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Ac electrical properties and dielectric relaxation of the new mixed crystal (Na0.8Ag0.2)2PbP2O7
Journal of Alloys and Compounds 486 (2009) 299–303
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Ac electrical properties and dielectric relaxation of the new mixed crystal (Na0.8 Ag0.2 )2 PbP2 O7 B. Louati ∗ , F. Hlel, K. Guidara Laboratoire de l’état solide, Faculté des Sciences de Sfax, B. P. 802, 3018 Sfax, Tunisia
a r t i c l e
i n f o
Article history: Received 23 December 2008 Received in revised form 18 June 2009 Accepted 19 June 2009 Available online 2 July 2009 Keywords: (Na0.8 Ag0.2 )2 PbP2 O7 X-ray diffraction ac conductivity Dielectric measurements
a b s t r a c t The new diphosphate compound containing sodium, silver and lead, (Na0.8 Ag0.2 )2 PbP2 O7 , has been synthesized and characterized by X-ray diffraction (XRD) and electrical technique. (Na0.8 Ag0.2 )2 PbP2 O7, is of triclinic symmetry with the space group P1¯ . The unit cell parameters are: a = 5.511(3) Å, b = 6.910(4) Å, c = 9.457(6) Å, ˛ = 105.72(4)◦ , ˇ = 96.81(5)◦ , = 108.40(4)◦ and V = 320.6(4) Å3 . The ac conductivity and dielectric properties of (Na0.8 Ag0.2 )2 PbP2 O7 compound have been studied at temperatures in the range 573–692 K and frequencies (300 Hz to 5 MHz). The ac conductivity data reveal that for high frequency ac (ω) is proportional to ωn . The values of the frequency exponent, n, were found to increase by increasing temperature. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Inorganic phosphates cover a large class of diverse materials whose applications include: catalysts, solid electrolytes for batteries [1–3], linear and non-linear optical components [4,5] and laser materials [6,7]. However, the study of phosphates has become more popular particularly, after the development of NASICON groups of fast ionic conductors [8–10]. Double phosphates of A2 BP2 O7 (A = alkaline ion and B = divalent cation) form a large family of materials [11–13]. The structures of these phosphates are diverse, and it is difficult to classify these materials as a function of classical fundamental criteria such as cation size, coordination number or chemical bonding. The Na2 PbP2 O7 crystal is one of the inorganic phosphates. The double phosphates Na2 PbP2 O7 have been prepared by melting using phosphate flux. Single crystals obtained are transparent and of parallelepipedic form. Na2 PbP2 O7 is of triclinic symmetry with the space group P1¯ (Z = 2) and the unit cell parame´˚ b = 6.942(4) A, ´˚ c = 9.440(4) A, ´˚ ˛ = 105.58(2)◦ , ters are a = 5.533(4) A,
ˇ = 97.03(4)◦ , = 108.32(4)◦ and V = 323.4(3)Å3 . The structure of Na2 PbP2 O7 consists of lamina parallel to (0 0 1) plan, constituting the tridimensional framework. An investigation of ionic conductivity properties revealed that the number of charge carriers is very small and the conduction in Na2 PbP2 O7 is low. A comparative study of electrical properties of ceramic and glassy Na2 PbP2 O7 has shown
∗ Corresponding author. E-mail address: bassem [email protected] (B. Louati). 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.06.148
that no conductivity notable variation is observed as a function of the crystalline or glassy state of Na2 PbP2 O7 [14]. Single crystals of Ag2 PbP2 O7 are isotype to Na2 PbP2 O7 . The unit ´˚ b = 7.008(8) A, ´˚ c = 10.018(9) A, ´˚ cell parameters are: a = 5.502(6) A, ˛ = 106.63(6)◦ , ˇ = 93.89(7)◦ , = 110.68(6)◦ and V = 340.8(6) Å3 . Ionic conductivity measurements of the crystalline Ag2 PbP2 O7 phase were carried out on powder samples. The Ag2 PbP2 O7 is characterized by a smaller E activation energy, a smaller Kohlrausch exponent, ˇ, and a slightly higher value of the glass decoupling index, log R (Tg ), resulting in a higher conductivity for the Agmaterial than for the Na-material. The better properties obtained for Ag2 PbP2 O7 can be attributed to the higher polarizability of Ag+ ions, more easily deformed (d10 configuration) to pass through the bottlenecks and consequently more mobile than the Na+ ions (rare gas type configuration) [15]. The aim of this study is to determine the influence of silver content on the electrical conductivity of the Na2 PbP2 O7 compound. The study focuses on the new mixed compound of composition (Na0.8 Ag0.2 )2 PbP2 O7 . The ac conductivity, ac , of the (Na0.8 Ag0.2 )2 PbP2 O7 sample was measured as a function of frequency and temperature with a view to study some electrical features. 2. Chemical preparation The (Na0.8 Ag0.2 )2 PbP2 O7 compound was synthesized by the classic ceramic method. The preparation technique which involves as a first step the mixing powders in an appropriate ratios and careful grinding using a mortar and pestle. The powders are pres-
300
B. Louati et al. / Journal of Alloys and Compounds 486 (2009) 299–303
Fig. 1. X-ray diffractogram of (Na0.8 Ag0.2 )2 PbP2 O7 in the 2 range 5–60◦ .
surised into pellets, heated once at 623 K for four hours and then at 800 K. At room temperature, the sample was characterized by its Xray powder pattern using a Phillips powder diffractometer PW ´˚ over a wide range of Bragg 1710 with CuK␣ radiation ( = 1.5405 A) ◦ ◦ angles (5 ≤ 2 ≤ 60 ). A pallet of about 8 mm diameter and about 1.8 mm thickness was used in the electrical measurements. Vacuum evaporated gold was used as electrode material. The ac conductivity measurements were performed with a Tegam 3550 impedance analyser (300 Hz to 5 MHz) which was also interfaced with a computer and a temperature controller. Measurements were carried out at temperatures from 573 K to 692 K.
Fig. 2. (a) and (b): The Cole–Cole plots of the impedance at several temperatures.
following expression
B=
3. Results and discussion 3.1. Crystalline parameters At room temperature, all the X-ray peaks were indexed in the triclinic system with P1¯ space group (a = 5.511(3) Å, b = 6.910(4) Å, c = 9.457(6) Å, ˛ = 105.72(4)◦ , ˇ = 96.81(5)◦ , = 108.40(4)◦ and V = 320.6(4) Å3 ) (Fig. 1). 3.2. Electrical properties
e2 a2h ϑ0 6k
N(T ) exp
S
k
(2)
where ah is the hopping distance, ϑ0 is an attempt frequency to overcome the potential barrier, N(T) is the charge carrier concentration and S is the migration entropy. The ac activation energy, E , is (0.72 ± 0.02) eV. In Table 1 we summarize the results of electrical study of Na2 PbP2 O7 [14], Ag2 PbP2 O7 [15] and (Na0.8 Ag0.2 )2 PbP2 O7 compounds. We note that the activation energy of the mixed compound is less than those of the parental compounds. However, the conduc-
Fig. 2(a) and (b) shows the plot of (−Z ) versus Z taken over the frequency range (300 Hz to 5 MHz) at different temperatures 573 K ≤ T ≤ 692 K. All the semicircles exhibit some depression instead of a semicircle centered on the x-axis. Such behaviour is indicative of non-Debye type of relaxation and it also manifests that there is a distribution of relaxation time instead of a single relaxation time in the material [16]. The values of bulk resistance (R) at different temperatures have been obtained from the intercept of the semicircular arcs on the real axis (Z ). It is observed that (R) decreases with rise in the temperature. The conductivity is obtained from (R) by means of the relation: =
e RS
(1)
where e/S represents the sample geometrical ratio. The temperature dependence of the conductivity is represented in Fig. 3 in the form of Ln (T) versus 1000/T. An Arrhenius type behaviour,T = Bexp(−E /kT), is shown in the temperature range 573 K ≤ T ≤ 692 K. The preexponential factor B can be given by the
Fig. 3. Dependence of Ln(T) on temperature for (Na0.8 Ag0.2 )2 PbP2 O7 compound.
B. Louati et al. / Journal of Alloys and Compounds 486 (2009) 299–303
301
Table 1 Electrical parameters of (Na0.8 Ag0.2 )2 PbP2 O7 and of ceramic and glassy Na2 PbP2 O7 and Ag2 PbP2 O7.
E (±0.02) eV (10−6 −1 cm−1 )
Na2 PbP2 O7 [14]
(Na0.8 Ag0.2 )2 PbP2 O7
Ag2 PbP2 O7 [15]
Ceramic
Glass
Ceramic
Ceramic
Glass
0.90 4
1.04 5
0.71 7.7
0.78 45
0.77 1189
tivities of these compounds at 300 ◦ C verify: Na2 PbP2 O7 < (Na0.8 Ag0.2 )2 PbP2 O7 < Ag2 PbP2 O7 The partial substitution of sodium by silver induces the reduction of activation energy and an increase in conductivity. 3.3. ac conductivity analysis The frequency variation of ac conductivity, ac (ω), at various temperatures is shown in Fig. 4. The ac (ω) increases with increase in frequency, which is a characteristic of ωn . The nature and mechanism of the conductivity dispersion in solids are generally analyzed using Jonscher’s power law; ac = dc + Aωn , where dc is the dc conductivity in particular range of temperature, A is a temperature dependent parameter and n is the temperature dependent exponent in the range of 0 ≤ n ≤ 1 [17–19]. The exponent n represents the degree of interaction between mobile ions with the lattices around them and the prefactor exponent A determines the strength of polarizability. The detailed analysis of ac (ω) of (Na0.8 Ag0.2 )2 PbP2 O7 suggests that the power law is obeyed. It is confirmed by the typical fit of the above equation to the experimental data (Fig. 4). According to Jonscher, the origin of frequency dependence of conductivity lies in the relaxation phenomenon arising due to mobile charge carriers. The low frequency dispersion attributes to the ac conductivity whereas the frequency independent plateau region of the conductivity pattern corresponds to dc conductivity of the material. The temperature at which grain resistance dominates over grain boundary resistance is marked by a change in slope of ac conductivity with frequency. The frequency at which change of slope takes place is known as the critical or hopping frequency. It corresponds to polaron hopping of charge species. The hopping frequency shifts to higher frequency side on increasing temperature. The charge species that have been accumulated at the grain boundaries have sufficient energy to jump over the barrier on increasing temperature [20,21].
Fig. 4. The dependence of ac conductivity ac (ω) on angular frequency at different temperatures for (Na0.8 Ag0.2 )2 PbP2 O7 sample.
Fig. 5. Temperature dependence of the frequency exponent n.
Fig. 5 shows the variation of n with temperature, which increases with temperature (0.47 ≤ n ≤ 0.69). The exponent is a measure of degree of interaction with the environment. Jonscher has shown that a non-zero n in the dispersive region of conductivity is due to the energy stored in the short-range collective motion of ions. A higher n implies that large energy is stored in such collective motions. In this work, exponent n increases with increasing temperature. Some glasses investigated by Ganguli et al. [22] exhibit similar trend for n as a function of temperature. Presently, we have no full explanation of this behaviour. A plot of −ln A against n (Fig. 6) indicates a linear temperatureindependent and structure insensitive correlation between the values of these two parameters. Such behaviour was observed in different types of materials and varied transport mechanism [23–25]. In the past few years, different scaling models have been proposed [26–29]. Among these models, we indicated the Ghosh’s model: ac (ω) =f dc
ω ωh
where h =( dc /A)n is used as scaling parameter for the frequency axis, is expected to be more appropriate for scaling the conductivity spectra of ionic conductors, since it takes into account the dependence of the conductivity spectra on structure and the pos-
Fig. 6. Correlation between–ln(A) and n. The line was best fitted to the experimental data points.
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B. Louati et al. / Journal of Alloys and Compounds 486 (2009) 299–303
Fig. 7. Plot of (/ dc ) versus (ω/ωh ) at different temperature.
Fig. 10. Variation of loss tangent (tan ı) with angular frequency at different temperatures.
carriers in the present compound is independent of temperature [30]. Fig. 8 shows the variation of ac with inverse of absolute temperature (1000/T) of (Na0.8 Ag0.2 )2 PbP2 O7 at different frequencies. The nature variation of ac over a wide temperature range supports the thermally activated transport of properties of the materials obeying Arrhenius equation: T = Bexp(−E /kT). It is observed that the ac conductivity of the material increases with rise in temperature, and shows the negative temperature coefficient of resistance behaviour. Fig. 9 shows the frequency dependence of the ac conduction activation energy for the conduction region. However, E remains constant in the low frequency range. At high frequency it decreases with increasing frequency. The obtained ac activation energy of the sample at low frequency is 0.72 eV. The activation energy involves the activation energies of formation of the vacant sites and migration of the mobile carriers. 3.4. Dielectric studies Fig. 8. Plot of ac conductivity versus 1000/T at different frequencies.
sible changes of the hopping distance experienced by the mobile ions [29]. Scaling the conductivity spectra for (Na0.8 Ag0.2 )2 PbP2 O7 sample in this way at different temperatures, merges on a single curve (Fig. 7) which implies that the relaxation dynamics of charge
Fig. 10 exhibits loss tangent (tan ı) variation with angular frequency and temperatures. The tangent loss peak showed a continuous trend of shifting towards high frequencies with rise in temperature. The tan ı increases with further rise in frequency, and shows a maximum at particular frequencies (fp ) for different tem-
Fig. 9. Frequency dependence of the ac activation energy of conduction.
Fig. 11. Temperature dependence of log (fp ) for (Na0.8 Ag0.2 )2 PbP2 O7 .
B. Louati et al. / Journal of Alloys and Compounds 486 (2009) 299–303
peratures because the active component (ohmic) of the current increases more rapidly than its reactive component (capacitive). At higher frequencies tan ı decreases with increasing frequency because the active component of the current is practically independent of frequency and the reactive component increases in proportion to the frequency [31]. The temperature dependence of (fp ) is plotted in Fig. 11. It is well described by the Arrhenius relation, fp = f0 exp(–Em /kT), where Em is the activation energy for conductivity, k is the Boltzmann constant and T is the temperature. The activation energy Em obtained from the tan ı spectra is about (0.68 ± 0.01) eV. The values of E calculated from conductivity and Em obtained from the tan ı spectra are close. 4. Conclusions In summary, in this work we have synthesized a new diphosphate compound of composition (Na0.8 Ag0.2 )2 PbP2 O7 by the classic ceramic method. The sample crystallizes in triclinic symmetry with P1¯ space group. The ac conductivity of (Na0.8 Ag0.2 )2 PbP2 O7 material was studied as a function of frequency and temperature ranges (300 Hz to 5 MHz) and (573–692 K), respectively. The ac conductivity showed a variation with frequency and it was found to obey Jonscher’s universal power law at different temperatures with n varies between 0.47 and 0.69. The activation energy of the compound was found to be (0.71 ± 0.02) eV for conduction process. References [1] L. Tortet, J.R. Gavarri, G. Nihoul, A.J. Dianoux, J. Solid State Ionics 97 (1997) 253. [2] B. Louati, K. Guidara, M. Gargouri, Physica Status Solidi B 241 (2004) 1994.
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[3] B. Louati, M. Gargouri, K. Guidara, T. Mhiri, J. Phys. Chem. Sol. 66 (2005) 762. [4] K. Sasaki, N. Ohno, Nonlinear Opt. 29 (2002) 615. [5] T. Fuyuki, K. Sasaki1, N. Ohno, J. Luminescence 112 (2005) 250. [6] H.G. Danielmeyer, G. Huber, W.W. Kruhler, J.F. Jesser, Appl. Phys. 2 (1973) 335. [7] H.P. Weber, T.C. Damen, H.G. Danielmeyer, C.C. Tofield, Appl. Phys. Lett. 22 (1973) 534. [8] H.Y.-P. Hong, Mater. Res. Bull. 11 (1976) 173. [9] J.B. Goodenough, H.Y.-P. Hong, J.P. Kafalas, Mater. Res. Bull. 11 (1976) 203. [10] J.P. Kafalas, R.J. Cava, in: P. Vashishta, J.N. Mundy, G.K. Shenoy (Eds.), Fast Transport in Solids, Elsevier, North-Holland, 1979, p. 419. [11] F. Erragh, A. Boukhari, E.M. Holt, Acta Crystallogr. C54 (1998) 1373. [12] A. El Maadi, A. Boukhari, E.M. Holt, J. Chem. Crystallogr. 25 (1995) 531. [13] F. Erragh, A. Boukhari, B. Elouadi, F. Abraham, J. Solid State Chem. 120 (1995) 23. [14] N. Dridi, A. Boukhari, J.M. Réau, E. Arbib, E.M. Holt, Solid State Ionics 127 (2000) 141. [15] N. Dridi, A. Boukhari, J.M. Réau, E. Arbib, E.M. Holt, Mater. Lett. 47 (2001) 212. [16] S. Sen, R.N.P. Choudhary, P. Pramanik, Phys. B 387 (2007) 56. [17] R.M. Hill, A.K. Jonscher, J. Non-Cryst. Solids 32 (1979) 53. [18] N.F. Mott, E.A. Davis, Electronic Processes in Non-Crystalline Materials, second ed., Clarendon Press, Oxford, 1979. [19] R.H. Chen, R.Y. Chang, S.C. Shern, J. Phys. Chem. Solids 63 (2002) 2069. [20] V. Biju, M.A. Khadar, J. Mater. Sci. 38 (2003) 4055. [21] S. Kurien, J. Mathew, S. Sebastian, S.N. Potty, K.C. George, Mater. Chem. Phys. 98 (2006) 470. [22] M. Ganguli, M.H. Bhat, K.J. Rao, Mater. Res. Bull. 34 (1999) 1757. [23] A.N. Papathanassiou, Mater. Lett. 59 (2005) 1634. [24] Z.C. Cramer, S. Brunklaus, E. Ratai, Y. Gao, Phys. Rev. Lett. 91 (2003) 266601. [25] A.N. Papathanassiou, J. Phys. Chem. Solids 66 (2005) 1849. [26] B. Roling, A. Happe, K. Funke, M.D. Ingram, Phys. Rev. Lett. 78 (1997) 2160. [27] D.L. Sidebottom, Phys. Rev. Lett. 82 (1999) 3653. [28] T.B. Schroder, J.C. Dyre, Phys. Rev. Lett. 84 (2000) 310. [29] A. Ghosh, A. Pan, Phys. Rev. Lett. 84 (2000) 2188. [30] A. Pan, A. Ghosh, Phys. Rev. B 66 (2002) 12301. [31] S. Chopra, S. Sharma, T.C. Goel, R.G. Mendiratta, Solid State Commun. 127 (2003) 299.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Ac electrical properties and dielectric relaxation of the new mixed crystal (Na0.8 Ag0.2 )2 PbP2 O7 B. Louati ∗ , F. Hlel, K. Guidara Laboratoire de l’état solide, Faculté des Sciences de Sfax, B. P. 802, 3018 Sfax, Tunisia
a r t i c l e
i n f o
Article history: Received 23 December 2008 Received in revised form 18 June 2009 Accepted 19 June 2009 Available online 2 July 2009 Keywords: (Na0.8 Ag0.2 )2 PbP2 O7 X-ray diffraction ac conductivity Dielectric measurements
a b s t r a c t The new diphosphate compound containing sodium, silver and lead, (Na0.8 Ag0.2 )2 PbP2 O7 , has been synthesized and characterized by X-ray diffraction (XRD) and electrical technique. (Na0.8 Ag0.2 )2 PbP2 O7, is of triclinic symmetry with the space group P1¯ . The unit cell parameters are: a = 5.511(3) Å, b = 6.910(4) Å, c = 9.457(6) Å, ˛ = 105.72(4)◦ , ˇ = 96.81(5)◦ , = 108.40(4)◦ and V = 320.6(4) Å3 . The ac conductivity and dielectric properties of (Na0.8 Ag0.2 )2 PbP2 O7 compound have been studied at temperatures in the range 573–692 K and frequencies (300 Hz to 5 MHz). The ac conductivity data reveal that for high frequency ac (ω) is proportional to ωn . The values of the frequency exponent, n, were found to increase by increasing temperature. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Inorganic phosphates cover a large class of diverse materials whose applications include: catalysts, solid electrolytes for batteries [1–3], linear and non-linear optical components [4,5] and laser materials [6,7]. However, the study of phosphates has become more popular particularly, after the development of NASICON groups of fast ionic conductors [8–10]. Double phosphates of A2 BP2 O7 (A = alkaline ion and B = divalent cation) form a large family of materials [11–13]. The structures of these phosphates are diverse, and it is difficult to classify these materials as a function of classical fundamental criteria such as cation size, coordination number or chemical bonding. The Na2 PbP2 O7 crystal is one of the inorganic phosphates. The double phosphates Na2 PbP2 O7 have been prepared by melting using phosphate flux. Single crystals obtained are transparent and of parallelepipedic form. Na2 PbP2 O7 is of triclinic symmetry with the space group P1¯ (Z = 2) and the unit cell parame´˚ b = 6.942(4) A, ´˚ c = 9.440(4) A, ´˚ ˛ = 105.58(2)◦ , ters are a = 5.533(4) A,
ˇ = 97.03(4)◦ , = 108.32(4)◦ and V = 323.4(3)Å3 . The structure of Na2 PbP2 O7 consists of lamina parallel to (0 0 1) plan, constituting the tridimensional framework. An investigation of ionic conductivity properties revealed that the number of charge carriers is very small and the conduction in Na2 PbP2 O7 is low. A comparative study of electrical properties of ceramic and glassy Na2 PbP2 O7 has shown
∗ Corresponding author. E-mail address: bassem [email protected] (B. Louati). 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.06.148
that no conductivity notable variation is observed as a function of the crystalline or glassy state of Na2 PbP2 O7 [14]. Single crystals of Ag2 PbP2 O7 are isotype to Na2 PbP2 O7 . The unit ´˚ b = 7.008(8) A, ´˚ c = 10.018(9) A, ´˚ cell parameters are: a = 5.502(6) A, ˛ = 106.63(6)◦ , ˇ = 93.89(7)◦ , = 110.68(6)◦ and V = 340.8(6) Å3 . Ionic conductivity measurements of the crystalline Ag2 PbP2 O7 phase were carried out on powder samples. The Ag2 PbP2 O7 is characterized by a smaller E activation energy, a smaller Kohlrausch exponent, ˇ, and a slightly higher value of the glass decoupling index, log R (Tg ), resulting in a higher conductivity for the Agmaterial than for the Na-material. The better properties obtained for Ag2 PbP2 O7 can be attributed to the higher polarizability of Ag+ ions, more easily deformed (d10 configuration) to pass through the bottlenecks and consequently more mobile than the Na+ ions (rare gas type configuration) [15]. The aim of this study is to determine the influence of silver content on the electrical conductivity of the Na2 PbP2 O7 compound. The study focuses on the new mixed compound of composition (Na0.8 Ag0.2 )2 PbP2 O7 . The ac conductivity, ac , of the (Na0.8 Ag0.2 )2 PbP2 O7 sample was measured as a function of frequency and temperature with a view to study some electrical features. 2. Chemical preparation The (Na0.8 Ag0.2 )2 PbP2 O7 compound was synthesized by the classic ceramic method. The preparation technique which involves as a first step the mixing powders in an appropriate ratios and careful grinding using a mortar and pestle. The powders are pres-
300
B. Louati et al. / Journal of Alloys and Compounds 486 (2009) 299–303
Fig. 1. X-ray diffractogram of (Na0.8 Ag0.2 )2 PbP2 O7 in the 2 range 5–60◦ .
surised into pellets, heated once at 623 K for four hours and then at 800 K. At room temperature, the sample was characterized by its Xray powder pattern using a Phillips powder diffractometer PW ´˚ over a wide range of Bragg 1710 with CuK␣ radiation ( = 1.5405 A) ◦ ◦ angles (5 ≤ 2 ≤ 60 ). A pallet of about 8 mm diameter and about 1.8 mm thickness was used in the electrical measurements. Vacuum evaporated gold was used as electrode material. The ac conductivity measurements were performed with a Tegam 3550 impedance analyser (300 Hz to 5 MHz) which was also interfaced with a computer and a temperature controller. Measurements were carried out at temperatures from 573 K to 692 K.
Fig. 2. (a) and (b): The Cole–Cole plots of the impedance at several temperatures.
following expression
B=
3. Results and discussion 3.1. Crystalline parameters At room temperature, all the X-ray peaks were indexed in the triclinic system with P1¯ space group (a = 5.511(3) Å, b = 6.910(4) Å, c = 9.457(6) Å, ˛ = 105.72(4)◦ , ˇ = 96.81(5)◦ , = 108.40(4)◦ and V = 320.6(4) Å3 ) (Fig. 1). 3.2. Electrical properties
e2 a2h ϑ0 6k
N(T ) exp
S
k
(2)
where ah is the hopping distance, ϑ0 is an attempt frequency to overcome the potential barrier, N(T) is the charge carrier concentration and S is the migration entropy. The ac activation energy, E , is (0.72 ± 0.02) eV. In Table 1 we summarize the results of electrical study of Na2 PbP2 O7 [14], Ag2 PbP2 O7 [15] and (Na0.8 Ag0.2 )2 PbP2 O7 compounds. We note that the activation energy of the mixed compound is less than those of the parental compounds. However, the conduc-
Fig. 2(a) and (b) shows the plot of (−Z ) versus Z taken over the frequency range (300 Hz to 5 MHz) at different temperatures 573 K ≤ T ≤ 692 K. All the semicircles exhibit some depression instead of a semicircle centered on the x-axis. Such behaviour is indicative of non-Debye type of relaxation and it also manifests that there is a distribution of relaxation time instead of a single relaxation time in the material [16]. The values of bulk resistance (R) at different temperatures have been obtained from the intercept of the semicircular arcs on the real axis (Z ). It is observed that (R) decreases with rise in the temperature. The conductivity is obtained from (R) by means of the relation: =
e RS
(1)
where e/S represents the sample geometrical ratio. The temperature dependence of the conductivity is represented in Fig. 3 in the form of Ln (T) versus 1000/T. An Arrhenius type behaviour,T = Bexp(−E /kT), is shown in the temperature range 573 K ≤ T ≤ 692 K. The preexponential factor B can be given by the
Fig. 3. Dependence of Ln(T) on temperature for (Na0.8 Ag0.2 )2 PbP2 O7 compound.
B. Louati et al. / Journal of Alloys and Compounds 486 (2009) 299–303
301
Table 1 Electrical parameters of (Na0.8 Ag0.2 )2 PbP2 O7 and of ceramic and glassy Na2 PbP2 O7 and Ag2 PbP2 O7.
E (±0.02) eV (10−6 −1 cm−1 )
Na2 PbP2 O7 [14]
(Na0.8 Ag0.2 )2 PbP2 O7
Ag2 PbP2 O7 [15]
Ceramic
Glass
Ceramic
Ceramic
Glass
0.90 4
1.04 5
0.71 7.7
0.78 45
0.77 1189
tivities of these compounds at 300 ◦ C verify: Na2 PbP2 O7 < (Na0.8 Ag0.2 )2 PbP2 O7 < Ag2 PbP2 O7 The partial substitution of sodium by silver induces the reduction of activation energy and an increase in conductivity. 3.3. ac conductivity analysis The frequency variation of ac conductivity, ac (ω), at various temperatures is shown in Fig. 4. The ac (ω) increases with increase in frequency, which is a characteristic of ωn . The nature and mechanism of the conductivity dispersion in solids are generally analyzed using Jonscher’s power law; ac = dc + Aωn , where dc is the dc conductivity in particular range of temperature, A is a temperature dependent parameter and n is the temperature dependent exponent in the range of 0 ≤ n ≤ 1 [17–19]. The exponent n represents the degree of interaction between mobile ions with the lattices around them and the prefactor exponent A determines the strength of polarizability. The detailed analysis of ac (ω) of (Na0.8 Ag0.2 )2 PbP2 O7 suggests that the power law is obeyed. It is confirmed by the typical fit of the above equation to the experimental data (Fig. 4). According to Jonscher, the origin of frequency dependence of conductivity lies in the relaxation phenomenon arising due to mobile charge carriers. The low frequency dispersion attributes to the ac conductivity whereas the frequency independent plateau region of the conductivity pattern corresponds to dc conductivity of the material. The temperature at which grain resistance dominates over grain boundary resistance is marked by a change in slope of ac conductivity with frequency. The frequency at which change of slope takes place is known as the critical or hopping frequency. It corresponds to polaron hopping of charge species. The hopping frequency shifts to higher frequency side on increasing temperature. The charge species that have been accumulated at the grain boundaries have sufficient energy to jump over the barrier on increasing temperature [20,21].
Fig. 4. The dependence of ac conductivity ac (ω) on angular frequency at different temperatures for (Na0.8 Ag0.2 )2 PbP2 O7 sample.
Fig. 5. Temperature dependence of the frequency exponent n.
Fig. 5 shows the variation of n with temperature, which increases with temperature (0.47 ≤ n ≤ 0.69). The exponent is a measure of degree of interaction with the environment. Jonscher has shown that a non-zero n in the dispersive region of conductivity is due to the energy stored in the short-range collective motion of ions. A higher n implies that large energy is stored in such collective motions. In this work, exponent n increases with increasing temperature. Some glasses investigated by Ganguli et al. [22] exhibit similar trend for n as a function of temperature. Presently, we have no full explanation of this behaviour. A plot of −ln A against n (Fig. 6) indicates a linear temperatureindependent and structure insensitive correlation between the values of these two parameters. Such behaviour was observed in different types of materials and varied transport mechanism [23–25]. In the past few years, different scaling models have been proposed [26–29]. Among these models, we indicated the Ghosh’s model: ac (ω) =f dc
ω ωh
where h =( dc /A)n is used as scaling parameter for the frequency axis, is expected to be more appropriate for scaling the conductivity spectra of ionic conductors, since it takes into account the dependence of the conductivity spectra on structure and the pos-
Fig. 6. Correlation between–ln(A) and n. The line was best fitted to the experimental data points.
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Fig. 7. Plot of (/ dc ) versus (ω/ωh ) at different temperature.
Fig. 10. Variation of loss tangent (tan ı) with angular frequency at different temperatures.
carriers in the present compound is independent of temperature [30]. Fig. 8 shows the variation of ac with inverse of absolute temperature (1000/T) of (Na0.8 Ag0.2 )2 PbP2 O7 at different frequencies. The nature variation of ac over a wide temperature range supports the thermally activated transport of properties of the materials obeying Arrhenius equation: T = Bexp(−E /kT). It is observed that the ac conductivity of the material increases with rise in temperature, and shows the negative temperature coefficient of resistance behaviour. Fig. 9 shows the frequency dependence of the ac conduction activation energy for the conduction region. However, E remains constant in the low frequency range. At high frequency it decreases with increasing frequency. The obtained ac activation energy of the sample at low frequency is 0.72 eV. The activation energy involves the activation energies of formation of the vacant sites and migration of the mobile carriers. 3.4. Dielectric studies Fig. 8. Plot of ac conductivity versus 1000/T at different frequencies.
sible changes of the hopping distance experienced by the mobile ions [29]. Scaling the conductivity spectra for (Na0.8 Ag0.2 )2 PbP2 O7 sample in this way at different temperatures, merges on a single curve (Fig. 7) which implies that the relaxation dynamics of charge
Fig. 10 exhibits loss tangent (tan ı) variation with angular frequency and temperatures. The tangent loss peak showed a continuous trend of shifting towards high frequencies with rise in temperature. The tan ı increases with further rise in frequency, and shows a maximum at particular frequencies (fp ) for different tem-
Fig. 9. Frequency dependence of the ac activation energy of conduction.
Fig. 11. Temperature dependence of log (fp ) for (Na0.8 Ag0.2 )2 PbP2 O7 .
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peratures because the active component (ohmic) of the current increases more rapidly than its reactive component (capacitive). At higher frequencies tan ı decreases with increasing frequency because the active component of the current is practically independent of frequency and the reactive component increases in proportion to the frequency [31]. The temperature dependence of (fp ) is plotted in Fig. 11. It is well described by the Arrhenius relation, fp = f0 exp(–Em /kT), where Em is the activation energy for conductivity, k is the Boltzmann constant and T is the temperature. The activation energy Em obtained from the tan ı spectra is about (0.68 ± 0.01) eV. The values of E calculated from conductivity and Em obtained from the tan ı spectra are close. 4. Conclusions In summary, in this work we have synthesized a new diphosphate compound of composition (Na0.8 Ag0.2 )2 PbP2 O7 by the classic ceramic method. The sample crystallizes in triclinic symmetry with P1¯ space group. The ac conductivity of (Na0.8 Ag0.2 )2 PbP2 O7 material was studied as a function of frequency and temperature ranges (300 Hz to 5 MHz) and (573–692 K), respectively. The ac conductivity showed a variation with frequency and it was found to obey Jonscher’s universal power law at different temperatures with n varies between 0.47 and 0.69. The activation energy of the compound was found to be (0.71 ± 0.02) eV for conduction process. References [1] L. Tortet, J.R. Gavarri, G. Nihoul, A.J. Dianoux, J. Solid State Ionics 97 (1997) 253. [2] B. Louati, K. Guidara, M. Gargouri, Physica Status Solidi B 241 (2004) 1994.
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