Novel CuFeS₂ pellet behaves like a portable signal transporting network: studies of immittance

Abstract

A novel synthesis of CuFeS₂ nanoparticles has been demonstrated here. This is the first time we have thoroughly investigated the frequency dependent dielectric behavior of iron-chalcopyrite (CuFeS₂) pellets (with σ_d.c. = 47.27 × 10⁻⁹ S cm⁻¹). The room temperature a.c. conductivity of the material has also been investigated in the frequency range 200 Hz–2 MHz. Frequency dependent impedance analysis of the material indicates the charging and discharging behavior of the capacitor. Throughout this report we have analyzed the frequency dependent complex impedance, electric modulus and the loss tangent of the CuFeS₂ pallet as series and parallel combinations of capacitors and resistors.

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1. Introduction

Chalcopyrite compounds such as CuAlS₂, CuInS₂, and CuFeS₂ are typical representatives of the ternary chalcogenide compounds. Nanocrystals of chalcopyrite have recently attracted great attention due to their important physical and chemical properties and promising potential applications in microelectronic devices.^1–6 Nanowires,⁷ nanorods, spherical particles⁸ and nano crystals⁹ have been synthesized to investigate the various properties of this compound for possible applications in photovoltaics,⁵ thermoelectric devices, and spintronic devices.⁶ The morphology dependent optical properties had been investigated for CuFeS₂.⁹ It was found that the optical band gap of the nanostructured material is comparably higher than the bulk materials. The investigation on size dependent thermal conductivity of the material revealed that the power factor and thermal conductivity have been greatly improved by decreasing the particle size.⁹

Tremendous efforts have been given on the development of new and easiest methods for synthesis of nanocrystalline composites which are expected to have important properties as building blocks for many novel functional chalcogenides.¹⁰ Different approaches have been reported on synthesis of CuFeS₂ nanomaterials – many of them are based on solvothermal reactions leading to the formation of powders.^11–14 Depending upon the choice of precursor and synthesis conditions, the nanocrystal exhibits either spherical or pyramidal morphology.

Though a lot of work has been done on CuFeS₂ composite, not much work on dielectric and impedance analysis of this chalcogenide nanocomposite have been reported so far. In this study we have synthesized CuFeS₂ by incorporating surfactant in hydrothermal method and studied its electrical behavior in pellet form. The complex impedance, complex electrical modulus and the loss-tangent were analyzed at room temperature from the capacitance versus frequency curve of a CuFeS₂ pellet. The frequency dependent immittance was analyzed by considering a series and a parallel combination of a capacitor and a resistor. We have investigated the response of frequency on a.c. conductivity in the frequency regime 200 Hz–2 MHz.

2. Experimental section

2.1. Materials and synthesis

In typical synthesis of CuFeS₂ nanomaterial, a mixture of 10 ml of 0.1 M FeCl₃ and 10 ml of 0.1 M CuCl₂ was taken into a glass beaker. 100 ml of 0.1 N Na₂S solution was also pre-prepared. By continuous stirring technique Na₂S solution was added drop wise with the mixture till a dark brown precipitate (ppt) was obtained. Drop wise a few amount of PVP [poly(vinyl-pyrrolidone)] were added as surfactant with the above mixture and stirred for 4 hours during precipitation. All the chemical reactions were carried out in open atmosphere. After collecting the ppt, it was transferred to a Teflon lined autoclave and was heated through overnight at temperature 140 °C. The baked ppt was collected and washed with ethanol and distilled water repeatedly and sequentially by centrifuge technique. The powder form of the synthesized material was collected and used for characterization by heating at 100 °C inside a vacuum oven.

2.2. Physical measurements

The structural characterizations of the synthesized material have been performed by the X-ray Diffraction (XRD), Transmission Electron Microscopy (TEM) and Field Emission Scanning Electron Microscopy (FESEM) technique. The XRD spectrum of the powder sample was recorded by Bruker D8 powder X-ray Diffractometer. The elemental analysis was performed by a 2400 Series II CHNS elemental analyzer of Perkin-Elmer. To get insight of the morphology of the material, the transmission electron microscopy (TEM) image was recorded by JEOL make instrument. The surface morphology and the composition were illustrated by FESEM image, TEM image, TEM-EDX, SEAD pattern recorded by FEI make Inspect F-50 microscope and transmission electron microscope of JEOL make. The thermal stability of the sample was investigated with DTG-60 thermogravimetric and differential thermal analyzer of Shimadzu.

A pellet of the synthesized material was prepared using a pelletizer. Thickness of the pellet was measured as 1 mm. Two silver contacts were made at both sides of the pellet. The capacitance was recorded as a function of frequency over a wide range (200 Hz–2 MHz) by a computer controlled LCR meter (precision LCR meter Agilent E4980) at room temperature. An input a.c. signal of amplitude 1 volt was applied across the pellet.

3. Results and discussions

Fig. 1 represents the powder X-ray diffraction pattern of the synthesized material. The responsible Bragg's diffraction peaks approved CuFeS₂,¹⁵ supported by the JCPDS Card no: 37-0471. The value of d_hkl and the corresponding intensity for the responsible (hkl) plane of the sample was detected with the help of X-Powder software. The estimated d_hkl and corresponding intensity of recorded XRD pattern are enlisted in Table 1. As the measured values of d_hkl (i.e. d_obs.) are quite identical with the standard JCPDS (d_standard), the system of synthesized CuFeS₂ is a tetragonal body centered lattice. To check the occurrence of other probable secondary phases like FeS₂ and Cu₂S within the synthesized composite, the XRD spectra (obtained from JCPDS data file with card no: 71-2219 and 84-1770) of FeS₂ and Cu₂S were compared with the recorded XRD pattern of CuFeS₂ and presented in Fig. 1. This indicates that probably there is no such secondary phases within the synthesized CuFeS₂. But still there is a possibility of occurrence of the amorphous residual carbon in the synthesized CuFeS₂ by using PVP. Fig. 2(a)–(c) represent the TEM image, SAED pattern and TEM-EDX spectra of the synthesized material respectively. The elemental composition of the material as obtained from the TEM-EDX was furnished in Table 2. The occurrence of residual carbon was detected from this EDX spectrum which might occur due to the carbon coated grid. For better estimation of residual carbon (C) the CHNS elemental analysis of the sample was performed. The residual C was found as 0.05% from the CHN analysis, which is very minute in comparison with the bulk material. Moreover, the selected area electron diffraction (SAED) of the sample indicates the diffraction spot corresponding to (112), (220) and (312) planes match with the above XRD pattern.

Fig. 1 Powder XRD pattern of CuFeS₂ and XRD spectra of FeS₂ (using JCPDS: 71-2219) and Cu₂S (using JCPDS: 84-1770).

Table 1 Comparison of d_hkl and corresponding intensity

2θ (degree)	(hkl)	dstandard (Å)	dobs. (Å)	Iobs. (a.u.)	Istandard (%)	(Iobs./Imax) × 100%
29.4	(112)	3.0390	3.1186	2693 (Imax)	100	100
48.6	(220)	1.8700	1.9119	1802	16	66
57.8	(312)	1.5926	1.6228	425	12	16

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Fig. 2 (a) TEM image; (b) SAED pattern and (c) TEM-EDX spectra of CuFeS₂.

Table 2 Elemental composition obtained from TEM-EDX

Element	Weight%	Atomic%
C K	0.79	2.28
S K	15.07	37.26
Fe K	39.03	26.17
Cu K	45.11	34.29
Total	100.00	100.00

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From the XRD pattern the average particle size was estimated as 12 nm by Debye Scherrer's approximation. In this approach L = Kλ/B cos θ had been considered.⁵ The notations contain their unique identity. Fig. 3 represents the SEM image of the material which depict that the size of the particles are in nanoscale.

Fig. 3 SEM image of CuFeS₂.

Thermal property of CuFeS₂ was studied by TGA spectra. The sample was heated at the rate of 10 °C min⁻¹ in nitrogen atmosphere. The thermal stability of the material was investigated within the temperature range 30 °C and 700 °C (shown in Fig. 4). The TGA curve shows trivial weight loss between 30 °C and 200 °C, which indicates that the sample is stable up to 200 °C. Very recently P. Kumar, et al. have synthesized Chalcopyrite CuFeS₂ which is stable up to 200 °C (ref. 16) and after that the sample started to decompose sharply. In our study, the sample was decomposed to 35% of its initial weight at temperature 700 °C.

Fig. 4 TGA curve.

Fig. 5 represents the capacitance versus frequency plot of the material in pellet form. It indicated that the capacitance initially falls sharply as the frequency increases and then saturates at some value as the frequency approaches 2 MHz. From this plot it is clear that the synthesized CuFeS₂ pellet, sandwiched between two conductive layers of silver behaves like a capacitor's dielectric medium consisting of dipoles. For a finite value of capacitive reactance the capacitance decreases towards saturation as the frequency increases for a certain applied field. Depending upon the occurrence of ionic dipoles and the compositional impurity (residual C) inside the synthesized sample, the system produces effective impedance into the device. Fig. 6 represents the exponential variation of impedance against frequency. The high capacitance and high impedance at lower frequencies may be attributed by the significant polarization of charge carriers. The dipoles cannot orient themselves at higher frequencies and hence the capacitance as well as impedance decreases. The ratio of low frequency to high frequency capacitance obtained from the curve is found to be close to 2 : 1 whereas the ratio of low frequency to high frequency impedance obtained from Fig. 6 is found to be 275 : 1. However, for Debye relaxation process the low frequency to the high frequency capacitance ratio is expected typically to be 3 : 1 (ref. 17) while the observed ratio in our case is 2 : 1. This may happen due to the occurrence of residual C inside the sample.

Fig. 5 Frequency dependent capacitance plot.

Fig. 6 Frequency dependent impedance plot.

The dielectric permittivity of the medium was evaluated with the help of the equation:

where C is the capacitance, L is the length and A is the effective area of the pellet. Fig. 7 represents the variation of dielectric permittivity of the sample with frequency at room temperature. The dielectric permittivity shows a decreasing trend. The decrease is rapid at lower frequency and it is slower and stable at higher frequency. The decrease of dielectric permittivity with increasing frequency is a normal dielectric behavior which is also observed by other researchers for various composites.^18–20 A composite system is considered as heterogeneous material that can experience interfacial polarization as predicted by Wagner.²¹ He pointed out that, at low frequency region, the movement of charge carriers trapped at interfacial region is influenced by inhomogeneous dielectric structure. At high frequency, the dominant mechanism contributing to dielectric constant is the hopping mechanism in their respective interstice under the influence of alternating current. The frequency of hopping between ions could not follow the frequency of applied field and hence it lags behind, therefore the values of dielectric constant reduces at higher frequency.²² A low loss factor is desirable for a dielectric material so that the dissipated electric power to the insulator is minimized. This type of consideration is very important for high power circuits operating at high speed. Dissipation factor is a ratio of the energy-dissipated to the energy-stored in the dielectric material. The more energy that is dissipated into the material, the less is carried to the final destination. This dissipated energy typically turns into heat or is radiated as radio frequency (RF) wave into the air. The optimal goal is to pass 100% of the original signal through the interconnecting network without any absorption in the dielectric medium. A high loss material means a little or no signal is left at the end of the transmission path. In order to retain maximum signal power, a low loss material should be used. The defect, space charge formation and lattice distortion is believed to produce an absorption current resulting in a loss factor.²²

Fig. 7 Dielectric constant vs. frequency curve.

The variation of loss tangent (tan δ) of our material with frequency at room temperature is shown in Fig. 8. This curve indicates that tan δ decreases with the increase in frequency and attains a minimum value which is general feature of polar dielectric materials.²³ The decreasing trend of loss tangent may be explained as follows: when the frequency of applied a.c. field is much larger than the hopping frequency of electron, the electron do not have an opportunity to jump at all and the loss of energy is small. In general, the local displacements of electronic charge carriers (jumping electrons in case of ceramic substrate) cause the dielectric polarization in materials. Since the dielectric polarization is similar to the conduction dominated by hopping, the marked decrease in tan δ is due to the decreasing ability of the jumping electron (charge carrier) to follow the alternating frequency of a.c. electric field beyond certain critical frequency. Fig. 8 illustrates that the dielectric loss (a part of the energy of an electric field dissipated as heat) decreased rapidly in lower frequency and saturated at higher frequency regime. It may arise in this manner depending upon two factors: the frequency dependent effective resistance of the material itself and the resistance of the electrodes (Ag). In lower frequency regime, the dielectric loss is maximum because the carrier transport through unpolarized material is controlled only by the applied field. Whereas in higher frequency regime the carrier transport phenomena through the pellet is governed by the field arisen due to the polarized dielectric medium under the applied field. These phenomena can be realized by impedance spectroscopy.

Fig. 8 Loss tangent vs. frequency curve.

The impedance spectroscopy technique is based on analyzing the a.c. response of a system to a sinusoidal perturbation, and subsequent calculation of impedance and related parameters as a function of frequency of the perturbation. Each parameter can be used to highlight a particular aspect of the materials. The electrical properties are often presented in terms of impedance (Z),^24–28 and electrical modulus (M).^29–32 The frequency dependence of dielectric properties of the materials is normally described in terms of complex impedance (Z), electric modulus (M) and dielectric loss tangent (tan δ) and is related to each other as:

Z = Z′ − jZ′′, M = M′ + jM′′

and

In this article we have analyzed the impedance spectroscopy of our sample by considering a series combination of resistor and capacitor. In this configuration the effective series impedance can be realized as

where,

The value of R is estimated as 4.56 × 10⁸ Ω from the saturation level of the |Z| vs. frequency (f) plot (Fig. 6). The value of Z′ remains constant with the increase in frequency whereas Z′′ decreases with the increase in frequency (Fig. 9). The impedance spectrum represents the Nyquist plot (Fig. 10). Fig. 11 represents the variation of loss tangent (as measured from the real and imaginary part of the complex impedance) with the change in frequency. The trend of gradually increasing loss tangent does not support the experimental curve (Fig. 8).

Fig. 9 Variation of Z′ and Z′′ for series CR circuit with respect to log ω.

Fig. 10 Nyquist plot for C–R series impedance.

Fig. 11 Z′/Z′′ vs. ω curve for CR series circuit.

Therefore we have analyzed the impedance spectroscopy of the sample by considering a parallel combination of resistor–capacitor. In this configuration the effective parallel impedance can be written as,

Fig. 12 represents the Z′ vs. ω curve. This curve exhibits that the value of Z′ decreases with increasing frequency and saturated at high frequency. This implies the possible release of space charge. This also indicates that there is every possibility of the existence of frequency relaxation process. The curve displays signal relaxation process, which implies the increase in a.c. conductivity with increasing frequency. The a.c. conductivity of the material is determined by the equation:

σ = 2πfεε₀ tan δ

Fig. 12 Z′ and Z′′ vs. ω plot for the CR parallel circuit.

Fig. 13 represents the a.c. conductivity against frequency curve, which supports the proclaimed interpretation by signal relaxation process. The conductivity pattern shows a frequency independent flat terrain in the low frequency region and exhibits dispersion at higher frequencies which occurred due to the polarization effect of the medium.³³ In lower frequency the drift of carriers is comparably low depending upon the effective resistance and the applied potential. Whereas in higher frequency regime the long range drift of the carriers is highly controlled by the polarized field of the sample and diffusion limited hopping. To some extent the anomalous variation of conductivity with frequency has been noticed. The variation of conductivity in those frequencies is attributed to the polarization effects at the electrode and electrolyte interface or it may arise due to the generation of heat in grain interior.^34,35

Fig. 13 Experimental and fitted curves of σ_a.c. vs. f.

Fig. 12 also shows the variation of imaginary part of impedance (Z′′) with frequency (ω) at room temperature. The Z′′ decreases with increase in frequency, which indicates the accumulation of space charge in the material. Fig. 14 illustrates the complex impedance spectrum (Nyquist plot) of the compound measured at 303 K over a wide range of frequency (200 Hz–2 MHz). The decrease in loss tangent (tan δ = Z′/Z′′) with increasing frequency (given in Fig. 15) approved the experimental curve (Fig. 11).

Fig. 14 Nyquist plot for C–R parallel impedance.

Fig. 15 Z′/Z′′ vs. ω curve for CR parallel circuit.

Fig. 14 indicates that the arc has a progressive tendency to become circular but at higher magnitude of impedance the Nyquist plot becomes straight line. This linearity may occur due to the thermal effect in grain interior. At this extent the complex impedance of the sample is considered as the parallel combination of resistor and capacitor.

The complex modulus formalism has been adopted to interpret the dynamical aspects of electrical transport phenomena. This technique also provides an insight into the electrical processes using the following relations of electrical modulus:

M = M′ + jM′′

The complex electric modulus is usually calculated from the impedance data using the following relations:

M′ = ωC₀Z′

and

M′′ = ωC₀Z′′

where C₀ = geometrical capacitance = ε₀A/L. The value of C₀ is measured as 0.125 pF.

Using the above modulus formalism the inhomogeneous nature of polycrystalline sample with bulk and grain boundary effects can easily be probed, which cannot be distinguished from complex impedance plots. The other major advantage of the electric modulus formalism is to suppress the effect of electrode. Fig. 16 shows the variation of M′ and M′′ as a function of frequency (ω) for the sample investigated at room temperature.

Fig. 16 M′ and M′′ vs. ω plot.

Fig. 16 exhibits that M′ approaches to zero in the low frequency region, and a continuous dispersion on increasing frequency, with a tendency to saturate at a maximum asymptotic value (i.e., M_∞) in the high frequency region. Such observation may possibly be related to a lack of restoring force governing the mobility of the charge carriers under the action of an induced electric field. This behavior supports the short range mobility of charge carriers.

Fig. 17 shows the complex modulus spectrum i.e., (M′′ vs. M′) of CuFeS₂ at temperature 303 K. The asymmetric semicircular arc observed earlier is now confirmed from this method. This may be due to the presence of electrical relaxation phenomena in the material. The curves don't form semicircles according to the prediction of ideal Debye model. Rather they possess the shape of deformed arcs with their centre positioned below the x-axis. This indicates the spread of relaxation with different mean time constants, and hence non-Debye type of relaxation in the material is confirmed. However the single semicircular arc confirms the formation of single-phase compound, which is also evident from XRD and SAED analysis. The modulus plane shows a progressive semicircle and its intercept on the real axis is the total capacitance contributed by the grain and grain boundaries. As the contribution of impurities inside the sample is beyond our task in this report, it is quite tough to evaluate exactly the total capacitance of the system. Nevertheless, it is confirmed from our M′′ vs. ω plot (Fig. 16) that the grain boundary effect is appreciably high.

Fig. 17 M′′ vs. M′ plot (Nyquist plot).

4. Conclusions

In present work, this is the first time we have synthesized CuFeS₂ nanoparticles and analyzed the a.c. response of a CuFeS₂ pallet and investigated the charge transport behavior by the analysis of complex impedance, electrical modulus and the loss tangent. We have studied the frequency dependant impedance of the pellet by considering a series and a parallel combination of a capacitor and a resistor. The analytical loss tangent vs. frequency curve has been supported by the experimental curve of loss tangent for the parallel combination of a resistor with a capacitor. Thus this pellet of CuFeS₂ can be applied as a prototype signal transporting network with ratio of capacitance at low frequency to high frequency as 2 : 1 and with the ratio of impedance at low frequency to high frequency as 275 : 1 in the frequency regime 200 Hz to 2 MHz.

Acknowledgements

The support of PURSE and FIST program of DST, Government of India is acknowledged.

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