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Characterization and transport properties of V2O5–Fe2O3–TeO2 glasses
Journal of Non-Crystalline Solids 351 (2005) 3139–3146 www.elsevier.com/locate/jnoncrysol
Characterization and transport properties of V2O5–Fe2O3–TeO2 glasses M.M. El-Desoky
*
Department of Physics, Faculty of Education, Suez Canal University, El-Arish, Egypt Received 13 February 2005; received in revised form 1 August 2005
Abstract IR, DSC, density and molar volume, and dc conductivity of the glasses in V2O5–Fe2O3–TeO2 system were reported. The network structure for the glass compositions with 65 and 62.5 mol%, V2O5 is built up of VO5 polyhedra, while the other glass compositions consist of VO4 polyhedra. Density and glass transition temperature were observed to decrease with an increase in V2O5 content. The glasses had conductivities ranging from 3.31 · 103 S m1 to 2.88 · 102 S m1 at 400 K for V2O5 = 50–65 mol%. The electrical conductivity was confirmed to be due to adiabatic small polaron hopping. The hopping carrier mobility varied from 0.587 · 105 cm2 V1 s1 to 6.904 · 105 cm2 V1 s1 at 400 K. The carrier density was evaluated to be 2.997 · 1019–7.298 · 1019 cm3. The conductivity was primarily determined by hopping carrier mobility. 2005 Elsevier B.V. All rights reserved. PACS: 61.43.Fs; 61.40
1. Introduction The dc conductivities of transition metal oxide (TMO), glasses have been targeted for extensive studies [1–7] because of their interesting semiconducting properties as well as for their probable technological applications. The conduction mechanism in these glasses was presumed to be by the small polaron hopping (SPH) process [8,9]. Vanadate glasses with a large concentration of V2O5 (>50 mol%), e.g. V2O5–P2O5 [10], V2O5– NiO–TeO2 [4] and V2O5–MnO–TeO2 [11], glasses are highly conductive. Hopping conduction of these glasses was generally known to be adiabatic for V2O5 content above 50 mol%, while, for V2O5 < 50 mol% conduction became non-adiabatic [12]. The effect of the second transition metal oxide on the conductivity was reported [4,11] and the glasses containing two kinds of transition *
Present address: Physics Department, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia. E-mail address: [email protected] 0022-3093/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2005.08.004
metal ions, e.g. V2O5–NiO–TeO2 [4] and V2O5–MnO– TeO2 [11] systems, have become the center of this conductivity study. These glasses showed relatively high conductivities of 104 S cm1 above 400 K [12]. Highly conductive tellurite glasses containing TMO have a potential applicability as electrical devices (e.g. memory switching and gas sensor). The objective of the present work is to study the compositional dependence of the structure and semiconducting properties of V2O5–TeO2 based glasses in view of MottÕs theory. V2O5–Fe2O3–TeO2 system is suitable for this purpose because of its wide glass formation region.
2. Experimental Reagent grade V2O5 (99.9%), Fe2O3 (99.9%) and TeO2 (99.99%) were used as raw materials. After mixing in air, a batch of 5 g with the prescribed compositions, the mixed mass of each glass composition was melted in platinum crucible for 1 h at 1050 K in an electric
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furnace. The melt was then poured on a thick copper block and immediately quenched by pressing with another similar copper block. Following this procedure, we obtained bulk glass of 2 · 2 cm2 size and about 1 mm in thickness. The amorphous nature of the glasses was ascertained from X-ray diffraction analysis. The error in the density is estimated as ±0.025 g/cm3. IR spectra of the glass samples were measured from 400 to 2000 cm1 by a conventional KBr pellet method on a Fourier transform infrared (FT–IR) spectrometer (Perkin-Elmer 1760 X). Differential scanning calorimeter (DSC) of the samples was investigated using Shimadzu DSC-50 with a heating rate of 20 C/min. The dc conductivity (r) of the asquenched glasses was measured at temperatures between 300 and 423 K. Silver paste electrodes deposited on both faces of the polished samples. The I–V characteristic between electrodes was recorded.
V2O5 (mol%) 50
Transmission
55
60
62.5
65
3. Results 3.1. IR spectra
3.2. DSC Fig. 2 shows the glass transition temperature, Tg, of the present glass system. From Fig. 2, it is clear that Tg decreased with increasing V2O5 content and lies between 570 K and 580 K. Also, the crystallization temperature, Tc, lies between 645 K and 657 K for the present glass compositions. It is known that the thermal stability of a glass depends on DT = Tc Tg of the glass [17]. This result is due to the fact that the present glasses were thermaly stable in comparison with the thermal stability of V2O5–MnO–TeO2 glasses [11], because the DT values of the present glasses (DT 76 K) were higher than those of V2O5–MnO–TeO2 glasses [11] (DT 60 K).
300 500 700 900 1100 1300 1500 1700 1900 2100
Wavenumber (cm)-1 Fig. 1. Room-temperature IR spectra for V2O5–Fe2O3–TeO2 glasses. 582
580
578
Tg (K)
The room temperature IR spectra in the region 400– 2000 cm1 of all glass compositions, are shown in Fig. 1. All the spectra show a water band at 1620–1630 cm1. The origin of this band might be due to the –OH bending mode and absorbed water [13,14]. Also, a weak band at 1000–1020 cm1 is observed for some glasses. This band is assigned to the vibrations of the isolated V@O vanadyl groups in VO5 trigomal bi-pyramids [13]. However, in the glass compositions containing 60–50 mol% V2O5 the band at 1000 cm1 vanishes completely.
576
574
572
570
568 48
50
52
54
56
58
60
62
64
66
68
V2O5 (mol%) Fig. 2. Composition dependence of glass transition temperature, Tg, for V2O5–Fe2O3–FeO2 glasses.
with the increase of vanadium oxide content in the glass compositions.
3.3. Density and molar volume 3.4. Electrical conductivity The composition dependence of the density of the present glass samples is shown in Fig. 3 and Table 1. It may be observed that density, d, decreases gradually
Fig. 4 shows the arrhenius plot of log (r) between 300 and 423 K. Deviation from a linear curve occurs around
M.M. El-Desoky / Journal of Non-Crystalline Solids 351 (2005) 3139–3146 -0.5
4.10
41.0
3141
-1.0 Vm
40.5
4.05
-1.5
4.00
39.5
3.95
39.0
3.90
38.5
3.85
38.0
3.80
-2.0
log σ (Sm-1)
40.0
d (g/cm3)
Vm (cm3/mol%)
d
-2.5 -3.0 -3.5
V2O5 mol% 50 55 60 62.5 65
-4.0 -4.5
37.5 48
50
52
54
56
58
60
62
64
66
-5.0 -5.5 2.2
3.75 68
2.4
2.6
V2O5 (mol%) Fig. 3. Composition dependence of density, d, and oxygen molar volume, Vm, for V2O5–Fe2O3–TeO2 glasses. Lines are drown connecting data symbols of each kind.
hD/2 (333–370 K, depending on concentration). Fig. 4 indicates the temperature dependent activation energy. The experimental conductivity data in such a situation is well described with an activation energy for conduction (W) given by Mott formula [8,9]. r ¼ r0 expðW =kT Þ;
2.8
3.0
3.2
3.4
3.6
1000/T (K)-1
ð1Þ
where r0 is a pre-exponential factor as discussed below. W values obtained from fitting of the linear part of the curves in Fig. 4 (high temperature regime) are given in Table 1. For these glass samples r2 = 0.9900 (r = is the correlation coefficient) and range = 1.02 · 105 S m1 in were obtained, which indicate a satisfactory fit. At temperature lower than 370 K the linearity between log (r) and 1/T deviated appreciably as seen from Fig. 4.
4. Discussion According to the mechanism suggested earlier [15], the iron ions occupy a position between V–O–V layers. This is why they have a direct influence on the isolated
Fig. 4. Temperature dependence of dc conductivity, r, for V2O5– Fe2O3–TeO2 glasses.
V@O bonds of VO5 groups according to scheme Fe– O–V. As a result of this, they should be longer and the frequencies of vibrations should be shifted towards the lower wavenumbers. A similar manner of interaction has been discussed concerning glasses, having a V2O5– TeO2 composition [16]. In the glass containing 62.5– 65 mol% V2O5 (i.e. lower Fe2O3 content), VO5 groups with unaffected V@O bonds are preserved along with the affected VO5 polyhedra [14]. With the increase of Fe2O3 (beyond 7.5 mol%), only affected VO5 polyhedra are obtained in the glass compositions containing 60– 50 mol% V2O5. This means that the network structure is build up of VO5 polyhedra for the glass compositions with higher V2O5 content [14]. However, as V2O5 content decreases the glass structure consists of VO4 polyhedra [13–15]. Finally, Dimitriv et al. [15] attributed the IR spectra absorption band in the range from 645 to 665 cm1, to TeO3 trigonal pyramids. Thermal stability of glasses is a result of glass structure. Generally, thermally stable glasses have a closely backed structure [12]. Inversely, the structure of thermally unstable glasses possesses a loose packing [12]. Thus, we assumed that the present glasses have a more closely packed structure. For vanadate glasses, when a
Table 1 Chemical composition and physical properties of V2O5–Fe2O3–TeO2 glasses Glass no.
1 2 3 4 5
Nominal composition (mol%) V2O5
Fe2O3
TeO2
50 55 60 62.5 65
20 15 10 7.5 5
30 30 30 30 30
W ± 0.01 (eV)
d ± 0.01 (g cm3)
N ± 0.01 (· 1022 cm3)
R ± 0.01 (nm)
hD ± 1 (K)
m0 ± 0.01 (· 1013 s1)
0.43 0.40 0.38 0.36 0.34
4.05 3.97 3.89 3.85 3.81
1.575 1.549 1.523 1.510 1.575
0.398 0.401 0.403 0.405 0.406
666 676 684 712 740
1.388 1.408 1.425 1.484 1.542
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layered-network structure including a VO4 polyhedra unit [13] increases in the concentration, the glasses form a closely backed structure [13,14], while the glasses form a loosely packed structure, when the network structure with VO5 polyhedra unit increases in concentration [13]. Since the present glasses became thermally stable by containing Fe2O3 substituted as MnO, we assumed that the glass structure containing VO5 units changed to the structure with VO4 units [5,14]. The relationship between density and composition of an oxide glass system can be expressed in terms of an apparent volume, Vm, occupied by 1 g atom of oxygen. The value of Vm has been calculated from the density and composition using the formula reported earlier [18] and its composition dependence is shown in Fig. 3. It is observed that Vm increases monotonically with an increase of V2O5 content in the composition which indicates that the topology of the network does not significantly change with composition. On the other hand, these trends can be explained rather simply as due to the replacement of a heavier cation (Fe) by a lighter one (V) [13,14]. Fig. 5 shows the plot of activation energy and electrical conductivity at constant temperature (403 K) as a function of V2O5 content. It is observed that as the percentage of V2O5 increases, the activation of electrical conduction decreases and electrical conductivity increases, in a linear manner. This is consistent qualitatively with Eq. (1) proposed for polaron hopping at high temperatures [8,9]. The high value of activation energy and low value of electrical conductivity are similar to those for V2O5–BaO–B2O3 and V2O5–NiO–TeO2 glasses [1,4].
Fig. 6 presents the variation in conductivity with increasing in V2O5 content at two temperatures (303 K and 403 K). This means a ratio of V4+ ion CV (=V4+/ Vtotal) increases, causing the activation energy, W, to decrease and electrical conductivity, r, to increase (Fig. 5). In V2O5–Fe2O3–TeO2 glasses of our present investigation, Fe2O3 addition lowered the conductivity. This means, Fe ion in the glass hindered the carrier transport [4,11]. Because Fe2O3 is not a glass network former, Fe ions are isolated in the glass network, which causes obstruction in the hopping of electrons due to the lack of oxygen bonds. A similar lowering of conductivity was also observed in V2O5–MnO–TeO2 [11], V2O5– NiO–TeO2 [4] and V2O5–CoO–TeO2 [16] glasses. In order to confirm the W–R relation, the V-ion density, N, was calculated using the following formula [21]: N ¼ 2½ðdWtV2 O5 =MW V2 O5 ÞN A ;
where d is the density, WtV2 O5 the weight fraction of V2O5, MW V2 O5 the molecular weight of V2O5 and NA is the Avogadro number, respectively. The relationship between N and mean distance, R, is generally described as follows: R ¼ ð1=N Þ
1=3
ð3Þ
.
The calculated values of R and N are summarized in Table 1. The relation between the activation energy (W) and the mean distance, R, between V ions is illustrated in Fig. 7 and Table 1. In the range of measurements, W depends on the site-to-site distance R. These results show that there is a prominent positive correlation between W and R between transition metal ions. This agrees with the results suggested by Sayer and Mansingh [6] and ElDesoky [4] which delineated the dependence of W on the
-2.6
0.44
-1.0
σ 0.42
-2.8
W
403 K
0.40
-2.0
-3.6 0.36 -3.8
log σ (Sm)-1
-3.4
W (eV)
-3.2 0.38
303 K
-1.5
-3.0
log σ (Sm-1)
ð2Þ
-2.5
-3.0
-3.5
0.34 -4.0 -4.0 0.32 48
50
52
54
56
58
60
62
64
66
-4.2 68
V2O5 (mol%)
-4.5 48
50
52
54
56
58
60
62
64
66
68
V2O5 (mol%) Fig. 5. Effect of V2O5 content on dc conductivity, r, and activation energy for different glass compositions. Lines are drown connecting data symbols of each kind.
Fig. 6. Effect of V2O5 content on dc conductivity, r, for different glass compositions. Lines are drown as guides for the eye.
M.M. El-Desoky / Journal of Non-Crystalline Solids 351 (2005) 3139–3146
Cv = V4+/Vtotal), a the tunneling factor (the ratio of wave function decay), WH the hopping energy and WD is the disorder energy defined as the difference of electronic energies between two hopping sites [19]. The density of state at Fermi level can be estimated from the following expression [19]:
0.44
0.42
0.40
W (eV)
3143
N ðEF Þ ¼ 3=4pR3 W .
ð7Þ
0.38
The results for the present glasses are listed in Table 2. The values of N(EF) are reasonable for localized states. In the adiabatic hopping regime, however, aR in Eq. (4) becomes negligible [17,19], then the conductivity, r, and the pre-exponential factor r0 in Eq. (4) is expressed by the following equations [8,9]:
0.36
0.34
0.32 0.396
0.399
0.402
0.405
r¼
0.408
R (nm)
m0 Ne2 R2 Cð1 CÞ expðW =kT Þ kT
ð8Þ
and Fig. 7. Effect of mean V-ion spacing, R, on activation energy, W, for different glass compositions.
mean distance between TM ions. A similar behavior was observed in V2O5–NiO–TeO2 [4] glasses. The logarithm of the conductivity (Fig. 4) shows linear temperature dependence up to a critical temperature hD/2 and then the slope changes with deviation from linearity and the activation energy is temperature dependent. Such a behavior is a feature of SPH [8,9]. So, we first discuss the thermal variation of conductivity assuming the SPH model [8,9] based on a strong coupling of electron with the lattice by a single phonon. This model gives in the non-adiabatic regime for TMO glasses as given by Eq. (1), viz. r¼
m0 Ne2 R2 Cð1 CÞ expð2aRÞ expðW =kT Þ. kT
ð4Þ
The activation energy W can be written as W ¼ W H þ W D =2 ðfor T > hD =2Þ; W ¼ W D ðfor T < hD =4Þ.
ð5aÞ ð5bÞ
The pre-exponential factor in Eq. (1) is given by r0 ¼ m0 Ne2 R2 Cð1 CÞ expð2aRÞ=kT ;
ð6Þ
where m0 is the optical phonon frequency (generally m0 ’ 1013 s1 [3,21], N the transition metal density, C the fraction of reduced transition metal ion (= Cv and
r0 ¼ m0 Ne2 R2 Cð1 CÞ=kT .
ð9Þ
From Eq. (8) r0 is independent of V2O5 concentration and hardly varies with V2O5 content [19]. Therefore, the dominant factor contributing to the conductivity should be W in the adiabatic regime [4,20]. For the present glasses, we calculated the term of r0 using experimental values in Table 1. Fig. 8 presents the effect of V2O5 concentration on r0, indicating almost unchanged value of r0 for V2O5:50–67.5 mol%. These results indicate that depends only on W in Eq. (7) in adiabatic regime for the present glasses as well as earlier glasses [20–22]. Then, based on this result, log at a given temperature is proportional to W and the log r–W relation should become log r = log r0 W/2.303kT from Eqs. (4) and (7). Fig. 10 shows the relationship between log l at 403 K and W. This relationship was linear for the present glasses. We filled the data to the relation log r vs. W for the present glasses by the least-square technique, and the slope of the regression line in Fig. 9 was obtained to be 12.33 eV1. This value is almost the same as the theoretical slope for the adiabatic hopping (tan h in Fig. 9), i.e. 12.33 eV1 (= 1/ 2.303 KT, T = 403 K). The equivalent temperature evaluated from the slope of regression line gave T = 408 K, which is nearly equal to the measured value T = 403 K. From the above results, we conclude the conduction of the present glasses to be due to adiabatic small polaron hopping of electrons. The adiabatic hopping was reported
Table 2 Polaron hopping parameters of V2O5–Fe2O3–TeO2 glasses Glass no.
WH ± 0.01 (eV)
ep ± 0.03
rp ± 0.001 (nm)
N(EF) (· 1021 eV1 cm3)
cp ± 0.1
1 2 3 4 5
0.40 0.38 0.36 0.35 0.32
47.48 49.56 52.10 53.36 58.36
0.160 0.161 0.162 0.163 0.164
3.79 4.93 9.59 9.98 10.49
13.92 13.03 12.20 11.38 10.02
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M.M. El-Desoky / Journal of Non-Crystalline Solids 351 (2005) 3139–3146
nearly the same as the values of V2O5–P2O5 [24] and V2O5–NiO–TeO2 glasses [4]. Thus, these estimated hD values indicate to be physically reasonable. Then, with the hD values, m0 was calculated using m0 = khD/h. The values of hD and m0 are summarized in Table 1. A polaron hopping model has been investigated by Holstein and co-workers [25] considering zero disorder energy and covering both the adiabatic and non-adiabatic hopping processes. On the basis of molecular crystal model, Emin and Holstein [25] have derived an expression for the dc conductivity
6
log σo (Sm-1)
5
4
3
r ¼ ð3e2 NR2 J 2 =2kT Þðp=kTW H Þð2aRÞ expðW H =kT Þ.
2
ð10Þ 1 48
50
52
54
56
58
60
62
64
66
68
V2O5 (mol%) Fig. 8. Effect of V2O5 content on pre-exponential factor, r0, for different glass compositions.
-1.2
-1.4
log σ (Sm-1)
-1.6
-1.8 Slope = -1/2.303 KT
r ¼ ð8m0 pe2 NR2 =3kT Þ exp½ðW H J Þ=kT ;
ð11Þ
where J is a polaron band width related to electron wave function overlap on the adjacent sites. The present experimental results follow Eq. (11) much more closely, with a thermal activation WH, which varies with Fe2O3 content. This model also provides an independent way of ascertaining the nature of hopping mechanism at high temperatures. The condition for the nature of hopping can be expressed by [26] 1=4 1=2 2kTW H hm0 J> ðadiabaticÞ ð12Þ p p and
-2.0
1=4 1=2 2kTW H hm0 J< p p
θ
-2.2
-2.4
-2.6 0.32
For the case of non-adiabatic hopping, while Emin and Holestein [26] have shown that for the case of adiabatic hopping
0.34
0.36
0.38
0.40
0.42
0.44
W (eV) Fig. 9. Effect of activation energy, W, on dc conductivity, r, at T = 403 K for different glass compositions.
for various vanadium tellurite glasses [21,22], and generally for V2O5 > 50 mol% [21,22]. The present glasses showed this conduction mode V2O5 P 50 mol%. As the adiabatic regime occurs at shorter V-ion spacing in high V2O5 concentration [21,22], the above result may be due to the effect of Fe ion on hopping between V-ions [23]. Next, we estimate the optical phonon frequency, m0, in Eq. (8) using the experimental data from Table 1, according to khD = hm0 (h is PlankÕs constant) [3,21]. To determine m0 for the different compositions, the Debye temperature hD was estimated by T > hD/2 (Eq. (5a)) using the hD values given in Table 1. hD of the present glasses was obtained to be 666–740 K, which was
ðnon-adiabaticÞ.
ð13Þ
The condition for the formation of small polaron is, however, given by J 6 WH/3. The limiting value of J calculated from the right-hand side of expression (12) or (13) at 400 K is of the order 0.0163–0.0165 eV, depending on the composition and therefore the condition for the existence of small polaron is satisfied. An unambiguous decision as to whether the polaron is actually in the adiabatic or in the non-adiabatic regime requires an estimate of the value of J, which can be obtained from [26] 3 1=2
J e3 ½N ðEF Þ=ðe0 ep Þ
.
ð14Þ
Using the values of N(EF) and ep from Table 2, Eq. (14) gives J 0.03 eV and thus adiabatic hopping theory is most appropriate to describe the polaronic conduction at high temperatures in the present glasses. Holstein [27] has suggested a method for calculating the polaron hopping energy WH 2
W H ¼ ð1=4N ÞRp ½cp hxp ;
ð15Þ
where [cp]2 is the electron–phonon coupling constant and xq is the frequency of the optical phonons of wave
M.M. El-Desoky / Journal of Non-Crystalline Solids 351 (2005) 3139–3146
number. Bogomolov et al. [28] have calculated the polaron radius rp for a nondispersive system of frequency t0 for Eq. (15) p1=3 R . ð16Þ rp ¼ 6 2
1 1 1 ¼ ; ep e1 eS
ð18Þ
eS and e1 are the static and high frequencies dielectric constants of the glass. An estimate of WH can be made from Eq. (17) from the known values of R and rp, while ep were estimated from cole–cole plot [29]. The values of WH and ep are given in Table 2. The values of small polaron coupling constant cp, a measure of electron–phonon interaction, given by the formula cp = 2WH/hm0 [8] were also evaluated for the present glasses. The estimated value of cp is 10.02– 13.92 (Table 2), which is larger than those for V2O5– Bi2O3 glasses doped with BaTiO3 (7.05–7.60) [30] and smaller than those for V2O5–NiO–TeO2 glasses (11.9– 18.65) [4]. The value of cp > 4 usually indicates a strong electron phonon interaction [19]. The hopping carrier mobility, l, and density, Nc were estimated for the present glasses. For adiabatic hopping regime, l is given by [31]. m0 eR2 l¼ ð19Þ expðW H =kT Þ kT then, l values were calculated for T = 400 K using the experimental data of m0, R and WH evaluated for different V2O5 concentration (Tables 1 and 2). Nc values were also evaluated using the formula r = eNcl. The results are shown in Fig. 10 and Table 3, indicating that the hopping mobility increases with V2O5 increase. The increase is expressed by the experimental relation l l0 exp[V2O5], similar to V2O5–MnO–TeO2 [11]. l values were evaluated to be (0.587–6.904) · 105 cm2 V1 s1 and Nc values 2.997 · 1019–7.298 · 1019 cm3, being the same order as those for V2O5– Sb2O3–TeO2 [21] and V2O5–MnO–TeO2 [11] glasses. Because the localization condition for hopping electrons is l 0.01 cm2 V1 s1 [31], the results mean that
2.0
5.0
1.5 4.5
4.0
log Nc (cm-3)
0.5 0.0
3.5
-0.5 3.0
2.5
2.0 48
50
52
54
56
µ
-1.0
Nc
-1.5
58
60
62
64
66
log µ (cm2 V-1 s-1)
1.0
The values of the polaron radii calculated from Eq. (16), using R from Table 1 is shown in Table 2 for the present glasses. Although the possible effect of disorder has been neglected in the above calculation, the small values of polaron radii suggest that the polarons are highly localized. These results are very similar to V2O5–NiO–TeO2 glasses [4]. The polaron hopping energy, WH, is given by [28] e2 1 1 WH ¼ ; ð17Þ 4ep rp R where
3145
-2.0 68
V2O5 (mol%) Fig. 10. Effect of V2O5 content on hopping carrier mobility, l, and density Nc for different glass compositions. Lines are drown connecting data symbols of each kind.
Table 3 Hopping carrier mobility and density of V2O5–Fe2O3–TeO2 glasses Glass no.
l (·105 cm2 V1 s1) (400 K)
Nc (·1019 cm3) (400 K)
1 2 3 4 5
0.587 ± 0.3 1.081 ± 0.4 1.972 ± 0.3 2.771 ± 0.4 6.904 ± 0.5
4.239 ± 0.2 3.330 ± 0.3 6.621 ± 0.3 7.298 ± 0.5 2.997 ± 0.2
electrons in the present glasses are localized mainly at V-ion site. Further, the nearly constant Nc 1019 cm3 indicates that the conductivity of the glasses is primarily determined by the hopping mobility [4,11]. The procedure suggested by Greaves [32] as a modification of MoltÕs model of the variable range hopping [19] could be applied at intermediate temperature and proposed the following expression for the dc conductivity: rT 1=2 ¼ A expðB=T 1=4 Þ;
ð20Þ
where A and B are constants and B is given by B ¼ 2:1½a3 =kN ðEF Þ
1=4
1/2
ð21Þ
. 1/4
A plot of ln(T ) vs. T is shown in Fig. 11. A good fit of the experimental data to expression (20) in the whole temperature range, suggesting that GreaveÕs variable range hopping may be valid in these glasses over the entire temperature range. The values of parameters A and B obtained from these curves are given in Table 4. Using the slope obtained from this linear relation and the value of N(EF) given in Table 2, we can apply expression (21) to calculate the factor a. These values of a and N(EF) are reasonable for the localized states [1,4,5].
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Greaves VRH model was found to be appropriate. The conduction was confirmed to obey the adiabatic small polaron hopping and was due to mainly electronic between V ions. The hopping carrier mobility varied from 0.587 · 105 cm2 V1 s1 to 6.904 · 105 cm2 V1 s1 at 400 K. The carrier density was evaluated to be 2.997 · 1019–7.298 · 1019 cm3. The dominant factor determining conductivity was the hopping carrier mobility in these glasses.
0.5 0.0
log σT1/2 (Sm-1 K1/2)
-0.5 -1.0 -1.5 -2.0
V2O5 (mol%) 50
-2.5
55 60
-3.0
References
62.5 -3.5 -4.0 0.215
65 0.220
0.225
0.230
T-1/4
0.235
0.240
0.245
(K-1/4)
Fig. 11. Relation between log(T1/2) and T1/4 for different glass compositions. Lines are drown by using the least-square technique for r values between 102 and 105 S m1.
Table 4 Parameters for Greaves variable-range hopping conduction of V2O5– Fe2O3–TeO2 glasses Glass no.
A ± 0.1 (S cm1 K1/2)
B ± 0.3 (K1/4)
a ± 0.001 (nm1)
1 2 3 4 5
21.32 21.43 21.44 20.63 19.24
100.43 100.233 97.864 93.349 87.081
0.075 0.069 0.065 0.063 0.062
5. Conclusions We have prepared semiconductive glasses in the system V2O5–Fe2O3–TeO2 by the press-quenching technique. IR, DSC, density and molar volume and dc conductivity of these glasses are reported. The network structure for the glass compositions with 65 and 62.5 mol% V2O5 is built up of VO5 polyhedra, while the other glass compositions consist of VO4 polyhedra. Density and glass transition temperature were observed to decrease with an increase in V2O5 content. The temperature dependence of the conductivity data has been analyzed in terms of different polaronic models. In high temperature region above hD/2 the Mott model of SPH between the nearest neighbors is consistent with the conductivity data, while at intermediate temperature the
[1] M.M. El-Desoky, Phys. Stat. Sol. (a) 195 (2) (2003) 422. [2] M.M. El- Desoky, S.M. Abo-Naf, J. Mater. Sci.: Mater. Electron. 15 (2004) 425. [3] M.M. El-Desoky, I. Kashif, Phys. Stat. Sol. (a) 194 (1) (2002) 89. [4] M.M. El-Desoky, J. Mater. Sci.: Mater. Electron. 14 (2003) 215. [5] A. Al-Shahrani, A. Al-Hajry, M.M. El-Desoky, Phys. Stat. Sol. (a) 300 (2003) 378. [6] M. Sayer, A. Mansingh, J. Non-Cryst. Solids 42 (1980) 357. [7] H.H. Qiu, T. Ito, H. Sakata, Mater. Chem. Phys. 58 (1999) 243. [8] N.F. Mott, Adv. Phys. 16 (1967) 49. [9] I.G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41. [10] M. Sayer, A. Manshingh, Phys. Rev. B 6 (1972) 4629. [11] K. Sega, Y. Kuroda, H. Sakta, J. Mater. Sci. 33 (1998) 1103. [12] H. Moi, T. Kitami, H. Sakata, J. Non-Cryst. Solids 168 (1994) 157. [13] S. Sen, A. Ghosh, J. Mater. Res. 15 (2000) 995. [14] S. Sen, A. Ghosh, J. Non-Cryst. Solids 258 (1999) 29. [15] V. Pimitrov, Y. Dimitiev, M. Arnaudov, D. Topalov, J. NonCryst. Solids 57 (1983) 147. [16] H. Sakata, K. Sega, B.K. Chaudhuri, Phys. Rev. B 50 (1999) 3230. [17] M.M. El-Desoky, N.M. Tashtoush, M.H. Habib, J. Mater. Sci.: Mater. Electron. 16 (2005) 533. [18] C.F. Drake, J.A. Stephens, B. Yates, J. Non-Cryst. Solids 28 (1978) 61. [19] N.F. Mott, E.A. Davis, Electronic Processes in Non-Crystalline Materials, Clarendon, Oxford, 1979. [20] H. Hirashima, H. Kurokawa, K. Mizobuchi, T. Yoshida, Glastech. Ber. 61 (1988) 151. [21] H. Mori, T. Kitami, H. Sakata, J. Non-Cryst. Solids 168 (1994) 157. [22] H. Mori, H. Sakata, Glastech. Ber. 68 (1995) 327. [23] K. Sega, H. Kasai, H. Sakata, Mater. Chem. Phys. 53 (1998) 28. [24] M.B. Field, J. Appl. Phys. 40 (1969) 2628. [25] L. Friedman, T. Holeston, Ann. Phys. 21 (1963) 494. [26] D. Emin, T. Holstein, Ann. Phys. (NY) 53 (1969) 439; L.D. Friedman, T. Holstein, Ann. Phys. (NY) 21 (1963) 494. [27] T. Holstein, Ann. Phys. 8 (1959) 343. [28] V.N. Bogomolov, E.K. Kudinev, U.N. Firsov, Sov. Phys. Solid State 9 (1968) 2502. [29] K.S. Cole, R.H. Cole, J. Chem. Phys. 9 (1941) 341. [30] A. Ghosh, J. Appl. Phys. 66 (1989) 2425. [31] M.H. Cohen, J. Non-Cryst. Solids 4 (1970) 391. [32] G.N. Greaves, J. Non-Cryst. Solids 11 (1973) 427.
Characterization and transport properties of V2O5–Fe2O3–TeO2 glasses M.M. El-Desoky
*
Department of Physics, Faculty of Education, Suez Canal University, El-Arish, Egypt Received 13 February 2005; received in revised form 1 August 2005
Abstract IR, DSC, density and molar volume, and dc conductivity of the glasses in V2O5–Fe2O3–TeO2 system were reported. The network structure for the glass compositions with 65 and 62.5 mol%, V2O5 is built up of VO5 polyhedra, while the other glass compositions consist of VO4 polyhedra. Density and glass transition temperature were observed to decrease with an increase in V2O5 content. The glasses had conductivities ranging from 3.31 · 103 S m1 to 2.88 · 102 S m1 at 400 K for V2O5 = 50–65 mol%. The electrical conductivity was confirmed to be due to adiabatic small polaron hopping. The hopping carrier mobility varied from 0.587 · 105 cm2 V1 s1 to 6.904 · 105 cm2 V1 s1 at 400 K. The carrier density was evaluated to be 2.997 · 1019–7.298 · 1019 cm3. The conductivity was primarily determined by hopping carrier mobility. 2005 Elsevier B.V. All rights reserved. PACS: 61.43.Fs; 61.40
1. Introduction The dc conductivities of transition metal oxide (TMO), glasses have been targeted for extensive studies [1–7] because of their interesting semiconducting properties as well as for their probable technological applications. The conduction mechanism in these glasses was presumed to be by the small polaron hopping (SPH) process [8,9]. Vanadate glasses with a large concentration of V2O5 (>50 mol%), e.g. V2O5–P2O5 [10], V2O5– NiO–TeO2 [4] and V2O5–MnO–TeO2 [11], glasses are highly conductive. Hopping conduction of these glasses was generally known to be adiabatic for V2O5 content above 50 mol%, while, for V2O5 < 50 mol% conduction became non-adiabatic [12]. The effect of the second transition metal oxide on the conductivity was reported [4,11] and the glasses containing two kinds of transition *
Present address: Physics Department, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia. E-mail address: [email protected] 0022-3093/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2005.08.004
metal ions, e.g. V2O5–NiO–TeO2 [4] and V2O5–MnO– TeO2 [11] systems, have become the center of this conductivity study. These glasses showed relatively high conductivities of 104 S cm1 above 400 K [12]. Highly conductive tellurite glasses containing TMO have a potential applicability as electrical devices (e.g. memory switching and gas sensor). The objective of the present work is to study the compositional dependence of the structure and semiconducting properties of V2O5–TeO2 based glasses in view of MottÕs theory. V2O5–Fe2O3–TeO2 system is suitable for this purpose because of its wide glass formation region.
2. Experimental Reagent grade V2O5 (99.9%), Fe2O3 (99.9%) and TeO2 (99.99%) were used as raw materials. After mixing in air, a batch of 5 g with the prescribed compositions, the mixed mass of each glass composition was melted in platinum crucible for 1 h at 1050 K in an electric
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furnace. The melt was then poured on a thick copper block and immediately quenched by pressing with another similar copper block. Following this procedure, we obtained bulk glass of 2 · 2 cm2 size and about 1 mm in thickness. The amorphous nature of the glasses was ascertained from X-ray diffraction analysis. The error in the density is estimated as ±0.025 g/cm3. IR spectra of the glass samples were measured from 400 to 2000 cm1 by a conventional KBr pellet method on a Fourier transform infrared (FT–IR) spectrometer (Perkin-Elmer 1760 X). Differential scanning calorimeter (DSC) of the samples was investigated using Shimadzu DSC-50 with a heating rate of 20 C/min. The dc conductivity (r) of the asquenched glasses was measured at temperatures between 300 and 423 K. Silver paste electrodes deposited on both faces of the polished samples. The I–V characteristic between electrodes was recorded.
V2O5 (mol%) 50
Transmission
55
60
62.5
65
3. Results 3.1. IR spectra
3.2. DSC Fig. 2 shows the glass transition temperature, Tg, of the present glass system. From Fig. 2, it is clear that Tg decreased with increasing V2O5 content and lies between 570 K and 580 K. Also, the crystallization temperature, Tc, lies between 645 K and 657 K for the present glass compositions. It is known that the thermal stability of a glass depends on DT = Tc Tg of the glass [17]. This result is due to the fact that the present glasses were thermaly stable in comparison with the thermal stability of V2O5–MnO–TeO2 glasses [11], because the DT values of the present glasses (DT 76 K) were higher than those of V2O5–MnO–TeO2 glasses [11] (DT 60 K).
300 500 700 900 1100 1300 1500 1700 1900 2100
Wavenumber (cm)-1 Fig. 1. Room-temperature IR spectra for V2O5–Fe2O3–TeO2 glasses. 582
580
578
Tg (K)
The room temperature IR spectra in the region 400– 2000 cm1 of all glass compositions, are shown in Fig. 1. All the spectra show a water band at 1620–1630 cm1. The origin of this band might be due to the –OH bending mode and absorbed water [13,14]. Also, a weak band at 1000–1020 cm1 is observed for some glasses. This band is assigned to the vibrations of the isolated V@O vanadyl groups in VO5 trigomal bi-pyramids [13]. However, in the glass compositions containing 60–50 mol% V2O5 the band at 1000 cm1 vanishes completely.
576
574
572
570
568 48
50
52
54
56
58
60
62
64
66
68
V2O5 (mol%) Fig. 2. Composition dependence of glass transition temperature, Tg, for V2O5–Fe2O3–FeO2 glasses.
with the increase of vanadium oxide content in the glass compositions.
3.3. Density and molar volume 3.4. Electrical conductivity The composition dependence of the density of the present glass samples is shown in Fig. 3 and Table 1. It may be observed that density, d, decreases gradually
Fig. 4 shows the arrhenius plot of log (r) between 300 and 423 K. Deviation from a linear curve occurs around
M.M. El-Desoky / Journal of Non-Crystalline Solids 351 (2005) 3139–3146 -0.5
4.10
41.0
3141
-1.0 Vm
40.5
4.05
-1.5
4.00
39.5
3.95
39.0
3.90
38.5
3.85
38.0
3.80
-2.0
log σ (Sm-1)
40.0
d (g/cm3)
Vm (cm3/mol%)
d
-2.5 -3.0 -3.5
V2O5 mol% 50 55 60 62.5 65
-4.0 -4.5
37.5 48
50
52
54
56
58
60
62
64
66
-5.0 -5.5 2.2
3.75 68
2.4
2.6
V2O5 (mol%) Fig. 3. Composition dependence of density, d, and oxygen molar volume, Vm, for V2O5–Fe2O3–TeO2 glasses. Lines are drown connecting data symbols of each kind.
hD/2 (333–370 K, depending on concentration). Fig. 4 indicates the temperature dependent activation energy. The experimental conductivity data in such a situation is well described with an activation energy for conduction (W) given by Mott formula [8,9]. r ¼ r0 expðW =kT Þ;
2.8
3.0
3.2
3.4
3.6
1000/T (K)-1
ð1Þ
where r0 is a pre-exponential factor as discussed below. W values obtained from fitting of the linear part of the curves in Fig. 4 (high temperature regime) are given in Table 1. For these glass samples r2 = 0.9900 (r = is the correlation coefficient) and range = 1.02 · 105 S m1 in were obtained, which indicate a satisfactory fit. At temperature lower than 370 K the linearity between log (r) and 1/T deviated appreciably as seen from Fig. 4.
4. Discussion According to the mechanism suggested earlier [15], the iron ions occupy a position between V–O–V layers. This is why they have a direct influence on the isolated
Fig. 4. Temperature dependence of dc conductivity, r, for V2O5– Fe2O3–TeO2 glasses.
V@O bonds of VO5 groups according to scheme Fe– O–V. As a result of this, they should be longer and the frequencies of vibrations should be shifted towards the lower wavenumbers. A similar manner of interaction has been discussed concerning glasses, having a V2O5– TeO2 composition [16]. In the glass containing 62.5– 65 mol% V2O5 (i.e. lower Fe2O3 content), VO5 groups with unaffected V@O bonds are preserved along with the affected VO5 polyhedra [14]. With the increase of Fe2O3 (beyond 7.5 mol%), only affected VO5 polyhedra are obtained in the glass compositions containing 60– 50 mol% V2O5. This means that the network structure is build up of VO5 polyhedra for the glass compositions with higher V2O5 content [14]. However, as V2O5 content decreases the glass structure consists of VO4 polyhedra [13–15]. Finally, Dimitriv et al. [15] attributed the IR spectra absorption band in the range from 645 to 665 cm1, to TeO3 trigonal pyramids. Thermal stability of glasses is a result of glass structure. Generally, thermally stable glasses have a closely backed structure [12]. Inversely, the structure of thermally unstable glasses possesses a loose packing [12]. Thus, we assumed that the present glasses have a more closely packed structure. For vanadate glasses, when a
Table 1 Chemical composition and physical properties of V2O5–Fe2O3–TeO2 glasses Glass no.
1 2 3 4 5
Nominal composition (mol%) V2O5
Fe2O3
TeO2
50 55 60 62.5 65
20 15 10 7.5 5
30 30 30 30 30
W ± 0.01 (eV)
d ± 0.01 (g cm3)
N ± 0.01 (· 1022 cm3)
R ± 0.01 (nm)
hD ± 1 (K)
m0 ± 0.01 (· 1013 s1)
0.43 0.40 0.38 0.36 0.34
4.05 3.97 3.89 3.85 3.81
1.575 1.549 1.523 1.510 1.575
0.398 0.401 0.403 0.405 0.406
666 676 684 712 740
1.388 1.408 1.425 1.484 1.542
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layered-network structure including a VO4 polyhedra unit [13] increases in the concentration, the glasses form a closely backed structure [13,14], while the glasses form a loosely packed structure, when the network structure with VO5 polyhedra unit increases in concentration [13]. Since the present glasses became thermally stable by containing Fe2O3 substituted as MnO, we assumed that the glass structure containing VO5 units changed to the structure with VO4 units [5,14]. The relationship between density and composition of an oxide glass system can be expressed in terms of an apparent volume, Vm, occupied by 1 g atom of oxygen. The value of Vm has been calculated from the density and composition using the formula reported earlier [18] and its composition dependence is shown in Fig. 3. It is observed that Vm increases monotonically with an increase of V2O5 content in the composition which indicates that the topology of the network does not significantly change with composition. On the other hand, these trends can be explained rather simply as due to the replacement of a heavier cation (Fe) by a lighter one (V) [13,14]. Fig. 5 shows the plot of activation energy and electrical conductivity at constant temperature (403 K) as a function of V2O5 content. It is observed that as the percentage of V2O5 increases, the activation of electrical conduction decreases and electrical conductivity increases, in a linear manner. This is consistent qualitatively with Eq. (1) proposed for polaron hopping at high temperatures [8,9]. The high value of activation energy and low value of electrical conductivity are similar to those for V2O5–BaO–B2O3 and V2O5–NiO–TeO2 glasses [1,4].
Fig. 6 presents the variation in conductivity with increasing in V2O5 content at two temperatures (303 K and 403 K). This means a ratio of V4+ ion CV (=V4+/ Vtotal) increases, causing the activation energy, W, to decrease and electrical conductivity, r, to increase (Fig. 5). In V2O5–Fe2O3–TeO2 glasses of our present investigation, Fe2O3 addition lowered the conductivity. This means, Fe ion in the glass hindered the carrier transport [4,11]. Because Fe2O3 is not a glass network former, Fe ions are isolated in the glass network, which causes obstruction in the hopping of electrons due to the lack of oxygen bonds. A similar lowering of conductivity was also observed in V2O5–MnO–TeO2 [11], V2O5– NiO–TeO2 [4] and V2O5–CoO–TeO2 [16] glasses. In order to confirm the W–R relation, the V-ion density, N, was calculated using the following formula [21]: N ¼ 2½ðdWtV2 O5 =MW V2 O5 ÞN A ;
where d is the density, WtV2 O5 the weight fraction of V2O5, MW V2 O5 the molecular weight of V2O5 and NA is the Avogadro number, respectively. The relationship between N and mean distance, R, is generally described as follows: R ¼ ð1=N Þ
1=3
ð3Þ
.
The calculated values of R and N are summarized in Table 1. The relation between the activation energy (W) and the mean distance, R, between V ions is illustrated in Fig. 7 and Table 1. In the range of measurements, W depends on the site-to-site distance R. These results show that there is a prominent positive correlation between W and R between transition metal ions. This agrees with the results suggested by Sayer and Mansingh [6] and ElDesoky [4] which delineated the dependence of W on the
-2.6
0.44
-1.0
σ 0.42
-2.8
W
403 K
0.40
-2.0
-3.6 0.36 -3.8
log σ (Sm)-1
-3.4
W (eV)
-3.2 0.38
303 K
-1.5
-3.0
log σ (Sm-1)
ð2Þ
-2.5
-3.0
-3.5
0.34 -4.0 -4.0 0.32 48
50
52
54
56
58
60
62
64
66
-4.2 68
V2O5 (mol%)
-4.5 48
50
52
54
56
58
60
62
64
66
68
V2O5 (mol%) Fig. 5. Effect of V2O5 content on dc conductivity, r, and activation energy for different glass compositions. Lines are drown connecting data symbols of each kind.
Fig. 6. Effect of V2O5 content on dc conductivity, r, for different glass compositions. Lines are drown as guides for the eye.
M.M. El-Desoky / Journal of Non-Crystalline Solids 351 (2005) 3139–3146
Cv = V4+/Vtotal), a the tunneling factor (the ratio of wave function decay), WH the hopping energy and WD is the disorder energy defined as the difference of electronic energies between two hopping sites [19]. The density of state at Fermi level can be estimated from the following expression [19]:
0.44
0.42
0.40
W (eV)
3143
N ðEF Þ ¼ 3=4pR3 W .
ð7Þ
0.38
The results for the present glasses are listed in Table 2. The values of N(EF) are reasonable for localized states. In the adiabatic hopping regime, however, aR in Eq. (4) becomes negligible [17,19], then the conductivity, r, and the pre-exponential factor r0 in Eq. (4) is expressed by the following equations [8,9]:
0.36
0.34
0.32 0.396
0.399
0.402
0.405
r¼
0.408
R (nm)
m0 Ne2 R2 Cð1 CÞ expðW =kT Þ kT
ð8Þ
and Fig. 7. Effect of mean V-ion spacing, R, on activation energy, W, for different glass compositions.
mean distance between TM ions. A similar behavior was observed in V2O5–NiO–TeO2 [4] glasses. The logarithm of the conductivity (Fig. 4) shows linear temperature dependence up to a critical temperature hD/2 and then the slope changes with deviation from linearity and the activation energy is temperature dependent. Such a behavior is a feature of SPH [8,9]. So, we first discuss the thermal variation of conductivity assuming the SPH model [8,9] based on a strong coupling of electron with the lattice by a single phonon. This model gives in the non-adiabatic regime for TMO glasses as given by Eq. (1), viz. r¼
m0 Ne2 R2 Cð1 CÞ expð2aRÞ expðW =kT Þ. kT
ð4Þ
The activation energy W can be written as W ¼ W H þ W D =2 ðfor T > hD =2Þ; W ¼ W D ðfor T < hD =4Þ.
ð5aÞ ð5bÞ
The pre-exponential factor in Eq. (1) is given by r0 ¼ m0 Ne2 R2 Cð1 CÞ expð2aRÞ=kT ;
ð6Þ
where m0 is the optical phonon frequency (generally m0 ’ 1013 s1 [3,21], N the transition metal density, C the fraction of reduced transition metal ion (= Cv and
r0 ¼ m0 Ne2 R2 Cð1 CÞ=kT .
ð9Þ
From Eq. (8) r0 is independent of V2O5 concentration and hardly varies with V2O5 content [19]. Therefore, the dominant factor contributing to the conductivity should be W in the adiabatic regime [4,20]. For the present glasses, we calculated the term of r0 using experimental values in Table 1. Fig. 8 presents the effect of V2O5 concentration on r0, indicating almost unchanged value of r0 for V2O5:50–67.5 mol%. These results indicate that depends only on W in Eq. (7) in adiabatic regime for the present glasses as well as earlier glasses [20–22]. Then, based on this result, log at a given temperature is proportional to W and the log r–W relation should become log r = log r0 W/2.303kT from Eqs. (4) and (7). Fig. 10 shows the relationship between log l at 403 K and W. This relationship was linear for the present glasses. We filled the data to the relation log r vs. W for the present glasses by the least-square technique, and the slope of the regression line in Fig. 9 was obtained to be 12.33 eV1. This value is almost the same as the theoretical slope for the adiabatic hopping (tan h in Fig. 9), i.e. 12.33 eV1 (= 1/ 2.303 KT, T = 403 K). The equivalent temperature evaluated from the slope of regression line gave T = 408 K, which is nearly equal to the measured value T = 403 K. From the above results, we conclude the conduction of the present glasses to be due to adiabatic small polaron hopping of electrons. The adiabatic hopping was reported
Table 2 Polaron hopping parameters of V2O5–Fe2O3–TeO2 glasses Glass no.
WH ± 0.01 (eV)
ep ± 0.03
rp ± 0.001 (nm)
N(EF) (· 1021 eV1 cm3)
cp ± 0.1
1 2 3 4 5
0.40 0.38 0.36 0.35 0.32
47.48 49.56 52.10 53.36 58.36
0.160 0.161 0.162 0.163 0.164
3.79 4.93 9.59 9.98 10.49
13.92 13.03 12.20 11.38 10.02
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M.M. El-Desoky / Journal of Non-Crystalline Solids 351 (2005) 3139–3146
nearly the same as the values of V2O5–P2O5 [24] and V2O5–NiO–TeO2 glasses [4]. Thus, these estimated hD values indicate to be physically reasonable. Then, with the hD values, m0 was calculated using m0 = khD/h. The values of hD and m0 are summarized in Table 1. A polaron hopping model has been investigated by Holstein and co-workers [25] considering zero disorder energy and covering both the adiabatic and non-adiabatic hopping processes. On the basis of molecular crystal model, Emin and Holstein [25] have derived an expression for the dc conductivity
6
log σo (Sm-1)
5
4
3
r ¼ ð3e2 NR2 J 2 =2kT Þðp=kTW H Þð2aRÞ expðW H =kT Þ.
2
ð10Þ 1 48
50
52
54
56
58
60
62
64
66
68
V2O5 (mol%) Fig. 8. Effect of V2O5 content on pre-exponential factor, r0, for different glass compositions.
-1.2
-1.4
log σ (Sm-1)
-1.6
-1.8 Slope = -1/2.303 KT
r ¼ ð8m0 pe2 NR2 =3kT Þ exp½ðW H J Þ=kT ;
ð11Þ
where J is a polaron band width related to electron wave function overlap on the adjacent sites. The present experimental results follow Eq. (11) much more closely, with a thermal activation WH, which varies with Fe2O3 content. This model also provides an independent way of ascertaining the nature of hopping mechanism at high temperatures. The condition for the nature of hopping can be expressed by [26] 1=4 1=2 2kTW H hm0 J> ðadiabaticÞ ð12Þ p p and
-2.0
1=4 1=2 2kTW H hm0 J< p p
θ
-2.2
-2.4
-2.6 0.32
For the case of non-adiabatic hopping, while Emin and Holestein [26] have shown that for the case of adiabatic hopping
0.34
0.36
0.38
0.40
0.42
0.44
W (eV) Fig. 9. Effect of activation energy, W, on dc conductivity, r, at T = 403 K for different glass compositions.
for various vanadium tellurite glasses [21,22], and generally for V2O5 > 50 mol% [21,22]. The present glasses showed this conduction mode V2O5 P 50 mol%. As the adiabatic regime occurs at shorter V-ion spacing in high V2O5 concentration [21,22], the above result may be due to the effect of Fe ion on hopping between V-ions [23]. Next, we estimate the optical phonon frequency, m0, in Eq. (8) using the experimental data from Table 1, according to khD = hm0 (h is PlankÕs constant) [3,21]. To determine m0 for the different compositions, the Debye temperature hD was estimated by T > hD/2 (Eq. (5a)) using the hD values given in Table 1. hD of the present glasses was obtained to be 666–740 K, which was
ðnon-adiabaticÞ.
ð13Þ
The condition for the formation of small polaron is, however, given by J 6 WH/3. The limiting value of J calculated from the right-hand side of expression (12) or (13) at 400 K is of the order 0.0163–0.0165 eV, depending on the composition and therefore the condition for the existence of small polaron is satisfied. An unambiguous decision as to whether the polaron is actually in the adiabatic or in the non-adiabatic regime requires an estimate of the value of J, which can be obtained from [26] 3 1=2
J e3 ½N ðEF Þ=ðe0 ep Þ
.
ð14Þ
Using the values of N(EF) and ep from Table 2, Eq. (14) gives J 0.03 eV and thus adiabatic hopping theory is most appropriate to describe the polaronic conduction at high temperatures in the present glasses. Holstein [27] has suggested a method for calculating the polaron hopping energy WH 2
W H ¼ ð1=4N ÞRp ½cp hxp ;
ð15Þ
where [cp]2 is the electron–phonon coupling constant and xq is the frequency of the optical phonons of wave
M.M. El-Desoky / Journal of Non-Crystalline Solids 351 (2005) 3139–3146
number. Bogomolov et al. [28] have calculated the polaron radius rp for a nondispersive system of frequency t0 for Eq. (15) p1=3 R . ð16Þ rp ¼ 6 2
1 1 1 ¼ ; ep e1 eS
ð18Þ
eS and e1 are the static and high frequencies dielectric constants of the glass. An estimate of WH can be made from Eq. (17) from the known values of R and rp, while ep were estimated from cole–cole plot [29]. The values of WH and ep are given in Table 2. The values of small polaron coupling constant cp, a measure of electron–phonon interaction, given by the formula cp = 2WH/hm0 [8] were also evaluated for the present glasses. The estimated value of cp is 10.02– 13.92 (Table 2), which is larger than those for V2O5– Bi2O3 glasses doped with BaTiO3 (7.05–7.60) [30] and smaller than those for V2O5–NiO–TeO2 glasses (11.9– 18.65) [4]. The value of cp > 4 usually indicates a strong electron phonon interaction [19]. The hopping carrier mobility, l, and density, Nc were estimated for the present glasses. For adiabatic hopping regime, l is given by [31]. m0 eR2 l¼ ð19Þ expðW H =kT Þ kT then, l values were calculated for T = 400 K using the experimental data of m0, R and WH evaluated for different V2O5 concentration (Tables 1 and 2). Nc values were also evaluated using the formula r = eNcl. The results are shown in Fig. 10 and Table 3, indicating that the hopping mobility increases with V2O5 increase. The increase is expressed by the experimental relation l l0 exp[V2O5], similar to V2O5–MnO–TeO2 [11]. l values were evaluated to be (0.587–6.904) · 105 cm2 V1 s1 and Nc values 2.997 · 1019–7.298 · 1019 cm3, being the same order as those for V2O5– Sb2O3–TeO2 [21] and V2O5–MnO–TeO2 [11] glasses. Because the localization condition for hopping electrons is l 0.01 cm2 V1 s1 [31], the results mean that
2.0
5.0
1.5 4.5
4.0
log Nc (cm-3)
0.5 0.0
3.5
-0.5 3.0
2.5
2.0 48
50
52
54
56
µ
-1.0
Nc
-1.5
58
60
62
64
66
log µ (cm2 V-1 s-1)
1.0
The values of the polaron radii calculated from Eq. (16), using R from Table 1 is shown in Table 2 for the present glasses. Although the possible effect of disorder has been neglected in the above calculation, the small values of polaron radii suggest that the polarons are highly localized. These results are very similar to V2O5–NiO–TeO2 glasses [4]. The polaron hopping energy, WH, is given by [28] e2 1 1 WH ¼ ; ð17Þ 4ep rp R where
3145
-2.0 68
V2O5 (mol%) Fig. 10. Effect of V2O5 content on hopping carrier mobility, l, and density Nc for different glass compositions. Lines are drown connecting data symbols of each kind.
Table 3 Hopping carrier mobility and density of V2O5–Fe2O3–TeO2 glasses Glass no.
l (·105 cm2 V1 s1) (400 K)
Nc (·1019 cm3) (400 K)
1 2 3 4 5
0.587 ± 0.3 1.081 ± 0.4 1.972 ± 0.3 2.771 ± 0.4 6.904 ± 0.5
4.239 ± 0.2 3.330 ± 0.3 6.621 ± 0.3 7.298 ± 0.5 2.997 ± 0.2
electrons in the present glasses are localized mainly at V-ion site. Further, the nearly constant Nc 1019 cm3 indicates that the conductivity of the glasses is primarily determined by the hopping mobility [4,11]. The procedure suggested by Greaves [32] as a modification of MoltÕs model of the variable range hopping [19] could be applied at intermediate temperature and proposed the following expression for the dc conductivity: rT 1=2 ¼ A expðB=T 1=4 Þ;
ð20Þ
where A and B are constants and B is given by B ¼ 2:1½a3 =kN ðEF Þ
1=4
1/2
ð21Þ
. 1/4
A plot of ln(T ) vs. T is shown in Fig. 11. A good fit of the experimental data to expression (20) in the whole temperature range, suggesting that GreaveÕs variable range hopping may be valid in these glasses over the entire temperature range. The values of parameters A and B obtained from these curves are given in Table 4. Using the slope obtained from this linear relation and the value of N(EF) given in Table 2, we can apply expression (21) to calculate the factor a. These values of a and N(EF) are reasonable for the localized states [1,4,5].
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M.M. El-Desoky / Journal of Non-Crystalline Solids 351 (2005) 3139–3146
Greaves VRH model was found to be appropriate. The conduction was confirmed to obey the adiabatic small polaron hopping and was due to mainly electronic between V ions. The hopping carrier mobility varied from 0.587 · 105 cm2 V1 s1 to 6.904 · 105 cm2 V1 s1 at 400 K. The carrier density was evaluated to be 2.997 · 1019–7.298 · 1019 cm3. The dominant factor determining conductivity was the hopping carrier mobility in these glasses.
0.5 0.0
log σT1/2 (Sm-1 K1/2)
-0.5 -1.0 -1.5 -2.0
V2O5 (mol%) 50
-2.5
55 60
-3.0
References
62.5 -3.5 -4.0 0.215
65 0.220
0.225
0.230
T-1/4
0.235
0.240
0.245
(K-1/4)
Fig. 11. Relation between log(T1/2) and T1/4 for different glass compositions. Lines are drown by using the least-square technique for r values between 102 and 105 S m1.
Table 4 Parameters for Greaves variable-range hopping conduction of V2O5– Fe2O3–TeO2 glasses Glass no.
A ± 0.1 (S cm1 K1/2)
B ± 0.3 (K1/4)
a ± 0.001 (nm1)
1 2 3 4 5
21.32 21.43 21.44 20.63 19.24
100.43 100.233 97.864 93.349 87.081
0.075 0.069 0.065 0.063 0.062
5. Conclusions We have prepared semiconductive glasses in the system V2O5–Fe2O3–TeO2 by the press-quenching technique. IR, DSC, density and molar volume and dc conductivity of these glasses are reported. The network structure for the glass compositions with 65 and 62.5 mol% V2O5 is built up of VO5 polyhedra, while the other glass compositions consist of VO4 polyhedra. Density and glass transition temperature were observed to decrease with an increase in V2O5 content. The temperature dependence of the conductivity data has been analyzed in terms of different polaronic models. In high temperature region above hD/2 the Mott model of SPH between the nearest neighbors is consistent with the conductivity data, while at intermediate temperature the
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