Dielectric study of Ba(Zn_1/3Nb_2/3)O₃ at low temperature

Dielectric study of Ba(Zn

Nb

)O

at low temperature

A K Himanshu, D C Gupta & T P Sinha⁺

School of Studies in Physics, Jiwaji University, Gwalior 474 011

†Department of Physics, Bose Institute, 93/1, APC Road, Kolkata 700 009 Received 18 October 2005; revised 23 January 2006; accepted 6 February 2006

The dielectric study of Ba(Zn1/3Nb2/3)O3 has been studied at low temperature in a frequency range 100 Hz-1 MHz and a temperature range from 145K to room temperature. An analysis of real and imaginary part of dielectric permittivity, imped- ance (Z), conductivity and electric modulus with frequency and temperature is performed, showing the polydispersive nature of the relaxation time in the sample as confirmed by the Cole-Cole plot of the dielectric permittivity and impedance. All these results suggest that the relaxation phenomenon seen in the configuration has been attributable to the damping of dipole oscillators due to the application of the external fields.

Keywords : Perovskite, Cole-Cole, Polydispersive, Impedance spectroscopy IPC Code: G01R27/26

1 Introduction

The complex pervoskites type compounds with the chemical formula of A²⁺(B' ²⁺ B" ⁵⁺)O₃ are of great technological interests. The examples include Ba(Zn1/3Nb2/3)O3 (BZN)(Ref.1) and Ba(Mg1/3Nb2/3)O3

(BMN)(Ref.2) for high frequency application, and Pb(Zn1/3Nb2/3)O3 (PZN) and Pb(Mg1/3Nb2/3)O3 (PMN) (Ref.3) show anomalously large dielectric constant (ε′) which makes them ideal in electrostitive acuators.

Barium zinc niobate, Ba(Zn1/3Nb2/3)O3 (BZN) and other related Ba-based mixed B-site cation perov- skites [Ba(B'1/3 B"2/3 ) O₃] are linear polar dielectric, as they adopt a structure with a long-range composi- tion order in which one plane of B′ atoms alternates with two planes of B″ atoms along the [111] direction.

We shall refer to this as 1:2_[111] structure^4,5. BZN has been known to have a cubic perovskite phase, how- ever the 1:2 ordered hexagonal structure was found⁶ for BZN sintered below 1350°C. On the other hand, weak X-ray reflections have been detected in various Pb compounds^7,8 such as PMN and Pb(Mg1/3Ta2/3)O3

(PMT)(Ref.9), that are indicative of a rocksalt-like 1:1 ordering. We will refer to this as 1:1[111]. The nature and strength of the atomic ordering have been shown to be crucial for the properties of this class of alloys.

The dielectric response of Ba-based mixed B-sites cation perovskites is known to be dependent on the long-range chemical ordering. The magnitude of both the dielectric constant (ε′) and dissipation factor (tanδ) has been reported to decrease with the in- creased order¹⁰.

Literature survey on Ba-based perovskites indicates that most of the research efforts have concentrated on the development of high dielectric constant (ε′) and a low dielectric loss (tanδ) in the frequency range 1-20 GHz for the potential application in the microwave dielectric resonators. However, the study on electrical properties of BZN in low frequency range (< 1 MHz) using alternating current impedance spectroscopy (ACIS) technique has received little attention. The ACIS is a very convenient and powerful experimental technique that enables us to correlate the electrical characterization of a material with its microstructure, and also helps to analyse and separate the contribu- tions, to the overall electrical properties, from various component (i.e., through grains, grains boundaries, interfaces, etc.) of polycrystalline materials in the wide frequency range. ACIS allows the measurement of capacitance (C) and the loss tanδ or real and imaginary impedance over a frequency range. From the measured capacitance and tanδ, four complex di- electric functions can be computed, impedance (Z^∗), permittivity (ε^∗), electric modulus (M^*) and admit- tance (Y^∗). For interpretation of the dielectric meas- urements, it is assumed that the sample behaviour can be represented by a time-invariant linear admittance.

In this case, if an alternating potential is applied across the sample, a phase shift θ between the current and voltage is induced due to the time dependence of the polarization process. If the current I and voltage V are considered to have a time variation of e^iωt, the

quantity V/I is a complex number with no time de- pendence and is called the complex impedance Z^∗, the real part (Z′) may be interpreted as resistance and the imaginary part Z″ may be interpreted as capacitance C with (Z^-1) = (1/R + jωC)^-1, where j = −1, C is the capacitance and ω is the angular frequency of the ac field. In this paper, we report the ACIS of our results on the electrical properties of BZN ceramics prepared by the solid-state reaction technique.

2 Experimental Details

BZN ceramics was prepared using the solid state reaction technique. Powders of BaCO₃ (reagent grade), ZnO (reagent grade) and Nb₂O₅ (reagent grade) were taken in the stoichiometric ratio and mixed in the presence of acetone for a day. The mix- ture was calcined in a Pt crucible at 1300^oC in air for 10 h and brought to room temperature under con- trolled cooling. The calcined powders were mixed

again and pressed into cylindrical discs using the polyvinyl alcohol as a binder. Finally, the cylindrical discs were sintered at 1350^oC for 5 h after the binder burnout at 450°C for 2 h. The sintered pellets were polished on different grades of emery papers to obtain parallel surfaces.

The X-ray powder diffraction pattern of the sample was taken at room temperature using Philips PW1877 automatic X-ray powder diffractometer. For the di- electric characterization, the sintered pellet was pol- ished and silver paste was used onto both sides of the pellet for electrical contacts. The temperature and fre- quency dependence of the dielectric characterization was carried out using LCR meter (HIOKI) in our laboratory, in the frequency range 50 Hz -1 MHz and in a temperature range 145K-room temperature. The temperature was controlled with a programmable oven. All the dielectric data were collected while heating at a rate of 0.5°C min^-1. These results were found to be reproducible.

Fig. 1—XRD pattern of BZN ceramic sintered at 1300°C

3 Results and Discussion

Figure 1 shows the X-ray diffractogram of the sample taken at room temperature. All the reflection peaks of the X-ray profiles were indexed showing the hexagonal structure of the sample at the room tem- perature. Our result agrees well¹¹ with the reported data for BZN. Figure 2(a-c) shows the frequency de- pendence of the real and imaginary part of the com- plex permittivity (ε′′) and loss tangent (tanδ) in the temperature range 145 - 290 K. The high value of ε′

and ε′′ and tanδ frequencies lower than 1 kHz which increases, in general, with decreasing frequency and increasing temperature may be attributable to free charge build-up at the interface between the sample and the electrode (space charge polarization). The Debye formula giving the complex permittivity re- lated to free dipole oscillating in an alternating field¹² is as follows:

* ' '' ( )

1 j s

j

∞ ∞

ε − ε ε = ε − ε = ε +

+ ωτ … (1)

The real part of ε∗ is

'

1 2 2

s ∞

∞

ε − ε ε = ε +

+ ω τ … (2)

Fig. 2(a)—Frequency dependence of ε′of BZN

Fig. 2(b)—Frequency dependence of ε″of BZN

Fig. 2(c)—Frequency dependence of tan δ of BZN

and the imaginary part of ε′ is

''

( ) 2 2

s ∞ 1

ε = ε − ε ωτ

+ ω τ … (3)

where εs and ε∞ are the low and high frequency values of ε′(ω), ω = 2πf, f being the measuring frequency, τ is the relaxation time. At very low frequencies (ω<<1/τ), dipoles follow the field and we have ε′ ≈ εs

(value of the dielectric constant at quasi-static fields).

As the frequency increases (with ω<1/τ), dipoles be- gin to lag behind the field and ε′ slightly decreases.

When frequency reaches the characteristic frequency (ω=1/τ), the dielectric constant drops (relaxation pro- cess). At very high frequencies (ω>>1/τ), dipoles can no longer follow the field and ε′ ≈ ε∞. Qualitatively, this is the behaviour observed in Fig. 1(a) and the ex- perimental results of Fig. 2(a) confirm Eq. (2). It is to be noted that at lower frequencies, there is a substan- tial increase in the dielectric constant that is attribut- able to a dipolar contribution to ε′(ω) from the hop- ping of cations between neighbouring atoms. It is ob- served from Fig. 2(a-c) that ε′, ε′′ and tanδ are very low as compared to Pb-based perovskite⁸ (PZN). The formation of very short Pb-O covalent bond in PZN, and the existing (unstable) analogous large Zn-O bonds in BZN, are probably the main quantitative rea- son for the larger relaxation energy found in PZN (1:2)[001] as compared to BZN (1:2)[001]. The energetics of the heterovalent BZN alloys is mainly driven by electrostatic interactions among the Zn and Nb atoms.

These electrostatic interactions lead to the stabiliza- tion of the 1:2 long-range ordered structure along [111] direction¹³. The ordered materials are character- ized by a temperature-independent dielectric response in the low frequency range less than 10⁹ Hz. It is ob- served from the frequency dependence of ε′, ε′′, tanδ in the frequency range 100 Hz – 1 MHz and the tem- perature range 145 - 290 K that the curve does not shift appreciably with the rise of temperature, indicat- ing that due to the long-range ordered formation of BZN, the dielectric response is independent of tem- perature, and consistent to the other report in the fre- quency range^14,15 below 10 ⁹ Hz.

The electrical conductivity effects give rise to higher values of ε′′ in Fig. 2(b), increasing with de- creasing frequency. A relation exists between σac and ε′′ which is given as σ_{ac =} ε₀ωε′′_, where σ_ac is the ac conductivity, ω = 2πf (f is the measuring frequency)

and ε₀ is the free space permittivity. Figure 3 shows the plot of frequency dependence ac-conductivity (σac) of BZN in the temperature range 145 - 290 K. The frequency spectra of the conductivity for BZN show a dispersion that increases with the increasing fre- quency and become independent of temperature in lower frequency regions. The almost overlap of 145, 202 and 290 K conductivity curves elucidate that the conductivity mechanism is independent of tempera- ture.

The width of loss peak shown in Fig. 2(b) cannot be accounted in terms of a monodispersive relaxation process, but points towards the possibility of relaxa- tion times. The complex dielectric data as shown in Fig. 2(a-b) are shown in Figure 4 in the ε′′(ω) versus ε′(ω) representation at 145 K. One standard way to analyse the experimental data is to fit to the Cole-Cole expression¹⁶.

1 (i )1

∗

∞ −α

ε = ε + Δε

+ ωτ … (4)

where Δε= ε_s-ε∞ is the dielectric relaxation strength, and α is the parameter describing the distribution of the relaxation times. It is apparent from Fig. 4 that the relaxation process differs from the mono-dispersive Debye process (for which α = 0). The parameter α as determined from the angle subtended by the radius of

Fig. 3—Frequency spectra of the conductivity for BZN

Fig. 4— Cole- Cole plot at temperature 145 K for BZN

the circle with the ε′-axis passing through origin of ε″-axis is 0.10. The value of α between 0 and 1 (0< α

< 1) indicates broad distribution of relaxation times in the system. The Cole-Cole plot confirms the polydis- persive nature of the dielectric relaxation time of BZN.

ACIS allow the separation of resistance related to the grain (bulk), and grain boundaries. A simple RC circuit in parallel gives rise to a semicircle in the complex plane (Z″ versus Z′; M″ versus M′) or a De- bye peak in the spectroscopic plot of the imaginary component (Z″, M″ versus logω). This is seen from equation for impedance of the circuit:

' '' (1/R j C) 1

∗ −

Ζ = Ζ − Ζ = + ω … (5)

where

'

1 ( )2

R Ζ = RC

+ ω … (6)

''

1 ( )2

R RC

RC

⎛ ω ⎞

Ζ = ⎜⎝ + ω ⎟⎠ … (7)

Figure 5(a and b) shows the frequency dependence of real and imaginary part of complex impedance (Z*) as a function of temperature from 145 to 290 K. The al- most overlap of the curve at these temperature indi- cates that the frequency dispersion is independent of temperature. The complex dielectric data shown in Fig. 5(a and b) and Fig. 6 in the Z″(ω) versus Z′(ω) representation. One of the convenient ways to analyse

Fig. 5(a)—Frequency dependence of Z' of BZN

Fig. 5(b)—Frequency dependence of Z″ of BZN

Fig. 6—Symmetrical Cole-Cole plots at 145 K and 290 K

the experimental data is to fit to the Cole-Cole plots.

In analogy to the symmetrical Cole-Cole distribution terms of a formal distribution times¹² is given by:

* 0

1

( )

1 ( ) R R Z R

i

∞ ∞−ϕ

= + −

+ ωτ … (8)

which is just the impedance of a resistance R _∞ in series with a parallel combination of a resistance R0 – R ∞ and a term called phase constant. Here R0 and R∞ are the values of resistance at low and high fre- quencies, respectively, and φ is a measure of the dis- tribution of relaxation times. The parameter φ can be determined from the location of the centre of the Cole-Cole circles, of which only an arc lies above the Z′-axis. Fig. 5 depicts a Cole-Cole plot between Z″

and Z′ at T = 145 K and 290 K for BZN. It is evident from this plot in Fig.5 that the relaxation process dif- fers from the mono-dispersive Debye process (for which φ = 0). The parameter φ, as determined from the angle subtended shows almost negligible change in the interval [0.10, 0.105] with the decrease of tem- perature from 290 to 145 K. The value of φ between 0 and 1 (0< φ<1), describes the broad distribution of relaxation times in the system. The Cole-Cole plots confirm the poly-dispersive nature of the dielectric relaxation of BZN. Further, in the presentation of complex impedance graph (Fig. 6), we expect a sepa- ration of the bulk phenomenon from the surface phe- nomenon (interfacial Maxwell-Wagner polarization).

For a bulk crystal containing interfacial boundary layer, one gets two arcs in the complex plane imped- ance plot: one for the bulk crystal and other for the interfacial boundary response. In Fig. 6, the absence of any second arc confirms that the polarization

mechanism in BZN correspond to bulk effect suggests that the Maxwell-Wagner polarization cannot be at the origin of the ε′ at low frequencies.

To analyse the conductivity relaxation property in depth, the complex permittivity (ε∗) is converted to the complex electric modulus M*(ω), because ε∗ is not completely suitable to describe the electrical properties of the sample. The real and imaginary part of M*(ω) can be calculated from ε∗(ω) as follows:

( ) 1 ' ''

M^∗ ω = _∗( )=M + jM

ε ω … (9)

the real part of M*(ω) is given as

' '

' 2 '' 2

M = ε

ε + ε … (10)

and the imaginary part of the M*(ω) is given as :

'' ''

'2 ''2

M = ε

ε + ε … (11)

Figure 7(a and b) shows the frequency dependence of M′(ω) and M″(ω) as a function of temperature.

M′(ω) shows a dispersion tending toward M∞ (the as- ymptotic value of M′(ω) at higher frequencies [Fig.

7(a)], and that M′(ω) approaches to zero at low fre- quencies, indicating that the electrode polarization gives a negligible low contribution to M′(ω) and

Fig. 7(a)—Frequency dependence of M' of BZN

Fig. 7(b)—Frequency dependence of M″ of BZN

being ignored when the permittivity data are ex- pressed in this form. Figure 7(b) can be used as a very convenient visual monitor of the electrical description of the sample and could provide a useful means to show the effect of changing conditions, i.e., tempera- ture and frequency, on the relaxation process ob- served in the sample. These plots show that a well- defined relaxation mechanism is in operation for tem- peratures as low to 145 K and 290 K. A shift in the fmax at constant M″ would imply variation in R but not C. On the other hand, the change in the value of M″max

with no variation in fmax would suggest a change in R and C. However, our data in the temperature range 145 - 290 K show almost negligible variations in both M″_max and f_max indicating no variation in C with the rise of temperature.

4 Conclusion

X-ray diffractogram of the BZN synthesized by the solid state reaction shows a hexagonal phase at room temperature. Analyses of the frequency dependence of the real and imaginary parts of the dielectric permit- tivity, impedance, conductivity, and electric modulus were performed in the temperature range 145-290 K, showing the polydispersive nature of relaxation time as confirmed by Cole-Cole plot of complex permittiv- ity and impedance. The frequency dependence of these results are found to be independent of tempera- ture. All these results suggest that the relaxation phe- nomenon seen in the configuration [Ba(Zn1/3Nb2/3)O3] has been attributable to the damping of dipole oscilla- tors due to the application of the external field.

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