Effect of porosity on dielectric properties of ZnO ceramics

Journal Pre-proof Effect of porosity on dielectric properties of ZnO ceramics Raphael Lucas de Sousa e Silva, A. Franco

PII:

S0955-2219(19)30876-3

DOI:

https://doi.org/10.1016/j.jeurceramsoc.2019.12.032

Reference:

JECS 12945

To appear in:

Journal of the European Ceramic Society

Received Date:

1 July 2019

Revised Date:

10 December 2019

Accepted Date:

15 December 2019

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Effect of porosity on dielectric properties of ZnO ceramics

Raphael Lucas de Sousa e Silva Instituto de Química Instituto de Física Universidade Federal de Goiás, Goiânia, Brazil

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A. Franco Jr. Instituto de Física Universidade Federal de Goiás, Goiânia, Brazil e-mail: {franco}@ufg.br

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Abstract

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Introduction

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In this study we investigated the effect of porosity level on the dielectric properties and conductivity of ZnO ceramic samples sintered by pressure-less solid-state reaction method. The relative permittivity (εr0 ) and, tangent loss value decreased gradually with increasing porosity, being 1.9 × 105 and 35.6 × 103 for sample with low porosity and high porosity level, respectively at room temperature. Also the tangent loss decreases with increasing porosity level being quite high (∼ 102 ) at low frequencies and, low (∼ 10−1 ) at high frequencies. The complex part of the relative permittivity results could be fitted to the Maxwell-Wagner (MW) model suggesting a poly-dispersive relaxation time. The frequency dependence-ac conductivity determined by means of dielectric data was strongly dependent of the porosity level. It decreases sharply with increasing porosity level is frequency independent- up to ∼ 104 − 105 Hz followed by an abrupt increase at higher frequencies. These data were discussed in terms ZnO defects such as Zn interstitial and oxygen vacancies present in the grain boundaries. Keywords : Porosity level, Dielectric permittivity, ZnO ceramics

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In the last years room temperature colossal dielectric permittivity (CP) have been subject of studies on wurtzite zinc oxide (ZnO) semiconductors materials [1]. In general the colossal dielectric permittivity response is attributed to the electronic inhomogeneous conduction mechanism within the material due to the production of absorption current in the thin grain boundary regions which accumulates charge at the interfaces and induces the Maxwell-Wagner interfacial polarization. Even though controlled sintering process produce dense ceramics they are not free from structural defects. While high pressure ZnO ceramics exhibited CP with low relative density and dielectric loss was mainly due to the enhanced MaxwellWagner poly-dispersive relaxation due to the highly porous ceramics [2]. On contrary, quite low room temperature dielectric permittivity (∼ 40 − 100, measured at f = 1 kHz) has been reported on rare earth doped ZnO ceramic materials [3, 4, 5] and Al-doped ZnO nanostructured powder [6] as well. In addition room temperature εr0 values are about ~103 (measured at f = 1 kHz) for dense Co2+ doped ZnO ceramics sintered by pressure-less solid state reaction method [7]. Despite of the wide discrepancy on published CP data in pure and/or co-doped ZnO ceramics, in overall, ones can state that the microstructure (for example porosity level) can affect drastically the dielectric properties of ZnO ceramics [8]. The dependence of dielectric permittivity (ε 0 ) on porosity level has been extensively explored using a number of empirical approximations [9, 10, 11, 12, 13, 14, 15, 16, 17]. In general, these models consider that the dielectric material is a composite system type consisting of two phases (a matrix with several pores) with different dielectric permittivities. The usual approach is to consider the dielectric material consisting of parallel layers with different dielectric permittivity. Two possibilities arise when an ac electric field is applied: (i) the electric field is perpendicular and (ii) parallel to the 0 0 plane of dielectrics which are described by ε =[εm − P(εm − 1)] and ε =[εm /P(εm − 1) + 1], respectively, where εm is the dielectric permittivity of matrix and P is the porosity. The model proposed by Maxwell-Garnet for the dielectric permittivity of ceramic materials basically consisted of a matrix with spherical pores that is described as [12, 11, 13]   3P (εr,m − 1) 0 (1) εr,p = εr,m × 1 − 2εr,m + 1 − P + Pεr,m

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0 and ε 0 are the relative dielectric permittivity of porous ceramics and the solid matrix, respectively, and P is the where εr,p r,m porosity. Nevertheless this model fails to fit relative dielectric permittivity data for higher porosity values (P > 0.10)[14]. While Bano et. all proposed another model taking in account the pore shape as "    2/3 # 1 p p 0 × εr,p = εr,m × 1 + − (2) 2/3 1/3 k k s s P (εr,m − 1) ks + 1

where ks is a parameter related to pore shape, ks = 1 for spherical pores, and ks = 0.5 for oval pores [15, 16, 17]. However, if the relative permittivity of the solid matrix ceramic is much larger compared to the porous phase, the term 2/3 1/(P1/3 (εr,m − 1) ks + 1) in Eq. 2 tents to zero leading to "  #  p 2/3 0 εr,p = εr,m × 1 − (3) ks kG

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Experimental procedure Sample preparation

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where is grain size parameter kG was taken in account as well [17]. Nevertheless, these empirical models some times fail to fit experimental data in a broad range of frequency. Certainly, this may be due to the fact that it takes in account only structural parameters which are most the sample preparation dependent. Therefore, in this work we investigated deeply the effect of porosity level on the dielectric properties such as colossal permittivity and conductivity in a large frequency range (20 Hz - 2 MHz) of three sets of ZnO ceramic sample: i) low; ii) median, and iii) high porosity levels sintered by pressure-less solid-state reaction method.

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Characterization

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Thus three sets of ZnO ceramic samples were sintered according to the level of porosity, i.e., low; median, and high porosity. All samples were prepared by pressure-less solid state reaction method using commercial ZnO powder of analytical grade (manufactured by Aldrich, New Jersey, USA). The powder was homogenized with small amount of dispersant (oleic acid) and binder (PVA), pressed uniaxially in a stainless steel die 2.5 mm thickness and 9 mm diameter to form compact pellets-green body. For low porosity samples, the pellets were cold isostatically pressed (CIP) with 350 MPa for 5 minutes then placed inside of a muffle furnace slowly heated (2 °C/min) up to 500 ºC with a dwelling of 30 min and (3 °C/min) up to 1000 ºC, 1150 °C and 1250 °C with a dwelling of 4 h and 10 h for each temperature. While for high porosity samples the pellets were not cold isostatically pressed following the same sinteting program. For further details please see suplementary flowchart, Fig. S1.

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The Archimedes’ principle was used to determine the relative density of all sintered ZnO ceramic samples. The structural parameters of ZnO ceramics were determined by a Shimadzu X-ray diffraction (XRD) (model 6000) with a scanning rate of 2º/min at time gap of 2s with CuKα (λ = 1.5418 Å) radiation for 2θ angles (20o ≤ 2θ ≤ 80o ) at room temperature (RT). The lattice parameters for ZnO samples were analyzed using the Rietveld refinement method [18] and crystalline phases were determined using GSAS-II software package [19]. The microstructure was analyzed by a JEOL Scanning Electron Microscope, model JSM 6610. The dielectric measurements were carried out using a computer controlled Agilent LCR meter (model EA 4890-A) operating in a broad frequency range, 20 Hz–2 MHz under 1.0 Vac signal at room temperature. A priori of each measurement, both surfaces of each pellet were polished down to 3 µm diamond then coated with silver paste. In order to obtain a better electrical contact all coated samples were placed inside of a muffle furnace and slowly heated at 350 °C for 30 minutes.

Result and discussions Structural properties

The relative density (or fractional closed porosity) of each sample determined by means of Archimedes’ principles were 98% (0.02 fractional porosity), 97% (0.03 fractional porosity) and 96% (0.04 fractional porosity) of bulk ZnO density. Hereon these samples with low porosity level are labeled as Z1, Z2, Z3 respectively. Samples with medium porosity level, 95% (0.05 fractional porosity) and samples with high porosity level, 89% (0.19 fractional porosity), 71% ( 0.29 fractional porosity) and 69% (0.31 fractional porosity) are labeled as Z5, Z6, and Z7, respectively. The sintering conditions and fractional porosity are displayed in Table 1. The laws for mass diffusion in the sintering process were related to compaction form, in which empty spaces with smaller dimensions favor grains growth. Fig. 1a exhibits the XRD patterns of the representative ZnO samples (high , medium and low porosity level, Z1, Z4 and Z7, respectively) obtained at room temperature. Even though the difference of porosity level the diffraction peaks 2

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Figure 1 (Color online) a) X-ray diffraction pattern and b) Rietveld refinement for representative ZnO ceramics. Sample Z1 (0.02 fractional porosity), sample Z4 (0.05 fractional porosity) and sample Z7 (0.31 fractional porosity).

g/cm3

CIP* No Yes Yes Yes Yes Yes Yes

3.860 4.840 4.990 5.330 5.380 5.430 5.510

Density (%) Fractional porosity 69 0.31 71 0.29 89 0.11 95 0.05 96 0.04 97 0.03 98 0.02

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Sintering conditions Temperature (ºC) Dwelling time (h) Z7 1000 4 Z6 1000 4 Z5 1000 10 Z4 1150 4 Z3 1150 10 Z2 1250 4 Z1 1250 10 *CIP - Cold Isostatic Pressing Sample

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Table 1 Some structural parameters of the ZnO ceramic obtained by Rietveld refinement and apparent density.

Structural parameters a (Å) c(Å) 3.2491(1) 5.2023(1) 3.2491(1) 5.2023(1) 3.2500(1) 5.2040(1) 3.2500(1) 5.2020(1) 3.2482(2) 5.2035(2) 3.2467(2) 5.2014(2) 3.2489(2) 5.2052(2)

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correspond to those typically found in hexagonal wurtzite structure (JCPDS PDF no. 01.075-0576 diffraction pattern card) of zinc oxide compounds. Reitveld refinements, Fig. 1b were employed to analyze the crystal structure of all samples and reaffirms that the sintering conditions did not alter the hexagonal wurtzite crystal structure of ZnO ceramics such as lattice parameters a ≈ 3.250A˚ and c ≈ 5.202Å ( ac = 1.6) shown in Table 1. However the color of sintered samples change according the porosity level as shown in Sumplemetary S2. Fig. 2 exhibits the SEM images of polished surface of representative samples Z5, Z4 and Z2. It is quite clear that the sintering conditions affects the porosity level and the grain morphology as well. The grain size significantly increases with increasing sintering temperature from ∼ 1.5 µm to ∼ 6 µm for 1000°C and 1250°C, respectively. For further details SEM images of fracture is shown in suplementary Fig. S3 Fig. ?? and a histograms of pores size distribution is shown in suplementary figure S4 Fig. ??) as well.

Dielectric properties

Fig. 3 shows the frequency dependence of real relative permittivity (εr0 ), imaginary relative permittivity (εr00 ) and dielectric loss (tanδ ) for ZnO samples at room temperature in log-log scale. It is clear that the dielectric properties of these samples are strongly influenced by the sample porosity level which is in accordance to previous studies[8, 20, 7],. For an specific frequency high porosity level materials exhibited lower εr0 values (εr0 ≈ 103 ) while lower porosity level materials the εr0 values was about two order of magnitude higher (εr0 ≈ 105 ) as shown in Fig. 3a. If some one consider that the ZnO ceramics is a dense matrix with random closed pores (filled with air) distributed inside the material, the relative permittivity values will decrease with the increase of porosity level since the relative permittivity of air is much lower than the ZnO dense ceramic. In fact the εr 0 values vary from 35.6 × 103 to 1.9 × 105 , for Z7 and Z1 samples at 103 Hz respectively (inset in Fig. 3a). Furthermore the dielectric loss also depends on the sample porosity levels and frequency as well, Fig. 3c. It decreases with porosity level being quite high (~102 ) at low frequencies and, low (~10−1 ) at high frequencies. 3

Figure 2 (Color online) SEM images of surface of ZnO ceramics sintered at different conditions. Fig. a) Sample Z5, Fig. b) sample Z4 and Fig. c) sample Z2 with magnification x800.

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Fig. 4a,b shows the dependence of εr0 on porosity at the frequency range 103 and 106 Hz respectively. Models described by Eq. 1, 2 and 3 were used to explain a behavior trend in ZnO ceramics. The plausible fittings were just with Eq. 2 and 3. The high porosity and irregular shape of the pores in Z6 and Z7 samples made the model of Eq. 1 not be satisfactory. However, at 103 Hz, ks values are 0.38 and 0.31 obtained by Eq. 2 and Eq. 3 respectively, indicating that pores shape is close to an elliptical shape. The approximate form of logarithmic decline and ks values indicates a uniform distribution in porous shape that is reinforced by SEM micrographics. Fig. 4b shown that at higher frequencies the pores and the dense matrix begin to behave in a similar way with low εr 0 values resulting in an approximation of the fittings of Eq. 2 and 3. In addition, εr 0 values for all samples sharply decrease with the increase of frequency. This may be due to the polarization as the reversals cannot keep up with the applied high-frequency ac electric field[21]. Maxwell-Wagner (MW) model describe this poly-dispersive relaxation and, on the basis of this the imaginary part of the permittivity can be written with the following expression [22], 1 (εs − ε∞ )ωτ + ωC0 (R1 + R2 ) 1 + ω 2τ 2

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ε” (ω) =

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where C (R 1+R ) is known as Ohmic conductivity (σdc ), ω is the angular frequency, τ is the relaxation time, εs and ε∞ are 0 1 2 the permittivity values in f = 0 Hz and f = ∞ Hz respectively. Fig. 5 exhibits the frequency dependence of ac conductivity (σac ) calculated from dielectric data using the following equation σac = εo ε 0 ω tan δ

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where εo is the dielectric permittivity in vacuum, is the relative dielectric permittivity of the material, ω angular frequency and tan δ dielectric loss. It is noticeable in Fig. 5 the frequency dependence of ac conductivity for all ZnO samples and the dispersion through the broad frequency range. High porosity level samples presented smaller regions of conductivity independent of the field frequency (≈ 104 Hz) after an abrupt increase in conductivity at higher frequencies, showing a high conductivity dependent on the field σac . Whereas dense samples presented larger regions of conductivity independent (σdc ) of the frequency and a moderate increase in the σac part above 105 Hz. This material can be fitted quite well with the Jonscher [21] power law written in terms of independent frequency, dc conductivity (σdc ), term as σac = σdc + Aω n

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where n is the frequency exponent which varies from 0 to 1 and A is the temperature dependent pre-exponential. The region corresponding to lower frequencies can be associated to the long-term translational hoping conduction responsible for dc conductivity. While for frequencies higher, ac conductivity is associated to the short-range translational and localized hoping conducting, Aω n term. The critical frequency, ωc , the frequency that links the frequency independent region to the frequency dependent region is the onset of the conductivity relaxation. In fact, this frequency can be assigned to the transition from long-range hopping to the short-range ionic motion occurs. The electric conductivity parameters and, relaxation time obtained by MW fitting are displayed in Table 2. It is clear that the dc conductivity term decreases with increasing porosity level. The relaxation time increases gradually with the porosity level. This is attributed to the presence of defects in ZnO ceramics such as Zn interstitial and oxygen vacancies segregated in grain boundary during the solid-state sintering process [20, 23].

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Figure 3 (Color online) (a) Real part of relative permittivity, (b) imaginary part of relative permittivity, and (c) dielectric loss versus frequency at room temperature.

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Fitting Eq. (1) Fitting Eq. (2) Fitting Eq. (3)

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Figure 4 (Color online) The dependence of dielectric permittivity on porosity.

Table 2 Some physical parameters of ac conductivity and relaxation time of ZnO ceramic samples with different porosity level.

Samples Z1 Z2 Z3 Z4 Z5 Z6 Z7

σdc (x10−3 Ωm)−1 298.83 151.47 130.36 90.1 19.54 15.77 95.61

Parameters A 1.23 × 10−4 6.76 × 10−5 1.16 × 10−4 3.83 × 10−9 9.35 × 10−9 3.43 × 10−6 1.24 × 10−5

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n 0.4 0.5 0.4 1.0 1.0 0.5 0.5

τ × (10−2 ) 1.892 1.800 1.862 2.082 2.356 2.156 2.014

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Figure 5 (Color online) Frequency dependence of ac conductivity on porosity.

Conclusions

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In this study the porosity level in ZnO ceramics was systematically controlled by the pressure-less solid-state reaction method. The relative permittivity (εr0 ) and, tangent loss value decreased gradually with increasing porosity, being 1.9 × 105 and 35.6×103 for sample with low porosity and high porosity level, respectively at room temperature. Also the tangent loss decreases with increasing porosity level being quite high (∼ 102 ) at low frequencies and, low (∼ 10−1 ) at high frequencies. The complex part of the relative permittivity results could be fitted to the Maxwell-Wagner (MW) model suggesting a poly-dispersive relaxation time. The frequency dependence-ac conductivity determined by means of dielectric data was strongly dependent of the porosity level. It decreases sharply with increasing porosity level is frequency independent- up to ∼ 104 − 105 Hz followed by an abrupt increase at higher frequencies. These data were discussed in terms ZnO defects such as Zn interstitial and oxygen vacancies present in the grain boundaries.

Acknowledgments

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We acknowledges the support provided by Conselho Nacional de Desenvolvimento Cientifico e Tecnológico (CNPq), Brazil with grant No. 435229/2018-4. One of us (A.F.Jr) is CNPq fellow under Grant No. 310440/2018-1. Also we thank to the FAPEG/CNPq with grant No. 201710267000535.

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