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Effect of sulfur addition on the transport properties of semiconducting iron phosphate glasses
Solid State Sciences 13 (2011) 1616e1622
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Effect of sulfur addition on the transport properties of semiconducting iron phosphate glasses M.M. El-Desoky a, *, F.A. Ibrahim b, M.Y. Hassaan c a
Physics Department, Faculty of Science, Suez Canal University, Suez, Egypt Department of Physics, Faculty of Education, Suez Canal University, Al-Arish, Egypt c Department of Physics, Faculty of Science, Al-Azhar University, Nasr City, 11884 Cairo, Egypt b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 January 2011 Received in revised form 27 May 2011 Accepted 10 June 2011 Available online 16 June 2011
Transport properties and redox state of iron in glasses with compositions Se (40 Fe2O3 e 60 P2O5)(mol %), where x ¼ 0, 2,4,6 and 8 (mass%), were studied. The overall features of the XRD curves confirm the amorphous nature of the present glasses. Sulfur acted as a reducing agent for redox reaction during glass synthesis and affected the conductivity. Mössbauer spectral analyses revealed that the Fe2þ ratio increases with increasing sulfur content. The high temperature above q/2 (qD Debye temperature) dependence of conductivity could be qualitatively explained by the small polaron hopping model. The physical parameters obtained from the best fits of this model are found reasonable and consistent with the glass compositions. The conduction is confirmed to be due to adiabatic small polaron hopping of electrons between iron ions. The electronephonon interaction coefficient gp was large (21.42e26.26). The estimated hopping mobility was low, 1.12 109e24.83 109 cm2 V1 s1 and increased with increasing S(mass%) content. Moreover, the low temperature (below q/2) conductivity could not be explained either by Mott’s or greaves variable e range hopping model giving rise to unusually large values of the density of states at the Fermi level compared to those of transition metal oxide glasses. The conductivity of the present glasses was primarily determined by hopping carrier mobility. Ó 2011 Elsevier Masson SAS. All rights reserved.
Keywords: Phosphate glasses Electrical conductivity Mössbauer spectral XRD SPH
1. Introduction Iron phosphate glasses of approximate composition 40Fe2O3e60P2O5 (mol%) have recently gained attention because of their potential use as host materials for vitrifying high level nuclear wastes [1]. The excellent chemical durability and high waste loading ability of these iron phosphate glasses are two of several features which make them attractive for nuclear waste vitrification. The properties and structure of iron phosphate glasses have been investigated [1e4], but the effect of sulfur ion on the properties and redox state of iron phosphate glasses have been rarely studied to our knowledge. Iron phosphate glasses melted in air are electronically conducting glasses [5e7]. Their electron conducting behavior is due to iron ions being in more than valance state, namely as Fe2þ and Fe3þ. Conduction in these glasses takes place by electrons hopping from low to high valance sites (from Fe2þ to Fe3þ). The charge transfer in such glasses is usually termed “small polaron hopping” (SPH) [8e10] and the electrical conductivity depends strongly upon the
* Corresponding author. E-mail address: [email protected] (M.M. El-Desoky). 1293-2558/$ e see front matter Ó 2011 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2011.06.012
distance between the irons [10]. In iron phosphate glasses, the charge carrier concentration is related to the total concentration of iron ions and to the ratio of Fe2þ ions to the total quantity of iron P (Fe2þ/ Fe) [3]. In the present study, considering that P2O5 is a glass network former and S acts as a reducing agent for redox reaction during the glass synthesis, and causes the conductivity of the glass to increase, an SeFe2O3eP2O5 system was selected. The redox state of iron ions in these glass compositions was determined by Mössbauer spectroscopy [10]. The electrical conduction mechanism of the glass was investigated by measuring its dc conductivity. 2. Experimental Glass samples were prepared from analytical reagent grade chemicals according to the formula Se (40 Fe2O3 e 60 P2O5)(mol %), where x ¼ 0, 2,4,6 and 8 (mass%). Batches that produced 20 g of glass were prepared by mixing reagent grade Fe2O3, P2O5 and S crystalline powders that were melted in platinum crucibles in air at 1200 C for 1 h with occasional stirring, when poured onto a polished copper block kept at room temperature and immediately pressed by a similar copper block.
M.M. El-Desoky et al. / Solid State Sciences 13 (2011) 1616e1622
The amorphous nature of the glasses was ascertained from X-ray diffraction analysis. The density of the glasses was measured by the Archimedes method using toluene as the immersion liquid. P The fraction of reduced transition metal ion (C ¼ Fe2þ/ Fe) in these glass compositions were determined by Mössbauer spectroscopy performed at room temperature using 57Co(Rh) source of 925 MBq [10].The Mössbauer spectroscopy results were described in detail in our previous paper [10]. The dc conductivity (s) of the as-quenched glasses was measured at temperatures between 303and 473K. Silver paste electrodes deposited on both faces of the polished samples. The IeV characteristic between electrodes was verified.
1617
-4 0 S(mass%)
-5
-1
log σ (Sm )
-6
2
``
4
``
6
``
8
``
-7
-8
-9
3. Results and discussion -10
3.1. XRD The X-ray diffraction (XRD) patterns of several compositions of the prepared samples are shown in Fig. 1. From the XRD studies it is observed that homogenous glasses are formed for S concentration between 0 and 8 mass%. The overall features of these XRD patterns confirm the amorphous nature of the present glasses. The XRD patterns (Fig. 1) indicate glassy behavior with a broad hump at 2q ¼ 20e22 . No peak corresponding to S is observed indicating that S has completely entered the glass matrix. 3.2. Electrical conductivity 3.2.1. Conductivity and activation energy The electrical conductivity (s) for several glass compositions is shown in Fig. 2 as a function of 1/T. Fig. 2 shows a linear temperature dependence up to a critical temperature qD/2 (qD Debye temperature) and then the slope changes with deviation from linearity and the activation energy is temperature dependent. Such a behavior is a feature of SPH [7e10]. However, above this temperature range, the variation of activation energy with temperature is negligibly small so that the behavior may be treated as activated. The activation energy and pre-exponential factor (so)
S (mass%)
-11 2.0
3
3.2
3.6
-1
10 /T(K ) Fig. 2. Temperature dependence of dc conductivity (s) for different glass compositions. The solid lines are calculated by using the least -square.
were obtained from the least square straight line fits of the data above 335K. The compositional dependence of the conductivity at 405K and the activation energy are shown in Fig. 3. A general trend observed in Fig. 3 is that the magnitude of the conductivity at fixed (405K) tends to be highest in those compositions having smallest activation energy, which is consistent with SPH mechanism [7,8]. The semiconducting behavior of iron phosphate [11], mixed alkali iron phosphate [3], iron lead borate [12] and iron tellurite [13] glasses were understood by SPH between iron ions under different valance states [8e10]. Fig. 4 shows the electrical conductivity (s) P and the fraction of reduced transition metal ion (C ¼ Fe2þ/ F) measured of our previous work [10] as a function of S (mass%) content in the present glasses. Fig. 4 shows the electrical conductivity (s) for the present glasses within an order of magnitude of that of iron phosphate glasses [3,11]. Since the electrical conduction in iron phosphate glasses is assumed [3,11] to be due to electron hopping from Fe2þ to Fe3þ sites, it is reasonable to assume that electron hopping also occurs in the sulfurecontaining iron phosphate glasses. Also, from Fig. 4 it is clear that the C increases with increasing S(mass%) content; a similar behavior is observed for the
8
-7.9
0.74
-8.2
W
0.72
6
Intensity (a.u)
2.8
2.4
σ -8.5
W(eV)
-8.8
-1
4
0.68 -9.1
2
log σ (Sm )
0.70
0.66 -9.4
0 0.64
-9.7
0.62
10
20
30
40
50
2θ (degree) Fig. 1. XRD for different glass compositions.
60
-10.0 0
1
2
3
4
5
6
7
8
S (mass%) Fig. 3. Effect of S content on dc conductivity at T ¼ 400K and activation energy (W) for different glass compositions.
1618
M.M. El-Desoky et al. / Solid State Sciences 13 (2011) 1616e1622
-8.0
0.140
-8.2
0.135
-8.4
0.130 0.125
-8.8 0.120
c
-1 log σ (Sm )
-8.6
-9.0 0.115 -9.2
C
σ
-9.4
0.110 0.105
-9.6 -9.8
0.100 0
1
2
3
4
5
6
7
8
s (mass%) Fig. 4. The dc conductivity (s) at 303K and TM ion ratio (C) for different glass compositions. Lines are drown as guides for the eye.
electrical conductivity results. This indicates that the mechanism of electrical conductivity of sulfur e containing iron phosphate glasses were understood by SPH between iron ions under different valance states [8e10]. Mott [7] has investigated the hopping conductivity in oxide glasses containing transition metal ions. The conductivity of the nearest neighbor at high temperatures (T > qD/2) is given by [7]
s¼
no Ne2 R2
Cð1 CÞexp ð2aRÞexp ðW=kTÞ kT ¼ so exp ðW=kTÞ
(1)
The pre-exponential factor (so) in Eq. (1) is given by
so ¼
no Ne2 R2 kT
Cð1 CÞexpð2aRÞ
(2)
where no is the optical phonon frequency, a is the tunneling factor (the ratio of wave function decay), N the transition metal density, C P the fraction of reduced transition metal ion (C ¼ Fe2þ/ Fe) and W is the activation energy for hopping conduction. Assuming a strong electronephonon interaction, Austin and Mott [8] have shown that
W ¼ WH þ WD =2 W ¼ WD
ðfor T >= qD =2Þ
ðfor T < qD =4Þ
(3a) (3b)
Where WH is the hopping energy, qD is the Debye temperature and WD is the disorder energy defined as the difference of electronic energies between two hopping sites [14] and is given by [15]
WD ¼
e2 =3s R L
(4)
where es is the static dielectric constant and L is a constant of order 0.3. The values of WD and W are summarized in Tables 1 and 2. In the adiabatic hopping regime, however, aR in Eq. (1) becomes negligible [14,16], then the conductivity (s) and the preexponential factor (so) in Eq. (1) is expressed by the following equations [7,8]
s¼
no Ne2 R2 kT
Cð1 CÞexp ðW=kTÞ
so ¼ no Ne2 R2 Cð1 C=kTÞ
From Eq. (6) so is independent of S (mass%) and hardly varies with it [14]. Therefore, the dominant factor contributing to the conductivity should be W in the adiabatic regime [16]. For the present glasses, we calculated the term of so using experimental values in Table 1. Fig. 5 presents the effect of S (mass%) concentration on so, indicating almost unchanged value of so for S ¼ 0e8 mass%. These results indicate that s depends only on W in Eq. (5) in adiabatic regime for the present glasses as well as previous glasses [17,18]. Then, based on this result, log s at a given temperature is proportional to W and the log seW relation should become log s ¼ log soeW/2.303 kT from Eqs. (1) and (5). Fig. 5 shows the relationship between log s at 405 K and W. This relationship was linear for the present glasses. We fitted the data to the relation log s vs. W for the present glasses by the least e square technique, and the slope of the regression line in Fig. 6 was obtained to be 12.26 eV1. This value almost the same as the theoretical slope for the adiabatic hopping (tan q in Fig. 6), i.e. 12.91 eV1 (¼ 1/ 2.303 kT, T ¼ 405 K). The equivalent temperature evaluated from the slope of regression line gave T ¼ 400K, which is nearly equal to the measured value T ¼ 405 K. From both these results, we conclude the conduction of the present glasses to be due to adiabatic small polaron hopping of electrons. Fig. 7Shows the relationship between activation energy (W) and the mean distance (R). Here we regarded R as the Fe e Fe ion spacing calculated from R ¼ N1/3, on the basis of the glass densities measured (Table 1). The values of (R) are listed in Table 1. The variation in the R was interpreted in terms of the structural changes that take place upon increasing the S content of the glasses [18]. In the range of measurements, W depends on the site e to e site distance R. This results shows 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 [19],Killias [20]and Austin and Garbet [21] delineated the dependence of W on the FeeOeFe site distance. Next, we estimate the optical phonon frequency, (no) in Eq.(5) using the experimental data from Table 1, according to kqD ¼ hno (h is the Plank’s constant) [17,18]. To determine no for the different compositions, the Debye temperature qD was estimated by T > qD/2(Eq. (3a)) using the TD values given in Table 1. qD of the present glasses was obtained to be 670e702K, which was nearly the same as the values of V2O5eNiOeTeO2 [18] and V2O5eP2O5 glasses [22]. Thus, these estimated qD values indicate to be physically reasonable. Then, with the qD values, no was calculated using no ¼ kqD/h. The values of qD and no are summarized in Table 1.
(5) (6)
3.2.2. Polaron hopping parameters In SPH conduction, the polaron band width (J) or the electron overlap integral obeys [19].
2kTWH 1=4 Zno 1=2 J> ðadiabaticÞ
p
J<
2kTWH
p
p
1=4
Zno
p
(7)
1=2 ðnon adiabaticÞ
(8)
For adiabatic hopping conduction, the hopping energy, WH, is given using J as
W WD =2xWH ¼ W=2 ¼
Wpy =2 J
(9)
where WP is the polaron binding energy, Wpy is the maximum polaron binding energy and WH depends on R [23]. By contrast, for non-adiabatic hopping conduction, WH is given as follows:
M.M. El-Desoky et al. / Solid State Sciences 13 (2011) 1616e1622
1619
Table 1 Chemical composition and physical properties of SeFe2O3eP2O5 glasses. Glass no.
Composition Fe2O3(mol%)
S (mass%)
P2O5(mol%)
1 2 3 4 5
40 40 40 40 40
0 2 4 6 8
60 60 60 60 60
W WD =2xWH ¼ Wpy =2
W (eV)
d (g cm
0.73 0.70 0.68 0.66 0.63
2.97 3.01 3.05 3.09 3.13
(10)
In order to determine the WH value of the present glasses, we evaluated the disorder energy (the difference of electronic energies between two hopping sites [7], WD ,(Eq. (4)) and activation energy, W (Table 1). WD at room temperature is recognized as below 0.05 eV for V2O5eTeO2 glasses [24] and below 0.09 eV for V2O5eBi2O3 glasses [35], or generally to be below 0.1 eV [25]. For the present system within the test temperature range, WD is assumed here to be 0.016e0.037 eV, as described in Table 2, we then obtain WH ¼ W e WD/2 ¼ 0.612e0.722 eV. For the present glasses, WH is nearly equal to W. Thus, from the WH values of the present glasses, the maximum value of Wpy /2 was obtained to be 0.722 eV. Then, the J values were estimated to be 0.11 eV by using WH, Wpy /2 and Eq. (9). Both WH and J values are given in Table 2. It is noted that the following criterion [26] should be satisfied for SPH conduction.
Wp’ =2 WH ¼ 3 3
(11)
The J values of the present glasses were obtained to be 0.11 eV, hence the above criterion was satisfied because the right-hand term in Eq. (10) was 0.24 eV. The right-hand term in Eqs. (7) and (8) where calculated to be 0.019 eV at 400 K. In the adiabatic regime for the present glasses, the criteria (Eqs. (7) and (10)) were satisfied, because J 0.11 eV. However, it should be noted that the J value was not estimated for S ¼ 0 mass%, because the maximum value of Wpy /2 is the hopping energy of 40Fe2O3e60P2O5 glass (mol%). Then, in the present study, the J value was assumed to be 0.02 eV, because the electrical conduction of the 40Fe2O3e60P2O5 glass (mol%). was concluded to be the adiabatic SPH from the discussion in the section 3.2. Next, using the mean spacing between the V- ions, R, calculated from the density (Table 1), polaron radius (rp) is given by [27].
6
NðEF Þ ¼
rp was then estimated to be rp ¼ 17.59e17.75 nm (Table 2) from R ¼ 43.67e44.04 nm (Table 1). The density of states for thermally activated electron hopping near the Fermi level is given from basic principles as [14,18].
R (nm)
qD(K)
no(1013 s1)
1.20 1.920 1.185 1.178 1.171
43.67 43.77 43.86 43.94 44.04
670 676 682 696 702
1.40 1.41 1.42 1.45 1.46
3=4pR3 W
(13)
3.2.3. Hopping carrier mobility and density The hopping carrier mobility (m) in the adiabatic and nonadiabatic hopping regions is described by the following equations [34]:
-5.5
-6.0
(12)
2
N (1022 cm3)
Using R and W values from Table 1, one can calculate N (EF) for the present glasses. It is clear that, the density of states N(EF) is the order of 1021 (eV1 cm3) [3,18]. The values of N(EF) are listed in Table 2. The N(EF) values are reasonable for the localized states [3,18]. The values of the tunneling factor (a) were computed from the pre- exponential factors (so) obtained from the least squares straight line fits of the data at high temperatures to Eq.(1) and using the experimental values of C and the other parameters shown in Table 1. The estimated a for these glasses a ¼ 19.08e20.10 nm1 (Table 2), which was similar to those for semiconducting oxide glasses [7,18,28]. The small polaron coupling constant (gp) a measure of the electronephonon interaction is given by gp ¼ 2WH/hno [7]. The estimated gp for these glasses was gp ¼ 21.42e26.26 (Table 2), which was similar to those for V2O5eMoOeTeO2 glasses [28] (gp ¼ 21-26), CaOeBaOeFe2O3eP2O5 glasses [3] (gp ¼ 21e29.2) and V2O5eMgOeTeO2 glasses [29] (21e33) but larger than those for V2O5eBi2O3 glasses doped with BaTiO3 [30] (gp ¼ 7e7.6). This indicates a strong electronephonon interaction in the present glasses [31e33].
-6.5 -1
rP ¼
p1=3 R
)
log σ (Sm )
j<
3
-7.0 Slope = -1/2.303 kT
-7.5
-8.0 Table 2 Polaron hopping parameters of SeFe2O3eP2O5 glasses.
θ
Glass no. WH(eV) WD(eV) rP(nm) J (eV) N(EF) a gp (1021 eV1 cm3) (nm1) 1 2 3 4 5
0.722 0.690 0.667 0.645 0.612
0.016 0.020 0.024 0.030 0.037
17.59 17.47 17.67 17.70 17.75
0.02 0.03 0.06 0.10 0.11
3.87 4.07 4.16 4.26 4.43
20.10 19.41 19.33 19.78 19.08
26.26 25.01 24.01 22.73 21.42
-8.5
-9.0 0.62
0.64
0.66
0.68
0.70
0.72
0.74
0.76
W (eV) Fig. 5. Effect of S content on pre-exponential factor (so) for different glass compositions.
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M.M. El-Desoky et al. / Solid State Sciences 13 (2011) 1616e1622 Table 3 Hopping carrier mobility and density of SeFe2O3eP2O5 glasses.
2.4
2.2
-1 log σ (Sm )
2.0
1.6
1.4
1.2
1.0 0
1
2
3
4
5
6
7
8
S (mass%) Fig. 6. Effect of activation energy (W) on dc conductivity (s) at T ¼ 405K for different glass compositions.
m ¼
no eR2 kT eR2 kT
! expðWH =kTÞðadiabaticÞ
(14)
! 1=2 p 1 J 2 expðW=kTÞ 4WH kT Z (15)
ðnon adiabaticÞ
The m values of the present glasses were calculated using the experimental data in Tables 1 and 2 and the result is given in Table 3. Also, the carrier density (Ne) values were calculated using the welleknown relation [35]
r ¼ Ne em
(16)
The values of m and Ne for various glass compositions are presented in Table 3. The carrier mobility (m) of the present system at
Nc (1020 cm3) (400 K)
1 2 3 4 5
1.12 2.61 4.92 9.66 24.83
1.11 1.9 1.6 1.95 1.55
400 K is very small (1.12 109 e 24.83 109 cm2 V1 s1), suggesting that electrons are highly localized at the Fe ion sites. Because the condition of the localized for the conductive electrons is generally for m < 102 cm2 V1 s1 [18], the formation of small polaron in these glasses was reconfirmed. From Fig. 8 it is seen that m increases with increasing S(mass%) content. The increase is expressed by the experimental relation m w moexp(S), similar to V2O5eNiOeTeO2 glasses [18]. Thus, the results indicate that the increase in the conductivity with increasing S(mass%) content is mainly due to an increase in the hopping carrier mobility of the glass. Furthermore, the nearly constant N w1020 cm3 indicates that the conductivity of the glasses is primarily determined by the hopping mobility [16,18]. 3.2.4. Variableerange hopping (VRH) models The slopes in the log(s) e 1/T relation (Fig. 2) changed at around 335K (above which the SPH law is valid). Such a case was found for binary glasses in the systems of V2O5eTeO2 [36] at 100K and ternary glasses V2O5eSrOeBi2O3 at 170K [37]. This phenomenon is attributed to the conduction mode changing from SPH to variable e range hopping (VRH) [7,38] with decrease in temperature. We then attempted to apply VRH [7,38] as reported for binary or ternary vanadate glasses [36,37]. However, the validity of such a high temperature range is not beyond question. But it has been pointed out that depending on the strength of coulomb interaction the expression for the density of states at the Fermi level N(EF) is modified and the VRH [7,38] may be applied even at high temperatures w 303K and above, though the VRH should actually be applicable in the low temperature regime (below qD/4) which is below 100K. For these glasses we, therefore, attempted to apply both the VRH models proposed by Mott [7] and Greaves [38] which
2.5
0.72
2.0
-1 -1
μ (x10- 8 cm V s )
0.74
1.5
2
0.70
W (eV)
m (109 cm2 V1 s1) (400 K)
1.8
o
m ¼
Glass no.
0.68
0.66
1.0
0.5 0.64
0.62 43.6
0.0 43.7
43.8
43.9
44.0
44.1
R(nm) Fig. 7. Effect of the mean distance (R) on activation energy (W) for different glass compositions.
0
1
2
3
4
5
6
7
8
S (mass%) Fig. 8. Effect of S content on hopping carrier mobility (m) for different glass compositions.
M.M. El-Desoky et al. / Solid State Sciences 13 (2011) 1616e1622 Table 4 Mott parameters for variable e range hopping conduction of SeFe2O3eP2O5 glasses. Glass no.
A (K1/4)
N(EF) (1023 eV1 cm3)
RVRH(nm)
1 2 3 4 5
29.74 27.55 25.26 25.43 24.48
0.22 0.49 0.51 0.63 0.82
0.55 0.46 0.44 0.42 0.39
1621
-0.3 -0.6
-1.2
1/2
-1
(Sm K )
-0.9
log σT
s ¼ B exp A=T1=4
1/2
is valid for the intermediate range of temperature. The expression for the conduction by the Mott VRH model [7] is based on a single optical phonon approach. In this model s is given by [7].
(17)
0 S mass%
-2.4
h i1=4 A ¼ 4 2a3 =9pkNðEF Þ
(18)
N(EF) is the density of states at the Fermi level. A (Table 4) are obtained from the slopes of the log s vs T1/4 (Fig. 9). Next, using N(EF) calculated from Eq. (17), the mean hopping in variable-range hopping (RVRH) (Table 4) is estimated as [7].
RVRH ¼ 91=4 =½8pNðEF ÞakT1=4
(19)
The values of N(EF) are given in Table 4, which is of order of 1023 eV1 cm3. This value of N(EF) is found to be large compared with those of the transition metal oxide glasses for which N(EF) is of the order 1019e1021 eV1 cm3 [3,13,18]. We shall now apply the Greaves law [38] of VRH is valid for the intermediate range of temperature (below qD/2). According to this model, the expression for the conductivity can be written as
sT
-1.8 -2.1
where
1=2
-1.5
0.215
``
4
``
6
``
8
``
0.220
0.225 -1/4
T Fig. 10. Relation between Log (sT
1/2
) and T
0.230
-1/4
(K
1/4
0.235
0.240
)
for different glass compositions.
Table (5) Parameters for Greaves variable e range hopping conduction of SeFe2O3eP2O5 glasses. Glass no.
B (K1/4)
N(EF) (1024 eV1 cm3)
1 2 3 4 5
15.44 14.49 14.37 13.57 13.16
0.48 0.68 0.71 0.84 1.05
-6.5
Fig. 10 shows the relationship log (s T1/2) against T1/4 drawn by rearranging the data from Fig. 1 The linear relationship confirms the Greaves VRH [38] in the intermediate temperature range. The values B obtained from these curves are given in Table 5. The N(EF) values were estimated from Eq. (20) using the values of a and B Tables 4 and 5, respectively. The values of the density of states at the Fermi level calculated from the parameter B of the Greaves model [38] given in Table 5 (w1024 eV1 cm3) are also found to be very large, compared to the usual semiconducting oxide glasses [3,13,18]. So none of these two VRH models are found suitable to explain the low temperature (below qD/2) conductivity data of these glasses. Thus we conclude that appearance of the VRH at T ¼ 303e473 K is rather unreasonable for the present glasses. So the experimental conductivity data above qD/2were fitted with SPH model proposed by Mott [7,8]. On the other hand, in the low temperature region (T < qD/2) the conduction is attributed to being electronic [31].
-7.0
4. Conclusion
¼ Aexp B=T1=4
(20)
where A and B, are constants. The slope B of log (sT1/2) vs. T1/4(Fig. 9) is given by
h i1=4 B ¼ 2:1 a3 =kNðEF Þ
(21)
-4.5 -5.0 -5.5 -6.0 -1
log σ (Sm )
-2.7 0.210
2
-7.5 0 S mass%
-8.0 -8.5 -9.0 -9.5
-10.0 0.210
0.215
2
``
4
``
6
``
8
``
0.220
0.225 -1/4
T
(K
1/4
Fig. 9. Relation between Log s and T
-1/4
0.230
0.235
0.240
)
for different glass compositions.
Semiconducting oxide glasses in the SeFe2O3eP2O5 system are fabricated by a press e quenching of glass melts using S, Fe2O3 and P2O5 row materials. Sulfur acted as a reducing agent for redox reaction during glass synthesis and affected the conductivity. Mössbauer spectral analyses revealed that the Fe2þ ratio increases with increasing sulfur content. From the conductivityetemperature relation, it was found that small polaron hopping model was applicable at the temperature above qD/2 (qD: the Debye temperature) regime; the electrical conduction at T > qD/2 was due to adiabatic small polaron hopping of electrons between iron ions. The electronephonon interaction coefficient gp was large (21.42e26.26). The estimated hopping mobility was low,
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M.M. El-Desoky et al. / Solid State Sciences 13 (2011) 1616e1622
1.12 109e24.83 109 cm2 V1 s1 and increased with increasing S(mass%) content. In the low temperature (below qD/2) regime, however, both Mott’s variable e range hopping and the Greaves’ intermediate range hopping models are found to be not applicable. References [1] D.E. Day, Z. Wu, C.S. Ray, P. Hrma, J. Non-Cryst. Solids 241 (1998) 1. [2] A. MoguS-Milankovi c, B. Santi c, S.C. Ray, D.E. Day, J. Non Cryst. Solids 263-264 (2000) 229. [3] M.M. El-desoky, I. Kashif, Phys. Stat. Sol.(a) 194 (No. 1) (2002) 89. [4] M.Y. Hassaan, M.M. El-Desoky, S.M. Salem, S.H. Salah, J. Radio. Nucl. Chem. 249 (2001) 595. [5] A. MoguS-Milankovi c, D.E. Day, J. Non. Cryst. Solids 162 (1993) 275. [6] A. MoguS-Milankovi c, B. Santi c, S.T. Rris, K. Furi c, D.E. Day, J. Non-Cryst. Solids 342 (2004) 97. [7] N.F. Mott, J. Non. Cryst. Solids 1 (1968) 1. [8] I.G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41. [9] M.M. El-Desoky, Shereief M. Abo- Naf, J. Mater. Sci. Mater. Electronics 15 (2004) 425. [10] M.M. El- Desoky., A. Al- Hajry, M. Tokunaga, T. Nishida, M.Y. Hassaan, Hyperfine Interact. 156/157 (2004) 547. [11] L. Murawski, O. Gzowski, Acta Phys. Polonica A50 (1976) 463. [12] I. Andelean, Solid State Commun. 27 (1978) 697. [13] H.H. Qiu, H. Sakata, T. Hirayama, J. Chin. Ceram. Soc. 24 (1996) 58. [14] N.F. Mott, E.A. Davis, Electronic Processes in Non-Crystalline Materials. Clarendon, Oxford, 1979.
[15] A. Miller, E. Abrahams, Phys. Rev. 120 (1969) 745. [16] K. Sega, Y. Kuroda, H. Sakata, J. Mater. Sci. 33 (1998) 1303. [17] H. Hirashima, H. Kurokawa, K. Mizobuchi, T. Yoshida, Glastech. Ber 61 (1988) 151. [18] M.M. El-Desoky, J. Mater. Sci. Mater. Electronics 14 (2003) 215. [19] M. Sayer, A. Mansingh, J. Non-Cryst. Solids 58 (1983) 91. [20] H.R. Killias, Phys. Lett. 20 (1966) 5. [21] I.G. Austin, E.S. Garbet, in: P.G. Le Comber, J. Mort (Eds.), Electronic and Structural Properties of Amorphorus Semiconductors, Academic Press, New York, 1973, p. 393. [22] M.B. Field, J. Appl. Phys. 40 (1969) 2628. [23] H. Hirashima, D. Arai, T. Yoshida, J. Am. Ceram. Soc. 68 (1985) 486. [24] V.K. Dhawan, A. Mansingh, M. Sayer, J. Non-Cryst. Solids 51 (1982) 87. [25] M. Sayer, A. Manshingh, Phys. Rev. B. 6 (1972) 4629. [26] D. Emin, T. Holstein, Ann. Phys. (NY) 53 (1969) 439. [27] V.N. Bogomolov, E.K. Kudinev, Y.A. . Firsov, Sov. Phys. Solid State 9 (1968) 2502 (Fiz. Tverd. Tela 9 (1967) 3175). [28] K. Sega, Y. Kuroda, H. Sakata, J. Mater. Sci. 33 (1998) 1303. [29] H. Satou, H. Sakata, Mater. Chem. Phys. 65 (2000) 186. [30] S. Chakraborty, M. Sadhukahn, D.K. Modak, B.K. Chaudhuri, J. Mater. Sci. 30 (1995) 5139. [31] M.M. El-Desoky, F.A. Ibrahim, A.G. Mostafa, M.Y. Hassaan, Mater. Res. Bull. 45 (2010) 1122. [32] M.M. El-Desoky, Mater. Chem. Phys. 119 (2010) 389. [33] M.M. El-Desoky, H.S.S. Zayed, F.A. Ibrahim, H.S. Ragab, Physica B. 404 (2009) 4125. [34] L. Murawaski, C.H. chung, J.D. Mackenzie, J. Non-Cryst. Solids 32 (1979) 91. [35] M.H. Cohen, J. Non-Crct. Solids 4 (1970) 391. [36] V.K. Dhawan, A. Mansingh, M. Sayer, J. Non-Cryst. Solids 51 (1982) 87. [37] H. Mori, K. Gotoh, H. Sakata, J. Non-Cryst. Solids 183 (1995) 122. [38] G.N. Greaves, J. Non-Crsyt. Solids 11 (1973) 427.
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Effect of sulfur addition on the transport properties of semiconducting iron phosphate glasses M.M. El-Desoky a, *, F.A. Ibrahim b, M.Y. Hassaan c a
Physics Department, Faculty of Science, Suez Canal University, Suez, Egypt Department of Physics, Faculty of Education, Suez Canal University, Al-Arish, Egypt c Department of Physics, Faculty of Science, Al-Azhar University, Nasr City, 11884 Cairo, Egypt b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 January 2011 Received in revised form 27 May 2011 Accepted 10 June 2011 Available online 16 June 2011
Transport properties and redox state of iron in glasses with compositions Se (40 Fe2O3 e 60 P2O5)(mol %), where x ¼ 0, 2,4,6 and 8 (mass%), were studied. The overall features of the XRD curves confirm the amorphous nature of the present glasses. Sulfur acted as a reducing agent for redox reaction during glass synthesis and affected the conductivity. Mössbauer spectral analyses revealed that the Fe2þ ratio increases with increasing sulfur content. The high temperature above q/2 (qD Debye temperature) dependence of conductivity could be qualitatively explained by the small polaron hopping model. The physical parameters obtained from the best fits of this model are found reasonable and consistent with the glass compositions. The conduction is confirmed to be due to adiabatic small polaron hopping of electrons between iron ions. The electronephonon interaction coefficient gp was large (21.42e26.26). The estimated hopping mobility was low, 1.12 109e24.83 109 cm2 V1 s1 and increased with increasing S(mass%) content. Moreover, the low temperature (below q/2) conductivity could not be explained either by Mott’s or greaves variable e range hopping model giving rise to unusually large values of the density of states at the Fermi level compared to those of transition metal oxide glasses. The conductivity of the present glasses was primarily determined by hopping carrier mobility. Ó 2011 Elsevier Masson SAS. All rights reserved.
Keywords: Phosphate glasses Electrical conductivity Mössbauer spectral XRD SPH
1. Introduction Iron phosphate glasses of approximate composition 40Fe2O3e60P2O5 (mol%) have recently gained attention because of their potential use as host materials for vitrifying high level nuclear wastes [1]. The excellent chemical durability and high waste loading ability of these iron phosphate glasses are two of several features which make them attractive for nuclear waste vitrification. The properties and structure of iron phosphate glasses have been investigated [1e4], but the effect of sulfur ion on the properties and redox state of iron phosphate glasses have been rarely studied to our knowledge. Iron phosphate glasses melted in air are electronically conducting glasses [5e7]. Their electron conducting behavior is due to iron ions being in more than valance state, namely as Fe2þ and Fe3þ. Conduction in these glasses takes place by electrons hopping from low to high valance sites (from Fe2þ to Fe3þ). The charge transfer in such glasses is usually termed “small polaron hopping” (SPH) [8e10] and the electrical conductivity depends strongly upon the
* Corresponding author. E-mail address: [email protected] (M.M. El-Desoky). 1293-2558/$ e see front matter Ó 2011 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2011.06.012
distance between the irons [10]. In iron phosphate glasses, the charge carrier concentration is related to the total concentration of iron ions and to the ratio of Fe2þ ions to the total quantity of iron P (Fe2þ/ Fe) [3]. In the present study, considering that P2O5 is a glass network former and S acts as a reducing agent for redox reaction during the glass synthesis, and causes the conductivity of the glass to increase, an SeFe2O3eP2O5 system was selected. The redox state of iron ions in these glass compositions was determined by Mössbauer spectroscopy [10]. The electrical conduction mechanism of the glass was investigated by measuring its dc conductivity. 2. Experimental Glass samples were prepared from analytical reagent grade chemicals according to the formula Se (40 Fe2O3 e 60 P2O5)(mol %), where x ¼ 0, 2,4,6 and 8 (mass%). Batches that produced 20 g of glass were prepared by mixing reagent grade Fe2O3, P2O5 and S crystalline powders that were melted in platinum crucibles in air at 1200 C for 1 h with occasional stirring, when poured onto a polished copper block kept at room temperature and immediately pressed by a similar copper block.
M.M. El-Desoky et al. / Solid State Sciences 13 (2011) 1616e1622
The amorphous nature of the glasses was ascertained from X-ray diffraction analysis. The density of the glasses was measured by the Archimedes method using toluene as the immersion liquid. P The fraction of reduced transition metal ion (C ¼ Fe2þ/ Fe) in these glass compositions were determined by Mössbauer spectroscopy performed at room temperature using 57Co(Rh) source of 925 MBq [10].The Mössbauer spectroscopy results were described in detail in our previous paper [10]. The dc conductivity (s) of the as-quenched glasses was measured at temperatures between 303and 473K. Silver paste electrodes deposited on both faces of the polished samples. The IeV characteristic between electrodes was verified.
1617
-4 0 S(mass%)
-5
-1
log σ (Sm )
-6
2
``
4
``
6
``
8
``
-7
-8
-9
3. Results and discussion -10
3.1. XRD The X-ray diffraction (XRD) patterns of several compositions of the prepared samples are shown in Fig. 1. From the XRD studies it is observed that homogenous glasses are formed for S concentration between 0 and 8 mass%. The overall features of these XRD patterns confirm the amorphous nature of the present glasses. The XRD patterns (Fig. 1) indicate glassy behavior with a broad hump at 2q ¼ 20e22 . No peak corresponding to S is observed indicating that S has completely entered the glass matrix. 3.2. Electrical conductivity 3.2.1. Conductivity and activation energy The electrical conductivity (s) for several glass compositions is shown in Fig. 2 as a function of 1/T. Fig. 2 shows a linear temperature dependence up to a critical temperature qD/2 (qD Debye temperature) and then the slope changes with deviation from linearity and the activation energy is temperature dependent. Such a behavior is a feature of SPH [7e10]. However, above this temperature range, the variation of activation energy with temperature is negligibly small so that the behavior may be treated as activated. The activation energy and pre-exponential factor (so)
S (mass%)
-11 2.0
3
3.2
3.6
-1
10 /T(K ) Fig. 2. Temperature dependence of dc conductivity (s) for different glass compositions. The solid lines are calculated by using the least -square.
were obtained from the least square straight line fits of the data above 335K. The compositional dependence of the conductivity at 405K and the activation energy are shown in Fig. 3. A general trend observed in Fig. 3 is that the magnitude of the conductivity at fixed (405K) tends to be highest in those compositions having smallest activation energy, which is consistent with SPH mechanism [7,8]. The semiconducting behavior of iron phosphate [11], mixed alkali iron phosphate [3], iron lead borate [12] and iron tellurite [13] glasses were understood by SPH between iron ions under different valance states [8e10]. Fig. 4 shows the electrical conductivity (s) P and the fraction of reduced transition metal ion (C ¼ Fe2þ/ F) measured of our previous work [10] as a function of S (mass%) content in the present glasses. Fig. 4 shows the electrical conductivity (s) for the present glasses within an order of magnitude of that of iron phosphate glasses [3,11]. Since the electrical conduction in iron phosphate glasses is assumed [3,11] to be due to electron hopping from Fe2þ to Fe3þ sites, it is reasonable to assume that electron hopping also occurs in the sulfurecontaining iron phosphate glasses. Also, from Fig. 4 it is clear that the C increases with increasing S(mass%) content; a similar behavior is observed for the
8
-7.9
0.74
-8.2
W
0.72
6
Intensity (a.u)
2.8
2.4
σ -8.5
W(eV)
-8.8
-1
4
0.68 -9.1
2
log σ (Sm )
0.70
0.66 -9.4
0 0.64
-9.7
0.62
10
20
30
40
50
2θ (degree) Fig. 1. XRD for different glass compositions.
60
-10.0 0
1
2
3
4
5
6
7
8
S (mass%) Fig. 3. Effect of S content on dc conductivity at T ¼ 400K and activation energy (W) for different glass compositions.
1618
M.M. El-Desoky et al. / Solid State Sciences 13 (2011) 1616e1622
-8.0
0.140
-8.2
0.135
-8.4
0.130 0.125
-8.8 0.120
c
-1 log σ (Sm )
-8.6
-9.0 0.115 -9.2
C
σ
-9.4
0.110 0.105
-9.6 -9.8
0.100 0
1
2
3
4
5
6
7
8
s (mass%) Fig. 4. The dc conductivity (s) at 303K and TM ion ratio (C) for different glass compositions. Lines are drown as guides for the eye.
electrical conductivity results. This indicates that the mechanism of electrical conductivity of sulfur e containing iron phosphate glasses were understood by SPH between iron ions under different valance states [8e10]. Mott [7] has investigated the hopping conductivity in oxide glasses containing transition metal ions. The conductivity of the nearest neighbor at high temperatures (T > qD/2) is given by [7]
s¼
no Ne2 R2
Cð1 CÞexp ð2aRÞexp ðW=kTÞ kT ¼ so exp ðW=kTÞ
(1)
The pre-exponential factor (so) in Eq. (1) is given by
so ¼
no Ne2 R2 kT
Cð1 CÞexpð2aRÞ
(2)
where no is the optical phonon frequency, a is the tunneling factor (the ratio of wave function decay), N the transition metal density, C P the fraction of reduced transition metal ion (C ¼ Fe2þ/ Fe) and W is the activation energy for hopping conduction. Assuming a strong electronephonon interaction, Austin and Mott [8] have shown that
W ¼ WH þ WD =2 W ¼ WD
ðfor T >= qD =2Þ
ðfor T < qD =4Þ
(3a) (3b)
Where WH is the hopping energy, qD is the Debye temperature and WD is the disorder energy defined as the difference of electronic energies between two hopping sites [14] and is given by [15]
WD ¼
e2 =3s R L
(4)
where es is the static dielectric constant and L is a constant of order 0.3. The values of WD and W are summarized in Tables 1 and 2. In the adiabatic hopping regime, however, aR in Eq. (1) becomes negligible [14,16], then the conductivity (s) and the preexponential factor (so) in Eq. (1) is expressed by the following equations [7,8]
s¼
no Ne2 R2 kT
Cð1 CÞexp ðW=kTÞ
so ¼ no Ne2 R2 Cð1 C=kTÞ
From Eq. (6) so is independent of S (mass%) and hardly varies with it [14]. Therefore, the dominant factor contributing to the conductivity should be W in the adiabatic regime [16]. For the present glasses, we calculated the term of so using experimental values in Table 1. Fig. 5 presents the effect of S (mass%) concentration on so, indicating almost unchanged value of so for S ¼ 0e8 mass%. These results indicate that s depends only on W in Eq. (5) in adiabatic regime for the present glasses as well as previous glasses [17,18]. Then, based on this result, log s at a given temperature is proportional to W and the log seW relation should become log s ¼ log soeW/2.303 kT from Eqs. (1) and (5). Fig. 5 shows the relationship between log s at 405 K and W. This relationship was linear for the present glasses. We fitted the data to the relation log s vs. W for the present glasses by the least e square technique, and the slope of the regression line in Fig. 6 was obtained to be 12.26 eV1. This value almost the same as the theoretical slope for the adiabatic hopping (tan q in Fig. 6), i.e. 12.91 eV1 (¼ 1/ 2.303 kT, T ¼ 405 K). The equivalent temperature evaluated from the slope of regression line gave T ¼ 400K, which is nearly equal to the measured value T ¼ 405 K. From both these results, we conclude the conduction of the present glasses to be due to adiabatic small polaron hopping of electrons. Fig. 7Shows the relationship between activation energy (W) and the mean distance (R). Here we regarded R as the Fe e Fe ion spacing calculated from R ¼ N1/3, on the basis of the glass densities measured (Table 1). The values of (R) are listed in Table 1. The variation in the R was interpreted in terms of the structural changes that take place upon increasing the S content of the glasses [18]. In the range of measurements, W depends on the site e to e site distance R. This results shows 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 [19],Killias [20]and Austin and Garbet [21] delineated the dependence of W on the FeeOeFe site distance. Next, we estimate the optical phonon frequency, (no) in Eq.(5) using the experimental data from Table 1, according to kqD ¼ hno (h is the Plank’s constant) [17,18]. To determine no for the different compositions, the Debye temperature qD was estimated by T > qD/2(Eq. (3a)) using the TD values given in Table 1. qD of the present glasses was obtained to be 670e702K, which was nearly the same as the values of V2O5eNiOeTeO2 [18] and V2O5eP2O5 glasses [22]. Thus, these estimated qD values indicate to be physically reasonable. Then, with the qD values, no was calculated using no ¼ kqD/h. The values of qD and no are summarized in Table 1.
(5) (6)
3.2.2. Polaron hopping parameters In SPH conduction, the polaron band width (J) or the electron overlap integral obeys [19].
2kTWH 1=4 Zno 1=2 J> ðadiabaticÞ
p
J<
2kTWH
p
p
1=4
Zno
p
(7)
1=2 ðnon adiabaticÞ
(8)
For adiabatic hopping conduction, the hopping energy, WH, is given using J as
W WD =2xWH ¼ W=2 ¼
Wpy =2 J
(9)
where WP is the polaron binding energy, Wpy is the maximum polaron binding energy and WH depends on R [23]. By contrast, for non-adiabatic hopping conduction, WH is given as follows:
M.M. El-Desoky et al. / Solid State Sciences 13 (2011) 1616e1622
1619
Table 1 Chemical composition and physical properties of SeFe2O3eP2O5 glasses. Glass no.
Composition Fe2O3(mol%)
S (mass%)
P2O5(mol%)
1 2 3 4 5
40 40 40 40 40
0 2 4 6 8
60 60 60 60 60
W WD =2xWH ¼ Wpy =2
W (eV)
d (g cm
0.73 0.70 0.68 0.66 0.63
2.97 3.01 3.05 3.09 3.13
(10)
In order to determine the WH value of the present glasses, we evaluated the disorder energy (the difference of electronic energies between two hopping sites [7], WD ,(Eq. (4)) and activation energy, W (Table 1). WD at room temperature is recognized as below 0.05 eV for V2O5eTeO2 glasses [24] and below 0.09 eV for V2O5eBi2O3 glasses [35], or generally to be below 0.1 eV [25]. For the present system within the test temperature range, WD is assumed here to be 0.016e0.037 eV, as described in Table 2, we then obtain WH ¼ W e WD/2 ¼ 0.612e0.722 eV. For the present glasses, WH is nearly equal to W. Thus, from the WH values of the present glasses, the maximum value of Wpy /2 was obtained to be 0.722 eV. Then, the J values were estimated to be 0.11 eV by using WH, Wpy /2 and Eq. (9). Both WH and J values are given in Table 2. It is noted that the following criterion [26] should be satisfied for SPH conduction.
Wp’ =2 WH ¼ 3 3
(11)
The J values of the present glasses were obtained to be 0.11 eV, hence the above criterion was satisfied because the right-hand term in Eq. (10) was 0.24 eV. The right-hand term in Eqs. (7) and (8) where calculated to be 0.019 eV at 400 K. In the adiabatic regime for the present glasses, the criteria (Eqs. (7) and (10)) were satisfied, because J 0.11 eV. However, it should be noted that the J value was not estimated for S ¼ 0 mass%, because the maximum value of Wpy /2 is the hopping energy of 40Fe2O3e60P2O5 glass (mol%). Then, in the present study, the J value was assumed to be 0.02 eV, because the electrical conduction of the 40Fe2O3e60P2O5 glass (mol%). was concluded to be the adiabatic SPH from the discussion in the section 3.2. Next, using the mean spacing between the V- ions, R, calculated from the density (Table 1), polaron radius (rp) is given by [27].
6
NðEF Þ ¼
rp was then estimated to be rp ¼ 17.59e17.75 nm (Table 2) from R ¼ 43.67e44.04 nm (Table 1). The density of states for thermally activated electron hopping near the Fermi level is given from basic principles as [14,18].
R (nm)
qD(K)
no(1013 s1)
1.20 1.920 1.185 1.178 1.171
43.67 43.77 43.86 43.94 44.04
670 676 682 696 702
1.40 1.41 1.42 1.45 1.46
3=4pR3 W
(13)
3.2.3. Hopping carrier mobility and density The hopping carrier mobility (m) in the adiabatic and nonadiabatic hopping regions is described by the following equations [34]:
-5.5
-6.0
(12)
2
N (1022 cm3)
Using R and W values from Table 1, one can calculate N (EF) for the present glasses. It is clear that, the density of states N(EF) is the order of 1021 (eV1 cm3) [3,18]. The values of N(EF) are listed in Table 2. The N(EF) values are reasonable for the localized states [3,18]. The values of the tunneling factor (a) were computed from the pre- exponential factors (so) obtained from the least squares straight line fits of the data at high temperatures to Eq.(1) and using the experimental values of C and the other parameters shown in Table 1. The estimated a for these glasses a ¼ 19.08e20.10 nm1 (Table 2), which was similar to those for semiconducting oxide glasses [7,18,28]. The small polaron coupling constant (gp) a measure of the electronephonon interaction is given by gp ¼ 2WH/hno [7]. The estimated gp for these glasses was gp ¼ 21.42e26.26 (Table 2), which was similar to those for V2O5eMoOeTeO2 glasses [28] (gp ¼ 21-26), CaOeBaOeFe2O3eP2O5 glasses [3] (gp ¼ 21e29.2) and V2O5eMgOeTeO2 glasses [29] (21e33) but larger than those for V2O5eBi2O3 glasses doped with BaTiO3 [30] (gp ¼ 7e7.6). This indicates a strong electronephonon interaction in the present glasses [31e33].
-6.5 -1
rP ¼
p1=3 R
)
log σ (Sm )
j<
3
-7.0 Slope = -1/2.303 kT
-7.5
-8.0 Table 2 Polaron hopping parameters of SeFe2O3eP2O5 glasses.
θ
Glass no. WH(eV) WD(eV) rP(nm) J (eV) N(EF) a gp (1021 eV1 cm3) (nm1) 1 2 3 4 5
0.722 0.690 0.667 0.645 0.612
0.016 0.020 0.024 0.030 0.037
17.59 17.47 17.67 17.70 17.75
0.02 0.03 0.06 0.10 0.11
3.87 4.07 4.16 4.26 4.43
20.10 19.41 19.33 19.78 19.08
26.26 25.01 24.01 22.73 21.42
-8.5
-9.0 0.62
0.64
0.66
0.68
0.70
0.72
0.74
0.76
W (eV) Fig. 5. Effect of S content on pre-exponential factor (so) for different glass compositions.
1620
M.M. El-Desoky et al. / Solid State Sciences 13 (2011) 1616e1622 Table 3 Hopping carrier mobility and density of SeFe2O3eP2O5 glasses.
2.4
2.2
-1 log σ (Sm )
2.0
1.6
1.4
1.2
1.0 0
1
2
3
4
5
6
7
8
S (mass%) Fig. 6. Effect of activation energy (W) on dc conductivity (s) at T ¼ 405K for different glass compositions.
m ¼
no eR2 kT eR2 kT
! expðWH =kTÞðadiabaticÞ
(14)
! 1=2 p 1 J 2 expðW=kTÞ 4WH kT Z (15)
ðnon adiabaticÞ
The m values of the present glasses were calculated using the experimental data in Tables 1 and 2 and the result is given in Table 3. Also, the carrier density (Ne) values were calculated using the welleknown relation [35]
r ¼ Ne em
(16)
The values of m and Ne for various glass compositions are presented in Table 3. The carrier mobility (m) of the present system at
Nc (1020 cm3) (400 K)
1 2 3 4 5
1.12 2.61 4.92 9.66 24.83
1.11 1.9 1.6 1.95 1.55
400 K is very small (1.12 109 e 24.83 109 cm2 V1 s1), suggesting that electrons are highly localized at the Fe ion sites. Because the condition of the localized for the conductive electrons is generally for m < 102 cm2 V1 s1 [18], the formation of small polaron in these glasses was reconfirmed. From Fig. 8 it is seen that m increases with increasing S(mass%) content. The increase is expressed by the experimental relation m w moexp(S), similar to V2O5eNiOeTeO2 glasses [18]. Thus, the results indicate that the increase in the conductivity with increasing S(mass%) content is mainly due to an increase in the hopping carrier mobility of the glass. Furthermore, the nearly constant N w1020 cm3 indicates that the conductivity of the glasses is primarily determined by the hopping mobility [16,18]. 3.2.4. Variableerange hopping (VRH) models The slopes in the log(s) e 1/T relation (Fig. 2) changed at around 335K (above which the SPH law is valid). Such a case was found for binary glasses in the systems of V2O5eTeO2 [36] at 100K and ternary glasses V2O5eSrOeBi2O3 at 170K [37]. This phenomenon is attributed to the conduction mode changing from SPH to variable e range hopping (VRH) [7,38] with decrease in temperature. We then attempted to apply VRH [7,38] as reported for binary or ternary vanadate glasses [36,37]. However, the validity of such a high temperature range is not beyond question. But it has been pointed out that depending on the strength of coulomb interaction the expression for the density of states at the Fermi level N(EF) is modified and the VRH [7,38] may be applied even at high temperatures w 303K and above, though the VRH should actually be applicable in the low temperature regime (below qD/4) which is below 100K. For these glasses we, therefore, attempted to apply both the VRH models proposed by Mott [7] and Greaves [38] which
2.5
0.72
2.0
-1 -1
μ (x10- 8 cm V s )
0.74
1.5
2
0.70
W (eV)
m (109 cm2 V1 s1) (400 K)
1.8
o
m ¼
Glass no.
0.68
0.66
1.0
0.5 0.64
0.62 43.6
0.0 43.7
43.8
43.9
44.0
44.1
R(nm) Fig. 7. Effect of the mean distance (R) on activation energy (W) for different glass compositions.
0
1
2
3
4
5
6
7
8
S (mass%) Fig. 8. Effect of S content on hopping carrier mobility (m) for different glass compositions.
M.M. El-Desoky et al. / Solid State Sciences 13 (2011) 1616e1622 Table 4 Mott parameters for variable e range hopping conduction of SeFe2O3eP2O5 glasses. Glass no.
A (K1/4)
N(EF) (1023 eV1 cm3)
RVRH(nm)
1 2 3 4 5
29.74 27.55 25.26 25.43 24.48
0.22 0.49 0.51 0.63 0.82
0.55 0.46 0.44 0.42 0.39
1621
-0.3 -0.6
-1.2
1/2
-1
(Sm K )
-0.9
log σT
s ¼ B exp A=T1=4
1/2
is valid for the intermediate range of temperature. The expression for the conduction by the Mott VRH model [7] is based on a single optical phonon approach. In this model s is given by [7].
(17)
0 S mass%
-2.4
h i1=4 A ¼ 4 2a3 =9pkNðEF Þ
(18)
N(EF) is the density of states at the Fermi level. A (Table 4) are obtained from the slopes of the log s vs T1/4 (Fig. 9). Next, using N(EF) calculated from Eq. (17), the mean hopping in variable-range hopping (RVRH) (Table 4) is estimated as [7].
RVRH ¼ 91=4 =½8pNðEF ÞakT1=4
(19)
The values of N(EF) are given in Table 4, which is of order of 1023 eV1 cm3. This value of N(EF) is found to be large compared with those of the transition metal oxide glasses for which N(EF) is of the order 1019e1021 eV1 cm3 [3,13,18]. We shall now apply the Greaves law [38] of VRH is valid for the intermediate range of temperature (below qD/2). According to this model, the expression for the conductivity can be written as
sT
-1.8 -2.1
where
1=2
-1.5
0.215
``
4
``
6
``
8
``
0.220
0.225 -1/4
T Fig. 10. Relation between Log (sT
1/2
) and T
0.230
-1/4
(K
1/4
0.235
0.240
)
for different glass compositions.
Table (5) Parameters for Greaves variable e range hopping conduction of SeFe2O3eP2O5 glasses. Glass no.
B (K1/4)
N(EF) (1024 eV1 cm3)
1 2 3 4 5
15.44 14.49 14.37 13.57 13.16
0.48 0.68 0.71 0.84 1.05
-6.5
Fig. 10 shows the relationship log (s T1/2) against T1/4 drawn by rearranging the data from Fig. 1 The linear relationship confirms the Greaves VRH [38] in the intermediate temperature range. The values B obtained from these curves are given in Table 5. The N(EF) values were estimated from Eq. (20) using the values of a and B Tables 4 and 5, respectively. The values of the density of states at the Fermi level calculated from the parameter B of the Greaves model [38] given in Table 5 (w1024 eV1 cm3) are also found to be very large, compared to the usual semiconducting oxide glasses [3,13,18]. So none of these two VRH models are found suitable to explain the low temperature (below qD/2) conductivity data of these glasses. Thus we conclude that appearance of the VRH at T ¼ 303e473 K is rather unreasonable for the present glasses. So the experimental conductivity data above qD/2were fitted with SPH model proposed by Mott [7,8]. On the other hand, in the low temperature region (T < qD/2) the conduction is attributed to being electronic [31].
-7.0
4. Conclusion
¼ Aexp B=T1=4
(20)
where A and B, are constants. The slope B of log (sT1/2) vs. T1/4(Fig. 9) is given by
h i1=4 B ¼ 2:1 a3 =kNðEF Þ
(21)
-4.5 -5.0 -5.5 -6.0 -1
log σ (Sm )
-2.7 0.210
2
-7.5 0 S mass%
-8.0 -8.5 -9.0 -9.5
-10.0 0.210
0.215
2
``
4
``
6
``
8
``
0.220
0.225 -1/4
T
(K
1/4
Fig. 9. Relation between Log s and T
-1/4
0.230
0.235
0.240
)
for different glass compositions.
Semiconducting oxide glasses in the SeFe2O3eP2O5 system are fabricated by a press e quenching of glass melts using S, Fe2O3 and P2O5 row materials. Sulfur acted as a reducing agent for redox reaction during glass synthesis and affected the conductivity. Mössbauer spectral analyses revealed that the Fe2þ ratio increases with increasing sulfur content. From the conductivityetemperature relation, it was found that small polaron hopping model was applicable at the temperature above qD/2 (qD: the Debye temperature) regime; the electrical conduction at T > qD/2 was due to adiabatic small polaron hopping of electrons between iron ions. The electronephonon interaction coefficient gp was large (21.42e26.26). The estimated hopping mobility was low,
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M.M. El-Desoky et al. / Solid State Sciences 13 (2011) 1616e1622
1.12 109e24.83 109 cm2 V1 s1 and increased with increasing S(mass%) content. In the low temperature (below qD/2) regime, however, both Mott’s variable e range hopping and the Greaves’ intermediate range hopping models are found to be not applicable. References [1] D.E. Day, Z. Wu, C.S. Ray, P. Hrma, J. Non-Cryst. Solids 241 (1998) 1. [2] A. MoguS-Milankovi c, B. Santi c, S.C. Ray, D.E. Day, J. Non Cryst. Solids 263-264 (2000) 229. [3] M.M. El-desoky, I. Kashif, Phys. Stat. Sol.(a) 194 (No. 1) (2002) 89. [4] M.Y. Hassaan, M.M. El-Desoky, S.M. Salem, S.H. Salah, J. Radio. Nucl. Chem. 249 (2001) 595. [5] A. MoguS-Milankovi c, D.E. Day, J. Non. Cryst. Solids 162 (1993) 275. [6] A. MoguS-Milankovi c, B. Santi c, S.T. Rris, K. Furi c, D.E. Day, J. Non-Cryst. Solids 342 (2004) 97. [7] N.F. Mott, J. Non. Cryst. Solids 1 (1968) 1. [8] I.G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41. [9] M.M. El-Desoky, Shereief M. Abo- Naf, J. Mater. Sci. Mater. Electronics 15 (2004) 425. [10] M.M. El- Desoky., A. Al- Hajry, M. Tokunaga, T. Nishida, M.Y. Hassaan, Hyperfine Interact. 156/157 (2004) 547. [11] L. Murawski, O. Gzowski, Acta Phys. Polonica A50 (1976) 463. [12] I. Andelean, Solid State Commun. 27 (1978) 697. [13] H.H. Qiu, H. Sakata, T. Hirayama, J. Chin. Ceram. Soc. 24 (1996) 58. [14] N.F. Mott, E.A. Davis, Electronic Processes in Non-Crystalline Materials. Clarendon, Oxford, 1979.
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