J. Mater. Sci. Technol., 2011, 27(10), 865-872.
Transport Properties of Kx V2 O5 ·nH2 O Nanocrystalline Films A.A. Bahgat† , H.A. Mady, A.S. Abdel Moghny, A.S. Abd-Rabo and Samia E. Negm Department of Physics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt [Manuscript received June 14, 2011, in revised form August 17, 2011]
Five different compositions of Kx V2 O5 ·nH2 O (where x=0.00, 0.0017, 0.0049, 0.0064 and 0.0091 mol) were prepared by the sol-gel process. Electrical conductivity and thermoelectric power were measured parallel to the substrate surface in the temperature range of 300–480 K. The electrical conductivity showed that all samples were semiconductors and that conductivity increased with increasing K content. The conductivity of the present system was primarily determined by hopping carrier mobility. The carrier density was evaluated as well. The conduction was confirmed to obey non-adiabatic small polaron hopping. The thermoelectric power or Seebeck effect, increased with increasing K ions content. The results obtained indicated that an n-type semiconducting behavior within the temperature range was investigated. KEY WORDS: Vanadium pentoxide xerogel; Nanocrystalline film; Electrical conductivity; Small polaron hopping
1. Introduction Vanadium oxides have a complex crystal system and consist of various morphology of vanadium and oxygen, and each is identifiable by its lattice structure and space group[1] . A further complication is the substantial variability in stoichiometry which is occurring in some structures. Temperature dependent semiconductor-to-metal phase transition has been observed in at least eight different types of vanadium oxides compounds and by which its thermochromic properties are explained[2] . Thin films of vanadium pentoxide have been prepared by various methods, such as sputtering[3] , chemical vapor deposition[4] , vacuum evaporation[5] and sol-gel technique[6–9] . If cost effective is of prime concern, sol-gel method is the preferred thin film fabrication technique for many applications. Vanadium oxide xerogels have been known for long time[10] . They can be described as nanocrystalline materials made of water molecules trapped within † Corresponding author. Prof., Ph.D.; E-mail address:
[email protected] (A.A. Bahgat).
a vanadium oxide network. They exhibit a wide range of electronic and ionic properties[10] . Conduction is achieved in transition metals oxides (TMO) by electrons hopping from low-valence, vanadium V4+ to high-valence vanadium V5+ , sites in the present case. This mechanism depends on the average distance between vanadium ions and the relative fraction of vanadium V4+ to vanadium V5+ ions[11] . Optical, electrical and thermoelectric power properties of Li1+ ions intercalated vanadium pentoxide, Lix V2 O5 ·nH2 O, films were studied recently[11,12] . It was shown recently that the xerogel specimens prepared by the V2 O5 melt-water quenching technique revealed that the conduction mechanism is due to non-adiabatic small polaron hopping[12] . On the other hand, a more recent study of the structure properties of Kx V2 O5 ·nH2 O xerogels shows nanocrystalline layer structure of rod like particles[13] . Volkov et al.[14] on the other hand have demonstrated that the electrical conductivity of pressed M2 V12 O30 ·nH2 O (M =K, Rb, Cs) samples is mainly due to charge transport across the V-O layers. While the interlayer spacing depends on the size of the hydrated M + cations and the degree of hydration.
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The main objective of the present work is to investigate the compositional dependence of the electrical conduction mechanism and thermoelectric power properties of Kx V2 O5 · nH2 O xerogel. 2. Experimental Five different compositions of Kx V2 O5 ·nH2 O (where x=0.00, 0.0017, 0.0049, 0.0064 and 0.0091 mol) have been prepared for the present investigation. Films of the investigated compounds were prepared by sol-gel technique (colloidal route). Generally, several methods may be followed to prepare V2 O5 ·nH2 O xerogel[6–12] . Typically, the most simple and cost effective methods are either by dissolving [9,13,15] V2 O5 in hydrogen peroxide H2 O2 or by pouring ◦ V2 O5 melt at 800 C in continually stirred distilled water[7,8] . Both routes produces xerogels of similar atomic structure, however they may show different properties when compared with analogous series of samples e.g. Lix V2 O5 ·nH2 O[12] . In the present study, vanadium pentoxide (V2 O5 ) (99.99%) and potassium hydroxide (KOH) (99.99%) in suitable proportions (mol%) were used as raw materials. A batch of (1.04 g) V2 O5 was dissolved in 80 ml of 17.5% hydrogen peroxide (H2 O2 ) at room temperature[9] . The solution was heated at 60◦ C with uninterrupted continuous stirring, where pH=3– 4. Water dissolved KOH (0.07 mol) was added to the V2 O5 gel drop by drop using a Pruitt up to the desired concentration according to the following chemical reaction[16] : V2 O5 + 2H2 O2 = 2HVO4 (peroxyvanadic acid) + H2 O 2HVO4 + (n − 1)H2 O = V2 O5 · nH2 O + O2 KOH → K+1 + (OH)− V2 O5 · nH2 O + x K+1 → Kx V2 O5 · nH2 O Vanadium pentoxide (V2 O5 ) and (V2 O5 -(x)KOH) gels can be synthesized via the condensation of aqueous solutions of (V2 O5 ) and (V2 O5 -(x)KOH). It is seems that the use of KOH restricts the obtained composition range (x=0.00, 0.0017, 0.0049, 0.0064 and 0.0091 mol) due to its chemical alkalinity effect, which increases the pH value above the suitable acidic requirements. Dip coating technique of Pyrex substrate was used to obtain films of thickness in the range of 250 to 320 nm as evaluated by optical interference method[17] . Structure properties of the obtained films were offered in a recent report[13] , where nanocrystalline thin film was observed as shown by the transmission electron microscopy (TEM)
Fig. 1 Typical room temperature TEM for the nanocrystalline V2 O5 ·nH2 O[13]
micrograph shown in Fig. 1[13] . On the other hand, the density of the V2 O5 ·nH2 O sample, which was left to dry independently under ambient conditions for one month, has been determined experimentally by Archimedes0 s rule using toluene as the immersion liquid. On the other hand, the dc electrical conductivity σdc was measured in the temperature range of 340– 460 K by the two probe method using silver painted electrodes. The thermoelectric power, TEP, of the samples was measured between two Cu-electrodes and two K-type thermocouples attached to the samples. Different electrical measurements were done in vacuum in order to eliminate any contribution from possible water adsorption[23] . 3. Results and Discussion 3.1 Density Generally, the density of any material is important for understanding the structure and many other properties. The density of Kx V2 O5 ·nH2 O system (0.0017≤x≤0.0091 mol) has been calculated theoretically using the relation ρ=ρ1 x1 + ρ2 x2 , where ρ1 and ρ2 are the density of K2 O[18] and V2 O5 ·nH2 O, and x1 and x2 are their fraction content, respectively. Figure 2 and Table 1 present the composition dependence of the density of the present samples. It is observed that the density increases gradually with increasing potassium content. In the current system, the density varies from 2.319 to 2.34 g/cm3 . The measured density as explained above for V2 O5 ·nH2 O sample was d=2.319 g/cm3 , which is in good agreement with that observed by Yao et al.[19] (2.25 g/cm3 ). This indicates that our sample structure follows the bilayer model proposed by Yao et al.[19] . The increase of the calculated density is small, about 0.8%, and is due to the small amounts of K-ions that intercalated within the V2 O5 ·nH2 O layers. The origin of this increase may be due to polarizing power strength (PPS), where generally PPS=ionic valance/square of ionic radius. As the PPS increases, the packing density would raise as the K content increases. One further point to be considered is due to the 1% unit cell volume reduction
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Table 1 Physical parameters of Kx V2 O5 ·nH2 O nanocrystals d /g·cm−3 ln(σ 375 /S·m−1 ) N/ ×1021 cm−3 R/nm W /eV σ o /×103 S·m−1 D k/ cm−1 , (FTIR)[13] ν o / ×1013 Hz (θD /2)/ K εp, (Optical)[11,17] r p /nm W H /eV N (E F )/×1021 eV−1 ·cm−3 γp J /eV, Eq. (14) J /eV, Eq. (15) µ/×10−4 cm2 ·V−1 ·s−1 , at 375 K N c /×1021 cm−3 , at 375 K ln(A/S·m−1 ·K−1/2 ) B /K1/4 α/×10−3 nm−1 C,(V4+ /Vtotal )
0.00/mol 2.319 3.77 7.676 0.5069 0.188 14.72 0.027 520.7 1.56 374 4.50 0.2043 0.050 9.750 1.547 0.0141 0.0257 2.876 9.427 31.624 109.518 2.15 0.10
0.0017/mol 2.320 3.71 7.680 0.5068 0.18 5.38 0.010 524.5 1.57 376 4.46 0.2042 0.051 10.189 1.568 0.0146 0.0258 3.413 7.481 28.537 96.465 1.84 0.11
2.340 PV
) -3
0.0064/mol 2.33 4.28 7.701 0.5063 0.16 6.46 0.0120 524.5 1.57 376 7.52 0.2040 0.029 11.497 0.919 0.010 0.0226 4.953 9.138 29.763 101.027 2.041 0.27
0.0091/mol 2.34 4.6 7.730 0.5058 0.156 6.63 0.0124 524.5 1.57 376 4.51 0.2038 0.049 11.826 1.531 0.0155 0.0260 8.146 8.700 30.025 100.559 2.047 0.63
the density was found to be 1.26 g/cm3 which is in support to the single layer model[6,20] . The amount per unit volume of vanadium ions N (cm−3 ) may be evaluated using the density by the relation:
2.345
d / (g cm
0.0049/mol 2.329 3.94 7.700 0.5064 0.182 5.24 0.0109 528.4 1.59 381 5.24 0.2041 0.043 10.101 1.299 0.0114 0.0250 2.838 11.324 32.013 107.778 2.131 0.12
2.335
2.330
N=
dpNA Aw
(1)
2.325
2.320
0.000
0.002
0.004
0.006
0.008
0.010
x / mol
Fig. 2 Compositional density dependence on K ions content of the Kx V2 O5 ·nH2 O xerogel films. PV indicates pure V2 O5 ·nH2 O gel
as evaluated from X-ray diffraction[13] and is due to the intercalation of K-ions. Whereas there is 0.8% density increase as obtained from the present work, and both these results are consistent even so the molecular weight is changed by only 0.2%. This may support our above interpretation concerning the strong PPS effect. On the other hand, the increase in the density with increasing K content is due to the loss of intercalated water and the increase of attractive interactions between the positively charged K ions and the negatively charged V2 O5 layers. The density of the present system is consistent with the ionic size, atomic weight and amount of different elements (K+ , V4+ , V5+ ) in the system[12] . In this respect a remark may be outlined; in comparison with the V2 O5 ·nH2 O xerogel sample prepared by the melt-water procedure[12] ,
where d is the density of the sample as evaluated above and presented in Table 1, p is the weight percentage of atoms, NA is the Avogadro0 s number and AW is the molecular weight. While the relationship between N and the mean inter-atomic distance R is generally described as: R = (1/N )1/3
(2)
The calculated values of R and N are summarized in Table 1. 3.2 Electrical conductivity Films with thicknesses 250, 190, 140, 300 and 320 nm are for x=0.0000, 0.0017, 0.0049, 0.0064 and 0.0091 mol, respectively[17] were used to study the effect of K content on the dc conductivity. Figure 3 shows a semiconducting temperature dependence of the electrical conductivity σ(T ), for Kx V2 O5 ·nH2 O system, which is the best being described by the relation[21] : σ(T ) = σo e
− kWT B
(3)
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6
0.20
x (mol)
T = 375 K
(a) 0.0000
5.0
(b) 0.0017
(e)
0.18
4.5
0.17
ln (
ln
4
W / eV
-1
(e) 0.0091
/ S m )
(d) 0.0064
-1
/ S m )
0.19
(c) 0.0049
5
4.0 3
(d)
0.16
(c) (a)
(b)
3.5
2 2.2
2.4
2.6
(1000/
2.8
3.0
3.2
T) / K
-1
Fig. 3 Electrical conductivity of the system Kx V2 O5 ·nH2 O system with 0≤x≤ 0.0091 mol. Measured data were collected in vacuum
here σ o is the pre-exponential factor, W is the activation energy, T is the absolute temperature and kB is the Boltzmann0 s constant. The electrical properties of Kx V2 O5 ·nH2 O system were investigated as a function of the degree of intercalation as shown in Fig. 3 in the temperature range of 300–460 K. The activation energys, W , and preexponential factor, σ o , were obtained from the least square straight line fits of the data. A general condition for transition metals oxides (TMO) semiconducting behavior is that the transition metal ion could exhibit several valence states such as V5+ and V4+ in V2 O5 , so that electronic conductivity takes place by electron hopping from low to higher valence state, V4+ →V5+ and vice versa[21] . The dc conductivity indicates that the activation energy, W , decreases while the magnitude of the conductivity increases with increasing K+1 content, as shown in Fig. 4 and given in Table 1. Figure 4 shows that the values of dc electrical conductivity at arbitrary selected temperature T =375 K increases as the potassium amount increases. This may be due to the small ionic size of the potassium ion when compared with that of H2 O group. Where, generally the high concentration of reduced state V4+ of vanadium ion is together with the effect of the polarizing power strength (PPS: attractive interaction between the positively charged alkali ions and the negatively charged V2 O5 layers)[22] . In general, PPS of potassium ions are higher than those for vanadium ions. Basically, the conduction mechanism is supposed to occur by electron hopping between TM-ions existing in different valence states in the amorphous and nanocrystalline materials. We thus are in favor of the option that electronic conductivity is the possible type describing the present system. This assumption is supported by the knowledge that the optical energy gap is about 0.40±0.02 eV in this system[17] as well as in comparable compositions[9,11] . This gap is twice as large as the activation energy, W , obtained from the present electrical conductivity measurements pre-
0.15 0.000
0.002
0.004
0.006
0.008
x / mol
Fig. 4 Effect of K content on dc conductivity (¥) for Kx V2 O5 ·nH2 O for 0≤x≤0.0091 mol at a selected temperature T equals to θD /2=375 K. The dependence of activation energy (o) of Kx V2 O5 ·nH2 O system on composition. The plotted curves are intended as guides to the eye
sented in Table 1 and shown in Fig. 4. The obtained values of σo in Eq. (3) are in the range of 14.72×103 –5.24×103 S·m−1 as obtained for the present system and are given in Table 1. According to the report of Mott and Davis[21] , the preexponential factor σo is given according to Anderson localization model as: e2 (4) ~a here ~ is the Plank0 s constant divided by 2π, e is the electronic charge, a is the distance between conducting centers and D=0.026 is a dimensionless constant which depends strongly on the coordination number of the centers[21] . Applying the obtained experimental data and considering a equals to R, the values of D were calculated and are given in Table 1. Those calculated values seem to be less than half of the theoretical one, when x>0.0. This may be due to that the hopping distance favors hopping to next nearest neighbors, NNN, rather than to the nearest neighbors, NN, as a consequence of K-ions intercalation. This is together with a probably larger effective coordination number for wavefunctions that are smaller only in certain directions[21] . The relatively small values of σ o obtained in the present work in comparison to the almost universal predicted value (104 to 105 S·m−1 )[21] may be an indication of a wide range of localized states as well as conduction by hopping. Additional explanation may be due to that if long-range fluctuations in potential exist, tunneling through the maximum is possible and σo would be smaller. σo = D
3.2.1 Nature of conduction mechanism The logarithm of the conductivity shows linear temperature dependence as shown in Fig. 3. Such behavior is a feature of small polaron hopping (SPH). If the interaction between electrons and optical phonons is strong enough, a small polaron will be formed and
A.A. Bahgat et al.: J. Mater. Sci. Technol., 2011, 27(10), 865–872
T
4.8
exp
= 375 K
Slope = -1/
T
ln(
-1
/ Sm )
cal
kT
cal
= 455 K
4.4
4.0
3.6
3.2 0.16
0.17
0.18
0.19
W / eV Fig. 5 Effect of activation energy W on dc conductivity at Texp =375 K for Kx V2 O5 ·nH2 O nanocrystals
at sufficiently high temperatures this will be moved by a hopping process[24] . Generally, the conduction mechanism may be described at relatively high temperatures (above the Debye temperature, θD /2, see Table 1) either as nonadiabatic or adiabatic small polaron hopping. Within the non-adiabatic regime, the electrons have a low chance of making the transfer during each excitation. The conductivity σ is given as in Eq. (3)[21,24] where the pre-exponential factor σ o is given by: 2
σo =
2
νo N e R C(1 − C)exp(−2αR) kB T
(5)
Fig. 5 for the present considered system. The values of the optical phonon frequency, ν o in Eqs. (5) and (8) were estimated using the experimental FTIR data[13] and are given in Table 1, according to ν o =kc where k is the wave number of the maximum IR absorption[13] and c is the velocity of light. Figure 5 shows the relationship between lnσ and W at an arbitrarily chosen experimental temperature of T =375 K. As can be seen that the data fall on a straight line for the whole range of W . From the slope of the plot, the value of the calculated temperature (Tc =455 K) is obtained, which is higher than the experimental temperature. This result supports nonadiabatic small polaron hopping mechanism[21] . Similar results were obtained recently on comparable thin films samples of the compositions Lix V2 O5 ·nH2 O[12] . 3.2.2 Small polaron hopping parameters If the interaction between electrons and optical phonons is strong enough, a small polaron will be formed and at sufficiently high temperatures (T >θD /2, see Table 1), this will move through a hopping process[25] . Holstein[25] has suggested a method for calculating the polaron hopping energy WH : ³ 1 ´X [γp ]2 ~ωp (9) WH = p 4N here [γp ]2 is the electron-phonon coupling constant and ω p is the frequency of the optical phonons. The polaron hopping energy, WH , can be calculated from theory and is given by[26] :
While the activation energy W can be written as: WH ≈ W = W = WH + WD /2 at low temperatures (T < θD /2) (6) W = WD at high temperatures (T > θD /2) (7) here ν o is the optical phonon frequency (∼1013 Hz, see Table 1), e is the electronic charge, N is the transition metal ion concentration, R is the average spacing between transition metal ions, C and 1–C are the fractions of the two transition metal ions (namely V4+ and V5+ ) as obtained from TEP results, see section 3.3 next, α is the tunneling factor, WH is the polaron hopping energy and WD is the disorder energy. On the other hand in the adiabatic case, the electrons oscillate backward and forward several times during each excitation of the lattice. However, αR in Eq. (5) approaches zero and the corresponding exponential function tends to one. Consequently, the pre-exponential factor σo in Eq. (3) is expressed by the following relation[21,24] : σo =
νo N e2 R2 C(1 − C) kB T
(8)
Therefore, lnσ=lnσ o −W/kB T , will demonstrates that the slope of lnσ at a fixed temperature vs activation energy, W , should be (kB Tc )−1 , as shown in
869
e2 ³ 1 1´ Wp = − 2 4εp rp R
(10)
While, 1 1 1 = − εp ε∞ εs where εs and ε∞ are the static and the high frequency dielectric constants, respectively. Generally εs >>ε∞ and we may consider εp ≈ε∞ . While rp is the small polaron radius which may be given as[26] : R ³ π ´1/3 1 ³ π ´1/3 = (12) 2 6N 2 6 Evaluation of WH can be made from Eq. (10) by the knowledge of R and rp , while εp was found from independent optical measurements[9,11,17] . The values of rp , εp and WH are given in Table 1. The small values of polaron radii suggest that the polarons are highly localized, which is in support to the conclusion derived for the values of σo given above. On the other hand, the density of states at Fermi level can be estimated from the following expression[21] : rp =
3 (13) 4πR3 W The obtained results for the present samples are listed in Table 1. N (EF ) =
870
A.A. Bahgat et al.: J. Mater. Sci. Technol., 2011, 27(10), 865–872
3.2.3 Nature of small polaron hopping (SPH) conduction An additional approach to illustrate the nature of small polaron hopping mechanism may be given in a more strict procedure, which is by studying the polaron band width parameter J. Where generally, in transition metal oxides (TMO) small polaron hopping (SPH) conduction mechanism is widely accepted[19,23] . This mechanism, SPH, is supported in the above section as the most accepted one to describe our present data. In this model the electrons behavior depends on what is known as the polaron band width parameter, J, or the electron overlap integral and which is given as[27] : J ≈ e3
h N (E ) i1/2 F (∈o εp )3
(14)
here ∈o is the free space permittivity, other parameters take their usual meaning. Generally, whether the conduction mechanism follows adiabatic or nonadiabatic regime can be discussed further in terms of this polaron band width parameter and which obeys either one of these inequalities[27] : J > (2kB T WH /π)1/4 (~νo /π)1/2 → adiabatic (15a)
J < (2kB T WH /π)1/4 (~νo /π)1/2 → non−adiabatic (15b) The limiting values of J as calculated from the right-hand side of Eq. (15a) or (15b), at e.g. T =375 K are in the order of 0.025 to 0.026 eV, respectively, depending on different composition. Alternatively, applying the values of N (EF ) and εp given in Table 1 to Eq. (14) gives J within the range of 0.0155 to 0.010 eV, as listed in Table 1. Accordingly, these results support the inequality given by Eq. (15b). Thus the non-adiabatic hopping mechanism is the most appropriate to describe the polaronic conduction of the present samples. This outcome is in support to the result obtained above in section 3.2.1. 3.2.4 Relation between activation energy and V–V spacing The relation between the activation energy, W , and the mean distance, R, between V ions is illustrated in Fig. 6 and Table 1 as well. As shown in Fig. 6, the activation energy, W , depends on the siteto-site distance, R. The effect of the dependence, σ(T ), upon potassium content in Kx V2 O5 ·nH2 O
0.22
/ eV
0.20
0.18
W
The values of the small polaron coupling constant γ p , as a measure of electron-phonon interaction is [21,24] given by the formula γ p =2WH /hν o . The values of γ p are listed in Table 1 as well. Typically, a value of γ p
