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Evidence of large hopping polaron conduction process in strontium doped calcium copper titanate ceramics
Physica B: Condensed Matter 556 (2019) 36–41
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Physica B: Condensed Matter journal homepage: www.elsevier.com/locate/physb
Evidence of large hopping polaron conduction process in strontium doped calcium copper titanate ceramics
T
S. Amhila,∗, E. choukria, S. Ben Moumena, A. Bourialb, L. Essaleha a Laboratory of Condensed Matter and Nanostructures (LMCN), Cadi-Ayyad University, Faculty of Sciences and Technology, Departement of Applied Physics, Marrakech, Morocco b Laboratoire Procédés, Métrologie, Matériaux pour l'Energie et Environnement (LP2M2E), Cadi-Ayyad University, Faculty of Sciences and Technology, Departement of Applied Physics, Marrakech, Morocco
A R T I C LE I N FO
A B S T R A C T
Keywords: CCTO Semi wet route Electrical properties OLPT
Strontium (Sr) doped Calcium Copper Titanate Ca1−xSrxCu3Ti4O12 with two values x = 0 and x = 0.05 commonly known as CSCTO ceramics have been obtained by using the semi wet route synthesis method. Rietveld refinement shows that the powders crystallize in the cubic perovskite related structure with Im3 space group. Scanning Electron Micrograph (SEM) analysis shows that the average grain size of ceramics becomes larger when Sr doping is considered. Both DC and AC electrical conductivity are investigated throughly in the temperature and frequency ranges between [373–653 K] and [20 Hz–1MHz], respectively. The values of the average activation energies for CSCTO-0 (x = 0) and CSCTO-5 (x = 0.05) were found to be 612 meV and 576 meV, respectively. In Fact, Sr doping has an effect on the broadening of the impurity band that can lead to a dramatic decrease in the activation conduction energy of CSCTO ceramics. A systematic study of AC electrical conductivity reveals that the predominant conduction mechanism existing in these ceramics is generated by large polaron hopping process. This mechanism has also been identified by the modulus analysis and confirmed by comparing the hopping polaron size with the lattice parameter.
1. Introduction Nowadays, it is becoming generally recognized that the demand for better performance, high density energy storage and low cost of electronic devices need an interest miniaturization and densification of capacitors in electronic based equipment. In fact, this phenomenon needs some capacitors that present thermal and frequency stability and good dielectric properties. Generally, perovskite materials are well known for their ability to produce high dielectric constant which had led to many important industrial applications in microelectronics and memory devices [1–3]. Lead-free perovskites such as BaFe0.5Nb0.5O3 and CaCu3Ti4O12 often called CCTO are found to be the most interesting materials for these applications [4]. Therefore, CCTO has attracted a great deal of attention due to its good physical properties, its highest dielectric constant (order of 105) and its good thermal stability over a wide range of temperature (100–600 K) and frequency independent in the frequency range of (103–106Hz) [1–3,5]. However, the only disadvantage of this material is its higher dielectric loss, thus the capacitor cannot hold a stored charge for more than a few seconds which limits its usage in device applications. In fact, there are various ways to reduce
∗
dielectric loss for CCTO materials, the most interesting technique is by ion doping at A or/and B sites, several studies have been reported with a variety of possible substitutions [2,6–8]. Various works have been done suggesting the important effect of Sr2+ doping ions on Ca-site, resulting to the good dielectric properties such as increasing the dielectric constant and decreasing the dielectric losses [9–12]. It is noted that CSCTO ceramics are usually prepared by a conventional solid-state method which needs relatively long reaction time and high calcination and sintering temperatures [6,10,13], the sol-gel method was also widely reported regarding its excellent chemical stoichiometry, homogeneity, and lower crystallization temperature, but it has a high cost of precursors which allowed us to avoid this method [13,14]. However, few ones used the wet chemistry method also named citrate-nitrate gel chemical method which is a type of combustion synthesis technique [15,16]. In this paper, this last method has been used due to its considerable advantages including lower sintering temperature and shorter reaction time [18]. To the best of our knowledge, several investigations have been reported to study the dielectric properties of Sr doped CCTO ceramics [9,10,14,15], but a few works on electrical properties and conduction mechanisms are reported in the literature for only non
Corresponding author. E-mail addresses: [email protected], [email protected] (S. Amhil).
https://doi.org/10.1016/j.physb.2018.12.032 Received 8 November 2018; Received in revised form 6 December 2018; Accepted 19 December 2018 Available online 04 January 2019 0921-4526/ © 2018 Elsevier B.V. All rights reserved.
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doped CCTO ceramics [16,17]. However, electrical measurements are the most sensitive and useful tool for understanding the conduction process in materials. Thus, the aim of this paper is to determine the different conduction mechanisms existing in the Sr doped CCTO ceramics by analyzing the temperature and frequency dependent electrical conductivity of the material. The large polaron hopping mechanism is identified to be the predominant conduction process through the analysis of the temperature dependence of power-law exponent s(T). This is also confirmed by considering the modulus formalism. The coherence length of polaron and lattice parameter are compared by means of structural data.
2. Experimental details 2.1. Sample preparation Polycrystalline samples Ca1−xSrxCu3Ti4O12 with x = 0 and x = 0.05 were synthesized by the semi-wet route. In this method, high purity chemicals copper nitrate (Cu(NO3)2,3H2O), calcium nitrates (Ca (NO3) 2, 4H2O) strontium nitrates (Sr(NO3)2) and titanium oxide (TiO2) were weighed in stoichiometric molar ratios. Solutions of metal nitrates were prepared in a baker using demineralized water. After that, solid TiO2 and a calculated amount of citric acid (C6H8O7) were added to the solution. The mixture was then heated using a hot plate with a magnetic stirrer at around 80 °C. About 2 h later and by removing the solvent a homogenous blue gel was formed and a spontaneous spark propagates on the surface of the material giving rise to voluminous porous and floppy brown powder. The xerogel (as prepared) was heat-treated at 800 °C for 12 h in air. After grinding, the calcined powders were pressed into discs of about 13 mm in diameter and 1 mm in thickness by mean of a hydraulic press applying pressure of 4 tonnes and the sintering was done at 1000 °C for 12 h. For the electrical measurements, the pellets are covered on both sides with silver (Ag) electrodes. The flow chart of the semi-wet method is represented in Fig. 1.
Fig. 2. Rietveld refinement of X-ray Diffraction pattern of undoped and Sr doped CCTO ceramics sintered at 1000 °C for 12 h collected at room temperature.
2.2. Sample characterization The crystal structure of CSCTO ceramics was investigated using the X-ray diffraction technique (XRD, Rigaku, smart lab) with Cu-Kα radiations (λ = 0.154098 nm) in a 2θ range from 20° to 70°, and a scan rate of 5°/min. Morphology and microstructure were observed on the surfaces of the ceramics with the scanning electron microscopy (SEM) (Vega3 TESCAN). The electrical characterization was carried out by impedance spectroscopy (IS) using HP4284A spectrometer with an applied AC voltage of 250 mV over a frequency range 20 Hz–1 MHz and a temperature range [373–653 K]. 3. Results and discussion 3.1. Structural and microstructural characteristics X-ray diffraction patterns of Ca1−xSrxCu3Ti4O12 (x = 0 (CSCTO-0) and x = 0.05(CSCTO-5)) ceramics at room temperature are shown in Fig. 2. The data were refined by the Rietveld technique using the Full Prof program. It is clearly shown that both ceramics CSCTO-0 and CSCTO-5 are formed without any secondary phases and a pure phase has been detected. In addition, CSCTO ceramics could be indexed to a cubic perovskite structure with Im3 space group according to JCPDS75-2188 [23] and satisfying the minimum value of the fitting parameter (χ2) in the program. The CSCTO lattice parameter was determined as a = 7.393 Å, a = 7.395 Å for CSCTO-0 and CSCTO-5 ceramics respectively which are in accordance with the results reported in the literature [9,19]. Therefore, as adding concentration of Sr2+, the CSCTO peaks positions shift to the lower angles (see inset Fig. 2(b)), this shift indicates the enhancement of the lattice which may be is caused by the substitution of Ca2+ (r(Ca2+) = 1.34 Å) cations by the larger cations of Sr2+ (r(Sr2+) = 1.44 Å) [9,14]. The scanning electron microscopic images of CSCTO ceramics are shown in Fig. 3(a and b). From this figures, it can be clearly seen that the samples have well distributed grains and exhibit a dense structure. It is noted that the grain size increased with the increase of the strontium content. Otherwise, the average crystallite size, D, was calculated from XRD data based on Debye Sherrer's method (see section 2.4). The results reveal that the crystallites size decreases from 139.4 nm to 82.7 nm when doping with Sr, then the possibility of having more crystallites is large which allows the grain growth in the presence of Sr, so we can say that Sr promotes the grain size and reduce the porosity as already observed in some works [6,20]. The average grain size of the CSCTO ceramics was calculated using ImageJ software and was
Mixing of metal nitrate solutions + solid TiO2 in stoichiometric amounts
Addition of citric acid to the mixed nitrate solutions
Mixing and drying at 80°C by a magnetic stirrer
Calcination in alumina Crucibles at 800°C for 10h Grinding
Pelletisation (Pressing) Sintering at 1000°C for 12h in air
Dielectric Measurements Fig. 1. Flow chart of the semi-wet method of CSCTO ceramics. 37
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Fig. 3. SEM micrograph of the fractured surface of the sintered ceramics (a) CSCTO-0, (b) CSCTO-5. Insets represent the distribution of grain size.
estimated to be 3.16 μm, for pure CSCTO and it was increased to 4.13 μm for CSCTO-5. The distribution of this two ceramics are shown in the inset of Fig. 3(a and b)). 3.2. Electrical conductivity Total electrical conductivity is calculated from the imaginary part of the dielectric constant (ε′ ′) according to the relation σtot = ωε0 ε′ ′, where ω is the angular frequency, ε0 is the permittivity of free space and ε′ ′ is the imaginary part of the dielectric constant, ε′ ′ is obtained from the values of measured capacity (Cp) and the measured values of loss tangent (D = tg δ) using the following equation [21]:
ε″ =
Cp d ε0 A
D
(1)
where d and A are the thickness and area of the ceramic. The frequency and temperature dependence of the total electrical conductivity of our samples (CSCTO-0, CSCTO-5) is shown in Fig. 4(a and b). It is given in log-log scale. From these figures we can observe that there are two distinct regions: For CSCTO-0, at lower temperatures (< 513 K), there is a small plateau in the low frequencies region followed by two regimes of dispersion in the high frequencies region. On and above 513 K, the conductivity shows a wide plateau region at low frequencies followed by one regime of dispersion in the high frequencies region. Further, the dispersive region shifts to the higher frequencies with increasing temperature. However, for CSCTO-5 we observe this behavior at a lower temperature (473 K) compared with the pur CCTO ceramic. These figures also show that the total conductivity σtot increases when the temperature increases from 373 K to 653 K for both ceramics, indicating that the electrical conduction processes are activated thermally. The phenomenon of conductivity dispersion is generally explained by Jonscher's law [22]:
σtot = σDC + Bω s
Fig. 4. Angular frequency dependence of the total electrical conductivity (σtot) at different temperatures for both ceramics: a) CSCTO-0, b) CSCTO-5.
(2)
Where σDC is the low frequency conductivity which can be obtained by extrapolating the low frequency plateau to zero frequency, B is a constant that depends on temperature which determines the strength of polarizability and the exponent s is frequency and temperature dependence, which represents the degree of interaction between mobile ions and the lattice and it is used to suggest the appropriate process for the conduction mechanism. Hence temperature dependence of this exponent for both ceramics was investigated later.
Fig. 5. Temperature dependence of DC electrical resistivity for both ceramics CSCTO. The straight lines indicate the linear behaviors of Ln ρ vs 1/T.
a little change of the slope around 512 K for CSCTO-0 and decreases for CSCTO-5 to achieve 470 K. It is clearly seen that the DC-resistivity decreases with the increase of Sr concentration. Hence, two different temperature regions can be observed in both ceramics associated with two activation energies that are calculated by using the Arrhenius law [23] and are indicated in Fig. 5. The average activation energies are thus deduced to be of the order of 612 meV and 576 meV for CSCTO-0 and CSCTO-5, respectively. The obtained values of activation energies are very close to the reported values of CSCTO [24]. It is clearly seen that the average energy decreases when adding Sr concentration.
3.2.1. DC resistivity DC electrical conductivity is closely related to DC-resistivity (which is more commonly used), thus, the values of DC resistivity (ρDC) can be obtained by extrapolating the low frequency plateau to zero frequency (Fig. 4a and b). The temperature dependence of DC electrical resistivity for both ceramics (CSCTO-0, and CSCTO-5) is shown in Fig. 5. From these curves, we can clearly see that the ceramics exhibit semiconducting nature for the studied temperature range [373 K–653 K] and 38
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However, the carrier doping by chemical substitution generally brings disorder in the system, which contributes to the broadening of the impurity band and that justifies the decrease of the average energy in the material. 3.2.2. AC conductivity AC electrical conductivity measurements are helpful in identifying the nature of the dominant conduction process in the material. In this way, the evolution of the exponent s with frequency and temperature is studied. According to the literature, many different models have been proposed to explain the behavior of the exponent s under an applied AC field [25]. In particular, four different conduction mechanisms have been considered:
• In • • •
the Quantum-mechanical tunneling (QMT) conduction mechanism, the exponent s increases slightly with temperature and predicts a value of s = 0.8. Correlated Barrier Hopping (CBH) conduction mechanism is a result of hopping of electrons between two sites over a coulombic potential well. In this case, the frequency exponent s was found to decrease with increasing temperature. Non-Overlapping Small Polaron Tunneling (NSPT) model, can be obtained when the addition of a charge carrier to a site causes a large local distortion which do not overlap, in this case, the exponent s is temperature dependent and it increased with increasing temperature. Overlapping Large Polaron Tunneling (OLPT) process, in which tunneling of polarons is the dominant mechanism, but where a considerable overlap of the polaron distortion clouds occurs. The frequency exponent s decreases with increasing temperature reaches a minimum and then increases again with increasing temperature. This mechanism appears to be the most appropriate model for this work (to be detailed in the next).
Fig. 6. Angular frequency dependence of the AC electrical conductivity (σAC) at various representative temperatures between 373 K and 653 K for a) CSCTO-0 and b) CSCTO-5 ceramics.
For our ceramics, the values of the frequency exponent s of both ceramics have been determined from the slopes of the curves Ln σAC = Ln(σtot − σDC) as a function of Ln(ω) in both regions that are shown in the Fig. 6(a and b). The variation of s with temperature for both ceramics is represented in Fig. 7. It is observed that there are two regions of temperatures in both two ceramics which can be described by the Overlapping Large Polaron Tunneling process. In region I (the low temperature region), it is clearly seen that the exponent s exhibits a minimum at a certain temperature which moves to the lower temperature from 427 K to 415 K when adding Sr concentration, this suggests the decrease of the polaron energy with adding Sr amount as reported in the literature for different values of polaron energies [26]. In fact, the polaron energy depends on the effective dielectric constant ε′ [27]. Hence, because of the high dielectric constant of Sr doped CCTO (ε′ = 1766.5 at 300 K and 1 KHz) (data not reported here) compared with CCTO-0 (ε′ = 35713.91 at 300 K and 1 KHz) (data not reported here), the energy associated with the charge transfer between the overlapping sites decreases when doping with Sr. In regards to the values of s, it is found that s stay less than a unity for both ceramics, and increases from 0.6 to 0.8 at 373 K when adding Sr concentration; this suggests that the ion Sr2+ exhibits a strong interaction with the lattice. Also it, is indicating a non debye behavior because for debye cases s = 1 [28]. In the other hand, for the region II, at higher temperatures, the minimum of OLPT process for CSCTO-5 can not be identified, this may be due to the increase of the spatial extention of the polaron (α) [25] which is attributed to the increment of the total conductivity in Sr doped CCTO ceramics. Therefore, the OLPT mechanism was also observed for Sr and Zn co-doped calcium copper titanate ceramic (Ca0.90Sr0.1Cu3Ti3.95Zn0.05O12) in the temperature range 303–483 K [28]. Hence, the existence of OLPT mechanism in CSCTO ceramics may be due to a reduced number of hopping charges that make the spatial extent of the polaron to extend to several interatomic distances
Fig. 7. The variation of frequency exponent (s) for CSCTO-0 and CSCTO-5 as a function of temperature, obtained from the slopes of the curves ln (σAC=σtot − σDC) = f(ln(ω)).
resulting in the formation of overlapping large polarons [29]. In order to confirm the existence of the OLPT mechanism in our samples, the modulus spectroscopy analysis has been studied.
3.3. Electric modulus analysis Electrical behavior can also be investigated by considering the complex electric modulus M*(ω) formalism, which provides an 39
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Table 1 Structural parameters, and the coherence length of polaron of the CSCTO system. x (Sr)
Lattice parameter a (Å)
Lattice Volume V (Å3)
Crystallite size (nm)
Lcoh (Å)
0 0.05
7.393(4) 7.395(1)
404.2 404.4
139.4 82.7
11.2 9.4
Lcoh ≈ D1/3 [31]. From the analysis of the shape of the XRD lines we determine the average crystallites size of each ceramics using DebyeSheerer's formula [4]:
D=
kλ βhkl cos(θ)
(3)
Where D is the crystallites size, k is a constant normally taken as 0.9, λ is the wavelength of Cukα radiation (λ = 1.54098 Å), βhkl is full width half maxima (FWHM) located at any 2θ in the pattern. The crystallite size was calculated from X-ray diffraction profiles of strong reflexions by measuring the full width at half maximum (FWHM). From the calculations, the average crystallites size of the CSCTO ceramics were found to be about 139.4 nm and 82.7 nm for CSCTO-0 and CSCTO5 respectively. Hence, we found that the values of coherence length (Lcoh≈ 11.2 Å, 9.4 Å) (see Table 1) is greater than the lattice constant (a = 7.393(4), 7.395(1) Å) for CSCTO-0 and CSCTO-5 respectively, indicating the predominance of the large polaron conduction process for both samples. 4. Conclusion In this Paper, Ca1−xSrxCu3Ti4O12 for pure (x = 0) and Sr doped (x = 0.05) have been synthesized by a chemical semi wet rout. Microstructural study showed that Sr concentration promotes grain growth in CSCTO ceramics. X-ray analysis indicated that theses ceramics crystallize in a cubic structure with Im3 space group. Both DC and AC electrical conductivity have been investigated. Therefore, variation of the exponent s with temperature, modulus analysis indicate that the dominant conduction process was attributed to the OLPT model for both ceramics in the temperature range of [373–673 K]. Finally, the predominance of the OLPT process is identified by comparing the coherence length of the polaron and the lattice parameter.
Fig. 8. Comparison of imaginary modulus and impedance with frequency at 373 K for a) CSCTO-0 and b) CSCTO-5.
alternative approach based on the polarization analysis [30]. However, this formalism takes into account both grain boundary (GB) and grain contributions in a coupled way. Hence, the formation of large polaron have been clarified when M″ and Z″ plotted as a function of frequency in log-log scale which is shown in Fig. 8(a and b) for both ceramics (CSCTO-0, and CSCTO-5) at 373 K. It is generally known that impedance and modulus formalism are used together to distinguish the microscopic processes responsible for localized dielectric relaxations (Short range hopping) and long-range conductions of charge carriers that is generally contributed to the large polaron [31], depending on how far apart the different dielectric functions appear on the frequency plane. From the Fig. 8(a and b), it is observed that the peaks of grains and grain boundary in Z″ and M″ spectra are nearly coinciding with each other showing the long range hopping of charge carriers [31]. Then, this confirms the formation of large polaron in CSCTO ceramics (CSCTO-0 and CSCTO-5).
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3.4. Determination of polaron size from X-Ray analysis In this section, we discuss the size of polarization cloud or what means the radius of polaron which is also called coherence length, Lcoh that gives information about the nature of the polaron that exists in the material and which contributes to the dielectric and electrical properties. We distinguish two types of polarons, small and large polarons, it depends on its radius Lcoh compared with the lattice constant a. If Lcoh < a, we talk about small polaron, by contrast, a large polaron can form when Lcoh > a [32]. Thus the coherence length depends on the crystallites size of materials to the one third power of crystallites size 40
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Evidence of large hopping polaron conduction process in strontium doped calcium copper titanate ceramics
T
S. Amhila,∗, E. choukria, S. Ben Moumena, A. Bourialb, L. Essaleha a Laboratory of Condensed Matter and Nanostructures (LMCN), Cadi-Ayyad University, Faculty of Sciences and Technology, Departement of Applied Physics, Marrakech, Morocco b Laboratoire Procédés, Métrologie, Matériaux pour l'Energie et Environnement (LP2M2E), Cadi-Ayyad University, Faculty of Sciences and Technology, Departement of Applied Physics, Marrakech, Morocco
A R T I C LE I N FO
A B S T R A C T
Keywords: CCTO Semi wet route Electrical properties OLPT
Strontium (Sr) doped Calcium Copper Titanate Ca1−xSrxCu3Ti4O12 with two values x = 0 and x = 0.05 commonly known as CSCTO ceramics have been obtained by using the semi wet route synthesis method. Rietveld refinement shows that the powders crystallize in the cubic perovskite related structure with Im3 space group. Scanning Electron Micrograph (SEM) analysis shows that the average grain size of ceramics becomes larger when Sr doping is considered. Both DC and AC electrical conductivity are investigated throughly in the temperature and frequency ranges between [373–653 K] and [20 Hz–1MHz], respectively. The values of the average activation energies for CSCTO-0 (x = 0) and CSCTO-5 (x = 0.05) were found to be 612 meV and 576 meV, respectively. In Fact, Sr doping has an effect on the broadening of the impurity band that can lead to a dramatic decrease in the activation conduction energy of CSCTO ceramics. A systematic study of AC electrical conductivity reveals that the predominant conduction mechanism existing in these ceramics is generated by large polaron hopping process. This mechanism has also been identified by the modulus analysis and confirmed by comparing the hopping polaron size with the lattice parameter.
1. Introduction Nowadays, it is becoming generally recognized that the demand for better performance, high density energy storage and low cost of electronic devices need an interest miniaturization and densification of capacitors in electronic based equipment. In fact, this phenomenon needs some capacitors that present thermal and frequency stability and good dielectric properties. Generally, perovskite materials are well known for their ability to produce high dielectric constant which had led to many important industrial applications in microelectronics and memory devices [1–3]. Lead-free perovskites such as BaFe0.5Nb0.5O3 and CaCu3Ti4O12 often called CCTO are found to be the most interesting materials for these applications [4]. Therefore, CCTO has attracted a great deal of attention due to its good physical properties, its highest dielectric constant (order of 105) and its good thermal stability over a wide range of temperature (100–600 K) and frequency independent in the frequency range of (103–106Hz) [1–3,5]. However, the only disadvantage of this material is its higher dielectric loss, thus the capacitor cannot hold a stored charge for more than a few seconds which limits its usage in device applications. In fact, there are various ways to reduce
∗
dielectric loss for CCTO materials, the most interesting technique is by ion doping at A or/and B sites, several studies have been reported with a variety of possible substitutions [2,6–8]. Various works have been done suggesting the important effect of Sr2+ doping ions on Ca-site, resulting to the good dielectric properties such as increasing the dielectric constant and decreasing the dielectric losses [9–12]. It is noted that CSCTO ceramics are usually prepared by a conventional solid-state method which needs relatively long reaction time and high calcination and sintering temperatures [6,10,13], the sol-gel method was also widely reported regarding its excellent chemical stoichiometry, homogeneity, and lower crystallization temperature, but it has a high cost of precursors which allowed us to avoid this method [13,14]. However, few ones used the wet chemistry method also named citrate-nitrate gel chemical method which is a type of combustion synthesis technique [15,16]. In this paper, this last method has been used due to its considerable advantages including lower sintering temperature and shorter reaction time [18]. To the best of our knowledge, several investigations have been reported to study the dielectric properties of Sr doped CCTO ceramics [9,10,14,15], but a few works on electrical properties and conduction mechanisms are reported in the literature for only non
Corresponding author. E-mail addresses: [email protected], [email protected] (S. Amhil).
https://doi.org/10.1016/j.physb.2018.12.032 Received 8 November 2018; Received in revised form 6 December 2018; Accepted 19 December 2018 Available online 04 January 2019 0921-4526/ © 2018 Elsevier B.V. All rights reserved.
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doped CCTO ceramics [16,17]. However, electrical measurements are the most sensitive and useful tool for understanding the conduction process in materials. Thus, the aim of this paper is to determine the different conduction mechanisms existing in the Sr doped CCTO ceramics by analyzing the temperature and frequency dependent electrical conductivity of the material. The large polaron hopping mechanism is identified to be the predominant conduction process through the analysis of the temperature dependence of power-law exponent s(T). This is also confirmed by considering the modulus formalism. The coherence length of polaron and lattice parameter are compared by means of structural data.
2. Experimental details 2.1. Sample preparation Polycrystalline samples Ca1−xSrxCu3Ti4O12 with x = 0 and x = 0.05 were synthesized by the semi-wet route. In this method, high purity chemicals copper nitrate (Cu(NO3)2,3H2O), calcium nitrates (Ca (NO3) 2, 4H2O) strontium nitrates (Sr(NO3)2) and titanium oxide (TiO2) were weighed in stoichiometric molar ratios. Solutions of metal nitrates were prepared in a baker using demineralized water. After that, solid TiO2 and a calculated amount of citric acid (C6H8O7) were added to the solution. The mixture was then heated using a hot plate with a magnetic stirrer at around 80 °C. About 2 h later and by removing the solvent a homogenous blue gel was formed and a spontaneous spark propagates on the surface of the material giving rise to voluminous porous and floppy brown powder. The xerogel (as prepared) was heat-treated at 800 °C for 12 h in air. After grinding, the calcined powders were pressed into discs of about 13 mm in diameter and 1 mm in thickness by mean of a hydraulic press applying pressure of 4 tonnes and the sintering was done at 1000 °C for 12 h. For the electrical measurements, the pellets are covered on both sides with silver (Ag) electrodes. The flow chart of the semi-wet method is represented in Fig. 1.
Fig. 2. Rietveld refinement of X-ray Diffraction pattern of undoped and Sr doped CCTO ceramics sintered at 1000 °C for 12 h collected at room temperature.
2.2. Sample characterization The crystal structure of CSCTO ceramics was investigated using the X-ray diffraction technique (XRD, Rigaku, smart lab) with Cu-Kα radiations (λ = 0.154098 nm) in a 2θ range from 20° to 70°, and a scan rate of 5°/min. Morphology and microstructure were observed on the surfaces of the ceramics with the scanning electron microscopy (SEM) (Vega3 TESCAN). The electrical characterization was carried out by impedance spectroscopy (IS) using HP4284A spectrometer with an applied AC voltage of 250 mV over a frequency range 20 Hz–1 MHz and a temperature range [373–653 K]. 3. Results and discussion 3.1. Structural and microstructural characteristics X-ray diffraction patterns of Ca1−xSrxCu3Ti4O12 (x = 0 (CSCTO-0) and x = 0.05(CSCTO-5)) ceramics at room temperature are shown in Fig. 2. The data were refined by the Rietveld technique using the Full Prof program. It is clearly shown that both ceramics CSCTO-0 and CSCTO-5 are formed without any secondary phases and a pure phase has been detected. In addition, CSCTO ceramics could be indexed to a cubic perovskite structure with Im3 space group according to JCPDS75-2188 [23] and satisfying the minimum value of the fitting parameter (χ2) in the program. The CSCTO lattice parameter was determined as a = 7.393 Å, a = 7.395 Å for CSCTO-0 and CSCTO-5 ceramics respectively which are in accordance with the results reported in the literature [9,19]. Therefore, as adding concentration of Sr2+, the CSCTO peaks positions shift to the lower angles (see inset Fig. 2(b)), this shift indicates the enhancement of the lattice which may be is caused by the substitution of Ca2+ (r(Ca2+) = 1.34 Å) cations by the larger cations of Sr2+ (r(Sr2+) = 1.44 Å) [9,14]. The scanning electron microscopic images of CSCTO ceramics are shown in Fig. 3(a and b). From this figures, it can be clearly seen that the samples have well distributed grains and exhibit a dense structure. It is noted that the grain size increased with the increase of the strontium content. Otherwise, the average crystallite size, D, was calculated from XRD data based on Debye Sherrer's method (see section 2.4). The results reveal that the crystallites size decreases from 139.4 nm to 82.7 nm when doping with Sr, then the possibility of having more crystallites is large which allows the grain growth in the presence of Sr, so we can say that Sr promotes the grain size and reduce the porosity as already observed in some works [6,20]. The average grain size of the CSCTO ceramics was calculated using ImageJ software and was
Mixing of metal nitrate solutions + solid TiO2 in stoichiometric amounts
Addition of citric acid to the mixed nitrate solutions
Mixing and drying at 80°C by a magnetic stirrer
Calcination in alumina Crucibles at 800°C for 10h Grinding
Pelletisation (Pressing) Sintering at 1000°C for 12h in air
Dielectric Measurements Fig. 1. Flow chart of the semi-wet method of CSCTO ceramics. 37
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Fig. 3. SEM micrograph of the fractured surface of the sintered ceramics (a) CSCTO-0, (b) CSCTO-5. Insets represent the distribution of grain size.
estimated to be 3.16 μm, for pure CSCTO and it was increased to 4.13 μm for CSCTO-5. The distribution of this two ceramics are shown in the inset of Fig. 3(a and b)). 3.2. Electrical conductivity Total electrical conductivity is calculated from the imaginary part of the dielectric constant (ε′ ′) according to the relation σtot = ωε0 ε′ ′, where ω is the angular frequency, ε0 is the permittivity of free space and ε′ ′ is the imaginary part of the dielectric constant, ε′ ′ is obtained from the values of measured capacity (Cp) and the measured values of loss tangent (D = tg δ) using the following equation [21]:
ε″ =
Cp d ε0 A
D
(1)
where d and A are the thickness and area of the ceramic. The frequency and temperature dependence of the total electrical conductivity of our samples (CSCTO-0, CSCTO-5) is shown in Fig. 4(a and b). It is given in log-log scale. From these figures we can observe that there are two distinct regions: For CSCTO-0, at lower temperatures (< 513 K), there is a small plateau in the low frequencies region followed by two regimes of dispersion in the high frequencies region. On and above 513 K, the conductivity shows a wide plateau region at low frequencies followed by one regime of dispersion in the high frequencies region. Further, the dispersive region shifts to the higher frequencies with increasing temperature. However, for CSCTO-5 we observe this behavior at a lower temperature (473 K) compared with the pur CCTO ceramic. These figures also show that the total conductivity σtot increases when the temperature increases from 373 K to 653 K for both ceramics, indicating that the electrical conduction processes are activated thermally. The phenomenon of conductivity dispersion is generally explained by Jonscher's law [22]:
σtot = σDC + Bω s
Fig. 4. Angular frequency dependence of the total electrical conductivity (σtot) at different temperatures for both ceramics: a) CSCTO-0, b) CSCTO-5.
(2)
Where σDC is the low frequency conductivity which can be obtained by extrapolating the low frequency plateau to zero frequency, B is a constant that depends on temperature which determines the strength of polarizability and the exponent s is frequency and temperature dependence, which represents the degree of interaction between mobile ions and the lattice and it is used to suggest the appropriate process for the conduction mechanism. Hence temperature dependence of this exponent for both ceramics was investigated later.
Fig. 5. Temperature dependence of DC electrical resistivity for both ceramics CSCTO. The straight lines indicate the linear behaviors of Ln ρ vs 1/T.
a little change of the slope around 512 K for CSCTO-0 and decreases for CSCTO-5 to achieve 470 K. It is clearly seen that the DC-resistivity decreases with the increase of Sr concentration. Hence, two different temperature regions can be observed in both ceramics associated with two activation energies that are calculated by using the Arrhenius law [23] and are indicated in Fig. 5. The average activation energies are thus deduced to be of the order of 612 meV and 576 meV for CSCTO-0 and CSCTO-5, respectively. The obtained values of activation energies are very close to the reported values of CSCTO [24]. It is clearly seen that the average energy decreases when adding Sr concentration.
3.2.1. DC resistivity DC electrical conductivity is closely related to DC-resistivity (which is more commonly used), thus, the values of DC resistivity (ρDC) can be obtained by extrapolating the low frequency plateau to zero frequency (Fig. 4a and b). The temperature dependence of DC electrical resistivity for both ceramics (CSCTO-0, and CSCTO-5) is shown in Fig. 5. From these curves, we can clearly see that the ceramics exhibit semiconducting nature for the studied temperature range [373 K–653 K] and 38
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However, the carrier doping by chemical substitution generally brings disorder in the system, which contributes to the broadening of the impurity band and that justifies the decrease of the average energy in the material. 3.2.2. AC conductivity AC electrical conductivity measurements are helpful in identifying the nature of the dominant conduction process in the material. In this way, the evolution of the exponent s with frequency and temperature is studied. According to the literature, many different models have been proposed to explain the behavior of the exponent s under an applied AC field [25]. In particular, four different conduction mechanisms have been considered:
• In • • •
the Quantum-mechanical tunneling (QMT) conduction mechanism, the exponent s increases slightly with temperature and predicts a value of s = 0.8. Correlated Barrier Hopping (CBH) conduction mechanism is a result of hopping of electrons between two sites over a coulombic potential well. In this case, the frequency exponent s was found to decrease with increasing temperature. Non-Overlapping Small Polaron Tunneling (NSPT) model, can be obtained when the addition of a charge carrier to a site causes a large local distortion which do not overlap, in this case, the exponent s is temperature dependent and it increased with increasing temperature. Overlapping Large Polaron Tunneling (OLPT) process, in which tunneling of polarons is the dominant mechanism, but where a considerable overlap of the polaron distortion clouds occurs. The frequency exponent s decreases with increasing temperature reaches a minimum and then increases again with increasing temperature. This mechanism appears to be the most appropriate model for this work (to be detailed in the next).
Fig. 6. Angular frequency dependence of the AC electrical conductivity (σAC) at various representative temperatures between 373 K and 653 K for a) CSCTO-0 and b) CSCTO-5 ceramics.
For our ceramics, the values of the frequency exponent s of both ceramics have been determined from the slopes of the curves Ln σAC = Ln(σtot − σDC) as a function of Ln(ω) in both regions that are shown in the Fig. 6(a and b). The variation of s with temperature for both ceramics is represented in Fig. 7. It is observed that there are two regions of temperatures in both two ceramics which can be described by the Overlapping Large Polaron Tunneling process. In region I (the low temperature region), it is clearly seen that the exponent s exhibits a minimum at a certain temperature which moves to the lower temperature from 427 K to 415 K when adding Sr concentration, this suggests the decrease of the polaron energy with adding Sr amount as reported in the literature for different values of polaron energies [26]. In fact, the polaron energy depends on the effective dielectric constant ε′ [27]. Hence, because of the high dielectric constant of Sr doped CCTO (ε′ = 1766.5 at 300 K and 1 KHz) (data not reported here) compared with CCTO-0 (ε′ = 35713.91 at 300 K and 1 KHz) (data not reported here), the energy associated with the charge transfer between the overlapping sites decreases when doping with Sr. In regards to the values of s, it is found that s stay less than a unity for both ceramics, and increases from 0.6 to 0.8 at 373 K when adding Sr concentration; this suggests that the ion Sr2+ exhibits a strong interaction with the lattice. Also it, is indicating a non debye behavior because for debye cases s = 1 [28]. In the other hand, for the region II, at higher temperatures, the minimum of OLPT process for CSCTO-5 can not be identified, this may be due to the increase of the spatial extention of the polaron (α) [25] which is attributed to the increment of the total conductivity in Sr doped CCTO ceramics. Therefore, the OLPT mechanism was also observed for Sr and Zn co-doped calcium copper titanate ceramic (Ca0.90Sr0.1Cu3Ti3.95Zn0.05O12) in the temperature range 303–483 K [28]. Hence, the existence of OLPT mechanism in CSCTO ceramics may be due to a reduced number of hopping charges that make the spatial extent of the polaron to extend to several interatomic distances
Fig. 7. The variation of frequency exponent (s) for CSCTO-0 and CSCTO-5 as a function of temperature, obtained from the slopes of the curves ln (σAC=σtot − σDC) = f(ln(ω)).
resulting in the formation of overlapping large polarons [29]. In order to confirm the existence of the OLPT mechanism in our samples, the modulus spectroscopy analysis has been studied.
3.3. Electric modulus analysis Electrical behavior can also be investigated by considering the complex electric modulus M*(ω) formalism, which provides an 39
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Table 1 Structural parameters, and the coherence length of polaron of the CSCTO system. x (Sr)
Lattice parameter a (Å)
Lattice Volume V (Å3)
Crystallite size (nm)
Lcoh (Å)
0 0.05
7.393(4) 7.395(1)
404.2 404.4
139.4 82.7
11.2 9.4
Lcoh ≈ D1/3 [31]. From the analysis of the shape of the XRD lines we determine the average crystallites size of each ceramics using DebyeSheerer's formula [4]:
D=
kλ βhkl cos(θ)
(3)
Where D is the crystallites size, k is a constant normally taken as 0.9, λ is the wavelength of Cukα radiation (λ = 1.54098 Å), βhkl is full width half maxima (FWHM) located at any 2θ in the pattern. The crystallite size was calculated from X-ray diffraction profiles of strong reflexions by measuring the full width at half maximum (FWHM). From the calculations, the average crystallites size of the CSCTO ceramics were found to be about 139.4 nm and 82.7 nm for CSCTO-0 and CSCTO5 respectively. Hence, we found that the values of coherence length (Lcoh≈ 11.2 Å, 9.4 Å) (see Table 1) is greater than the lattice constant (a = 7.393(4), 7.395(1) Å) for CSCTO-0 and CSCTO-5 respectively, indicating the predominance of the large polaron conduction process for both samples. 4. Conclusion In this Paper, Ca1−xSrxCu3Ti4O12 for pure (x = 0) and Sr doped (x = 0.05) have been synthesized by a chemical semi wet rout. Microstructural study showed that Sr concentration promotes grain growth in CSCTO ceramics. X-ray analysis indicated that theses ceramics crystallize in a cubic structure with Im3 space group. Both DC and AC electrical conductivity have been investigated. Therefore, variation of the exponent s with temperature, modulus analysis indicate that the dominant conduction process was attributed to the OLPT model for both ceramics in the temperature range of [373–673 K]. Finally, the predominance of the OLPT process is identified by comparing the coherence length of the polaron and the lattice parameter.
Fig. 8. Comparison of imaginary modulus and impedance with frequency at 373 K for a) CSCTO-0 and b) CSCTO-5.
alternative approach based on the polarization analysis [30]. However, this formalism takes into account both grain boundary (GB) and grain contributions in a coupled way. Hence, the formation of large polaron have been clarified when M″ and Z″ plotted as a function of frequency in log-log scale which is shown in Fig. 8(a and b) for both ceramics (CSCTO-0, and CSCTO-5) at 373 K. It is generally known that impedance and modulus formalism are used together to distinguish the microscopic processes responsible for localized dielectric relaxations (Short range hopping) and long-range conductions of charge carriers that is generally contributed to the large polaron [31], depending on how far apart the different dielectric functions appear on the frequency plane. From the Fig. 8(a and b), it is observed that the peaks of grains and grain boundary in Z″ and M″ spectra are nearly coinciding with each other showing the long range hopping of charge carriers [31]. Then, this confirms the formation of large polaron in CSCTO ceramics (CSCTO-0 and CSCTO-5).
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