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AC and DC conductivity study of KPb4(PO4)3 compound using impedance spectroscopy
Accepted Manuscript AC and DC conductivity study of KPb4(PO4)3 compound using impedance spectroscopy Rabiaa Chtourou, Bassem Louati, Kamel Guidara PII:
S0925-8388(17)32892-X
DOI:
10.1016/j.jallcom.2017.08.163
Reference:
JALCOM 42920
To appear in:
Journal of Alloys and Compounds
Received Date: 6 June 2017 Revised Date:
9 August 2017
Accepted Date: 16 August 2017
Please cite this article as: R. Chtourou, B. Louati, K. Guidara, AC and DC conductivity study of KPb4(PO4)3 compound using impedance spectroscopy, Journal of Alloys and Compounds (2017), doi: 10.1016/j.jallcom.2017.08.163. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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AC and DC conductivity study of KPb4(PO4)3 compound using impedance spectroscopy Rabiaa Chtourou*, Bassem Louati, Kamel Guidara Laboratory of spectroscopic characterization and optic materials, University of Sfax, Faculty of Sciences B.P. 1171, 3000, Sfax-TUNISIA
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*[email protected]
Abstract
Orthophosphate KPb4(PO4)3 compound was synthesized by the conventional solid-state reaction . The phase formation of the compound was confirmed from the powder X-ray
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diffraction. Vibrational study confirms the existence of [PO4]3− group. The impedance spectroscopy measurements was realized with Compact disc, Φ= 8mm diameter and 1.2 mm
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thickness in the range temperature (659–708)K and frequency (209Hz to 1 MHz), respectively. As well, the impedance spectra are well adjusted to an equivalent circuit formed by a serial combination of three cells. It was found that the non-overlapping small polaron tunneling (NSPT) model is suitable to describe the conduction mechanism in this compound. Keywords: Orthophosphate, Electrical properties, Ac conductivity, NSPT model
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1. Introduction
Design and discovery of new materials that can be used diverse areas of science and technology are attracted much attention as one of research issues. Many strategies and methods have been used to synthesize new compounds.
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Among what materials, the compounds of the apatite type have been studied in the literature. These materials can be used for various applications, such as catalysts [1], ionic exchangers
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for harmful ions [2] and luminescent materials [3-5] as well as in optoelectronics [6] and biomaterials [7]. Considerably, they are also attracting attention as a new class of oxide ion conductors [8-10].Usually, the general chemical formula of this compounds is M10(YO4)6X2 this family of apatite has been crystallized in hexagonal system with space group P63/m [11, 12]. Several authors has been are interested to demonstrate the structure of apatite .The structure is describe as follows. The YO4 tetrahedrons are arranged around the 63 screw axes forming columns around the crystallographic c axis with X ions on the axis [10]. In one cell, the ten cations are distributed on two sites where six of them fill the (6h) sites making equilateral triangles and the remaining four cations occupy the (4f) sites. The coordination number is seven for the (6h) cations, six O and one X; while is nine (Oxygen atoms) for the 1
ACCEPTED MANUSCRIPT (4f) cations building trigonal tri-capped prisms stacked in columns in the [001] direction. In the last few years; several studies were limited to lacunar Apatites, with lack of X anion and the general formula APb4(XO4)3, (A= Li, Na, Ag), have already been widely studied. A large number of cations combinations were proposed by several authors. It is been shown that the cation Pb2+ have a crucial role by preserving the apatite's network, which is related to the
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presence of the electronic doublets 6s2 that compensate for the Coulomb imbalance due to the existence of the anion gap in the tunnels of the apatite structure[13]. In this paper, we are interested to studying a one element of this group the KPb4(PO4)3.The structure study of this compound was reported previously in 1980 by MATHEW and ALL .In this paper we are
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interested first of all to perform the structural characterization using X-ray diffraction and Raman spectroscopy of the composition of lead phosphate apatite of potassium, secondly we are study electrical properties according of temperature and frequency. We are determined the
2. Experimental procedure
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appropriate model responsible for the conduction mechanism in KPb4(PO4)3 compound.
KPb4(PO4)3 sample has been carried out by the standard solid state reaction method at high temperature. The starting materials were mixed and ground in an agate mortar according to the following chemical reaction:
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4PbO+1/2K2CO3+3[(NH4)2HPO4 ]→ KPb4(PO4)3+1/2CO2+18/4H2O+6NH3 First of all, the powder obtained was heated in a crucible to 573K to eliminate NH3, CO2, and H2O. Then, the obtained compound was again ground, pressed in pellet pressed in to a disc
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form with Φ=8 mm diameter and 1.2 mm thickness using 3 t/cm2 uniaxial pressure and heated at 873K. Finally the sample was cooled at a rate of 5 °C / min at room temperature. The initial
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characterization of this compound was performed out using powder X-ray diffraction (XRD), in utilize a Phillips powder diffractometer with copper radiation Kα (λKα=1.5405 Å) over a wide range of Bragg angles (10°≤2θ≤80°). Furthermore, unit cell parameter for this powder was established by the least square method from the powder data. The Raman spectrum of KPb4(PO4)3
was
recorded
at
room
temperature
using
a
single
monochromatic
spectrophotometer Notch filter(Labram HR800) equipped with a laser-ionized helium using the red exciting ray (λ=633 nm). Electrical impedances measurements were performed using two gold electrodes configuration and recorded in the frequency ranging (209 Hz to 1 MHz) using a TEGAM 3550 ALF automatic bridge monitored by a microcomputer and a
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ACCEPTED MANUSCRIPT temperature controller. Measurements were carried out in the temperature range from (659708)K. 3. Results and discussion 3.1. Crystalline parameters
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The X-ray powder diffraction (XRD) pattern recorded at room temperature for the KPb4(PO4)3 sample is shown in Figure 1 we found that our sample can be indexed in the hexagonal system with space group P63/m (ITA No.176) and the structural model indicators converged to RBragg = 7.01% and χ2 =3.95. The corresponding lattice parameters and unit cell
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volume obtained from Rietveld refinement are a=b= 9.731(5) Å, c= 7.1986(7) Å and V= 610.75(5) Ǻ³.The unit cell parameters are in good agreement with the literature values [14];
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revealing the existence of one phase.
Figure 2 shows the projection of the structure of the title compound along [001]. The main feature of this structure is the way the [PO4]3− tetrahedra are packed to delimit hexagonal tunnels running along the c-direction. The structure of KPb4 (PO4)3 can be described by the distinction of the two types of channels.
•One with a small section, which corresponds to a mixed site (4f position), occupied by an
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equal number of Na+ and Pb2+ cations (Na and Pb2). The latter cations are coordinated to nine oxygen anions belonging to six distinct tetrahedra, and to three much further oxygen anions having almost the same elevation as Na and Pb2
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•The other with larger section (6h position), which is totally occupied by lead cations (Pb1). These cations are inserted into six fold sites that constitute the walls of the tunnels. Their
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coordination spheres are delimited by six oxygen ions common to five [PO4]3− tetrahedra. Analysis of the bond lengths in [PO4]3- tetrahedra determines the average value of the P-O distances (P-O2 = 1.525Å (2), P-O1 = 1.538 Å, P-O3=1.585 Å) is agreement monophosphate of that found for ions [14]. In addition, the O- P -O angles vary between 108.4 and 111.65 °, with a mean value (107.92 °) almost identical to that of a regular [ PO4]
3-
tetrahedron [14].
This can be confirmed by the four distances P-O, which are very close. In the structure of our apatite O3 has a special role: on one hand it concerns the longest P-O bond [P- O3= 1.585 Å] and secondly to the shorter length of Pb-O [Pb1 -O3 2.47 Å]. 3.2 Raman spectroscopy analysis 3
ACCEPTED MANUSCRIPT The Raman spectrum is analyzed with a view to study the vibrational modes of the phosphate groups. The factors that might be considered are the mass and the size of the cation. Factor group analysis [14] of KPb4(PO4)3 hexagonal structures (P63/m) shows that the normal modes of vibration can be classified among the irreducible representations of C6h as
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Γ=12Ag+8E1g+12E2g+8Au+12Bu+8Bg+12E1u+8E2u Where the internal mode contribution of the (PO4) groups to the Raman active vibrations is Γ P O 4 =6Ag(ν1+ν2+2ν3+2ν4)+3E1g(ν2+ν3+ν4)+6E2g(ν1+ν2+2ν3+2ν4)+3Au(ν2+ν3+ν4)+6E1u(ν1+ν2+ 2ν3+2ν4)
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Were the g and the u modes are Raman active.
The Raman spectrum is reported in Figure 3. The attribution of mode has been interpreted on
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the basis of similar compounds [15]. The observed bands may be classified as follows: K/PbO, Pb-O external modes as well as the rotations and translations of the internal modes of the [PO4]3- groups. A series of band was observed in (389–584) cm-1 region is attributed to O–P– O bending vibrations with ν2 from (389 to 424 cm-1) and ν4 from (582 to 584cm-1). In high frequency the bands observed is assigned to P–O stretching modes ν3 from (979 to 1026cm-1)
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and ν1 observed around 935cm-1. The wavenumbers and the corresponding assignments are listed in Table1.
3.3. Electrical property study
The Complex impedance spectroscopy is a useful method to analyze the frequency-dependent
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electric properties of a compound by the application of an ac signal as input perturbation [16]. Furthermore, this investigation confirms separation between the bulk, grain boundaries, and
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electrode electrolyte interface properties. The experimental data can be characterize in terms of three possible complex formalisms such as the complex impedance (Z*), the electric complex modulus (M*), and the complex permittivity (ε*). These parameters are related to each other as follows: Z*= Z’- jZ”
(1)
M*= M’+ jM”= jω0Z*
(2)
ε*= ε’+jε”= (M*)-1
(3)
Where Z’= |Z| cosΦ and Z”= |Z | sinΦ
(4)
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ACCEPTED MANUSCRIPT ωo is the angular frequency (2πf), Co is the vacuum capacitance of the measuring cell and electrodes with an air gap in place of the sample, Co= εo/k; here, εo is the permittivity of free space and k= e/d, where e is the thickness, and d is the area of the sample [17]. Figure 4 shows the complex impedance spectra of KPb4(PO4)3 compound for some representative temperatures. It is remarkable that all the diagrams show certain degree of
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decentralization. The observed decentralization in Nyquist diagram is due to the heterogeneity of the sample which can be related to several phenomena such as the nature of the interface, the size of the crystals, the change of porosity [18]. This confirms that the type of relaxation in this material is non-Debye. The evolution of – Z″= f (Z′) curves show clearly the
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diminution of the resistance with the temperature. The conductivity of this material was deduced from the resistance R by the relation σ= [e/(R*S)] where e, S, and R are respectively the thickness, the surface of the pellets, and the resistance. Impedance spectra were fitted
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satisfactorily with an equivalent circuit model consisting by three elements. The first consists of parallel combination of resistance (Rg), capacitance (Cg) and a constant phase element CPEg, the second of parallel combination of resistance (Rgb) and a constant phase element CPEgb, whereas the third consists of capacitance (Celec). The confirmation of the choice of the circuit equivalent is justified by the figures (5, 6) which shows the variations of the
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experimental values of Z′ and Z″ versus the simulated ones using the parameters of the equivalent circuit model. The accumulation of these curves proves a linear behavior with a slope equal to the unity.
Electrical resistance for of the studied powder was assessed as a function of temperature,
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conductivity for the grain interior, grain boundary, and total conductivity was determined. The mechanism of ionic conduction in the KPb4(PO4)3 compound is well described by the
σ
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Arrhenius equation :
( g, gb,tot )
*
Ea( g, gb ,tot ) T = B( g , gb ,tot ) exp − K BT
(5)
Where Ea is activation energy for conduction, B is the pre-exponential factor, T is absolute temperature, and KB is Boltzmann constant. Figure 7 shows plots of Ln (σdcg,gb,tot T) versus 1000/T of bulk electrical conductivity (σg), grain boundary conductivity (σgb), and total conductivity (σtot). From this law, the activation energy for bulk, grain boundary, and total conductivity are about (0.98±0.05) eV, (1.10±0.05) eV, and (1.08±0.05) eV, respectively. In addition, this figure shows that the total conductivity 5
ACCEPTED MANUSCRIPT of the compound is less than the bulk conductivity but greater than the grain boundaries one, proving the existence of a partial blockage of the charge carriers by the grain boundaries. In other words, the conductivity of the compound is limited by the grain boundaries conductivity in the material.
3.4.1 Ac conductivity
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3.4. Frequency-dependent conductivity measurements
The ac conductivity of ionic materials at diffrent temperature is usually described by the universal power law Jonscher’s expressed as [19]:
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σ ac (ω ) = σ dc + Aω s
(6)
Where σdc is the sample direct current conductivity, A is a temperature dependent parameter
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determines the strength of polarisability and s is the slope of the high frequency dispersion data, is used to determine of interaction between mobile ions with the environments surrounding them.
To the dispersive region of the AC conductivity, the crossover frequency from DC is known as hopping frequency, ωh, and it can be elaborate forthwith from AC conductivity data using
σ ωh = dc A
1
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the following equation [20]. s
(7)
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The hopping frequency is temperature dependent obeying the Arrhenius relation:
− E hop KT
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ωh = ω0 exp
(8)
It can be seen frome Figure 8 that a linear relation can be deduced from the above equation when ln (ωh) versus 1000/T graph is plotted in the temperature range (659–708)K. Linear adjustment of this relation has given that the hopping activation energy is found to be Eh= (1.3±0.02) eV. This value is different to her given from dc conductivity; this presupposes that the mobility of the charge carrier is not due to a simple hopping mechanism in the investigated material. In the past few years, various scaling models have been proposed [21, 22]. Among them, we interested in the model of Ghosh [21]
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ACCEPTED MANUSCRIPT ω σ ac (ω ) = f σ dc ωh
(9)
Figure 9present the variation σac/σdc versus ω/ωh at different temperatures of KPb4(PO4)3. It is apparent that the scaled conductivity σac/σdc consolidates on a single curve which involve that the conduction transport mechanism is independent of temperature [23].
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3.4.2 Theory of conduction mechanism
The plot of the exponent s at different temperatures for our sample is shown in Figure 10 with the straight line fit to the relation and shows an increase of s with increase of temperature.
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The electrical conduction mechanism has been resolved by temperature behaviour of the value of s based on the application of various models [24- 27] that have been proposed.
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The quantum mechanical tunneling (QMT) model: The exponent s is well-nigh equal to 0.8 and increases slightly with increasing temperature or it is independent of temperature. This model is inconsistent with results the obtained.
The correlated barrier hopping (CBH) model: Where charge carriers hop between sites separating them and predict a decrease in the value of s with increase in temperature .Is not
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suitable with the results of our materials.
The overlapping large polaron tunneling (OLPT) model: The exponent s depends on both frequency and temperature and it decline with the rise in temperature to a minimum value then increases with increasing temperature. This is not observed experimentally.
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The non-overlapping small polaron tunneling (NSPT) model: The exponent s which is temperature dependent increased with the increase in temperature. It seems plausible to use
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the NSPT model since this is the case observed in our data In the NSPT model, the frequency exponent s and the expression for the AC conductivity are established by: s = 1−
4 k BT Wm − k BT ln(ωτ 0 )
(10)
Where Wm is the polaron hopping energy and τ0 is a characteristic relaxation time which is in the order of an atom vibrational period τ0 =10-13 s. [28].
σ ac =
(π e ) ² kBTα −1ω N ( EF ) ² Rω4 12
(11) 7
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Rω =
1 1 Wm ln − 2α ωτ 0 kBT
(12)
Whither α-1 is the spatial extension of the polaron, N(EF) is the density of states near the
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Fermi level, and Rω is the tunneling distance. Figure 11 demonstrate the logarithm of the conductivity as a function temperature at different frequencies. It is evident from the plots that the theoretical calculations of the conductivity (fits) are in excellent accord well with the experimental data (symbol).
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The values of parameters N(EF), α and the tunneling distance Rω calculation from linear fit to the data points are shows in figure (12,13). When the frequency is increased the values of α
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and N(EF) are increased as well [29]. However, the values of Rω are decreased [30]. These results confirm that the conductivity increases with increase in frequency. As a matter of fact, in this model is apparent that the values of Rω are vary in the range of (3.91 Å to 2.21 Å) this values are comparable with the interatomic spacing K–K distances which was found to be 3.44(Å) [31, 32]. From this finding we can deduce that the conduction
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process is ensured by a small polaron along the [001] tunnels. 4. Conclusion
The potassium lead apatite KPb4(PO4)3 was synthesized by the solid-state reaction method and characterized by X-ray diffraction and Raman spectroscopy. Its structure has been
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determined by Rietveld, adopting the space group P63/m (ITA No. 176). The Raman spectrum is recorded and interpreted on the basis of the structural peculiarities of the [PO4]3- present in
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the crystal lattice. The performed studies allowed us to establish the electrical properties of KPb4(PO4)3 compound. Two semicircles are observed in the impedance plot, indicating the presence of two relaxations processes in the studied compound associated with the grain and grain boundary. Consequently, an equivalent electrical circuit for the electrochemical cell with KPb4(PO4)3 was proposed. The variation of AC conductivity as a function of frequency at different temperatures is found to obey Jonscher's universal power law. In addition the electrical conductivity of the title compound has been theoretically supported by the NSPT model. Acknowledgments
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ACCEPTED MANUSCRIPT This work is financially supported by the Ministry of Higher Education and Scientific Research of Tunisia. References [1]Y. Matsumura, S. Sugiyama, H. Hayashi, J B. Moat, J. Solid. Stat. Chem. 114 (1995) 138.
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[2] T. Suzuki, Gypsum. Lime 204 (1986) 314. [3] B. M.J. Smet, J. Mater. Chem. Phys. 16 (1987) 283. [4] G. Blasse, J. Mater. Chem. Phys. 16 (1987) 201.
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[5] M. Tachihante , D. Zanbon, J. C. Cousseins, J. Eur Solid State Inorg. Chem. 33 (1996) 713.
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[6] L. D. Deloach, S. A. Payne, L. K. Smith., W.L. Kway, W.F. Krupke, J. Opt. Soc. Am B : Opt. Phys. 11 (1994) 269.
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[12] P.P Mokoena, I.M. Nagpure , V. Kumar, R. E. Kroo , E.J .Olivier , J. H. Neethling, H. C. Swart , O.M. Ntwaeaborw, J. Solid. Stat. Chem. 998 (2014) 1003. [13] M. El Koumiri, S Oishi, S Sato, L. El Ammari, B. Elouadi, J. Mater. Res. Bull. 35 (2000) 503. [14] M. Azrour, M. Azdouz, B. Manoun, R. Essehli, S. Benmokhtar, L. Bih, L. ElAmmari, A. Ezzahi, A. Ider, A.AitHou, J. Solid. Stat. Chem. 72 (2011) 1199. [15] S. Chemlal, A. Bouhaouss, M. Ferhat, J. C. Lacout, J. Chim. Phys. 88 (1991) 1901. 9
ACCEPTED MANUSCRIPT [16] S. Kulkarni , B.M. Nagabhushana , N. Parvatikar , A. Koppalkar ,C. Shivakumara , R. Damle, Materials Research Bullettin. 50 (2014) 197. [17] A. Muller, E.J. Baran, R.O. Carter, Struct. 26 (1976) 81. [18] Thesis Charlotte. Mellier. Université. Nantes (2011).
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Figures Captions
Figure 1: The Rietveld refinement for the KPb4(PO4)3 sample at room temperature: The dotted line indicates experimental data and calculated data are represented by black continuous lines. The lowest curve in blue shows the difference between experimental and calculated patterns. The vertical bars in green indicate the Bragg positions. Figure 2: projection of the structure of KPb4(PO4)3 compound along [001]. Figure 3: Raman spectrum of KPb4(PO4)3 recorded at room temperature. Figure 4: Plots of the impedance data at several temperatures for KPb4(PO4)3 compound. Figure 5: Measured and simulated values of the real part of the complexes impedance of the KPb4(PO4)3 compound. 10
ACCEPTED MANUSCRIPT Figure 6: Plot of experimental values versus simulated values of imaginary part Z’’ KPb4(PO4)3. Figure 7: Temperature dependence of Ln (σdcT). Figure 8: Variations of ln (ωh) as a function of 1000/T of KPb4(PO4)3.
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Figure 9: Plot of (σac/σdc) versus (ω/ωh) at different temperatures of KPb4(PO4)3. Figure 10: Variation of the universal exponent s as a function of temperature.
Figure 11: Logarithm of the conductivity as a function of temperature at different frequencies of KPb4(PO4)3 sample .
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Figure 12: Variation of the parameters α (Å-1) and N(EF) (eV-1cm-3) according to the frequency (NSPT model).
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Figure 13: Variation of the parameter Rω(Å) according to the frequency (NSPT model). Table caption:
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Table 1 Assignments of observed Raman bands in KPb4(PO4)3.
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ACCEPTED MANUSCRIPT Table. 1 Raman(cm-1)
Assignments
64 85 128 158 205
s Vs m m m
389 424
m m
ν2 (PO43-)
545 572 584
m w s
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Intensity
External modes
935
s
979 1026
s m
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K/Pb-O, Pb-O
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ν4(PO43-)
ν1 (PO43-)
ν3(PO43-)
Vs: very strong, s: strong, m: medium and w: weak
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ν2: symmetetric stretching, ν4: antisymmetric stretching, ν1: symmetetric bending,
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ν3: antisymmetric bending.
1
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Figure 1
Figure 2
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Figure 4
2
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1,2x10
659K 667K 674K 683K 691K 699K 708K fit
6
1,0x10
5
Z' experimental(Ω)
8,0x10
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6,0x10
5
4,0x10
5
0,0 0,0
5
2,0x10
5
5
4,0x10
6,0x10
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8,0x10
6
1,0x10
6
1,2x10
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Z' simuleted(Ω)
Figure5
5
5x10
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659K 667K 674K 683K 691K 699K 708K fit
5
5
5
2x10
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3x10
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Z''experimental(Ω)
4x10
5
1x10
0 0
5
1x10
5
2x10
5
3x10
5
4x10
5
5x10
Z''simuleted(Ω) Figure 6 3
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-4 Grain Grain Boundary Total conductivity Fit
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-6
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-7
-8
-9
-10
-11 1,38
1,44
1,47
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1,41
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-1
-1
Ln (σdc*T).(Ω cm K)
-5
1,50
1,53
1,56
-1
1000/T(K )
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Figure 7
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14,7 14,4
Linear Fit of Data1_D
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h
Ln(ω)
14,1 13,8 13,5
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13,2
12,6 1,38
1,41
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12,9
1,44
1,47
1,50
1,53
1,56
-1
1000/T(K )
659K 667K 674K 683K 691K 699K 708K
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Figure 8
ac
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σ /σ
dc
10
5
0 10
-1
10
0
10
1
ω/ωh
Figure 9
5
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0,60
0,58
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0,56
s
0,54
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0,52
0,48 650
660 s
670
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0,50
680
690
700
710
T(K)
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Figure 10
Figure 11 6
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10
32,2
3,0x10
32,0
Ln(NEf)
α
31,8
−1
10
2,5x10
10
2,0x10
-3
Ln(N )(eV cm )
31,6
10
31,2
-1
α(Å )
1,5x10
31,0
10
1,0x10
30,8
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Ef
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This paper deals with electrical properties and conduction mechanisms of the orthophosphate compound KPb4(PO4)3.
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- Ac conductivity data affirm that for high frequencies σac is proportional to ωs. - The non-overlapping small polaron tunneling is the appropriate conduction mechanism of KPb4(PO4)3 compound.
S0925-8388(17)32892-X
DOI:
10.1016/j.jallcom.2017.08.163
Reference:
JALCOM 42920
To appear in:
Journal of Alloys and Compounds
Received Date: 6 June 2017 Revised Date:
9 August 2017
Accepted Date: 16 August 2017
Please cite this article as: R. Chtourou, B. Louati, K. Guidara, AC and DC conductivity study of KPb4(PO4)3 compound using impedance spectroscopy, Journal of Alloys and Compounds (2017), doi: 10.1016/j.jallcom.2017.08.163. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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AC and DC conductivity study of KPb4(PO4)3 compound using impedance spectroscopy Rabiaa Chtourou*, Bassem Louati, Kamel Guidara Laboratory of spectroscopic characterization and optic materials, University of Sfax, Faculty of Sciences B.P. 1171, 3000, Sfax-TUNISIA
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*[email protected]
Abstract
Orthophosphate KPb4(PO4)3 compound was synthesized by the conventional solid-state reaction . The phase formation of the compound was confirmed from the powder X-ray
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diffraction. Vibrational study confirms the existence of [PO4]3− group. The impedance spectroscopy measurements was realized with Compact disc, Φ= 8mm diameter and 1.2 mm
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thickness in the range temperature (659–708)K and frequency (209Hz to 1 MHz), respectively. As well, the impedance spectra are well adjusted to an equivalent circuit formed by a serial combination of three cells. It was found that the non-overlapping small polaron tunneling (NSPT) model is suitable to describe the conduction mechanism in this compound. Keywords: Orthophosphate, Electrical properties, Ac conductivity, NSPT model
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1. Introduction
Design and discovery of new materials that can be used diverse areas of science and technology are attracted much attention as one of research issues. Many strategies and methods have been used to synthesize new compounds.
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Among what materials, the compounds of the apatite type have been studied in the literature. These materials can be used for various applications, such as catalysts [1], ionic exchangers
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for harmful ions [2] and luminescent materials [3-5] as well as in optoelectronics [6] and biomaterials [7]. Considerably, they are also attracting attention as a new class of oxide ion conductors [8-10].Usually, the general chemical formula of this compounds is M10(YO4)6X2 this family of apatite has been crystallized in hexagonal system with space group P63/m [11, 12]. Several authors has been are interested to demonstrate the structure of apatite .The structure is describe as follows. The YO4 tetrahedrons are arranged around the 63 screw axes forming columns around the crystallographic c axis with X ions on the axis [10]. In one cell, the ten cations are distributed on two sites where six of them fill the (6h) sites making equilateral triangles and the remaining four cations occupy the (4f) sites. The coordination number is seven for the (6h) cations, six O and one X; while is nine (Oxygen atoms) for the 1
ACCEPTED MANUSCRIPT (4f) cations building trigonal tri-capped prisms stacked in columns in the [001] direction. In the last few years; several studies were limited to lacunar Apatites, with lack of X anion and the general formula APb4(XO4)3, (A= Li, Na, Ag), have already been widely studied. A large number of cations combinations were proposed by several authors. It is been shown that the cation Pb2+ have a crucial role by preserving the apatite's network, which is related to the
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presence of the electronic doublets 6s2 that compensate for the Coulomb imbalance due to the existence of the anion gap in the tunnels of the apatite structure[13]. In this paper, we are interested to studying a one element of this group the KPb4(PO4)3.The structure study of this compound was reported previously in 1980 by MATHEW and ALL .In this paper we are
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interested first of all to perform the structural characterization using X-ray diffraction and Raman spectroscopy of the composition of lead phosphate apatite of potassium, secondly we are study electrical properties according of temperature and frequency. We are determined the
2. Experimental procedure
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appropriate model responsible for the conduction mechanism in KPb4(PO4)3 compound.
KPb4(PO4)3 sample has been carried out by the standard solid state reaction method at high temperature. The starting materials were mixed and ground in an agate mortar according to the following chemical reaction:
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4PbO+1/2K2CO3+3[(NH4)2HPO4 ]→ KPb4(PO4)3+1/2CO2+18/4H2O+6NH3 First of all, the powder obtained was heated in a crucible to 573K to eliminate NH3, CO2, and H2O. Then, the obtained compound was again ground, pressed in pellet pressed in to a disc
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form with Φ=8 mm diameter and 1.2 mm thickness using 3 t/cm2 uniaxial pressure and heated at 873K. Finally the sample was cooled at a rate of 5 °C / min at room temperature. The initial
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characterization of this compound was performed out using powder X-ray diffraction (XRD), in utilize a Phillips powder diffractometer with copper radiation Kα (λKα=1.5405 Å) over a wide range of Bragg angles (10°≤2θ≤80°). Furthermore, unit cell parameter for this powder was established by the least square method from the powder data. The Raman spectrum of KPb4(PO4)3
was
recorded
at
room
temperature
using
a
single
monochromatic
spectrophotometer Notch filter(Labram HR800) equipped with a laser-ionized helium using the red exciting ray (λ=633 nm). Electrical impedances measurements were performed using two gold electrodes configuration and recorded in the frequency ranging (209 Hz to 1 MHz) using a TEGAM 3550 ALF automatic bridge monitored by a microcomputer and a
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ACCEPTED MANUSCRIPT temperature controller. Measurements were carried out in the temperature range from (659708)K. 3. Results and discussion 3.1. Crystalline parameters
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The X-ray powder diffraction (XRD) pattern recorded at room temperature for the KPb4(PO4)3 sample is shown in Figure 1 we found that our sample can be indexed in the hexagonal system with space group P63/m (ITA No.176) and the structural model indicators converged to RBragg = 7.01% and χ2 =3.95. The corresponding lattice parameters and unit cell
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volume obtained from Rietveld refinement are a=b= 9.731(5) Å, c= 7.1986(7) Å and V= 610.75(5) Ǻ³.The unit cell parameters are in good agreement with the literature values [14];
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revealing the existence of one phase.
Figure 2 shows the projection of the structure of the title compound along [001]. The main feature of this structure is the way the [PO4]3− tetrahedra are packed to delimit hexagonal tunnels running along the c-direction. The structure of KPb4 (PO4)3 can be described by the distinction of the two types of channels.
•One with a small section, which corresponds to a mixed site (4f position), occupied by an
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equal number of Na+ and Pb2+ cations (Na and Pb2). The latter cations are coordinated to nine oxygen anions belonging to six distinct tetrahedra, and to three much further oxygen anions having almost the same elevation as Na and Pb2
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•The other with larger section (6h position), which is totally occupied by lead cations (Pb1). These cations are inserted into six fold sites that constitute the walls of the tunnels. Their
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coordination spheres are delimited by six oxygen ions common to five [PO4]3− tetrahedra. Analysis of the bond lengths in [PO4]3- tetrahedra determines the average value of the P-O distances (P-O2 = 1.525Å (2), P-O1 = 1.538 Å, P-O3=1.585 Å) is agreement monophosphate of that found for ions [14]. In addition, the O- P -O angles vary between 108.4 and 111.65 °, with a mean value (107.92 °) almost identical to that of a regular [ PO4]
3-
tetrahedron [14].
This can be confirmed by the four distances P-O, which are very close. In the structure of our apatite O3 has a special role: on one hand it concerns the longest P-O bond [P- O3= 1.585 Å] and secondly to the shorter length of Pb-O [Pb1 -O3 2.47 Å]. 3.2 Raman spectroscopy analysis 3
ACCEPTED MANUSCRIPT The Raman spectrum is analyzed with a view to study the vibrational modes of the phosphate groups. The factors that might be considered are the mass and the size of the cation. Factor group analysis [14] of KPb4(PO4)3 hexagonal structures (P63/m) shows that the normal modes of vibration can be classified among the irreducible representations of C6h as
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Γ=12Ag+8E1g+12E2g+8Au+12Bu+8Bg+12E1u+8E2u Where the internal mode contribution of the (PO4) groups to the Raman active vibrations is Γ P O 4 =6Ag(ν1+ν2+2ν3+2ν4)+3E1g(ν2+ν3+ν4)+6E2g(ν1+ν2+2ν3+2ν4)+3Au(ν2+ν3+ν4)+6E1u(ν1+ν2+ 2ν3+2ν4)
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Were the g and the u modes are Raman active.
The Raman spectrum is reported in Figure 3. The attribution of mode has been interpreted on
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the basis of similar compounds [15]. The observed bands may be classified as follows: K/PbO, Pb-O external modes as well as the rotations and translations of the internal modes of the [PO4]3- groups. A series of band was observed in (389–584) cm-1 region is attributed to O–P– O bending vibrations with ν2 from (389 to 424 cm-1) and ν4 from (582 to 584cm-1). In high frequency the bands observed is assigned to P–O stretching modes ν3 from (979 to 1026cm-1)
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and ν1 observed around 935cm-1. The wavenumbers and the corresponding assignments are listed in Table1.
3.3. Electrical property study
The Complex impedance spectroscopy is a useful method to analyze the frequency-dependent
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electric properties of a compound by the application of an ac signal as input perturbation [16]. Furthermore, this investigation confirms separation between the bulk, grain boundaries, and
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electrode electrolyte interface properties. The experimental data can be characterize in terms of three possible complex formalisms such as the complex impedance (Z*), the electric complex modulus (M*), and the complex permittivity (ε*). These parameters are related to each other as follows: Z*= Z’- jZ”
(1)
M*= M’+ jM”= jω0Z*
(2)
ε*= ε’+jε”= (M*)-1
(3)
Where Z’= |Z| cosΦ and Z”= |Z | sinΦ
(4)
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decentralization. The observed decentralization in Nyquist diagram is due to the heterogeneity of the sample which can be related to several phenomena such as the nature of the interface, the size of the crystals, the change of porosity [18]. This confirms that the type of relaxation in this material is non-Debye. The evolution of – Z″= f (Z′) curves show clearly the
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diminution of the resistance with the temperature. The conductivity of this material was deduced from the resistance R by the relation σ= [e/(R*S)] where e, S, and R are respectively the thickness, the surface of the pellets, and the resistance. Impedance spectra were fitted
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satisfactorily with an equivalent circuit model consisting by three elements. The first consists of parallel combination of resistance (Rg), capacitance (Cg) and a constant phase element CPEg, the second of parallel combination of resistance (Rgb) and a constant phase element CPEgb, whereas the third consists of capacitance (Celec). The confirmation of the choice of the circuit equivalent is justified by the figures (5, 6) which shows the variations of the
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experimental values of Z′ and Z″ versus the simulated ones using the parameters of the equivalent circuit model. The accumulation of these curves proves a linear behavior with a slope equal to the unity.
Electrical resistance for of the studied powder was assessed as a function of temperature,
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conductivity for the grain interior, grain boundary, and total conductivity was determined. The mechanism of ionic conduction in the KPb4(PO4)3 compound is well described by the
σ
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Arrhenius equation :
( g, gb,tot )
*
Ea( g, gb ,tot ) T = B( g , gb ,tot ) exp − K BT
(5)
Where Ea is activation energy for conduction, B is the pre-exponential factor, T is absolute temperature, and KB is Boltzmann constant. Figure 7 shows plots of Ln (σdcg,gb,tot T) versus 1000/T of bulk electrical conductivity (σg), grain boundary conductivity (σgb), and total conductivity (σtot). From this law, the activation energy for bulk, grain boundary, and total conductivity are about (0.98±0.05) eV, (1.10±0.05) eV, and (1.08±0.05) eV, respectively. In addition, this figure shows that the total conductivity 5
ACCEPTED MANUSCRIPT of the compound is less than the bulk conductivity but greater than the grain boundaries one, proving the existence of a partial blockage of the charge carriers by the grain boundaries. In other words, the conductivity of the compound is limited by the grain boundaries conductivity in the material.
3.4.1 Ac conductivity
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3.4. Frequency-dependent conductivity measurements
The ac conductivity of ionic materials at diffrent temperature is usually described by the universal power law Jonscher’s expressed as [19]:
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σ ac (ω ) = σ dc + Aω s
(6)
Where σdc is the sample direct current conductivity, A is a temperature dependent parameter
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determines the strength of polarisability and s is the slope of the high frequency dispersion data, is used to determine of interaction between mobile ions with the environments surrounding them.
To the dispersive region of the AC conductivity, the crossover frequency from DC is known as hopping frequency, ωh, and it can be elaborate forthwith from AC conductivity data using
σ ωh = dc A
1
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the following equation [20]. s
(7)
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The hopping frequency is temperature dependent obeying the Arrhenius relation:
− E hop KT
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ωh = ω0 exp
(8)
It can be seen frome Figure 8 that a linear relation can be deduced from the above equation when ln (ωh) versus 1000/T graph is plotted in the temperature range (659–708)K. Linear adjustment of this relation has given that the hopping activation energy is found to be Eh= (1.3±0.02) eV. This value is different to her given from dc conductivity; this presupposes that the mobility of the charge carrier is not due to a simple hopping mechanism in the investigated material. In the past few years, various scaling models have been proposed [21, 22]. Among them, we interested in the model of Ghosh [21]
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(9)
Figure 9present the variation σac/σdc versus ω/ωh at different temperatures of KPb4(PO4)3. It is apparent that the scaled conductivity σac/σdc consolidates on a single curve which involve that the conduction transport mechanism is independent of temperature [23].
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3.4.2 Theory of conduction mechanism
The plot of the exponent s at different temperatures for our sample is shown in Figure 10 with the straight line fit to the relation and shows an increase of s with increase of temperature.
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The electrical conduction mechanism has been resolved by temperature behaviour of the value of s based on the application of various models [24- 27] that have been proposed.
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The quantum mechanical tunneling (QMT) model: The exponent s is well-nigh equal to 0.8 and increases slightly with increasing temperature or it is independent of temperature. This model is inconsistent with results the obtained.
The correlated barrier hopping (CBH) model: Where charge carriers hop between sites separating them and predict a decrease in the value of s with increase in temperature .Is not
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suitable with the results of our materials.
The overlapping large polaron tunneling (OLPT) model: The exponent s depends on both frequency and temperature and it decline with the rise in temperature to a minimum value then increases with increasing temperature. This is not observed experimentally.
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The non-overlapping small polaron tunneling (NSPT) model: The exponent s which is temperature dependent increased with the increase in temperature. It seems plausible to use
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the NSPT model since this is the case observed in our data In the NSPT model, the frequency exponent s and the expression for the AC conductivity are established by: s = 1−
4 k BT Wm − k BT ln(ωτ 0 )
(10)
Where Wm is the polaron hopping energy and τ0 is a characteristic relaxation time which is in the order of an atom vibrational period τ0 =10-13 s. [28].
σ ac =
(π e ) ² kBTα −1ω N ( EF ) ² Rω4 12
(11) 7
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Rω =
1 1 Wm ln − 2α ωτ 0 kBT
(12)
Whither α-1 is the spatial extension of the polaron, N(EF) is the density of states near the
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Fermi level, and Rω is the tunneling distance. Figure 11 demonstrate the logarithm of the conductivity as a function temperature at different frequencies. It is evident from the plots that the theoretical calculations of the conductivity (fits) are in excellent accord well with the experimental data (symbol).
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The values of parameters N(EF), α and the tunneling distance Rω calculation from linear fit to the data points are shows in figure (12,13). When the frequency is increased the values of α
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and N(EF) are increased as well [29]. However, the values of Rω are decreased [30]. These results confirm that the conductivity increases with increase in frequency. As a matter of fact, in this model is apparent that the values of Rω are vary in the range of (3.91 Å to 2.21 Å) this values are comparable with the interatomic spacing K–K distances which was found to be 3.44(Å) [31, 32]. From this finding we can deduce that the conduction
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process is ensured by a small polaron along the [001] tunnels. 4. Conclusion
The potassium lead apatite KPb4(PO4)3 was synthesized by the solid-state reaction method and characterized by X-ray diffraction and Raman spectroscopy. Its structure has been
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determined by Rietveld, adopting the space group P63/m (ITA No. 176). The Raman spectrum is recorded and interpreted on the basis of the structural peculiarities of the [PO4]3- present in
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the crystal lattice. The performed studies allowed us to establish the electrical properties of KPb4(PO4)3 compound. Two semicircles are observed in the impedance plot, indicating the presence of two relaxations processes in the studied compound associated with the grain and grain boundary. Consequently, an equivalent electrical circuit for the electrochemical cell with KPb4(PO4)3 was proposed. The variation of AC conductivity as a function of frequency at different temperatures is found to obey Jonscher's universal power law. In addition the electrical conductivity of the title compound has been theoretically supported by the NSPT model. Acknowledgments
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ACCEPTED MANUSCRIPT This work is financially supported by the Ministry of Higher Education and Scientific Research of Tunisia. References [1]Y. Matsumura, S. Sugiyama, H. Hayashi, J B. Moat, J. Solid. Stat. Chem. 114 (1995) 138.
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[2] T. Suzuki, Gypsum. Lime 204 (1986) 314. [3] B. M.J. Smet, J. Mater. Chem. Phys. 16 (1987) 283. [4] G. Blasse, J. Mater. Chem. Phys. 16 (1987) 201.
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[5] M. Tachihante , D. Zanbon, J. C. Cousseins, J. Eur Solid State Inorg. Chem. 33 (1996) 713.
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[6] L. D. Deloach, S. A. Payne, L. K. Smith., W.L. Kway, W.F. Krupke, J. Opt. Soc. Am B : Opt. Phys. 11 (1994) 269.
[7] C. Ohtsuki, T. Kokubo, T. Yamamuro, J. Non-Cryst. Solids. 143 (1992) 8492. [8] L. Leon-Reina, M. E. Martin-Sedeno, E. R. Losilla, A. Caberza, M. Martinez- Lara, S. Bruque, F. M. B. Marques, D. V. Sheptvakov, M. A. G. Aranda, J Chem. Mater. 15 (2003)
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[10] B. Orayech, A. Faik, G. A. Lopez, O. Fabelo, J. M. Igartua J. Appl. Cryst. 48 (2015).
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[12] P.P Mokoena, I.M. Nagpure , V. Kumar, R. E. Kroo , E.J .Olivier , J. H. Neethling, H. C. Swart , O.M. Ntwaeaborw, J. Solid. Stat. Chem. 998 (2014) 1003. [13] M. El Koumiri, S Oishi, S Sato, L. El Ammari, B. Elouadi, J. Mater. Res. Bull. 35 (2000) 503. [14] M. Azrour, M. Azdouz, B. Manoun, R. Essehli, S. Benmokhtar, L. Bih, L. ElAmmari, A. Ezzahi, A. Ider, A.AitHou, J. Solid. Stat. Chem. 72 (2011) 1199. [15] S. Chemlal, A. Bouhaouss, M. Ferhat, J. C. Lacout, J. Chim. Phys. 88 (1991) 1901. 9
ACCEPTED MANUSCRIPT [16] S. Kulkarni , B.M. Nagabhushana , N. Parvatikar , A. Koppalkar ,C. Shivakumara , R. Damle, Materials Research Bullettin. 50 (2014) 197. [17] A. Muller, E.J. Baran, R.O. Carter, Struct. 26 (1976) 81. [18] Thesis Charlotte. Mellier. Université. Nantes (2011).
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[30] L.J. De Jongh, W.D. Van Amstel, A.R. Miedema, J. Physica. 58 (1972) 277. [31] EI. Get’man, S. N. Loboda, A.V. Ignatov, V. V. Prisedsky, M. A. B. Abdul Jabar, L.I.
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Ardanova, J. Inorg. Chem. 55 (2016) 2165.
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Figures Captions
Figure 1: The Rietveld refinement for the KPb4(PO4)3 sample at room temperature: The dotted line indicates experimental data and calculated data are represented by black continuous lines. The lowest curve in blue shows the difference between experimental and calculated patterns. The vertical bars in green indicate the Bragg positions. Figure 2: projection of the structure of KPb4(PO4)3 compound along [001]. Figure 3: Raman spectrum of KPb4(PO4)3 recorded at room temperature. Figure 4: Plots of the impedance data at several temperatures for KPb4(PO4)3 compound. Figure 5: Measured and simulated values of the real part of the complexes impedance of the KPb4(PO4)3 compound. 10
ACCEPTED MANUSCRIPT Figure 6: Plot of experimental values versus simulated values of imaginary part Z’’ KPb4(PO4)3. Figure 7: Temperature dependence of Ln (σdcT). Figure 8: Variations of ln (ωh) as a function of 1000/T of KPb4(PO4)3.
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Figure 9: Plot of (σac/σdc) versus (ω/ωh) at different temperatures of KPb4(PO4)3. Figure 10: Variation of the universal exponent s as a function of temperature.
Figure 11: Logarithm of the conductivity as a function of temperature at different frequencies of KPb4(PO4)3 sample .
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Figure 12: Variation of the parameters α (Å-1) and N(EF) (eV-1cm-3) according to the frequency (NSPT model).
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Figure 13: Variation of the parameter Rω(Å) according to the frequency (NSPT model). Table caption:
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Table 1 Assignments of observed Raman bands in KPb4(PO4)3.
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Assignments
64 85 128 158 205
s Vs m m m
389 424
m m
ν2 (PO43-)
545 572 584
m w s
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Intensity
External modes
935
s
979 1026
s m
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K/Pb-O, Pb-O
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ν4(PO43-)
ν1 (PO43-)
ν3(PO43-)
Vs: very strong, s: strong, m: medium and w: weak
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ν2: symmetetric stretching, ν4: antisymmetric stretching, ν1: symmetetric bending,
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ν3: antisymmetric bending.
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659K 667K 674K 683K 691K 699K 708K fit
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659K 667K 674K 683K 691K 699K 708K fit
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-4 Grain Grain Boundary Total conductivity Fit
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Figure 8
ac
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0,54
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0,52
0,48 650
660 s
670
M AN U
0,50
680
690
700
710
T(K)
AC C
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Figure 10
Figure 11 6
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10
32,2
3,0x10
32,0
Ln(NEf)
α
31,8
−1
10
2,5x10
10
2,0x10
-3
Ln(N )(eV cm )
31,6
10
31,2
-1
α(Å )
1,5x10
31,0
10
1,0x10
30,8
SC
Ef
-1
RI PT
31,4
30,6
30,2 7
8
9
M AN U
30,4
10
11
12
13
9
5,0x10
0,0
14
Ln(f)Hz
AC C
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Figure 12
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RI PT
4,0
SC
3,0
M AN U
Rω(Å)
3,5
2,0
TE D
2,5
6
9
12
15
Figure 13
AC C
EP
Ln(f)Hz
8
ACCEPTED MANUSCRIPT Highlights
This paper deals with electrical properties and conduction mechanisms of the orthophosphate compound KPb4(PO4)3.
AC C
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TE D
M AN U
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- Ac conductivity data affirm that for high frequencies σac is proportional to ωs. - The non-overlapping small polaron tunneling is the appropriate conduction mechanism of KPb4(PO4)3 compound.