-ray powder diffraction, XRD using an automated Shimadzu diffractometer XRD 6000, Cu Ka radiation, with data recorded in the 2q range 10e70 at scan speed 0.1 /min. For electrical property measurements, BMN powders were pressed into pellets 8 mm diameter and ~1.5 mm thick using a uniaxial hydraulic press prior to sintering at 1075 C for 24 h. The relative pellet density was ˃ 90% of that calculated from the XRD data and unit cell contents. Au paste was used as electrodes which was smeared on opposite faces and hardened by heating to 600 C. Impedance spectroscopy, IS measurements at low temperature, 10e320 K were performed using an Agilent E4980A with Intelligent Temperature Controller, ITC 503S over the frequency range 1 kHz to 1 MHz; high temperature, 373e1073 K measurements used a HP4192A impedance analyser over the frequency range 10 Hz-1 MHz. IS data were modelled with various equivalent electrical circuits using ZView software. 3. Results and discussion 3.1. Electrical properties measured at fixed frequency and variable temperature Phase-pure BMN pyrochlores show excellent insulating properties with high ε0 in the range 167e204 and low tan d of 104 103 at ambient temperature, ~28 C [12]. In order to determine and understand their electrical behaviour at sub-ambient temperature in particular, composition Bi3.55Mg1.78Nb2.67O13.78 with the highest ε0 , 204, was chosen for detailed study. The data are presented first in the traditional way for relaxors as fixed frequency plots of ε0 and tan d against temperature in the range 10e320 K, Fig. 1. The ε0 data show broad maxima whose temperature, Tmax, increases with frequency and whose magnitude at the maximum, ε0 max decreases with increasing Tmax. Thus, the magnitudes of ε0 max, Tmax at frequencies of 1 kHz, 10 kHz, 100 kHz and 1 MHz are 212, 146 K; 211, 164 K; 210, 180 K and 209, 204 K, respectively, Fig. 1(a). At temperatures above ~230 K, the ε0 data are frequencyindependent, Fig. 1(a). The tan d data show maxima whose value increases with both frequency and temperature but are also frequency-independent above ~230 K, Fig. 1(b).
Fig. 1. (a) The dielectric constant, ε0 and (b) dielectric loss, tan d of Bi3.55Mg1.78Nb2.67O13.78 at four fixed frequencies in the temperature range of 10e320 K.
For a ferroelectric material that transforms into a paraelectric state above its Curie temperature, Tc, ε’ should follow the CurieWeiss law: 1/ε’ ¼ (T - T0)/C
(1)
where T0 is the Curie-Weiss temperature and C is the Curie-Weiss constant. Frequency-independent ε0 data were obtained above ~230 K and are plotted at four fixed frequencies, assuming CurieWeiss law behaviour, in Fig. 2; from these high temperature ε0 data and the large, negative To values, i.e. below 0 K (estimated from extrapolation), ferroelectric behaviour is not expected at lower temperatures. The dispersive character of ε’ below Tm, Fig. 1(a) is typical of relaxors and is usually attributed to the formation of polar nanodomains. The Burns temperature, TB, is identified as the onset of polar domain formation at which the dispersion becomes noticeable on cooling [14] and is approximately 200 K from Fig. 2. The difference between Tm and TB, given by Refs. [4,15e17]:
D Tm ¼ TB - Tm
(2)
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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linear relationship, but with scatter of the data and some evidence of curvature, for the four measuring frequencies with approximate slopes of 1.54, 1.36, 1.34 and 1.63. Since 1 < g < 2, this indicates that a diffuse phase transition in BMN pyrochlore could occur. The data may also be analysed using the Vogel-Fulcher equation: fmax ¼ f0 exp [-Ea/k(Tmax - Tvf)]
Fig. 2. The inverse of dielectric constant as a function of temperature at four fixed frequencies.
Has values at 1 kHz, 10 kHz, 100 kHz and 1 MHz of 76 K, 62 K, 48 K and 26 K, respectively and is attributed to the diffuse nature of the phase transition at these temperatures. The characteristic features of a diffuse phase transition include (i) a broadened peak of ε0 versus temperature, (ii) a relatively large separation of temperature between the maxima of the real, ε0 and imaginary, ε” parts of the dielectric spectrum, (iii) a deviation from Curie-Weiss law in the vicinity of Tm and (iv) a frequency dispersion of both ε0 and tan d in the transition region which leads to a frequency dependence of Tmax [4]. For a relaxor ferroelectric with a diffuse phase transition, a modified Curie-Weiss law is used: (1/ε’ e 1/εmax) ¼ (T e Tm)g/C
(3)
where g and C are the diffuseness degree and Curie constant, respectively. The parameter g gives information on the character of the phase transition: g ¼ 1 indicates Curie-Weiss behaviour for a first order ferroelectric; g ¼ 2 indicates a completely diffuse phase transition in an ideal relaxor ferroelectric [4,15,17]. The plots of ln (1/ε’ e 1/εmax) against ln (T - Tmax), Fig. 3, show an approximately
-8
1 kHz 10 kHz 100 kHz 1 MHz
(4)
where k is Boltzmann’s constant, 8.617 105 eV K1, fmax is the frequency of the peak maximum at Tmax and Tvf is an adjustable parameter that is presumed to represent freezing of the nanodomains. In this case, Fig. 4, a value of 10 K for Tvf gives a good fit; the activation energy, Ea ¼ 0.12 eV is obtained from an Arrhenius plot using the same data, Fig. 4 inset. Table 1 summarises the various parameters that may be used to describe the temperaturedependent, fixed-frequency, dielectric constant data. These analyses follow traditional procedures using fixed frequency data to characterise relaxors; from the results, it is not clear whether BMN is also ferroelectric although from the large negative values of To obtained from Fig. 2, ferroelectric behaviour is not expected. The second method of data analysis is to present variable frequency IS data at constant temperature. This is standard procedure in IS studies of electroceramics, but as far as we are aware, has been used on only two other occasions for relaxors [1,14]. IS data are presented and analysed in Figs. 5e9 and used the same experimental data sets as Figs. 1e4. 3.2. Variable frequency impedance data In Fig. 5, capacitance, C0 , data obtained from the impedance measurements are shown as a function of frequency over the temperature range, 10e1073 K. At the lowest temperatures, C0 increases with increasing temperature and decreases with increasing frequency (a,b). At lower frequencies, a frequency-independent plateau is seen increasingly at temperatures above ~100 K (b). For temperatures 200 K, C0 is independent of frequency over the range 103e106 Hz (c) but its value decreases with increasing temperature (c,d) up to the highest temperatures studied. Above ~873 K, (d), an additional low frequency dispersion is seen in the C0 data. An apparent drop in C’ plateau of ~5 pF for fixed frequency at 1 kHz and 1 MHz is discernible over the range ~200e673 K (e).
1.54 1.36 1.34 1.63
l n (1 / ' - 1 /
m
)
-10
-12
-14 1
2
3 4 ln (T - Tm) / K
5
6
Fig. 3. ln (1/ε’ - 1/εmax) against ln (T - Tm) of Bi3.55Mg1.78Nb2.67O13.78 at different frequencies.
Fig. 4. Frequencies and temperatures of ε0 max with fits to the Vogel-Fulcher equation as fmax as a function of Tmax. The inset (i) shows the Arrhenius plot of log fm as a function of 1/(Tm e Tvf).
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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Table 1 The temperatures for which the maximum dielectric constant (Tm), maximum dielectric constant (ε0 max), diffuseness constant (g), and Burns temperature (TB) at different frequencies. Frequency (Hz)
TB (K)
Tm (K)
ε0 max
g
1k 10 k 100 k 1M
222 226 228 230
146 164 180 204
212 211 210 209
1.54 1.36 1.34 1.63
Admittance or conductivity, Y0, data extracted from the same IS datasets, are plotted against frequency in fixed temperature format in Fig. 6. Below ~240 K, Y0 data were frequency-dependent at all temperatures (a,b). Between ~240 and 623 K, the conductivities were too low to measure accurately, < ~107 U1 cm1, at any frequency (not shown). Above ~623 K, Y0 data were again measurable, but were now frequency-independent and Y’ increased with temperature (c). At the lowest temperatures, 10e40 K (a), Y0 data show linear,
Fig. 5. Capacitance, C0 as a function of frequency for five temperature ranges (a) 10e100 K, (b) 110e210 K, (c) 220e320 K, (d) 373e1073 K and (e) C0 plateau as a function of temperature.
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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Fig. 6. Admittance, Y0 as a function of frequency for temperature ranges (a) 10e120 K, (b) 130e240 K and (c) 623e1073 K.
power law dependence and increase with increasing temperature at a given frequency. At higher temperatures, the Y0 data start to show curvature with an increasing slope at lower frequencies, but the overall Y0 values increase by a small amount. This continues until ~120 K (a), above which, the Y’ data start to decrease and above ~240 K were too small to measure (b). At all temperatures up to 240 K, therefore, the ac conductivity was clearly measurable but there was no evidence of a limiting, low frequency, dc conductivity. Above ~623 K, the dc conductivity became measurable for the first time and was independent of frequency (c).
3.3. Interpretation of variable frequency impedance data (a) Equivalent circuit modelling In order to analyse variable frequency IS data, the first step is to find an equivalent circuit that accurately represents the data. This is followed by fitting data to the circuit to extract values of the component parameters. The final step is to assign the parameters to specific features or properties of the sample. Selection of the correct equivalent circuit is an essential but non-trivial exercise since, in general, it is always possible to fit a particular data set to more than one circuit and the equations used to extract R and C values depend on the circuit used. Our approach is to: first, make a visual
inspection of the IS data in various formats, such as C0 and Y’ against frequency; second, assign circuit elements to key features of each response and gradually build the overall equivalent circuit; third, evaluate how the sample parameters vary with, for example, sample processing conditions, temperature and composition. If accurate values of circuit parameters are required, perform computer fitting to the circuit and examine the quality of the fits, either visually or from the residuals as a function of frequency. The inter-relationships between the various formalisms that may be used for representing impedance data are given by Ref. [18]: M* ¼ juCo Z* ¼ (ε* or C*)1 ¼ juCo (Y* or A*)1
(5)
where j ¼ √-1 and M*, Z*, ε* and Y* are the complex electric modulus, impedance, permittivity and admittance. Each of the four complex formalisms has real and imaginary components such that: Formalism ¼ (real) þ j(imaginary)
(6)
Data can be represented as complex plane plots (or Argand diagrams) of (imaginary) vs (real), usually on linear scales, or as spectroscopic (Nyquist) plots of one component against frequency. The ratio: (imaginary)/(real) is also often plotted against frequency, especially for the permittivity formalism, and is known as dielectric
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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Fig. 7. Equivalent circuits showing different R, C, CPE combinations (a) master circuit, (b) below ~ 60 K, (c) ~80 Ke~220 K, (d) > ~220 K, (e) > ~673 K, (f) dielectric relaxation.
loss or tan d. In order to use these various methods of data presentation to gain an overview of the impedance response of the material, knowledge of the appropriate equivalent circuit is not necessary, but to subsequently extract values of component R and C parameters, knowledge of the equivalent circuit, and associated equations, is essential. Using an appropriate choice of methods and plots to analyse the data shown in Figs. 5 and 6, the following key conclusions were drawn: (i) From the Y0 data, BMN is a dc electrical insulator below 240 K; nevertheless, ac conductivities can be measured. To model these, either a series combination of a resistance and a capacitance, in which the capacitance blocks the inability for dc conduction to occur, or a frequency-dependent resistance, is required. (ii) At the lowest temperatures, plots of log Y0 vs log f are almost linear and indicate a power law component in the equivalent circuit which could be represented by a constant phase element, CPE, whose admittance, Y*, is given by: Y* ¼ Aun þ jBun ¼ Y’ þ jY”
(7)
where u is the angular frequency, 2pf and A, B are inter-related by A/B ¼ tan (np/2)
(8)
The CPE is effectively, a parallel combination of a variable
resistance and capacitance; Y’ therefore represents the frequency dependence of the resistive component of the CPE, Aun. The value of n is ~0.96 which means that the CPE is mainly capacitive in nature at these temperatures. (iii) At temperatures > ~90 K, the increased slope, with value > 1, in log Y’/log f plots at low frequencies, indicates the need for an additional capacitive element in series with the CPE. This is because the maximum possible value of n for a CPE is 1. For an ideal circuit consisting of two elements in series, the low frequency slope that connects their impedance responses can have a value as high as 2. (iv) C0 data at temperatures of 220 Ke573 K are frequencyindependent over the entire measurement range, Fig. 5 (c, d) and are therefore represented by a simple, frequencyindependent capacitance; any associated parallel or leakage resistance was too high to measure, >107 U cm, as shown by presentation of the same data in the format log Y’/log f: the observed Y0 data were effectively background noise associated with the internal impedance of the measuring instrumentation. The presence of this same capacitance is seen in low frequency C0 data for temperatures as low as 90 K, Fig. 5 (a), although the full capacitance plateau was not seen due to frequency limitations of the equipment. This capacitance is referred to as the low frequency capacitance, C2, in subsequent discussions. (v) In the low temperature C0 data, Fig. 5(a), there is some evidence from the small amount of curvature of the log C’/log f
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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Fig. 8. Fit of the 20 K, 150 K, 240 K data to circuit in Figs. 5 and 6.
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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Fig. 9. Temperature dependence of (a) capacitance C1, (b) capacitance C2, (c) CPE1 and the n values, (d) resistance R1 and (e) Arrhenius conductivity plots of Y0 as a function of temperature for temperature range 623e1073 K.
plots that a second, frequency-independent plateau may exist at the highest frequencies which would correspond to the limiting, high frequency capacitance of the sample, C∞, referred to here as C1 [19]. Its value is estimated to be 2e3 pF.
The frequency-dependent C0 data at the lowest temperatures therefore represent the summation of two contributions, from the CPE and C1, which are in parallel and are given by:
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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C’ ¼ (B/Co) un1 þ C1/Co
(9)
With increasing temperature, the capacitance dispersion leading to the high frequency C1 plateau moves to higher frequency and C1 moves off-scale. Thus, at e.g. 50 K, C0 is dominated by the CPE component, Bun and the plot of log C’/log f is linear with slope (n1) ¼ 0.04. With further increase in temperature, the capacitance dispersion represented by the CPE also moves off-scale and only the low frequency capacitance, C2, is seen, Fig. 5(b and c), for temperatures >~210 K. A master circuit that incorporates points (i) to (v) and was shown to fit low temperature data for other pyrochlore relaxors [1,14] is given in Fig. 7(a). However, this circuit simplifies in various ways, depending on temperature. Element C1 can be quantified only at the lowest temperatures, Table 2; it represents the limiting high frequency capacitance of the sample and gives a value of ~30 for the permittivity, ε∞, using: ε∞¼εoε0 A/l
(10)
where εo is the permittivity of free space 8.854 1014 Fcm1 and A/l is the geometric factor of the sample in units of cm. For data in the range 10e70 K, R1 was too large to measure, the additional series capacitance C2 was not needed and the equivalent circuit simplifies to that given in Fig. 7(b). For temperatures above ~60 K, data are still dominated by the CPE, but evidence for series capacitance C2 is increasingly seen and resistance R1 is required to obtain good fits to the experimental data. C1 no longer makes any significant contribution to the impedance data and circuit Fig. 7(c) therefore becomes appropriate. The value of R1 decreases rapidly with increasing temperature and above ~220 K, R1 is sufficiently small that the circuit reduces to that of a single capacitor, C2, Fig. 7(d).
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For the parallel R1-CPE1 component of the circuits shown in Fig. 7(a,c), the two possible contributions to the ac conductivity are R1 1 and CPE1, since Y’ is given by: n Y’ ¼ R1 1 þ A1 u
(11)
This ac conductivity is localised and in series with capacitance C2 which effectively blocks any possibility of long range conduction. The presence of C2 is shown by log C’/log f plots at low frequencies for temperatures > ~90 K, Fig. 5(a,b) and also in the curvature at low frequencies in log Y’/log f plots for temperatures > ~40 K, Fig. 6(a,b). With increasing temperature, the Y’ conductivity spectrum is displaced to higher frequency as shown clearly in Fig. 6(b) and is off-scale >~240 K. This is because the net effect of a decrease in R1 (and increase in A1) with increasing temperature, Table 2, is to decrease the time constant (RC product) of the series combination of R1 and C2 and therefore, to increase the relaxation frequency, umax, given by umaxRC ¼ 1, associated with this series combination. When the ac conductivity can no longer be measured above ~240 K, the equivalent circuit simplifies to that of a single capacitor, Fig. 7(d), as shown by the data in Fig. 5(c). At much higher temperatures, >~623 K, Y0 data show wide ranges of frequency-independent conductivity, Fig. 6(c) which is evidence for long range, dc conduction through the sample. Circuit Fig. 7(d) is therefore modified to add a leakage resistance, R2 in parallel with capacitance C2. At still higher temperatures, above ~773 K, Fig. 5(d), C’ increases at low frequencies; this is attributed to polarisation at the sample e electrode interface. The equivalent circuit Fig. 7(d) is therefore modified further to add an additional capacitance, C3, that represents the blocking of charge carriers at the electrode-sample interface, Fig. 7(e). A selection of fits to equivalent circuits is shown in Fig. 8. In Fig. 8(a,b) are shown spectroscopic plots for Y0 and C0 for circuit
Table 2 Fitting data of Bi3.55Mg1.78Nb2.67O13.78 using various circuit parameters from 10 K to 320 K. Temperature (K) 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320
R1 (U cm) x 105
C1 (F cm1) 1012
C2 (F cm1) 1011
2.95 2.42 1.95 1.27 3.95 101 1.15 106 1.50 107 7.84 5.99 15.6 2.40 1.18 5.02 101 2.11 101 9.00 102 3.97 102 1.82 102 7.69 103 3.47 103 1.56 103 6.95 104
1.59 1.69 1.83 1.82 1.85 1.87 1.87 1.87 1.87 1.87 1.86 1.86 1.85 1.85 1.84 1.84 1.83 1.83 1.82 1.82 1.81 1.80 1.79 1.79 1.78
A1 (U1cm1rad1) x 106
n
9.08 106 1.09 105 1.25 105 1.44 105 1.67 105 1.86 105 2.05 105 6.98 104 9.14 104 1.10 103 2.19 103 4.30 103 1.03 102 2.66 102 7.37 102 2.01 101 5.52 101 1.27 2.66 3.37 1.65
0.963 0.962 0.961 0.962 0.962 0.961 0.958 0.813 0.801 0.789 0.762 0.733 0.696 0.655 0.613 0.571 0.530 0.501 0.476 0.477 0.529
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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Fig. 7(b) at 20 K. In Fig. 8(c,d), similar plots for circuit Fig. 7(c) at 150 K are shown. In Fig. 8(e) the spectroscopic plot for C0 for circuit Fig. 7(d) at 240 K is shown. It was not always appropriate to allow free refinement of all the circuit parameters simultaneously. This was because first, the B component of CPE1 was a frequency dependent capacitance which was fitting the same C0 data as C2 and second, the A component of CPE1 was fitting the same Y’ data as R1. Nevertheless, the broad conclusions of the analyses are clear and are summarised in Fig. 9 as the temperature dependence of the various circuit parameters. (b) Assignment of equivalent circuit parameters The temperature dependence of A1, n, C1, C2 and R1, Fig. 9 and can be described and interpreted as follows: Capacitance C1 is attributed to the bulk lattice polarisation; it has a value of ~3 pF, representing a value for ε∞ of ~30, which is a typical value for a polar dielectric. Capacitance C2 is also small and decreases gradually with temperature. It represents the blocking of charge displacement associated with R1 1 and A1. These charge displacements are very small, represent a tiny fraction of an interatomic bond distance and cannot be construed as an ionic conduction process. C2 is not a conventional blocking capacitance such as occurs at sample-electrode interfaces, therefore. Resistance R1 is attributed to the difficulty of the localised charge displacements, which is increasingly frozen-in at the lowest temperatures; R1 decreases rapidly with rising temperature and has little effect on the sample impedance above ~220 K. Hence, at ac measuring frequencies, the lattice polarisation is represented by C2 at high temperatures but by C1 at low temperatures. The n parameter gives the relative contribution of frequencydependent resistances and capacitances to the CPE. It decreases from ~0.96 at the lowest temperatures where the CPE is largely capacitive to ~0.48 at 200 K where R and C contribute equally to the CPE. The A1 parameter reflects the localised atomic motions that contribute to the CPE and gives similar information to the parameter R1. Thus, the ac conductivity values represented by A1 increase by > 5 orders oCCf magnitude between ~50 and 200 K as the polar regions become unfrozen and start to break up. R2 represents long range conductivity through the sample at high temperature; it is in parallel with blocking capacitance C2. Clearly, R2 has a different origin to that responsible for R1 and A1; from the presence of series capacitance C3 at higher temperatures, it is likely that R2 represents either electronic conduction or, more probably, conduction of oxide ions; further work is required to clarify the high temperature conduction mechanism. (c) Correlation of electrical properties with the structure of BMN pyrochlore In BMN pyrochlore, Mg2þ cations are probably distributed at random over both A- and B-sites with general formula, (Bi3.55Mg0.45) (Mg1.33Nb2.67)O13.78. Either of the crystallographic A and B sites could be responsible for polarity of the crystal structure and possible nanodomain formation. Thus, the eight-coordinated A-site contains two ions, Bi and Mg, of very different size and coordination requirements and the possibility exists for off-centre displacement of the smaller Mg2þ ions. The octahedral B-site also contains a mixture of two ions of different size and charge [1]; polarisation associated with mixed occupancy of octahedral sites by Mg and Nb in the perovskite structure of PMN, lead magnesium
niobate is well-established and could therefore occur in the present BMN sample. A third possibility is that one of the oxygen sites, often written as O’, shows positional disorder in pyrochlores and could contribute to polarisation. Assuming that at least one of the above three polarisation processes is responsible for the low temperature relaxor properties, the possibility exists for the individual polarisation steps to act cooperatively, leading to polar domain formation. For instance, it has been suggested that relaxation in pyrochlores might stem from the hopping of dynamically disordered A-site cations and O0 ions among the closely-spaced possible positions [6,7]. The interaction between the cations at the disordered A-sites and the O’ ions could cause the formation of localised dipoles within the structure that reorient in an external ac field. In addition, inhomogeneous distribution of Mg2þ may cause additional random fields leading to multiwell potentials with a wide distribution of heights that contribute to a broad dielectric relaxation [6,7] and the variable R and C components of the CPE. Cooperative alignment within domains may, however, be limited to short distances only because of frustration associated with inhomogeneities in the structure and/or local composition. In addition, the magnitude of the high temperature lattice polarisation, C2, is small and therefore, the charge displacements associated with polar domains are likely to be very small. Resistance R1 represents a thermally-activated, local displacement with activation energy 0.26 eV above ~160 K, Fig. 9(b). We see no evidence that R1 is associated with long range conduction but instead, is associated with local atomic displacements within a polar region or, perhaps, with domain wall migration. Our interpretation of R1, C1, and their temperature dependencies, is that the material possesses some kind of polar nanodomain structure that is effectively frozen-in at low temperature. With increasing temperature, domain relaxation processes commence as shown by a reduction in resistance R1. At temperatures around 170e220 K, the domains break up as R1 becomes negligibly small. BMN pyrochlore shows similar relaxor behaviour to other pyrochlores such as BZN, BZT, BZNT, BNN [1,6e9]. Their relaxor electrical properties are intermediate between those of (i) first order ferroelectrics which show sharp dielectric constant maxima as a function of temperature and (ii) dielectric materials which show very little temperature dependence of dielectric constant [1,19e21]. In the absence of the frequency-dependent relaxor characteristics, the electrical properties could be referred to the classic dielectric relaxation circuit shown in Fig. 7(f). This has a low frequency capacitance dominated by C2, a high frequency capacitance dominated by C1, and a relaxation at intermediate frequencies controlled by the magnitude of R1 and the R1C2 time constant. Superposed on this circuit is the frequency dependencies of R and C represented by the CPE; hence, the key component that determines the frequencydependent relaxor characteristics is the CPE. 4. Conclusions 1. BMN pyrochlore is a relaxor but is not ferroelectric. A CurieWeiss plot of high temperature capacitance data shows no indication of any ferroelectric transition at lower temperatures; also, low temperature capacitance data show no evidence of any capacitance maximum that could be associated with a Curie temperature. 2. The dielectric properties have been satisfactorily modelled using equivalent circuit analysis. The key circuit element responsible for the frequency-dependence of the permittivity, that is characteristic of a relaxor such as BMN, is a constant phase element which, in its ideal form, is a parallel, frequency-dependent, resistance and capacitance combination.
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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3. Low temperature relaxor behaviour can be derived from an ideal dielectric relaxation equivalent circuit that consists of a parallel RC element in series with a capacitor. The two capacitances represent the lattice polarisation at the low and high frequency limits, that respectively, are with and without, the contribution from the lattice relaxation. This ideal dielectric relaxation circuit is modified for a relaxor by inclusion of a CPE in the circuit. 4. The atomic displacements responsible for relaxor behaviour are very small and are likely to be at least an order of magnitude less than those involved in the ferroelectric switching of BaTiO3. These displacements are, however, thermally activated with activation energy, 0.29 eV, that essentially controls the range of temperature range over which relaxor behaviour is observed. Several types of possible atomic displacement within the pyrochlore structure can be identified. 5. The relaxor effect in BMN is seen only below ~220 K. At higher temperatures, BMN is an excellent insulator. At much higher temperatures, above ~600 K, the dielectric behaviour becomes leaky, probably due to the onset of oxide ion conduction. Acknowledgments The financial support from The Universiti Putra Malaysia through Putra Research Grant Scheme is gratefully acknowledged. The authors would like to extend their utmost gratitude to Prof. A.R. West for his invaluable technical advices, insightful suggestions and sponsorship for P.Y. Tan’s three-month research attachment at The University of Sheffield, UK. References [1] R.A.M. Osman, A.R. West, Electrical characterization and equivalent circuit analysis of (Bi1.5Zn0.5)(Nb0.5Ti1.5)O7 pyrochlore, a relaxor ceramic, J. Appl. Phys. 109 (2011), 074106. [2] Z.Y. Cheng, R.S. Katiyar, X. Yao, A.S. Bhalla, Temperature dependence of the dielectric constant of relaxor ferroelectrics, Phys. Rev. B 57 (1998) 8166e8177. [3] H.Q. Fan, S.M. Ke, Relaxor behaviour and electrical properties of high dielectric constant materials, Sci. China Ser. E Technol. Sci. 52 (2009) 2180e2185.
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[4] X.G. Tang, K.H. Chew, H.L.W. Chan, Diffuse phase transition and dielectric tunability of Ba(ZryTi1-y)O3 relaxor ferroelectric ceramics, Acta Mater. 52 (2004) 5177e5183. [5] L.E. Cross, Relaxor ferroelectrics: an overview, Ferroelectrics 151 (1994) 305e320. [6] C. Ang, Z. Yu, H.J. Youn, C.A. Randall, A.S. Bhalla, L.E. Cross, J. Nino, M. Lanagan, Low-temperature dielectric relaxation in the pyrochlore (Bi3/4Zn1/4)2(Zn1/4Ta3/ 4)2O7 compound, Appl. Phys. Lett. 80 (2002) 4807e4809. [7] S. Kamba, V. Porokhonskyy, A. Pashkin, V. Bovtun, J. Petzelt, Anomalous broad dielectric relaxation in Bi1.5Zn1.0Nb1.5O7 pyrochlore, Phys. Rev. B 66 (2002), 054106. [8] J.C. Nino, M.T. Lanagan, C.T. Randall, Dielectric relaxation in Bi2O3-ZnO-Nb2O5 cubic pyrochlore, J. Appl. Phys. 89 (2001) 4512e4516. n, Y. Liu, R.L. Withers, X. Wei, M.M. Elcombe, The disor[9] B.H. Nguyen, L. Nore dered structures and low temperature dielectric relaxation properties of two misplaced-displacive cubic pyrochlores found in the Bi2O3-MIIO-Nb2O5 (M ¼ Mg and Ni) systems, J. Solid State Chem. 180 (2007) 2558e2565. [10] L. Li, X. Zhang, L. Ji, P. Ning, Q. Liao, Dielectric properties and electrical behaviors of tunable Bi1.5MgNb1.5O7 thin films, Ceram. Int. 38 (2012) 3541e3545. [11] D.P. Cann, C.A. Randall, T.R. Shrout, Investigation of the dielectric properties of bismuth pyrochlores, Solid State Commun. 100 (1996) 529e534. [12] P.Y. Tan, K.B. Tan, C.C. Khaw, Z. Zainal, S.K. Chen, M.P. Chon, Phase equilibria and dielectric properties of Bi3þ(5/2)xMg2-xNb3-(3/2)xO14-x cubic pyrochlores, Ceram. Int. 40 (2014) 4237e4246. [13] P.Y. Tan, K.B. Tan, C.C. Khaw, Z. Zainal, S.K. Chen and M.P. Chon, Manuscript in Preparation. , A.R. West, Bismuth zinc niobate pyrochlore, a relaxor[14] R.A.M. Osman, N. Maso like non-ferroelectric, J. Am. Ceram. Soc. 95 (2012) 296e302. [15] W. Zuo, R. Zuo, W. Zhao, Phase transition behavior and electrical properties of lead-free (Bi0.5K0.5)TiO3-LiNbO3 relaxor ferroelectric ceramics, Ceram. Int. 39 (2013) 725e730. ski, J. Koperski, Dielectric [16] M. Adamczyk, Z. Ujma, L. Szymczak, A. Soszyn properties and relaxation of Bi-doped (Pb0.75Ba0.25)(Zr0.70Ti0.30)O3 ceramics, Mater. Sci. Eng., B 136 (2007) 170e176. [17] H. Yang, F. Yan, Y. Lin, T. Wang, F. Wang, Y. Wang, L. Guo, W. Tai, H. Wei, Leadfree BaTiO3-Bi0.5Na0.5TiO3-Na0.73Bi0.09NbO3 relaxor ferroelectric ceramics for high energy storage, J. Eur. Ceram. Soc. 37 (2017) 3303e3311. [18] A.R. West, D.C. Sinclair, N. Hirose, Characterisation of electrical materials, especially ferroelectrics, by impedance spectroscopy, J. Electroceram. 1 (1997) 65e71. [19] M.A. Hernandez, N. Maso, A.R. West, On the correct choice of equivalent circuit for fitting bulk impedance data of ionic/electronic conductors, Appl. Phys. Lett. 108 (2016) 152901. [20] G.A. Samara, The relaxational properties of compositionally disordered ABO3 perovskites, J. Phys. Condens. Matter 15 (2003) R367eR411. [21] L.E. Cross, Relaxor ferroelectrics, Ferroelectrics 76 (1987) 241e267.
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Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore P.Y. Tan a, K.B. Tan a, *, C.C. Khaw b, Z. Zainal a, S.K. Chen c, O.J. Lee d, M.P. Chon a a
Department of Chemistry, Faculty of Science, Universiti Putra Malaysia, 43400, UPM Serdang, Selangor, Malaysia Department of Mechanical and Material Engineering, Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, 53300, Kuala Lumpur, Malaysia c Department of Physics, Faculty of Science, Universiti Putra Malaysia, 43400, UPM Serdang, Selangor, Malaysia d School of Fundamental Science, Universiti Malaysia Terengganu, 21300, Kuala Terengganu, Terengganu, Malaysia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 June 2019 Received in revised form 30 September 2019 Accepted 4 October 2019 Available online xxx
Phase-pure Bi3.55Mg1.78Nb2.67O13.78, BMN pyrochlore was prepared by conventional solid-state reaction at 1025 C for 2e3 days. Electrical properties measured by impedance spectroscopy over the range 10 e1073 K showed relaxor behaviour with a maximum dielectric constant, ε0 max of 209 at its temperature maximum, Tmax of 204 K. Impedance data were analysed by fixed-frequency sweeps of dielectric constant and tan d and variable frequency scans at fixed temperature. Low temperature data were modelled using the classic dielectric relaxation circuit that consists of a resistance in combination with series and parallel capacitances, but modified to include a constant phase element that introduced variable resistances and capacitances into the equivalent circuit. There was no evidence of ferroelectric behaviour, either from extrapolation of high temperature Curie-Weiss plots or the temperature-dependence of low temperature capacitance data. At intermediate temperatures, ~240e623 K, BMN is an insulator with resistivity >10 MU cm. Above ~623 K, it is a modest electrical conductor, activation energy 1.07 eV; the charge carriers are probably oxide ions. © 2019 Elsevier B.V. All rights reserved.
Keywords: Pyrochlore Dielectric Relaxor Equivalent circuit modelling
1. Introduction Much attention has been given to ferroelectrics with diffuse phase transition, DPT and/or relaxor characteristics. One feature of relaxors is a broad peak of dielectric constant as a function of temperature, unlike first order ferroelectrics which exhibit a sharp dielectric constant maximum, ε0 max at the Curie temperature, Tc. A second feature is frequency-dependent dielectric constant over a wide temperature range that includes the peak maximum. Consequently, ε0 max is both temperature- and frequency-dependent and a single Tmax cannot be identified for relaxors. By contrast, Tmax coincides with Tc for first order ferroelectrics and a symmetry change occurs at the ferroelectric-paraelectric phase transition. It is not clear from the literature whether relaxor materials are also ferroelectric; undoubtedly, some are but not necessarily in all cases. Relaxors are used in multilayer ceramic capacitors as they have high dielectric constant which varies little over a wide range of temperatures [1,2]. Relaxors with complex perovskite structure are
* Corresponding author. E-mail address: [email protected] (K.B. Tan).
usually lead-based, e.g. PbMg1/3Nb2/3O3 (PMN), PbZn1/3Nb2/3O3 (PZN), PbSc1/2Nb1/2O3 (PSN) and PbSc1/2Ta1/2O3 (PST) [3e5]. Class II dielectrics have dielectric constants, ε0 in the range 2000e20000, whereas class I dielectrics have lower ε’, typically in the range 5e500. Recently, Bi-based pyrochlore relaxors have been explored as possible class I dielectrics. Examples include: (Bi1.5Zn0.5) (Zn0.5Ta1.5)O7, BZT; (Bi1.5Zn0.5) (Zn0.5Nb1.5)O7, BZN; (Bi1.5Zn0.5). (Nb0.5Ti1.5)O7, BZNT. Their ε0 max and Tm values are in the range ~76e~160 and ~150e~190 K, respectively [1,6e8]. Replacement of Zn by other divalent cations, e.g. Mg and Ni yielded Bi1.667Mg0.70Nb1.52O7, BMN and Bi1.667Ni0.75Nb1.5O7, BNN with ε0 max values of ~172 at ~190 K and ~118 at ~220 K, respectively [9]. Pyrochlores in the BMN system have high ε’ and low dielectric loss, tan d which lead to possible microwave dielectric applications [9e12]. Previous studies indicated relaxor behaviour at low temperature [9] but the composition studied may have been a mixture of the cubic pyrochlore, Bi5Nb3O15 and BiNbO4 according to our unpublished phase diagram results [13]: it was found that BMN pyrochlore form a quadrilateral-shaped solid solution area in the Bi2O3eMgO e Nb2O5 phase diagram which could be described best using the general formula, Bi3.36þxMg1.92-yNb2.72-xþyO13.76-xþ(3/2) y: 0.01 x 0.20; 0.00 y 0.16. Assuming full occupancy of the
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Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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cation sites, x and y quantify the cation composition, with creation of either oxygen vacancies or interstitials for charge compensation, through two possible mechanisms: (i) x Bi3þ 4 x Nb5þ þ x O2 and (ii) y Mg2þ 4 y Nb5þ þ 3y/2 O2 [12,13]. The objectives of the present study are to (i) characterise phasepure, relaxor-like BMN, (ii) study its low temperature electrical properties, (iii) determine the most appropriate equivalent circuit to satisfactorily model the impedance data, (iv) provide a physical interpretation of the relaxor behaviour and (v) determine whether BMN is ferroelectric or non-ferroelectric. The composition chosen was x ¼ 0.19, y ¼ 0.14. 2. Experimental Bi3.55Mg1.78Nb2.67O13.78 was prepared by conventional solidstate reaction. The starting materials were reagent-grade powders, Bi2O3 (Alfa Aesar, 99.99%), MgO (Aldrich, 99%) and Nb2O5 (Alfa Aesar, 99.9%). All oxides were dried before use: Bi2O3 at 300 C and the others at 600 C. The reagents were weighed, mixed with acetone in an agate mortar, dried, transferred to a Pt boat and heated in air at 300 C for 1 h, followed by 600 C for 1 h to ensure the Bi2O3 reacted to form less-volatile intermediates. This allowed subsequent firing at higher temperatures without significant loss of Bi. The powders were heated at 800 C overnight followed by 1025 C for 2e3 days with intermediate regrinding. The BMN product, Bi3.55Mg1.78Nb2.67O13.78, was confirmed to be single phase by X-ray powder diffraction, XRD using an automated Shimadzu diffractometer XRD 6000, Cu Ka radiation, with data recorded in the 2q range 10e70 at scan speed 0.1 /min. For electrical property measurements, BMN powders were pressed into pellets 8 mm diameter and ~1.5 mm thick using a uniaxial hydraulic press prior to sintering at 1075 C for 24 h. The relative pellet density was ˃ 90% of that calculated from the XRD data and unit cell contents. Au paste was used as electrodes which was smeared on opposite faces and hardened by heating to 600 C. Impedance spectroscopy, IS measurements at low temperature, 10e320 K were performed using an Agilent E4980A with Intelligent Temperature Controller, ITC 503S over the frequency range 1 kHz to 1 MHz; high temperature, 373e1073 K measurements used a HP4192A impedance analyser over the frequency range 10 Hz-1 MHz. IS data were modelled with various equivalent electrical circuits using ZView software. 3. Results and discussion 3.1. Electrical properties measured at fixed frequency and variable temperature Phase-pure BMN pyrochlores show excellent insulating properties with high ε0 in the range 167e204 and low tan d of 104 103 at ambient temperature, ~28 C [12]. In order to determine and understand their electrical behaviour at sub-ambient temperature in particular, composition Bi3.55Mg1.78Nb2.67O13.78 with the highest ε0 , 204, was chosen for detailed study. The data are presented first in the traditional way for relaxors as fixed frequency plots of ε0 and tan d against temperature in the range 10e320 K, Fig. 1. The ε0 data show broad maxima whose temperature, Tmax, increases with frequency and whose magnitude at the maximum, ε0 max decreases with increasing Tmax. Thus, the magnitudes of ε0 max, Tmax at frequencies of 1 kHz, 10 kHz, 100 kHz and 1 MHz are 212, 146 K; 211, 164 K; 210, 180 K and 209, 204 K, respectively, Fig. 1(a). At temperatures above ~230 K, the ε0 data are frequencyindependent, Fig. 1(a). The tan d data show maxima whose value increases with both frequency and temperature but are also frequency-independent above ~230 K, Fig. 1(b).
Fig. 1. (a) The dielectric constant, ε0 and (b) dielectric loss, tan d of Bi3.55Mg1.78Nb2.67O13.78 at four fixed frequencies in the temperature range of 10e320 K.
For a ferroelectric material that transforms into a paraelectric state above its Curie temperature, Tc, ε’ should follow the CurieWeiss law: 1/ε’ ¼ (T - T0)/C
(1)
where T0 is the Curie-Weiss temperature and C is the Curie-Weiss constant. Frequency-independent ε0 data were obtained above ~230 K and are plotted at four fixed frequencies, assuming CurieWeiss law behaviour, in Fig. 2; from these high temperature ε0 data and the large, negative To values, i.e. below 0 K (estimated from extrapolation), ferroelectric behaviour is not expected at lower temperatures. The dispersive character of ε’ below Tm, Fig. 1(a) is typical of relaxors and is usually attributed to the formation of polar nanodomains. The Burns temperature, TB, is identified as the onset of polar domain formation at which the dispersion becomes noticeable on cooling [14] and is approximately 200 K from Fig. 2. The difference between Tm and TB, given by Refs. [4,15e17]:
D Tm ¼ TB - Tm
(2)
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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linear relationship, but with scatter of the data and some evidence of curvature, for the four measuring frequencies with approximate slopes of 1.54, 1.36, 1.34 and 1.63. Since 1 < g < 2, this indicates that a diffuse phase transition in BMN pyrochlore could occur. The data may also be analysed using the Vogel-Fulcher equation: fmax ¼ f0 exp [-Ea/k(Tmax - Tvf)]
Fig. 2. The inverse of dielectric constant as a function of temperature at four fixed frequencies.
Has values at 1 kHz, 10 kHz, 100 kHz and 1 MHz of 76 K, 62 K, 48 K and 26 K, respectively and is attributed to the diffuse nature of the phase transition at these temperatures. The characteristic features of a diffuse phase transition include (i) a broadened peak of ε0 versus temperature, (ii) a relatively large separation of temperature between the maxima of the real, ε0 and imaginary, ε” parts of the dielectric spectrum, (iii) a deviation from Curie-Weiss law in the vicinity of Tm and (iv) a frequency dispersion of both ε0 and tan d in the transition region which leads to a frequency dependence of Tmax [4]. For a relaxor ferroelectric with a diffuse phase transition, a modified Curie-Weiss law is used: (1/ε’ e 1/εmax) ¼ (T e Tm)g/C
(3)
where g and C are the diffuseness degree and Curie constant, respectively. The parameter g gives information on the character of the phase transition: g ¼ 1 indicates Curie-Weiss behaviour for a first order ferroelectric; g ¼ 2 indicates a completely diffuse phase transition in an ideal relaxor ferroelectric [4,15,17]. The plots of ln (1/ε’ e 1/εmax) against ln (T - Tmax), Fig. 3, show an approximately
-8
1 kHz 10 kHz 100 kHz 1 MHz
(4)
where k is Boltzmann’s constant, 8.617 105 eV K1, fmax is the frequency of the peak maximum at Tmax and Tvf is an adjustable parameter that is presumed to represent freezing of the nanodomains. In this case, Fig. 4, a value of 10 K for Tvf gives a good fit; the activation energy, Ea ¼ 0.12 eV is obtained from an Arrhenius plot using the same data, Fig. 4 inset. Table 1 summarises the various parameters that may be used to describe the temperaturedependent, fixed-frequency, dielectric constant data. These analyses follow traditional procedures using fixed frequency data to characterise relaxors; from the results, it is not clear whether BMN is also ferroelectric although from the large negative values of To obtained from Fig. 2, ferroelectric behaviour is not expected. The second method of data analysis is to present variable frequency IS data at constant temperature. This is standard procedure in IS studies of electroceramics, but as far as we are aware, has been used on only two other occasions for relaxors [1,14]. IS data are presented and analysed in Figs. 5e9 and used the same experimental data sets as Figs. 1e4. 3.2. Variable frequency impedance data In Fig. 5, capacitance, C0 , data obtained from the impedance measurements are shown as a function of frequency over the temperature range, 10e1073 K. At the lowest temperatures, C0 increases with increasing temperature and decreases with increasing frequency (a,b). At lower frequencies, a frequency-independent plateau is seen increasingly at temperatures above ~100 K (b). For temperatures 200 K, C0 is independent of frequency over the range 103e106 Hz (c) but its value decreases with increasing temperature (c,d) up to the highest temperatures studied. Above ~873 K, (d), an additional low frequency dispersion is seen in the C0 data. An apparent drop in C’ plateau of ~5 pF for fixed frequency at 1 kHz and 1 MHz is discernible over the range ~200e673 K (e).
1.54 1.36 1.34 1.63
l n (1 / ' - 1 /
m
)
-10
-12
-14 1
2
3 4 ln (T - Tm) / K
5
6
Fig. 3. ln (1/ε’ - 1/εmax) against ln (T - Tm) of Bi3.55Mg1.78Nb2.67O13.78 at different frequencies.
Fig. 4. Frequencies and temperatures of ε0 max with fits to the Vogel-Fulcher equation as fmax as a function of Tmax. The inset (i) shows the Arrhenius plot of log fm as a function of 1/(Tm e Tvf).
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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Table 1 The temperatures for which the maximum dielectric constant (Tm), maximum dielectric constant (ε0 max), diffuseness constant (g), and Burns temperature (TB) at different frequencies. Frequency (Hz)
TB (K)
Tm (K)
ε0 max
g
1k 10 k 100 k 1M
222 226 228 230
146 164 180 204
212 211 210 209
1.54 1.36 1.34 1.63
Admittance or conductivity, Y0, data extracted from the same IS datasets, are plotted against frequency in fixed temperature format in Fig. 6. Below ~240 K, Y0 data were frequency-dependent at all temperatures (a,b). Between ~240 and 623 K, the conductivities were too low to measure accurately, < ~107 U1 cm1, at any frequency (not shown). Above ~623 K, Y0 data were again measurable, but were now frequency-independent and Y’ increased with temperature (c). At the lowest temperatures, 10e40 K (a), Y0 data show linear,
Fig. 5. Capacitance, C0 as a function of frequency for five temperature ranges (a) 10e100 K, (b) 110e210 K, (c) 220e320 K, (d) 373e1073 K and (e) C0 plateau as a function of temperature.
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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Fig. 6. Admittance, Y0 as a function of frequency for temperature ranges (a) 10e120 K, (b) 130e240 K and (c) 623e1073 K.
power law dependence and increase with increasing temperature at a given frequency. At higher temperatures, the Y0 data start to show curvature with an increasing slope at lower frequencies, but the overall Y0 values increase by a small amount. This continues until ~120 K (a), above which, the Y’ data start to decrease and above ~240 K were too small to measure (b). At all temperatures up to 240 K, therefore, the ac conductivity was clearly measurable but there was no evidence of a limiting, low frequency, dc conductivity. Above ~623 K, the dc conductivity became measurable for the first time and was independent of frequency (c).
3.3. Interpretation of variable frequency impedance data (a) Equivalent circuit modelling In order to analyse variable frequency IS data, the first step is to find an equivalent circuit that accurately represents the data. This is followed by fitting data to the circuit to extract values of the component parameters. The final step is to assign the parameters to specific features or properties of the sample. Selection of the correct equivalent circuit is an essential but non-trivial exercise since, in general, it is always possible to fit a particular data set to more than one circuit and the equations used to extract R and C values depend on the circuit used. Our approach is to: first, make a visual
inspection of the IS data in various formats, such as C0 and Y’ against frequency; second, assign circuit elements to key features of each response and gradually build the overall equivalent circuit; third, evaluate how the sample parameters vary with, for example, sample processing conditions, temperature and composition. If accurate values of circuit parameters are required, perform computer fitting to the circuit and examine the quality of the fits, either visually or from the residuals as a function of frequency. The inter-relationships between the various formalisms that may be used for representing impedance data are given by Ref. [18]: M* ¼ juCo Z* ¼ (ε* or C*)1 ¼ juCo (Y* or A*)1
(5)
where j ¼ √-1 and M*, Z*, ε* and Y* are the complex electric modulus, impedance, permittivity and admittance. Each of the four complex formalisms has real and imaginary components such that: Formalism ¼ (real) þ j(imaginary)
(6)
Data can be represented as complex plane plots (or Argand diagrams) of (imaginary) vs (real), usually on linear scales, or as spectroscopic (Nyquist) plots of one component against frequency. The ratio: (imaginary)/(real) is also often plotted against frequency, especially for the permittivity formalism, and is known as dielectric
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Fig. 7. Equivalent circuits showing different R, C, CPE combinations (a) master circuit, (b) below ~ 60 K, (c) ~80 Ke~220 K, (d) > ~220 K, (e) > ~673 K, (f) dielectric relaxation.
loss or tan d. In order to use these various methods of data presentation to gain an overview of the impedance response of the material, knowledge of the appropriate equivalent circuit is not necessary, but to subsequently extract values of component R and C parameters, knowledge of the equivalent circuit, and associated equations, is essential. Using an appropriate choice of methods and plots to analyse the data shown in Figs. 5 and 6, the following key conclusions were drawn: (i) From the Y0 data, BMN is a dc electrical insulator below 240 K; nevertheless, ac conductivities can be measured. To model these, either a series combination of a resistance and a capacitance, in which the capacitance blocks the inability for dc conduction to occur, or a frequency-dependent resistance, is required. (ii) At the lowest temperatures, plots of log Y0 vs log f are almost linear and indicate a power law component in the equivalent circuit which could be represented by a constant phase element, CPE, whose admittance, Y*, is given by: Y* ¼ Aun þ jBun ¼ Y’ þ jY”
(7)
where u is the angular frequency, 2pf and A, B are inter-related by A/B ¼ tan (np/2)
(8)
The CPE is effectively, a parallel combination of a variable
resistance and capacitance; Y’ therefore represents the frequency dependence of the resistive component of the CPE, Aun. The value of n is ~0.96 which means that the CPE is mainly capacitive in nature at these temperatures. (iii) At temperatures > ~90 K, the increased slope, with value > 1, in log Y’/log f plots at low frequencies, indicates the need for an additional capacitive element in series with the CPE. This is because the maximum possible value of n for a CPE is 1. For an ideal circuit consisting of two elements in series, the low frequency slope that connects their impedance responses can have a value as high as 2. (iv) C0 data at temperatures of 220 Ke573 K are frequencyindependent over the entire measurement range, Fig. 5 (c, d) and are therefore represented by a simple, frequencyindependent capacitance; any associated parallel or leakage resistance was too high to measure, >107 U cm, as shown by presentation of the same data in the format log Y’/log f: the observed Y0 data were effectively background noise associated with the internal impedance of the measuring instrumentation. The presence of this same capacitance is seen in low frequency C0 data for temperatures as low as 90 K, Fig. 5 (a), although the full capacitance plateau was not seen due to frequency limitations of the equipment. This capacitance is referred to as the low frequency capacitance, C2, in subsequent discussions. (v) In the low temperature C0 data, Fig. 5(a), there is some evidence from the small amount of curvature of the log C’/log f
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Fig. 8. Fit of the 20 K, 150 K, 240 K data to circuit in Figs. 5 and 6.
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Fig. 9. Temperature dependence of (a) capacitance C1, (b) capacitance C2, (c) CPE1 and the n values, (d) resistance R1 and (e) Arrhenius conductivity plots of Y0 as a function of temperature for temperature range 623e1073 K.
plots that a second, frequency-independent plateau may exist at the highest frequencies which would correspond to the limiting, high frequency capacitance of the sample, C∞, referred to here as C1 [19]. Its value is estimated to be 2e3 pF.
The frequency-dependent C0 data at the lowest temperatures therefore represent the summation of two contributions, from the CPE and C1, which are in parallel and are given by:
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C’ ¼ (B/Co) un1 þ C1/Co
(9)
With increasing temperature, the capacitance dispersion leading to the high frequency C1 plateau moves to higher frequency and C1 moves off-scale. Thus, at e.g. 50 K, C0 is dominated by the CPE component, Bun and the plot of log C’/log f is linear with slope (n1) ¼ 0.04. With further increase in temperature, the capacitance dispersion represented by the CPE also moves off-scale and only the low frequency capacitance, C2, is seen, Fig. 5(b and c), for temperatures >~210 K. A master circuit that incorporates points (i) to (v) and was shown to fit low temperature data for other pyrochlore relaxors [1,14] is given in Fig. 7(a). However, this circuit simplifies in various ways, depending on temperature. Element C1 can be quantified only at the lowest temperatures, Table 2; it represents the limiting high frequency capacitance of the sample and gives a value of ~30 for the permittivity, ε∞, using: ε∞¼εoε0 A/l
(10)
where εo is the permittivity of free space 8.854 1014 Fcm1 and A/l is the geometric factor of the sample in units of cm. For data in the range 10e70 K, R1 was too large to measure, the additional series capacitance C2 was not needed and the equivalent circuit simplifies to that given in Fig. 7(b). For temperatures above ~60 K, data are still dominated by the CPE, but evidence for series capacitance C2 is increasingly seen and resistance R1 is required to obtain good fits to the experimental data. C1 no longer makes any significant contribution to the impedance data and circuit Fig. 7(c) therefore becomes appropriate. The value of R1 decreases rapidly with increasing temperature and above ~220 K, R1 is sufficiently small that the circuit reduces to that of a single capacitor, C2, Fig. 7(d).
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For the parallel R1-CPE1 component of the circuits shown in Fig. 7(a,c), the two possible contributions to the ac conductivity are R1 1 and CPE1, since Y’ is given by: n Y’ ¼ R1 1 þ A1 u
(11)
This ac conductivity is localised and in series with capacitance C2 which effectively blocks any possibility of long range conduction. The presence of C2 is shown by log C’/log f plots at low frequencies for temperatures > ~90 K, Fig. 5(a,b) and also in the curvature at low frequencies in log Y’/log f plots for temperatures > ~40 K, Fig. 6(a,b). With increasing temperature, the Y’ conductivity spectrum is displaced to higher frequency as shown clearly in Fig. 6(b) and is off-scale >~240 K. This is because the net effect of a decrease in R1 (and increase in A1) with increasing temperature, Table 2, is to decrease the time constant (RC product) of the series combination of R1 and C2 and therefore, to increase the relaxation frequency, umax, given by umaxRC ¼ 1, associated with this series combination. When the ac conductivity can no longer be measured above ~240 K, the equivalent circuit simplifies to that of a single capacitor, Fig. 7(d), as shown by the data in Fig. 5(c). At much higher temperatures, >~623 K, Y0 data show wide ranges of frequency-independent conductivity, Fig. 6(c) which is evidence for long range, dc conduction through the sample. Circuit Fig. 7(d) is therefore modified to add a leakage resistance, R2 in parallel with capacitance C2. At still higher temperatures, above ~773 K, Fig. 5(d), C’ increases at low frequencies; this is attributed to polarisation at the sample e electrode interface. The equivalent circuit Fig. 7(d) is therefore modified further to add an additional capacitance, C3, that represents the blocking of charge carriers at the electrode-sample interface, Fig. 7(e). A selection of fits to equivalent circuits is shown in Fig. 8. In Fig. 8(a,b) are shown spectroscopic plots for Y0 and C0 for circuit
Table 2 Fitting data of Bi3.55Mg1.78Nb2.67O13.78 using various circuit parameters from 10 K to 320 K. Temperature (K) 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320
R1 (U cm) x 105
C1 (F cm1) 1012
C2 (F cm1) 1011
2.95 2.42 1.95 1.27 3.95 101 1.15 106 1.50 107 7.84 5.99 15.6 2.40 1.18 5.02 101 2.11 101 9.00 102 3.97 102 1.82 102 7.69 103 3.47 103 1.56 103 6.95 104
1.59 1.69 1.83 1.82 1.85 1.87 1.87 1.87 1.87 1.87 1.86 1.86 1.85 1.85 1.84 1.84 1.83 1.83 1.82 1.82 1.81 1.80 1.79 1.79 1.78
A1 (U1cm1rad1) x 106
n
9.08 106 1.09 105 1.25 105 1.44 105 1.67 105 1.86 105 2.05 105 6.98 104 9.14 104 1.10 103 2.19 103 4.30 103 1.03 102 2.66 102 7.37 102 2.01 101 5.52 101 1.27 2.66 3.37 1.65
0.963 0.962 0.961 0.962 0.962 0.961 0.958 0.813 0.801 0.789 0.762 0.733 0.696 0.655 0.613 0.571 0.530 0.501 0.476 0.477 0.529
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Fig. 7(b) at 20 K. In Fig. 8(c,d), similar plots for circuit Fig. 7(c) at 150 K are shown. In Fig. 8(e) the spectroscopic plot for C0 for circuit Fig. 7(d) at 240 K is shown. It was not always appropriate to allow free refinement of all the circuit parameters simultaneously. This was because first, the B component of CPE1 was a frequency dependent capacitance which was fitting the same C0 data as C2 and second, the A component of CPE1 was fitting the same Y’ data as R1. Nevertheless, the broad conclusions of the analyses are clear and are summarised in Fig. 9 as the temperature dependence of the various circuit parameters. (b) Assignment of equivalent circuit parameters The temperature dependence of A1, n, C1, C2 and R1, Fig. 9 and can be described and interpreted as follows: Capacitance C1 is attributed to the bulk lattice polarisation; it has a value of ~3 pF, representing a value for ε∞ of ~30, which is a typical value for a polar dielectric. Capacitance C2 is also small and decreases gradually with temperature. It represents the blocking of charge displacement associated with R1 1 and A1. These charge displacements are very small, represent a tiny fraction of an interatomic bond distance and cannot be construed as an ionic conduction process. C2 is not a conventional blocking capacitance such as occurs at sample-electrode interfaces, therefore. Resistance R1 is attributed to the difficulty of the localised charge displacements, which is increasingly frozen-in at the lowest temperatures; R1 decreases rapidly with rising temperature and has little effect on the sample impedance above ~220 K. Hence, at ac measuring frequencies, the lattice polarisation is represented by C2 at high temperatures but by C1 at low temperatures. The n parameter gives the relative contribution of frequencydependent resistances and capacitances to the CPE. It decreases from ~0.96 at the lowest temperatures where the CPE is largely capacitive to ~0.48 at 200 K where R and C contribute equally to the CPE. The A1 parameter reflects the localised atomic motions that contribute to the CPE and gives similar information to the parameter R1. Thus, the ac conductivity values represented by A1 increase by > 5 orders oCCf magnitude between ~50 and 200 K as the polar regions become unfrozen and start to break up. R2 represents long range conductivity through the sample at high temperature; it is in parallel with blocking capacitance C2. Clearly, R2 has a different origin to that responsible for R1 and A1; from the presence of series capacitance C3 at higher temperatures, it is likely that R2 represents either electronic conduction or, more probably, conduction of oxide ions; further work is required to clarify the high temperature conduction mechanism. (c) Correlation of electrical properties with the structure of BMN pyrochlore In BMN pyrochlore, Mg2þ cations are probably distributed at random over both A- and B-sites with general formula, (Bi3.55Mg0.45) (Mg1.33Nb2.67)O13.78. Either of the crystallographic A and B sites could be responsible for polarity of the crystal structure and possible nanodomain formation. Thus, the eight-coordinated A-site contains two ions, Bi and Mg, of very different size and coordination requirements and the possibility exists for off-centre displacement of the smaller Mg2þ ions. The octahedral B-site also contains a mixture of two ions of different size and charge [1]; polarisation associated with mixed occupancy of octahedral sites by Mg and Nb in the perovskite structure of PMN, lead magnesium
niobate is well-established and could therefore occur in the present BMN sample. A third possibility is that one of the oxygen sites, often written as O’, shows positional disorder in pyrochlores and could contribute to polarisation. Assuming that at least one of the above three polarisation processes is responsible for the low temperature relaxor properties, the possibility exists for the individual polarisation steps to act cooperatively, leading to polar domain formation. For instance, it has been suggested that relaxation in pyrochlores might stem from the hopping of dynamically disordered A-site cations and O0 ions among the closely-spaced possible positions [6,7]. The interaction between the cations at the disordered A-sites and the O’ ions could cause the formation of localised dipoles within the structure that reorient in an external ac field. In addition, inhomogeneous distribution of Mg2þ may cause additional random fields leading to multiwell potentials with a wide distribution of heights that contribute to a broad dielectric relaxation [6,7] and the variable R and C components of the CPE. Cooperative alignment within domains may, however, be limited to short distances only because of frustration associated with inhomogeneities in the structure and/or local composition. In addition, the magnitude of the high temperature lattice polarisation, C2, is small and therefore, the charge displacements associated with polar domains are likely to be very small. Resistance R1 represents a thermally-activated, local displacement with activation energy 0.26 eV above ~160 K, Fig. 9(b). We see no evidence that R1 is associated with long range conduction but instead, is associated with local atomic displacements within a polar region or, perhaps, with domain wall migration. Our interpretation of R1, C1, and their temperature dependencies, is that the material possesses some kind of polar nanodomain structure that is effectively frozen-in at low temperature. With increasing temperature, domain relaxation processes commence as shown by a reduction in resistance R1. At temperatures around 170e220 K, the domains break up as R1 becomes negligibly small. BMN pyrochlore shows similar relaxor behaviour to other pyrochlores such as BZN, BZT, BZNT, BNN [1,6e9]. Their relaxor electrical properties are intermediate between those of (i) first order ferroelectrics which show sharp dielectric constant maxima as a function of temperature and (ii) dielectric materials which show very little temperature dependence of dielectric constant [1,19e21]. In the absence of the frequency-dependent relaxor characteristics, the electrical properties could be referred to the classic dielectric relaxation circuit shown in Fig. 7(f). This has a low frequency capacitance dominated by C2, a high frequency capacitance dominated by C1, and a relaxation at intermediate frequencies controlled by the magnitude of R1 and the R1C2 time constant. Superposed on this circuit is the frequency dependencies of R and C represented by the CPE; hence, the key component that determines the frequencydependent relaxor characteristics is the CPE. 4. Conclusions 1. BMN pyrochlore is a relaxor but is not ferroelectric. A CurieWeiss plot of high temperature capacitance data shows no indication of any ferroelectric transition at lower temperatures; also, low temperature capacitance data show no evidence of any capacitance maximum that could be associated with a Curie temperature. 2. The dielectric properties have been satisfactorily modelled using equivalent circuit analysis. The key circuit element responsible for the frequency-dependence of the permittivity, that is characteristic of a relaxor such as BMN, is a constant phase element which, in its ideal form, is a parallel, frequency-dependent, resistance and capacitance combination.
Please cite this article as: P.Y. Tan et al., Non-ferroelectric relaxor properties of BMN, Bi3.55Mg1.78Nb2.67O13.78 pyrochlore, Journal of Alloys and Compounds, https://doi.org/10.1016/j.jallcom.2019.152576
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3. Low temperature relaxor behaviour can be derived from an ideal dielectric relaxation equivalent circuit that consists of a parallel RC element in series with a capacitor. The two capacitances represent the lattice polarisation at the low and high frequency limits, that respectively, are with and without, the contribution from the lattice relaxation. This ideal dielectric relaxation circuit is modified for a relaxor by inclusion of a CPE in the circuit. 4. The atomic displacements responsible for relaxor behaviour are very small and are likely to be at least an order of magnitude less than those involved in the ferroelectric switching of BaTiO3. These displacements are, however, thermally activated with activation energy, 0.29 eV, that essentially controls the range of temperature range over which relaxor behaviour is observed. Several types of possible atomic displacement within the pyrochlore structure can be identified. 5. The relaxor effect in BMN is seen only below ~220 K. At higher temperatures, BMN is an excellent insulator. At much higher temperatures, above ~600 K, the dielectric behaviour becomes leaky, probably due to the onset of oxide ion conduction. Acknowledgments The financial support from The Universiti Putra Malaysia through Putra Research Grant Scheme is gratefully acknowledged. The authors would like to extend their utmost gratitude to Prof. A.R. West for his invaluable technical advices, insightful suggestions and sponsorship for P.Y. Tan’s three-month research attachment at The University of Sheffield, UK. References [1] R.A.M. Osman, A.R. West, Electrical characterization and equivalent circuit analysis of (Bi1.5Zn0.5)(Nb0.5Ti1.5)O7 pyrochlore, a relaxor ceramic, J. Appl. Phys. 109 (2011), 074106. [2] Z.Y. Cheng, R.S. Katiyar, X. Yao, A.S. Bhalla, Temperature dependence of the dielectric constant of relaxor ferroelectrics, Phys. Rev. B 57 (1998) 8166e8177. [3] H.Q. Fan, S.M. Ke, Relaxor behaviour and electrical properties of high dielectric constant materials, Sci. China Ser. E Technol. Sci. 52 (2009) 2180e2185.
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[4] X.G. Tang, K.H. Chew, H.L.W. Chan, Diffuse phase transition and dielectric tunability of Ba(ZryTi1-y)O3 relaxor ferroelectric ceramics, Acta Mater. 52 (2004) 5177e5183. [5] L.E. Cross, Relaxor ferroelectrics: an overview, Ferroelectrics 151 (1994) 305e320. [6] C. Ang, Z. Yu, H.J. Youn, C.A. Randall, A.S. Bhalla, L.E. Cross, J. Nino, M. Lanagan, Low-temperature dielectric relaxation in the pyrochlore (Bi3/4Zn1/4)2(Zn1/4Ta3/ 4)2O7 compound, Appl. Phys. Lett. 80 (2002) 4807e4809. [7] S. Kamba, V. Porokhonskyy, A. Pashkin, V. Bovtun, J. Petzelt, Anomalous broad dielectric relaxation in Bi1.5Zn1.0Nb1.5O7 pyrochlore, Phys. Rev. B 66 (2002), 054106. [8] J.C. Nino, M.T. Lanagan, C.T. Randall, Dielectric relaxation in Bi2O3-ZnO-Nb2O5 cubic pyrochlore, J. Appl. Phys. 89 (2001) 4512e4516. n, Y. Liu, R.L. Withers, X. Wei, M.M. Elcombe, The disor[9] B.H. Nguyen, L. Nore dered structures and low temperature dielectric relaxation properties of two misplaced-displacive cubic pyrochlores found in the Bi2O3-MIIO-Nb2O5 (M ¼ Mg and Ni) systems, J. Solid State Chem. 180 (2007) 2558e2565. [10] L. Li, X. Zhang, L. Ji, P. Ning, Q. Liao, Dielectric properties and electrical behaviors of tunable Bi1.5MgNb1.5O7 thin films, Ceram. Int. 38 (2012) 3541e3545. [11] D.P. Cann, C.A. Randall, T.R. Shrout, Investigation of the dielectric properties of bismuth pyrochlores, Solid State Commun. 100 (1996) 529e534. [12] P.Y. Tan, K.B. Tan, C.C. Khaw, Z. Zainal, S.K. Chen, M.P. Chon, Phase equilibria and dielectric properties of Bi3þ(5/2)xMg2-xNb3-(3/2)xO14-x cubic pyrochlores, Ceram. Int. 40 (2014) 4237e4246. [13] P.Y. Tan, K.B. Tan, C.C. Khaw, Z. Zainal, S.K. Chen and M.P. Chon, Manuscript in Preparation. , A.R. West, Bismuth zinc niobate pyrochlore, a relaxor[14] R.A.M. Osman, N. Maso like non-ferroelectric, J. Am. Ceram. Soc. 95 (2012) 296e302. [15] W. Zuo, R. Zuo, W. Zhao, Phase transition behavior and electrical properties of lead-free (Bi0.5K0.5)TiO3-LiNbO3 relaxor ferroelectric ceramics, Ceram. Int. 39 (2013) 725e730. ski, J. Koperski, Dielectric [16] M. Adamczyk, Z. Ujma, L. Szymczak, A. Soszyn properties and relaxation of Bi-doped (Pb0.75Ba0.25)(Zr0.70Ti0.30)O3 ceramics, Mater. Sci. Eng., B 136 (2007) 170e176. [17] H. Yang, F. Yan, Y. Lin, T. Wang, F. Wang, Y. Wang, L. Guo, W. Tai, H. Wei, Leadfree BaTiO3-Bi0.5Na0.5TiO3-Na0.73Bi0.09NbO3 relaxor ferroelectric ceramics for high energy storage, J. Eur. Ceram. Soc. 37 (2017) 3303e3311. [18] A.R. West, D.C. Sinclair, N. Hirose, Characterisation of electrical materials, especially ferroelectrics, by impedance spectroscopy, J. Electroceram. 1 (1997) 65e71. [19] M.A. Hernandez, N. Maso, A.R. West, On the correct choice of equivalent circuit for fitting bulk impedance data of ionic/electronic conductors, Appl. Phys. Lett. 108 (2016) 152901. [20] G.A. Samara, The relaxational properties of compositionally disordered ABO3 perovskites, J. Phys. Condens. Matter 15 (2003) R367eR411. [21] L.E. Cross, Relaxor ferroelectrics, Ferroelectrics 76 (1987) 241e267.
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