dc Conductivity and dielectric properties of V 2 O 5 -Bi 2 O 3 -ZnO glass

Transcription

1 Indian Journal of Pure & Applied Physics Vol. 45, January 2007, pp dc Conductivity and dielectric properties of V 2 O 5 -Bi 2 O 3 -ZnO glass D K Shukla & S Mollah * Department of Physics, Aligarh Muslim University, Aligarh * smollah@rediffmail.com Received 1 March 2006; accepted 26 October 2006 Semiconducting oxide glass with composition 40V 2 O 5-40Bi 2 O 3-20ZnO is prepared by rapid quenching method. The glassy phase is confirmed from X-ray diffraction (XRD) pattern which shows a broad hump around 2θ = 30 o. The dc conductivity of the glass has been measured in the temperature range K and compared with that of other vanadium and copper based zinc oxide containing glasses. The dc conductivity is due to non-adiabatic small polaron hopping conduction which is confirmed from the fitting of the conductivity data with different polaronic hopping models. The frequency (75 khz - 30 MHz) dependent dielectric constant of the glass decreases first and then increases with the increase of frequency at room temperature. The anomaly in frequency dependent dielectric constant at ~ 5 MHz may be due to the displacement and/or orientational motion of BiO 3 and BiO 6 structural units present in the glass. Keywords: Glass, dc Conductivity, Polaronic hopping models, Dielectric properties, V 2 O 5 -Bi 2 O 3 -ZnO, Semiconducting oxide glass IPC Code: G01R 1 Introduction The research on transition-metal oxide (TMO) glasses is continuing since long time due to their many technological applications 1. The dc conduction in TMO glasses is the reason of transfer of electrons from the lower valence to the higher valence states of the transition-metal ions (TMI). The electrical conduction is controlled by strong electron-phonon interaction and resulting in the formation of small polarons 2-4. This is observed in many TMO glasses 5-9. Generally, small-polaron hopping 2,3 (SPH) model can explain the dc conduction and transport properties of vanadate glasses At temperatures below θ D /2 (where θ D = Debye temperature), the three-dimensional (3D) variable-range hopping (VRH) conduction 13 takes place as the polaron binding energy is less than k B T where k B is the Boltzmann constant and T is the absolute temperature. The effect of vanadium has been well studied in different glasses with Bi 2 O 3 as the glass former 11. The conduction in these glasses takes place by the transfer of electrons from V 4+ to V 5+ ions. Again, ZnO has been extensively used as a key catalyst in many important photo catalysis processes 14,15 as it easily produces the electron-hole pair by the exposure of ultraviolet (UV) light which is necessary for photo processes. It also improves the glazing durability of the glasses and is very powerful even with its least possible presence. In order to understand its importance and applicability, ZnO has been added in bismuth vanadate glass to study its transport and dielectric properties. The present paper reports the dc conductivity and frequency dependent dielectric properties of V 2 O 5 -Bi 2 O 3 -ZnO glass. 2 Experimental Details Reagent grade chemicals of V 2 O 5, Bi 2 O 3 and ZnO (with purity more that 99%) were mixed at stoichiometric ratio (i.e. 40 mol % V 2 O 5, 40 mol % Bi 2 O 3 and 20 mol % ZnO) and ground in an agate mortar for two hours. The mixture was heated at 500 o C for two hours to evaporate the moisture (if any), cooled and again ground. It was once more sintered at 800 o C for four hours. Finally, the grinded mixed oxide was melted at a temperature of 1100 o C in a high temperature programmable muffle furnace for one hour and stirred several times for better mixing. The melt was then rapidly quenched in air between two highly polished copper blocks placed at room temperature. This gave the opaque glass with shining surfaces. The glass sample was then annealed at 250 o C to remove the micro-cracks (if any) during formation. A small amount of the glass was powdered for the measurement of X-ray diffraction (XRD). Glassy phase of the sample was confirmed from XRD pattern as it showed a broad hump at 2θ ~ 30 o. Both

2 SHUKLA & MOLLAH: DIELECTRIC PROPERTIES OF V 2 O 5 -Bi 2 O 3 -ZnO GLASS 53 surfaces of a properly shaped glass were highly polished and cleaned by acetone. Subsequently, the surfaces were coated with silver paste and heat-treated at 100 o C for four hours to stabilize the electrodes. The dc conductivity of the sample was measured by using a Keithley Digital Multimeter (Model 2000) in the temperature range K. The frequency (75 khz-30 MHz) dependence of dielectric constant was quantified by Hewlett Packard (Agilent) 4285 A precision LCR meter at room temperature. 3 Results and Discussion 40V 2 O 5-40Bi 2 O 3-20ZnO glass has a density (ρ) ~ g cm -3 and an apparent molar volume occupied by 1 g atom of oxygen (V * o ) ~ cm 3 gm - 1 atom -1 (Table 1). V * o is calculated from the formula V * o = M/ρn, where M is the molecular weight calculated from the composition and n is the number * of atoms in one formula unit. The values of ρ and V o are consistent with other bismuth-vanadate glasses. The dc conductivity (σ dc ) of 40V 2 O 5-40Bi 2 O 3-20ZnO glass can be explained by a polaron hopping mechanism (in the non-adiabatic approximation) with the following formula 2-4 : σ dc = (σ o /T) exp (-W/k B T),...(1) where σ o = ν ph Ne 2 R 2 C v (1 - C v ) exp(-2αr)/k B, N is the number of transition-metal ions (TMIs) per unit volume, C v is the ratio of the transition-metal (TM) ion concentration in the low valence state to the total TM ion concentration, ν ph is an optical-phonon frequency (~10 13 Hz), e is the electronic charge, R the Table 1 Some important parameters of 40V 2 O 5-40Bi 2 O 3-20ZnO glass Density ρ (gm cm -3 ) V o * (cm 3 gm -1 atom -1 ) Analyzed TMI N (10 22 cm -3 ) 1.31 TMI spacing R (Å) 4.2 Polaron radius r p (Å) 1.69 Disorder energy W d (ev) Polaron-hopping energy W h (ev) 0.32 Debye Temperature θ D (K) 846 Phonon frequency ν ph (Hz) Small-polaron coupling constant (γ p ) m p /m * average V-V spacing (~ N -1/3 ), α the wave function decay constant, W the activation energy, k B the Boltzmann constant and T is the absolute temperature. Some of the important parameters of the glass are given in Table 1. It should be mentioned here that the integral I = exp (-2αR) reduces to 1.0 in the adiabatic case. The activation energy W is given by 2-4 : W = W h + W d /2 for T > θ D /2 and = W d for T < θ D /4, (2) where θ D is the Debye temperature and is given by hν ph = k B θ D, h being the Planck constant, W h is the polaron-hopping energy equal to W p /2, W p is the polaron binding energy and W d is the disorder energy arising from the energy difference of the neighbouring sites. W h is estimated from the relation 2-4 : W h = W p /2 = (e 2 / 4ε p ) (r p -1 - R -1 ) (3) where r p is the polaron radius and ε p is the effective dielectric constant (ε p = ε = n 2, n is the refractive index of the glass). The value of n is ~ 1.995, which can be determined from the measurement of Brewster s angle. The calculated value of W h is then found to be ~ 0.32 ev (Table 1). The r p for the present glass is found to be ~ 1.69 Å. The disorder energy W d is obtained from the Millar-Abraham theory 2,16,17 W d = 0.3e 2 /ε s R, (4) where ε s is the static dielectric constants of the glass at high temperature and low frequency. We would like to mention that W d may exist between the initial and final sites due to variations in the local arrangements of ions 10. It is proposed by Mott 2 that the carriers, having insufficient energy to hop to the nearest neighbours will hop further afield to find sites of comparable energy, in spite of a smaller electronic overlap. This approach leads to the dependence of W d on R [Eq. (4)]. In another approach 17, it is more appropriate to use an extrapolation of the lowfrequency dielectric constant ε s (~ 20-30) from electrical measurements down to zero frequency, for the calculation of W d of vanadate glasses. However, for the estimate of W h from Eq. (3), the value of 1/ε p (= 1/ε - 1/ε s ) has been proposed by Israd 17 taking ε and ε s, respectively, as the limiting values above and below the phonon frequency (10 13 Hz). For this case, ε s is taken as the limiting high-frequency (10 10 Hz)

3 54 INDIAN J PURE & APPL PHYS, VOL 45, JANUARY 2007 value (~ 8) from electrical measurements 17. We assume here ε s = 30, and this value is reasonable as ε s ~ at 500 Hz for V 2 O 5 -MnO-TeO 2 glasses 18 and ε s ~20-30 for the vanadate glasses 17. The calculated value of W d is then found to be ~ ev (Table 1). Figure 1 shows the inverse temperature variation of log 10 (σ dc ) and log 10 (σ dc T). At 450, 500 and 560 K temperatures, the dc conductivity of the glass is found to be , and ohm -1 cm -1, respectively (Table 2). The slopes of the curves (Fig. 1) change slightly with T at high temperatures, indicating little modification of the activation energy W. The temperature where the linearity of the curves of log 10 (σ dc ) versus 10 3 /T and log 10 (σ dc T) versus 10 3 /T (Fig. 1) deviates are taken as θ D /2 wherever θ D is the Debye temperature ~ 846 K (Table 1), consistent with other vanadate glasses. From Holstein s relation 19, it can be inferred whether the hopping conduction is in the adiabatic or non-adiabatic region. According to this relation, the polaron bandwidth J should obey the following conditions: J > H for adiabatic hopping and < H for non-adiabatic hopping conduction, (5) where H = (2k B TW h /π) 1/4 (hν ph /π) 1/2 (6) The condition for small-polaron formation is J < W h /3. An evaluation of J can be made from the approximate relation 19 for high-temperatures: J(T) 0.67hν ph (T/θ D ) 1/4 = 0.027(T/θ D ) 1/4 (7) and for ground-state bandwidth J(0) = 3hν ph = 0.12 ev. Taking ν ph = Hz, it is found that H (500 K) ~ ev and J (500 K) ~ ev (Table 2). Again, W h /3 is ~ ev. Since J (500 K) is less than both H (500 K) and W h /3, we conclude that dc conduction in this glass occurs by small-polaron hopping in the non-adiabatic regime. Similar relation for H and J is also valid at other temperatures (Table 2). In another Table 2 Some important parameters of 40V 2 O 5-40Bi 2 O 3-20ZnO glass obtained from the dc conductivity data at 450 K at 500 K at 560 K σ dc (ohm -1 cm -1 ) W (ev) W/W / W/W / (Theoretical) H J Fig. 1 Inverse temperature variation of log 10 (σ dc ) & log 10 (σ dc T) of V 2 O 5 -Bi 2 O 3 -ZnO glass

4 SHUKLA & MOLLAH: DIELECTRIC PROPERTIES OF V 2 O 5 -Bi 2 O 3 -ZnO GLASS 55 approach, J has been calculated from the relation J e 3 [N(ε F )]/ε 3/2 P where N(ε F ) is the density of states at the Fermi level and is found to be ~ 0.02 ev which is also less than the values of H at all measured temperatures. This again confirms the non-adiabatic hopping in the glasses. This is consistent with the report of Sakata et al. 20 and Mori et al. 21 who found the adiabatic small-polaron hopping conduction in V 2 O 5 containing tellurite glasses for V 2 O 5 > 50 mol% and non-adiabatic small-polaron hopping conduction for V 2 O 5 < 50 mol%. The small-polaron coupling constant γ p, which is a measure of electron-phonon interaction in these glasses, can be estimated from the relation 2-4 γ p = 2W h /hν ph. The value for γ p, using ν ph = Hz, is estimated to be ~ (Table 1). Therefore, the present glass has a strong electron-phonon interaction as it is indicated 3 for γ p > 4. The ratio of the polaron mass m p to the rigid-lattice effective mass m * is obtained by 2 : m p = (h 2 /8π 2 JR 2 ) exp(γ p ) = m * exp(γ p ) (8) The calculated value of m p /m * is ~ (Table 1), is very large and once more indicates strong electron-phonon interaction in this glass. According to Schnakenberg 22, a single opticalphonon process replaces the multi-phonon processes with lowering temperature and the activation energy for conduction follows: W/W / = [tanh (hν ph /4k B T)]/(hν ph /4k B T) (9) where W / is the high-temperature activation energy. W/W / varies from 0.98 to 1.0 (Table 2). The temperature variation of theoretical as well as experimental W/W / is shown in Fig. 2. Similar behaviour is also observed for other vanadate and TMO glasses 5-9. The lowering of activation energy with decrease of temperature (Fig. 2) is consistent with the polaron hopping model for dc conduction. Consequently, the dc conduction in this glass system can be well explained by non-adiabatic small-polaron hopping conduction. In intermediate temperature range (between θ D /4 and θ D /2), Greaves 23,24 suggested variable-range hopping (VRH) conduction and derived an expression for the conductivity as: σ dc T 1/2 = L exp (-Q/T 1/4 ) (10) where Q and L are constants. The slope of log 10 (σ dc T 1/2 ) versus T -1/4 plot is given by Q = 2.1[α 3 /k B N(E F )] 1/4 = 2.4[W d (αr) 3 /k B ] 1/4 (11) Figure 3 shows that log 10 (σ dc T 1/2 ) versus T -1/4 plot is tending to be non-linear at lower temperatures. Thus, the VRH model 2,23,24 is not suitable for explaining the dc conductivity data of this glass at temperatures lower than θ D /2. At room temperature, the frequency (75 khz-30 MHz) dependent dielectric constant of the glass decreases followed by an increase with the increase of frequency (Fig. 4). Inset of Figure 4 shows that an Fig. 2 Plot of W/W / versus 10 3 /T for the V 2 O 5 -Bi 2 O 3 -ZnO glass. The theoretical curve is obtained from Eq. (9) Fig. 3 Log 10 (σ dc T 1/2 ) versus T -1/4 curve for V 2 O 5 -Bi 2 O 3 -ZnO glass

5 56 INDIAN J PURE & APPL PHYS, VOL 45, JANUARY 2007 explained to be due to the displacement and/or orientational motion of the structural units of BiO 3 and BiO 6. Acknowledgement D K Shukla is grateful to Inter-University Accelerator Centre (IUAC) formerly known as Nuclear Science Centre (NSC), New Delhi, for providing him a fellowship. The facility given by IUAC to measure the dielectric properties of the glass is thankfully acknowledged. Fig. 4 Plot of frequency dependent (75 khz-30 MHz) dielectric constant of the V 2 O 5 -Bi 2 O 3 -ZnO glass at room temperature. Inset shows an anomaly that occurs at a frequency of ~ 5 MHz anomaly occurs at a frequency of 5 MHz. Similar anomaly was also observed in Ba 1-x K x BiO 3 glass at room temperature 25 which was attributed to be associated with the orientational motion of the BiO 3 or BiO 6 structural units present in the glass. The orientational motions of the structural units may give rise to structural instability and different phase transitions. Kristoffel et al. 26 have described the importance of such structural instability arising from strong electron-phonon interactions that lead to the high static dielectric constant. Therefore, the anomaly of dielectric constant around 5 MHz may be due to the orientational motion of the structural units of BiO 3 and BiO 6. Further increase of dielectric constant above 5 MHz is consistent with that of other TMO and vanadate glasses 5-8, Conclusions The 40V 2 O 5-40Bi 2 O 3-20ZnO glass is prepared by melt quenching, and its dc conductivity as well as dielectric properties are investigated. VRH model (below θ D /2) cannot explain the dc conductivity data. From Mott-Austin s SPH model 2,3, Holstein s condition 19 and Schnakenberg s suggestion 22, it is established that transport of electrons in this glassy system occurs by small-polaron hopping conduction in the non-adiabatic regime for temperatures above θ D /2 (~500 K, for the present glass). The anomaly in frequency dependent dielectric constant at 5 MHz is References 1 Sakurai Y & Yamaki J, J Electrochem Soc, 132 (1985) Mott N F, J Non-crystalline Solids, 1 (1968) 1. 3 Austin I G & Mott N F, Adv Phys, 18 (1969) Mott N F & Davis E A, Electronic processes in non crystalline materials 2 nd Ed, (Oxford University Press, Clarendon), (1979). 5 Som K K, Mollah S, Bose K & Chaudhuri B K, Phys Rev B, 45 (1992) Mollah S, Som K K, Bose K, Chakraborty A K & Chaudhuri B K, Phys Rev B, 46 (1992) Mollah S, Som K K, Chakraborty S, Bera A K, Chatterjee S, Banerjee S & Chaudhuri B K, Phys Rev B, 51 (1995) Chatterjee S, Banerjee S, Mollah S & Chaudhuri B K, Phys Rev B, 53 (1996) Mollah S, Hirota K, Sega K, Chaudhuri B K & Sakata H, Philos Mag, 84 (2004) Sayer M & Mansingh A, Phys Rev B, 6 (1972) Ghosh A & Chaudhuri B K, J Non-crystalline Solids, 83 (1986) Mori H, Kitami T & Sakata H, J Non-crystalline Solids, 168 (1994) Mott N F, Philos Mag, 19 (1969) Cheng H C & Wu N L, J Photochem Photobiol A Chem, 172 (2005) Hadj S N, Bouhelassaa M, Bekkouche S & Boultii A, Desalination, 166 (2004) Miller A & Abrahams E, Phys Rev, 120 (1960) Isard J O, J Non-crystalline Solids, 42 (1980) Pal M, Sega K, Chaudhuri B K & Sakata H, unpublished data. 19 Holstein T, Ann Phys, 8 (1959) 325 & Sakata H, Amano M & Yagi T, J Non-crystalline Solids, 194 (1996) Mori H, Matsuno H & Sakata H, J Non-crystalline Solids, 276 (2000) Shnakenberg J, Phys Status Solidi, 28 (1968) Greaves G N, J Non-crystalline Solids, 11 (1973) Greaves G N, J Non-crystalline Solids, 51 (1982) Mollah S, Bera A K, Chakraborty S & Chaudhuri B K, Phys Rev B, 49 (1994) Kristoffel N N & Konsin P, Phys Status Solidi, 28 (1968) 731.