Sajal Chandra Mazumdar¹, Sanjib Datta¹, Farhad Alam^2
1Department of Physics, Comilla University, Cumilla, Bangladesh.
²Department of Physical Sciences, Independent University, Bangladesh, Dhaka-1229, Bangladesh.
DOI: 10.4236/jamp.2022.106138   PDF    HTML   XML   172 Downloads   830 Views   Citations

Abstract

The novel polycrystalline Bi_0.85Gd_0.15Cu_xFe_1-xO₃ (x = 0, 0.025, 0.05, 0.075, 0.10) multiferroics are synthesized by the usual solid-state reaction route. The synthesis of the desired phase has been verified by the X-ray Diffraction (XRD) patterns. With major structural phases, few traces of secondary phases of Bi₂Fe₄O₉ and Bi₂₅FeO₄₀ appear for all the compositions. A discontinuous series of structural changes with varying compositions are observed for the doped samples. The bulk density (ρ_B) increases with Cu content reaches the highest at x = 0.05 and then declines. The complex initial permeability and dielectric characterizations are performed by Wayne Kerr Impedance Analyzer. The x = 0.05 samples having maximum density exhibit the highest permeability (μ_i’) implying a close relation between μ_i’ and the density. The reduction of μ_i’ at higher Cu concentration is due to the low density of the samples associated with the increased intragranular pores. The dielectric constant (ε’) is measured against frequency in the range 1 kHz - 10 MHz. It is perceived that ε’ falls with the rise in frequency up to 100 kHz. This dielectric dispersion is observed at a lower frequency as a result of interfacial polarization outlined by Maxwell-Wagner. The maximum ε’ is obtained for x = 0.025 composition. In the low-frequency range, the AC conductivity σ_AC is practically independent of frequency and resembles the DC conductivity (σ_DC). In the vicinity of high frequency recognized as the hopping region, σ_AC rises since the conductive grains are more active at high frequencies. The co-doping with Gd and Cu in BiFeO₃ ceramics enhances the magnetic and dielectric properties of the ceramics and hence can be utilized for fabricating multifunctional devices.

Keywords

X-Ray Diffraction, Permeability, Dielectric Constant, Conductivity

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1. Introduction

Multiferroic materials have lately achieved great attraction because of their versatile device applications and triggering new physics. Multiferroics combine various primary ferroic orders in a single phase [1]. Conventionally, multiferroics unite ferroelectricity and ferromagnetism or, more liberally, with every kind of magnetism [2]. The major attractive feature of multiferroic ceramic is their reputed magnetoelectric (ME) coupling, while a ferroic property is by and large improved by means of the conjugate field (magnetic fields alter magnetization, electric fields alter polarization, and likewise). A magnetic field can adjust the electric polarization and an electric field can adjust the magnetization in a multiferroic [2].

In the recent past, the utilization of ferroelectric materials to transfer light into mechanical, electrical, or chemical energy has enticed vast attention for understanding the mechanisms in addition to applications in photovoltaic, photocatalytic, and photo-transducer devices [3] - [9]. The huge prospects for applications emanated from their distinctive ferroelectric properties and the spontaneous electric polarization owing to the disruption of powerful inversion symmetry [10]. Ferroelectrics can furthermore serve as novel candidates for photocatalysis with comparable advantages and mechanisms. Several researchers have established that ferroelectric resources can perform improved photocatalysis than their counterparts. Among all the multiferroics, BiFeO₃ (BFO) is an extensively studied material owing to its ferroelectric and magnetic transition temperature well above room temperature (RT) [11] [12]. In the last few years, a huge struggle has been put to gain both durable ferroelectric (FE) and ferromagnetic (FM) polarizations. The stereo-chemically active 6s² lone pair of Bi³⁺ is accountable for the ferroelectric process in BFO while the remnant moment from the canted Fe³⁺ spins’ structure is accountable for the weak ferromagnetic property of BFO [13]. The interaction between fields of magnetic and electric occurs as a result of lattice distortion of BFO on the application of an electric or a magnetic field [14]. This puts forward novel paths to the recommendation and appliance of information storage, spintronics, sensors, etc. The foremost troubles of BFO and additional resources of this family are their huge leakage current density originating from charge defects, non-stoichiometry and impurity phases in BFO which creates it complicated to achieve a well-saturated ferroelectric hysteresis loop and small dielectric loss and hence obstructs its sensible applications [15] [16] [17]. In order to enhance the electrical properties of BFO, a number of research teams have tried to substitute with trivalent rare-earth ions such as La³⁺, Er³⁺, Dy³⁺, Sm³⁺ and Tb³⁺ at the Bi site of BFO [13] [18] [19]. The substitution has emanated in the decrease of the leakage current as well as upgrading of ferroelectric properties of BFO reasonably. In addition, a few results confirmed that better ferroelectric parameters were strongly interconnected to the structural change resulting from rare earth doping [20] [21] [22]. Doping at Bi³⁺ site with rare earth and alkaline earth metal elements and doping at Fe³⁺ site with transition metal elements have been lately studied [23] [24] [25] [26] [27] and improved multiferroic properties have been reported. Li et al. studied the effect of La and Mn co-doping in BFO on structural and multiferroic properties of BFO [24]. The saturation magnetization and saturation polarization were found to be improved due to the co-doping. The effect of Nd and Mn co-doping on electrical and magnetic properties of BFO was investigated by Hu et al. [27]. The enhanced ferromagnetic property was attained owing to the structural transition from orthorhombic to tetragonal. The doping reduced the leakage current significantly and hence improved the ferroelectric property. In the present research, we would like to investigate the response of Gd³⁺ and Cu²⁺ doping at Bi and Fe site of BFO respectively to the structural and multiferroic properties of BFO.

2. Experimental

2.1. Sample Preparation

The multiferroic Bi_0.85Gd_0.15Cu_xFe_1−xO₃ (BGCFO) ceramics have been synthesized using conventional ceramic method. The various steps of the sample preparation method are shown in Figure 1. The high purity powers of Bi₂O₃ (99.9%), Gd₂O₃ (99.9%), CuO (99.9%) and Fe₂O₃ (99.9%) are utilized as basic material for producing BGCFO ceramics. At first, the required stoichiometric constituents are weighted and the weighted powders are blended thoroughly by grinding. Grinding is performed to decrease the particle size to the micro level to facilitate the solid-state reaction to occur by atomic diffusion. In this case, mortar and pestle are utilized for grinding. Samples have been grinded for 6 hours. In hand milling process, particle size is decreased due to the friction of the powder with the pestle. Finer particles can lessen the sintering temperature and time remarkably. The grinded powders are fired at 750˚C for 4 hours. For a better degree of uniformity, the fired powders were grinded again for 2 hours. Before making disk and toroid shaped samples 1 - 2 drops (depending on the amount of sample) of polyvinyl alcohol (PVA) are added as a binder. The disk and toroid shaped

samples are made using a uniaxial hydraulic press with a pressure of 10 kN and 15 kN, respectively. These disk and toroid shaped samples are sintered at 825˚C for 4 hours with a heating rate of 10˚C per minute.

2.2. Characterization

X-ray diffraction is a non-catastrophic technique for detection and quantitative determination of different structural phases of any material. To investigate crystalline phases of the samples PHILIPS PW 3040 X’pert PRO X-ray diffractometer has been used. The samples are exposed to CuK_α radiation of wavelength, λ = 1.54178 Å with a primary beam of 40 kV and 30 mA with 0.02˚ sampling pitch and 1.0 second data collection step.

A 2θ scan is taken from 20˚ to 70˚ to obtain probable elementary peaks and Ni filter is applied to diminish CuK_α radiation.

The X-ray density ${\rho }_x$ is measured applying the following expression:

${\rho }_x=\frac{nM}{N_{A}V}\text{g}/{\text{cm}}^{\text{3}}$ (1)

where, n is the number of atoms per unit cell, N_A is Avogadro’s number (6.02 ´ 10²³ mol⁻¹), M is the molecular weight, V is volume of the unit cell. The porosity is calculated from the equation

$P\left(\%\right)=\frac{{\rho }_x-{\rho }_B}{{\rho }_x}\times 100\%$ (2)

where, ${\rho }_B$ is the bulk density which is measured by the formula:

${\rho }_B=\frac{m}{\pi r^{2}t}$ (3)

where m is the mass, r is the radius and t is the thickness of the pellet or ring [28].

Frequency dependent dielectric and magnetic characterization was performed at room temperature (RT) using WAYNE KERR Impedance Analyzer (Model No. 6500B). The real and imaginary part of complex initial permeability are calculated using the formulae:

${{\mu }^{\prime }}_i=L_S/L_0$ (4)

${{\mu }^{\prime }}_i={{\mu }^{″}}_i\tan \delta$ (5)

where L_S and L₀ are the self-inductances of the sample with and without the core L₀ is derived from the formula:

$L_0=\frac{{\mu }_0{N}^{2}S}{\pi \bar{d}}$ (6)

Here N is the number of turns of the coil (N = 5), S is the cross-sectional area and $\bar{d}=\left(d_1+d_2\right)/2$ is the average diameter, where d₁ and d₂ are the inner and outer diameter of the toroidal shaped sample, respectively [29]. With a Vibrating Sample Magnetometer (VSM) the magnetic characterization of BBFSO is made at a maximum applied field of ±1 T at RT. The pellets are painted for dielectric measurements with conducting silver paste on both sides to confirm good electrical connection. The dielectric constant, ${\epsilon }^{\prime }$, is computed using the relation:

${\epsilon }^{\prime }=\frac{Ct}{{\epsilon }_{0}A}$ (7)

where C, A and ɛ₀ are the capacitance of the pellet, the cross-sectional area of the electrode and the permittivity of free space, respectively.

The ac conductivity of the samples is estimated with the formula:

${\sigma }_{ac}=\omega {\epsilon }_0{\epsilon }^{\prime }\tan \delta$ (8)

where $\omega$ is the angular frequency and $\tan \delta$ is the dielectric loss. Real part ( $M^{\prime }$ ) of dielectric modulus are computed applying the formulae:

$M^{\prime }=\frac{{\epsilon }^{\prime }}{{{\epsilon }^{\prime }}^2+{{\epsilon }^{″}}^2}$ (9)

3. Results and Discussion

3.1. Structural Characterization, Density and Porosity

The XRD patterns of BGCFO ceramics are illustrated in Figure 2(a). The peaks in the XRD patterns have been pointed out with their equivalent miller indices. The XRD patterns verified the synthesis of desired ceramics with few trace of impurity phases of Bi₂Fe₄O₉ and Bi₂₅FeO₄₀ [30] appeared for all the compositions. The undoped sample exhibits orthorhombic perovskite structure. A discontinuous series of structural changes with varying composition are observed for the doped samples as illustrated in Figure 2(b). The compositionx = 0.025 exhibits rhombohedral structure and the other doped samples exhibit orthorhombic structure. The inconsistence structural change is due to the inhomogeneous diffusion of Cu in the lattice.

Figure 3 indicates the change of ${\rho }_x$, ${\rho }_B$ and P as a function of composition sintered at 825˚C. The ${\rho }_x$ is maximum for x = 0.025 which may be due to the structural transition. The ${\rho }_B$ increases with Cu content reaches the highest at x = 0.05 and then reduces. The increase in ${\rho }_B$ with Cu content is because of the fact that Cu stimulates grain development [31]. The decrease in ${\rho }_B$ at higher

Cu content may be due to the expanded intragranular porosity resulting from higher rate of grain growth. Porosity degrades the material quality and high value of porosity is undesirable. The lowest P is obtained for x = 0.05 composition.

3.2. Complex Initial Permeability

Permeability is one of the leading factors used in assessing magnetic materials. Figure 4 indicates the change of ${{\mu }^{\prime }}_i$ with frequency of BGCFO as a function of composition. The ${{\mu }^{\prime }}_i$ persists quite steady over the whole frequency range for all the compositions. This is owing to the fact that their cut-off frequency falls outside the investigated frequency scale. The cut-off frequency is the frequency at which ${{\mu }^{\prime }}_i$ gains 71% of its starting value. The above findings concurs well with the Globus model [32], which correlates the resonance frequency with permeability as given by ${\left({\mu }_i-1\right)}^{1/2}{f}_r=\text{constant}$. Conforming to this relationship, the higher the value of ${\mu }_i$, the lower the value of $f_r$ and vice-versa. The ${{\mu }^{\prime }}_i$ goes up with Cu content up to x = 0.5 and then falls with additional rise in Cu content in the composition. The samples having maximum density show the highest ${{\mu }^{\prime }}_i$ indicating a close relation between ${{\mu }^{\prime }}_i$ and the density. The reduction of ${{\mu }^{\prime }}_i$ at higher Cu concentration is because of the low density and defect of the samples resulting from the increased intragranular porosity.

Figure 5 indicates the change of $\tan {\delta }_M$ with frequency of BGCFO in the frequency range 100 kHz - 120 MHz. It is noticed from the figure that lowest $\tan {\delta }_M$ is obtained at higher frequency for all the compositions. The alteration of RQF in terms of frequency is revealed in Figure 6. For applied implementation the RQF is frequently taken as a measure of performance. It is detected that RQF rises with the frequency and tends to show a peak at high frequency. The highest RQF is attained for the sample with x = 0.05 for which the highest density is obtained.

3.3. Dielectric Property

Figure 7 illustrates the alteration of ${\epsilon }^{\prime }$ with frequency of BGCFO in the

frequency range 1 kHz - 10 MHz. It is perceived that ${\epsilon }^{\prime }$ goes down with rising frequency up to 100 kHz. This dielectric dispersion at low-frequency is due to Maxwell-Wagner [33] [34] type interfacial polarization in agreement with Koop’s phenomenological theory [35]. The interfacial polarization develops because of the heterogeneities of the sample following from porosity, interfacial defects and grain structure. These heterogeneities are produced in the sample during high temperature calcination and firing procedure. At higher frequencies, the ${\epsilon }^{\prime }$ persists approximately frequency independent owing to the incapability of electric dipoles to go along the rapid change of the alternating applied electric field [36]. These frequency independent values are known as the static dielectric constant. The alteration of ${\epsilon }^{\prime }$ with composition at 1 kHz frequency is indicated in Figure 8. The ${\epsilon }^{\prime }$ first goes up with Cu content and then goes down. The maximum ${\epsilon }^{\prime }$ is obtained for x = 0.025 composition. Figure 9 demonstrates the change of $\tan {\delta }_E$ with frequency. The $\tan {\delta }_E$ is often ascribed to ion relocation, ion oscillation and distortion and electric polarization. Ion relocation is predominantly significant and strongly influenced by temperature and frequency. The losses owing to ion relocation rise at low-frequency and the temperature rises. The samples show low loss at high frequency because of the less mobility of charge carriers and might be useful for microwave applications.

3.4. Complex Impedance Spectra Analysis

Figure 10 indicates the change of $M^{\prime }$ with frequency of the samples. The value of $M^{\prime }$ is low in the lower frequency part disclosing the relief of polaron hopping and minor function of electrode effect [37] [38]. The value of $M^{\prime }$ rises with frequency for all the samples and shows a sharp rise at high frequency. This is because of the incapability of several dipoles to follow up the rapid varying electric field at high frequency.

3.5. AC Conductivity

The ${\sigma }_{AC}$ is an essential factor for interpretation the conduction process in different materials. Figure 11 demonstrates the change of ${\sigma }_{AC}$ with frequency at RT in the frequency range 1 kHz - 1 MHz. In lower part of the frequency, the conductivity is nearly frequency independent which resembles DC conductivity ( ${\sigma }_{DC}$ ). The reason is that the resistive grain borders are more active at lower frequencies in agreement with the Maxwell–Wagner double layer model for dielectrics. However, in the higher frequency side (above 10 kHz) known as the hopping region, ${\sigma }_{AC}$ rises [39] because at higher frequencies the conductive grains become more active thereby increasing hopping of charge carriers [40] and obeys the following Joncher’s law: ${\sigma }_{AC}\left(\omega \right)={\sigma }_0+A{\omega }^s$, where ${\sigma }_{AC}\left(\omega \right)$ is the total electrical conductivity, ${\sigma }_0$ is the frequency-independent dc conductivity, A is a temperature-dependent pre exponential factor known as the Universal Dynamic Response (UDR) [41] and s is the power law exponent which usually varies between 0 and 1 depending on the temperature. Alteration of $\log {\sigma }_{AC}$ in terms of $\log \omega$ is depicted in Figure 12. The $\log {\sigma }_{AC}$ rises almost linearly with $\log \omega$ for all the samples. The conduction mechanism in the low-frequency dispersive region mostly depends on the long-range hopping associated with grain boundaries [42] and that in the high frequency dispersive region is because of the restricted or reorientational short-range hopping inside the grain [42] [43].

4. Conclusion

The multiferroic BGCFO ceramics are synthesized by a cost-effective solid-state reaction technique. The XRD patterns verify the synthesis of the desired structural phase with few traces of impurity phases of Bi₂Fe₄O₉ and Bi₂₅FeO₄₀. The composition x = 0.025 exhibits rhombohedral structure and the other doped samples exhibit orthorhombic structure. The ${\rho }_x$ is maximum for x = 0.025, which may be due to the structural transition. The ${\rho }_B$ increases with Cu content reaches a maximum at x = 0.05 and then decreases. The ${{\mu }^{\prime }}_i$ rises with Cu content up to x = 0.5 and then falls with an additional rise in Cu content in the composition. The samples having maximum ${\rho }_B$ exhibit the highest ${{\mu }^{\prime }}_i$ and RQF implying a direct relation of ${{\mu }^{\prime }}_i$ and RQF with ${\rho }_B$. The dispersive character of ${\epsilon }^{\prime }$ at lower frequencies is due to Maxwell-Wagner type interfacial polarization. At higher frequencies, the ${\epsilon }^{\prime }$ persists nearly constant with frequency owing to the incapability of electric dipoles to follow up the rapid variation of the applied alternating electric field. The maximum ${\epsilon }^{\prime }$ is obtained for x = 0.025 composition. The samples exhibit low loss at high frequency on account of the low mobility of charge carriers and can be used for microwave applications. In the low-frequency region, ${\sigma }_{AC}$ remains almost constant but in the high frequency hopping region, ${\sigma }_{AC}$ increases as the conductive grains are more active at high frequencies.

Acknowledgements

The authors greatly acknowledge Comilla University, Cumilla and University Grant Commission of Bangladesh for providing research grants for this work.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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