Dielectric Studies And Cole-Cole Plot Analysis Of Silver .
Vol. 3(1), pp.1-9, February 2014Available online at http://www.accessinterjournals.org/ajpsISSN 2354-2438 Copyright 2013 Access International JournalsFull Length Research PaperDielectric studies and Cole-Cole plot analysis of silverion conducting glassesFathy Salman, Reda Khalil and Hany HazaaPhysics Department, Faculty of Science, Benha University, Benha, Egypt.Corresponding author. E-mail: FATHY.SALMAN@fsc.bu.edu.egTel: 201005357846Accepted 12 December, 2013Silver ion conducting glasses are the first solid electrolytes to be used in solid-state electro-chemicaldevices for low specific energy applications. These glasses represent potential candidates for energystorage devices and solid state batteries. Silver phosphate glasses of the compositions xAgI – 40Ag2O(50-x)P2O5-10Fe2O3 mole% [x 0,5, 10,15, 20, 30] were prepared by quenching method and studied bymeans of AC measurements in the frequency range (50 Hz-5 MHz) and temperature range (303 -550 K).Dielectric peaks appeared between glass transition T g and the crystallization temperature T c. Thedielectric peaks change against temperature agree well with the exothermic peak change in DTA results.The study of frequency dependence of both dielectric constant ε' and dielectric loss ε" showed adecrease of both quantities with increasing frequency indicating a normal behavior of dielectrics. ColeCole plots are drawn with ε' and ε". From the Cole-Cole plot parameters like optical dielectric constant,static dielectric constant, average relaxation time, and molecular relaxation time are evaluated.Key words: Dielectric properties, Cole-Cole plot, silver ion conducting glasses.INTRODUCTIONSuperionic conductors of AgI – Ag2O – P2O5 have drawnparticular interest in recent years (Minami et al., 1980;Takahashi, 1998; Tatsumisago et al., 1993; Krasowskiand Garbarczyk,1996). The high mobility of silver ion andthe relatively simple structure of the glass network makethe materials useful objects for the fast ion transportstudies in the glassy phase. These glasses representpotential canadidates for energy storage devices andsolid state batteries (Chowdari et al., 1995; Funke, 1993).So far, the main concern has been focused on electricalproperties. It is assumed that such investigation is thebest way to recognize the details of ion transport.Dielectric measurements on ionic materials give usefulinformation about dynamical processes involving ionicmotion (Funke, 1993). Most of the disordered materialsshow a dielectric relaxation that cannot be described byan exponential decay with a characteristic single decaytime (Debye-like decay). The relaxation times in thesematerials follow the so called Kohlrausch-William-Watts(KWW) function (Minami, 1987; Pogg and Kohlrausch,1854).The aim of this work is to study dielectric properties andto analysis Cole-Cole plots technique for a series of somesilver phosphate glasses in which P2O5 is replaced by AgIup to 20 mole% to obtain parameters like opticaldielectric constant, static dielectric constant, averagerelaxation time, and molecular relaxation time.EXPERIMENTAL WORKSilver phosphate glasses of the compositions xAgI –
Adv. J. Phys. Sci.240Ag2O-(50-x)P2O5-10Fe2O3 mole% [x 0, 10, 20] wereprepared using NH4H2PO4, AgI, Ag2O and Fe2O3 asstarting materials (with purity not less than 99.8%). Thepractical applications of phosphate glasses are oftenlimited due to their poor chemical durability. It was foundthat, the chemical durability of this kind of theses glassesincreases dramatically with the addition of Fe2 O3 (Reis etal., 2002). With the addition of Fe2 O3 into phosphateglasses, the P-O-P bonds are replaced by more chemicaldurable P-O-Fe2 and / or P-O-Fe3 bonds (Yu, etal.,1997; Baia et al., 2002; Montagne et al., 1996). Theraw materials are weighted to the desired concentrationsand the batches are mixed well and then melted inporcelain crucibles using an electric furnace at 950 C for6 h with frequent stirring to ensure completehomogeneity. The melts are quenched between two precooled copper plates to form glass samples. Thedielectric measurements are carried out on the silverpaste coated pellets by using s programmable automaticRCL meter (Hioki 3532LCR Hi TESTER) in frequencyrange (50 Hz - 5 MHz) and temperature range (303-550)K. Differential Thermal Analysis (DTA) was performed instatic air atmosphere with a constant heating rate of 10K/min in a temperature range of 298-873K usingShimadzu DT-50. The DTA thermogrames for all samplesare shown in Figure 1. The values of the glass transitiontemperature (Tg) and the crystallization temperature (Tc)for samples under investigation are listed in Table (1).RESULTS AND DISCUSSIONDielectric behaviorThe dielectric relaxation as a whole is the result of themovement of dipoles (dielectric relaxation) and electriccharges (ionic relaxation) due to an applied alternatingelectric field. Debye relaxation model has been widelyemployed to describe the response of molecules to anapplied field.The Debye equation in its simplest form of the complexdielectric constant, assuming a single relaxation time τo,is given by ' j ' ' s 1 j o(1)where εs is the low frequency of ε' (the static dielectricconstant) and ε is the high frequency of ε' (the opticaldielectric constant), ω is the applied angular frequency(ω 2πf).Then we have the real part ε' (dielectric constant) andthe imaginary part ε'' (dielectric loss) as follow: s 21 2 o(2) s 21 2 o(3)The temperature and frequency dependences of thedielectric constant ε' and the dielectric loss ε" are studiedin the frequency range (50 Hz - 5 MHz) and temperaturerange (303-523K) for samples with x 0, 10 and 20.Figures 2(a, b) illustrate the variation of both dielectricconstant ε' and the dielectric loss constant ε" withtemperature at different frequencies (sample x 20 as anexample). In these figures, it is observed that both ε' andε" exhibit peaks against temperatures indicating dipolarrelaxation character. The comparison of the maximumpeaks with the differential thermal analysis (DTA)indicates that the beginning of the maxima correspondingto the glass transition temperature (Tg). These dielectricpeaks exist between Tg and Tc temperatures where thecrystallization finishes in DTA results. The appearedpeaks for samples x 0, 10, and 20, was noticed at Tg 375, 365, and 360 K respectively.Figures 3(a, b) illustrates the variation of dielectricconstant ε' and the dielectric loss constant ε" withfrequencies (log f) for composition x 20 at differenttemperatures. The dielectric constant ε' is higher at lowfrequencies then decreases sharply with frequency andafter that it remains almost constant over the entirefrequency range. In the case of ε", it is very similar naturelike of dielectric constant ε', decreases rapidly andbecomes almost constant afterwards. This behaviorindicates a normal behavior of the dielectric. Thedecrease of dielectric constants in higher frequencyregion may be due to the fact that the dipoles cannotfollow up the fast variation of the applied field. The highervalues of ε' and ε" at lower frequencies may be due tocontribution from all the four types (space charge, dipole,ionic and electronic polarization ) of polarizations, but athigher frequencies, only ionic and electronic polarizationcontribute. Generally, the high value of dielectric constantat low frequencies is attributed to the interfacial ionicpolarizations due to localized Ag ion motion within theglass network (Chowdari and Radhakrishnan, 1989). Thedecrease of dielectric constant ε' , with increasingfrequency means that, the response of the permanentdipoles decreases as the frequency increases and thecontribution of charge carriers (ions) towards thedielectric constant decreases (Bergo and Pontuschka,2007; Graca et al., 2003).Cole-Cole plot analysisA simple evaluation of the Debye Equations (3) and (4)shows that the relation between ε' and ε" of the complexdielectric constant (ε )٭ is the equation of a circle. Byeliminating (ωτ), these two Equations (2, 3) can becombined and written in the form of a circle:
and K. Yamada, Appl. Phys. Lett.91, (2007) 052912.Salman et al.3TCExoTgX 30X 20X 15X 10 EX 5X 0Endo000373473373573673T, K4735737738736739737731073873973Figure 1. DTA curves for the glass system (50-x) P2O5-xAgI-40Ag2O-10Fe2O3, [x 10730,5,10,15,20,30].2 522 3Figure (1) : DTA curves for the glass system (50-x) P O -xAgI-40Ag O-10Fe O , [x 0,5,10,15,20,30] .Table 1. The valuesTg,10Fe2 O3,[x 0,5,10,15,20,30].x AgI0510152030 s 2 Tg K375.89371.14365.76360.27359.55356.8122 s 2 TCforTC K761.12754.96725.26715.82613.32528.052(4)This gives a semicircle plot of ε' against ε" with a centeron the real axis and intersects it at values ε and εsrespectively. The top of this semicircle corresponds toωτ 1. This plot confirms Debye theory.Cole and Cole (Graca et al., 2003) found for aconsiderable number of liquids and solids that the valuesof ε" fell below the semicircle but could be represented bya semicircle arc intersecting the real axis at the values ofthe glasssystem (50-x)P2O5-xAgI-40Ag2 O-εs3333-ε 17354065-ε and εs. The center of the circle of which this arc was apart lay below the real axis and the diameter drawnthrough the center from the ε point made an angle α 2with the real axis. Cole and Cole suggested that in thiscase the complex dielectric constant might follow theempirical relation of the form: s 1 1 j (5)
Adv. J. Phys. Sci.4Figure 2a. Temperature dependence of the dielectric constant for samplex 20 at different frequencies.Figure 2b. Temperature dependence of the dielectric loss constant for samplex 20 at different frequencies.Where τ is the average relaxation time and α is thespreading factor of actual relaxation time τo (0 α 1).When α equals to zero the dielectric has only onerelaxation time.The Cole-Cole plots is obtained from the dependence ε'on ε" on the complex plane at temperatures range (303500K). The Cole-Cole plots method are used to test theeffect of compositions xAgI – 40Ag2O-(50-x)P2O5-
Salman et al.5Figure 3a. Frequency dependence of the dielectric constant for sample x 20 atdifferent temperatures.Figure 3b. frequency dependence of the dielectric constant for sample x 20different temperatures.10Fe2O3 mole% [x 0, 5, 10, 15, 20] on type of dielectricconstant at room temperature (303K), (Figure 4). Eachatplot is represented by a semicircle arc with a centrebelow ε'-axis. The dielectric parameters ε and εs are
Adv. J. Phys. Sci.6Figure 4. Cole-Cole plots for glassy samples with x 5, 10, and 15 at 303 K.Table 2. The calculated values of εs, ε and τ calculated from Cole-Cole plot and τm from Equation(9).T, C5060708090100110120130140F, 50000εs49484442383532282625evaluated as the high- and low-frequency intercepts ofexperimental ε' with the real axis of Cole-Cole plot (Tableε 2222222222 30353837404734333337τ, .86E-073.12E-071.59E-071.28E-07τm, .86E-041.57E-046.88E-055.13E-052). At higher frequencies, all the data at differentcompositions converge in one point that represents a
Salman et al.7Figure 5. Cole-Cole plots for sample x 20 at different temperatures.unique value of optical dielectric constant ε . The reasonfor ionic value of ε is that the alternating field oscillatesto rapidly for the dipole to follow and so the dipoleremains essentially stationary and consequentially thedipolar polarization vanishes. The low frequencyintercepts εs shift to a higher value as P2O5 is replaced bythe AgI up to 20 mol%. This means that the increasing ofAgI concentration in the glassy system is to increasesilver ion in the glass matrix and excess ionic jumps atlower frequency in the field direction.The Cole-Cole analysis (Figure 5) is also used to obtainthe relaxation time of relaxation process. The averagerelaxation time may be calculated from the relation:v1 u(6)Where v is the distance on the Cole-Cole plot between εsand an experimental point, and u is the distance betweenthe experimental point and ε . From the Cole-Cole plotthe parameters like optical dielectric constant ε , staticdielectric constant εs, average relaxation time τ,molecular relaxation time τm are evaluated and listed inTable (2). The average relaxation time τ is plotted againsttemperature for studied glasses (Figure 6). The relaxationtime is thermally activated and follows closely the Em / KT Arrhenius relation; m o e, with values ofactivation energies listed in Table (2).On the molecular level, the molecular relaxation timeτm can be estimated by employing the following Equation(Montagne et al., 1996) by substituting the value of τ: 2 s 3 s m (7)The obtained molecular relaxation time is listed in Table
Adv. J. Phys. Sci.8Figure 6. Temperature dependence of the relaxation time for samples.2. According to this Table, values of the relaxation timesof the studied glasses are very near to that of amorphousbulk chalcogenide semiconductors and oxide glasses(Chowdari and Radhakrishnan, 1989; Bergo andPontuschka, 2007; Graca et al., 2003). The relaxationtime is fast at high temperatures and increasesdramatically at low temperatures, suggesting a freezingof electric dipoles at low temperatures (Ahmad andYamada, 2007).ConclusionsSilver phosphate glasses of the compositions xAgI –40Ag2O-(50-x)P2O5-10Fe2O3 mole% [x 0, 5, 10, 15, 20,30] was prepared using melt-quenching technique. Theglass transition temperature (Tg) changes with silveriodide concentration increasing reflecting the formation ofthe most opened network structure. It has been observedthat both ε and εs decrease with increasing frequencyindicating a normal behavior of dielectrics. It is noticedfrom Cole-Cole plots that the increasing of AgIconcentration in the glassy system is to increase thestatic dielectric constant which may act as electricdipoles. From the Cole-Cole plot parameters the averagerelaxation time and molecular relaxation time areevaluated. The relaxation time is found to be fast at hightemperatures and increases dramatically at lowtemperatures, suggesting a freezing of electric dipoles atlow temperatures.REFERENCESAhmad MM and Yamada K (2007). Superionic PbSnF4: Agiant dielectric constant material, Appl. Phys. Lett.91(5): 052912-3.Baia L, Stefan R, Kiefer W, Pop J, Simom SJ(2002).Structural investigations of copper doped B2O3–Bi2O3glasses with high bismuth oxide content, J. Non-Cryst.Solids 303(3): 379-386.Bergo P, Pontuschka WM, Prison JM (2007). Dielectricproperties of P2O5–Na2O–Li2O glasses containing WO3,CoO or Fe2O3. Solid State Communications 141(10):545-547.Borsa F, Torgeson DR, Martin SW, Patel HK (1992).Relaxation and fluctuations in glassy ctivity measurements. Phys. Rev. B 46(25): 795800.Chowdari BV, Mok KF, Xie JM, Gopalakrisnan R (1995).Electrical and structural studies of lithiumfluorophosphate glasses. Solid State Ionics 76(3-4):
Salman et al.189-198.Chowdari BVR, Radhakrishnan K (1989). Electrical andelectrochemical characterization of Li 2O:P2O5:Nb2O5based solid electrolytes. J. Non-Cryst.Sol. 110(1): 101110.Funke K (1993). Jump relaxation in solid electrolytes,Prog. Solid State Chem. 22(2): 111-195.Graca M, Valente MA, Ferreira da silva MG (2003).Electrical properties of lithium niobium silicate glasses.J. Non-Cryst. Solids 325(1-3): 267-274.Krasowski K, Garbarczyk JE (1996). XRD, DSC, andadmittance spectroscopy studies on some AgI-Ag2OV2O5 Superionic Glasses. Phys. Stat. Sol. (a) 158: k13k16.Minami T, Imazawa K, Tanaka M (1980). Formationregion and characterization of superionic conductingglasses in the systems AgI-Ag2O-MxOy. J. Non-Cryst.Solids 42(1-3): 469-476.Minami TJ (1987). Recent progress in superionicconducting glasses. J. Non-Cryst. Solids 95-96(part1):107-118.Montagne I, Palavit G, Mairesse G (1996). 31P MAS NMRand FTIR and analysis of (50-x/2)Na2O.xBi2O3.(50-x/2)P2O5 glasses. Phys. Chem. Glasses 37(5): 206-211.9Pogg R, Kohlrausch F (1854). Theorie des elektrischenRückstandes in der Leidener Flasche, Ann. Phys.Chem. 91: 179–214.Reis ST, Faria DLA, Martinelli JR, Pontuschka WM, DayDE, Partini CSM (2002). Structural features of lead ironphosphate glasses. J. Non-Cryst. Solids 304(1-3): 188194.Takahashi H, Shishitsuka K, Shimojo Y, Ishii Y (1998).Characteristic features of ionic conduction in AgI–Ag2O–V2O5 glasses. Solid State Ionics 113-115: 685690.Tatsumisago M, Taniguchi A, Minami T (1993).Formation of Frozen α-Agl in Twin-Roller-QuenchedAgl Ag2 O MxOy (MxOy WO3, V2O5) Glasses atAmbient Temperature. J. Am. Cer. Soc. 76(11): 235–237.Yu X, Day DE, Long GJ, Brow RK (1997). Properties andstructure of sodium-iron phosphate glasses. J. NonCryst. Solids 215(1): 21-31.
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