Ionics (2010) 16:673–679 DOI 10.1007/s11581-010-0477-3
ORIGINAL PAPER
Electrical properties of TiO2: equilibrium vs dynamic electrical conductivity Tadeusz Bak · Janusz Nowotny · James Stranger
Received: 18 June 2010 / Revised: 9 August 2010 / Accepted: 12 September 2010 / Published online: 6 October 2010 © Springer-Verlag 2010
Abstract The present work reports semiconducting properties of high purity TiO2 determined in the gas/solid equilibrium, as well as during controlled heating and cooling in the range 300–1,273 K. The activation energy of the electrical conductivity is considered in terms of the activation enthalpy of the formation of ionic defects and the activation enthalpy of the mobility of electronic defects. These data, determined from the dynamic electrical conductivity experiments, are compared to the electrical conductivity data determined in equilibrium. It is shown that only the equilibrium electrical conductivity data for high-purity TiO2 are well defined. It is shown that the activation energy of the electrical conductivity determined in equilibrium differs substantially from that for the dynamic electrical conductivity data during cooling and heating. It is concluded that the formation enthalpy term determined from the dynamic conductivity data is determined by the heating/cooling rate rather than materials’ properties. Keywords Titanium dioxide · Defect disorder · Electrical conductivity
T. Bak · J. Nowotny (B) Solar Energy Technologies, College of Health and Science, University of Western Sydney, Locked Bag 1797, Penrith South DC, New South Wales 1797, Australia e-mail:
[email protected] T. Bak e-mail:
[email protected] J. Stranger College of Health and Science, University of Western Sydney, Locked Bag 1797, Penrith South DC, New South Wales 1797, Australia
Introduction According to the pioneering work of Fujishima and Honda [1], titanium dioxide is a promising material which can be applied as a photocatalyst for solar water purification and as a photoelectrode for solar water splitting. The discovery of Fujishima and Honda resulted in an increasing interest in TiO2 [2–16]. The studies aim to enhance photocatalytic performance of TiO2 through the modification of its properties. Recent studies of the authors indicate that photocatalytic properties of TiO2 are closely related to semiconducting properties, which are determined by defect disorder [17–20]. Therefore, the formation of photocatalysts with enhanced performance requires better understanding of semiconducting properties of TiO2 . An important property of oxide semiconductors, such as TiO2 , is the temperature dependence of electrical conductivity that can be considered in terms of the activation energy of electrical conductivity. There has been an accumulation of data indicating that the activation energy of electrical conductivity for oxides, including TiO2 , depends substantially on oxygen activity [21–24]. These data are shown in Fig. 1. As seen, the reported activation energies exhibit a substantial scatter. The scatter may result from the following effects: 1. Non-equilibrium conditions. The electrical conductivity data are well defined only when they correspond to the gas/solid equilibrium. This requires knowledge of the equilibration kinetics and the chemical diffusion data. The latter can be used to select the required time of equilibration. However, the reported electrical conductivity data are not associated with the chemical diffusion data.
674
Ionics (2010) 16:673–679
Basic relationships and definition of terms ACTIVATION ENERGY, Eσ [kJ/mol]
220
TiO2
Defect disorder
200
180
160
Balachandran & Eror, 1988 (PC) Marucco et al., 1981 (SC) Odier et al., 1975 (SC) Blumenthal at al., 1966 (SC, c) Blumenthal et al., 1966 (SC, c)
140
120
-10
-5
0
5
The properties of TiO2 , including its semiconducting properties, are closely related to the concentration of point defects, including ionic defects, such as oxygen vacancies, titanium vacancies, and titanium interstitials, and electronic defects (electrons and electron holes) [17–20]. Using the Kröger–Vink notation [25], the formation of defects at elevated temperatures may be described by the following defect equilibria [17]:
log p(O2) [p(O2) in Pa]
(1)
Fig. 1 Literature data on the activation energy of electrical conductivity for TiO2
(2) Consequently, they may not correspond to thermodynamic equilibrium. 2. Effect of impurities. The electrical conductivity of semiconductors is very sensitive to the presence of aliovalent ions, forming donors or acceptors. While the activation energies of electrical conductivity in Fig. 1 are reported for undoped TiO2 , the effect of unintentional dopants (impurities) is unknown, as the reports did not provide information on concentration of impurities. As seen in Fig. 1, the activation energy, Eσ , for TiO2 assumes 170 kJ/mol in strongly reduced conditions, increases to a maximum value of 210 kJ/mol with increased oxygen activity, and then decreases to 125 kJ/mol in oxidising conditions (air). However, due to a large scatter of reported results, there is a need to generate the activation energy data that are well defined. This can be achieved by the determination of electrical conductivity in the gas/solid equilibrium (when the specimen is well defined) for a high-purity TiO2 . The specific aim of the present paper is to study the elctrical conductivity of high-purity TiO2 in equilibrium at 1,273 K, as well as during cooling and heating with a controlled rate in the temperature range 300–1,273 K. The obtained data are considered in terms of the activation enthalpy of formation of ionic defects, such as oxygen vacancies, and the activation enthalpy of motion of electronic defects. The experimental part is preceded by the definition of terms used in the consideration of defect disorder, electrical conductivity, and the effects of cooling.
(3)
(4)
(5) where e and h• denote electron and electron hole, respectively. These defects must satisfy the charge neutrality condition, which can be expressed as: •• 2 VO + 3 Tii••• + 4 Tii•••• + A , + D• + p = n + 4 VTi
(6)
where n and p denote the concentrations of electrons and electron holes, respectively, and [D• ] and [A ] are the concentrations of singly ionized donor- and acceptor-type foreign ions introduced as dopants or impurities. The equilibria 1–5 may be considered in terms of the mass action law. Then, the respective equilibrium constants are expressed as follows: •• 2 1 n p(O2 ) 2 K1 = VO
(7)
K2 = Tii••• n3 p(O2 )
(8)
K3 = Tii•••• n4 p(O2 )
(9)
Ionics (2010) 16:673–679
675
(10)
Ki = np,
(11)
where the square brackets represent the concentrations of ionic defects (molar fractions). Using the combination of Eqs. 7–11 and the charge neutrality condition 6, the concentrations of both electronic and ionic defects may be expressed as a function of the p(O2 ) [18, 26].
TC
T
Eσ =
log σ
4 K4 = VTi p p(O2 )−1
2 m
Δ Hf + Δ H m
Eσ = ΔHm
Electrical conductivity Electrical conductivity is the product of both concentration and mobility terms. The electrical conductivity of n-type semiconductor may be expressed by the following formula: σ = enμn ,
GAS/SOLID EQUILIBRIUM
1/T
(12)
where e is the elementary charge, n is the concentration of electrons and μn is their mobility. It has been shown that the slope of log σ vs log p(O2 ) relationship for TiO2 at elevated temperatures depends on the oxygen activity range. In strongly reduced conditions ( p(O2 ) < 10−5 Pa) and in oxidised conditions ( p(O2 ) > 10 Pa), the slope is −1/6 and −1/4, respectively [17]. As electrical conductivity is the product of mobility and concentration terms, the effect of temperature on both of them may be expressed by the following respective forms [27]: Hm μn = const exp − RT 1 m
n = const p(O2 ) exp −
(13)
2 H f m
RT
,
(14)
where the parameter const includes equilibrium constants, Hm is the activation enthalpy of motion of electrons, m is the parameter related to the ionisation degree of defects and H f is the enthalpy of the formation of defects. Consequently, the effect of temperature on the electrical conductivity may be expressed in the following form: σ = const exp −
2 H f m
+ Hm RT
(15)
QUENCHED REGIME
Fig. 2 Schematic representation of the effect of temperature on electrical conductivity
Therefore, the activation energy of electrical conductivity is equal to: Eσ =
2 H f + Hm m
(16)
Effect of cooling The effect of cooling on electrical conductivity is schematically represented in Fig. 2 [27]. As seen, the activation energy of the electrical conductivity at higher temperatures (above the Tc level) has a complex physical meaning, as it involves both Hm and H f terms [17]. However, the activation energy of the quenched system (below the Tc level) is determined only by the Hm term. Thus, determined mobility term may then be used for the calculation of the formation term H f from the activation energy of the electrical conductivity determined at T > Tc , if the parameter m is known. As it has been shown above, the parameter m for TiO2 in reduced and oxidised conditions is 6 and 4, respectively.
Brief overview of literature data There has been an accumulation of the electrical conductivity data for TiO2 [21–24, 28–43]. The effect of oxygen activity on the activation energy of the electrical
676
Ionics (2010) 16:673–679
conductivity for undoped (but not necessarily pure) TiO2 is shown in Fig. 1 [21–24]. As seen, these data exhibit a large scatter that may be related to the following effects: Ef fect of impurities Electrical properties are very sensitive to the content of impurities, especially of aliovalent ions [19]. Therefore, the data on the impurity analysis (frequently not reported) is essential to compare the data on electrical conductivity. Ef fect of microstructure The effect of microstructure and the local properties of grain boundaries on electrical conductivity may be substantial. Ef fect of contacts The determination of well-defined data of electrical conductivity requires that the electrode contacts exhibit ohmic behaviour. Equilibrium vs nonequilibrium data Only the data determined in equilibrium are well defined. In many instances, the literature reports do not allow to assess whether the equilibrium was reached. In order to minimise the above effects, the present work reports the electrical conductivity data for highpurity TiO2 , including single crystal and polycrystalline specimens, obtained using the four-probe method. The data on the activation energy of the electrical conductivity, which was determined in the gas/solid equilibrium, are shown in Fig. 3. These data indicate that the overall effect of p(O2 ) on the activation energy is similar to that in Fig. 1. As seen, the activation energy values for polycrystalline specimen are higher than for the single crystal. The difference between the two is consistent with the effect of grain boundaries, which
220
are enriched with donor-type defects, such as oxygen vacancies and titanium interstitials [17]. While it is clear that the data in equilibrium are well defined, so far, little is known on the effect of colling/heating on the temperature coefficient of the electrical conductivity. The aim of the present work is to assess the effect of fast and slow colling/heating on the activation energy of the electrical conductivity for both reduced and oxidised TiO2 of high purity.
Experimental The polycrystalline specimen of TiO2 was prepared from high-purity (99.999%) titanium isopropoxide, Ti[(CH2 )2 (CH2 OH)]4 . All vessels used for the processing were made of polypropylene or platinum in order to prevent silicon contamination. Deionized water, in the amount required by the reaction, was slowly added into the titanium isopropoxide/ethanol mixture leading to TiO2 precipitation. The powder was cold pressed (200 MPa) into 15-mm-diameter pellets and then sintered at 1,423 K for 12 h. The scanning electron microscopy micrograph of the studied specimen is shown in Fig. 4. The electrical properties were studied using a rectangular prism specimen of dimensions 2 × 5 × 10 mm that was cut from the sintered pellet. The total concentration of acceptor-type cation impurities was 34 ppm, and the concentration of anions (mostly chlorine) was 20 ppm. The electrical conductivity, σ , was measured using a high-temperature Seebeck probe [20]. The external (current) probes were formed of platinum plates attached to the 2 × 5 mm sides of the specimen. A spring mechanism, located outside the high-temperature zone, was used to maintain effective galvanic contact between
Eσ [kJ/mol]
200
180 POLYCRYSTAL
160 SINGLE CRYSTAL
140
120
TiO2 -8
-6
-4
-2
0
2
4
log p(O 2) [p(O2) in Pa]
Fig. 3 Activation energy of electrical conductivity as a function of oxygen activity for TiO2 single crystal and polycrystalline specimen
Fig. 4 SEM micrograph of high purity, polycrystalline TiO2 specimen
Ionics (2010) 16:673–679
677
1400
1200
1000
900
T [K] 800
700
600
0
TiO2 (PC) HEATING (500 deg/h) p(O2) = 10 Pa
-1 -1
-1
log σdynamic [σ in Ω m ]
the electrodes and the specimen. The voltage electrodes were formed of two platinum wires wrapped around the specimen and welded to the connecting wires. The distance between these electrodes was 6.6 mm. Prior to the measurements of the electrical conductivity, the specimen was equilibrated at the initial temperature of the measurements in argon ( p(O2 ) = 10 Pa) or in the argon–hydrogen–water vapour mixture (its oxygen activity was temperature dependent). At each temperature, the specimen was annealed until its electrical conductivity assumed a constant value for several hours. The details of the applied experimental procedure are described elsewhere [20].
-2
-3
-4 Eσ = 130.3 kJ/mol
-5
0.8
1.0
1.2
1.4
1.6
-1
1000/T [K ]
Results
Fig. 6 Changes of electrical conductivity of polycrystalline TiO2 during heating in argon
The present study included the following experimental procedures: –
–
Slow cooling (50 K/h) of the specimen annealed in argon. The obtained results are shown in Fig. 5. As seen, the slope of log σ vs log p(O2 ) exhibits a good linearity in the range 750–1,273 K (below 750 K, the resistance of the specimen becomes comparable to that of the sample holder). The activation energy of electrical conductivity is 166.8 kJ/mol. Fast heating (500 K/h) of the specimen in argon. These data are shown in Fig. 6. As seen, the slope of log σ vs log p(O2 ) again exhibits a good linearity in the range 700–1,200 K, with the activation energy of electrical conductivity equal 130.3 kJ/mol. Below 600 K, the resistance of the specimen is too high to be measured accurately; above 1,200 K, the
–
–
sample apparently has a tendency to reach a new equilibrium. Slow cooling (50 K/h) of the specimen annealed in reduced conditions ( p(O2 ) < 10−5 Pa). As seen in Fig. 7, the plot log σ vs log p(O2 ) exhibits two slopes with activation energies 47.8 kJ/mol above 1,000 K and 1.8 kJ/mol below 800 K. Fast heating (500 K/h) of the specimen in reducing atmosphere ( p(O2 ) < 10−5 Pa). Figure 8 shows that two activation energies of electrical conductivity are observed during this experiment: 104.9 kJ/mol above 1,100 K and 1.8 kJ/mol below 1,000 K.
According to the discussion in the section ‘Effect of cooling’, the low-temperature activation energy of
T [K] 1400
1200
1000
900
800
T [K]
700
1400 1000 800
IN EQUILIBRIUM AT 1273 K
TiO2 (PC)
-2
-3
-4
Eσ = 166.8 kJ/mol
-10
TiO2 (PC)
Pa
COOLING (50 deg/h) Ar + H2(1%) + H2O
2.2
-1
-1
-1
COOLING (50 deg/h) p(O2) = 10 Pa
log σdynamic [σ in Ω m ]
p(O2) = 1.1·10
-1
-1
400
2.4
0
log σdynamic [σ in Ω m ]
600
Eσ = 47.8 kJ/mol
2.0 Eσ = 1.8 kJ/mol
1.8
-5
0.8
1.0
1.2
1.4
-1
1000/T [K ]
Fig. 5 Changes of electrical conductivity of polycrystalline TiO2 during cooling in argon
1.0
1.5
2.0 -1 1000/T [K ]
2.5
3.0
Fig. 7 Changes of electrical conductivity of polycrystalline TiO2 during cooling in the mixture argon–hydrogen–water vapour
678
Ionics (2010) 16:673–679 T [K] 1400
1000 800
600
IN EQUILIBRIUM AT 1273 K -10 p(O2) = 1.1·10 Pa
TiO2 (PC)
–
HEATING (500 deg/h) Ar + H2(1%) + H2O
2.2
-1
log σdynamic [σ in Ω m ]
determination of the H f term, the following assumptions has been made:
400
–
-1
Eσ = 104.9 kJ/mol
2.0
– Eσ = 1.8 kJ/mol
1.8
1.0
1.5
2.0 -1 1000/T [K ]
2.5
3.0
Fig. 8 Changes of electrical conductivity of polycrystalline TiO2 during heating in the mixture argon–hydrogen–water vapour
electrical conductivity can be interpreted as the enthalpy of motion, Hm . The defect formation enthalpy term, determined in equilibrium from the electrical conductivity data for high-purity TiO2 in Fig. 3, is shown in Fig. 9. In the
The parameter mσ at low and high p(O2 ) is 6 and 4, respectively. The mobility term determined in the present work is Hm = 1.8 kJ/mol. The mobility term is independent of oxygen activity, p(O2 ).
As seen, the enthalpy term increases with decreasing p(O2 ). Assuming that the predominant defects are oxygen vacancies, the dependence H f vs log p(O2 ) indicates that the energy needed to form these defects increases with their concentration. As also seen in Fig. 9, the formation enthalpy determined from the dynamic data of the electrical conductivty differs substantialy from those related to thermodynamic equilibrium. The apparent values of the enthalpy of defect formation are 140 and 310 kJ/mol, determined during cooling and heating, respectively, in reducing conditions and 260 and 330 kJ/mol for heating and cooling, respectively, in oxidising conditions. Clearly, these values strongly depend on the conditions of the experiment.
Conclusions 500
The present work assessed both the dynamic data of the electrical conductivity for TiO2 , determined during cooling and heating at the controlled rate, and the electrical conductivity determined in the gas/solid equilibrium. It is shown that the defect formation enthalpy, determined from the equilibrium data for high-purity TiO2 , is well defined and increases with the concentration of the predominant defects, oxygen vacancies. However, the formation enthalpy term determined from the dynamic electrical conductivity depends on the cooling/heating rate and is not well defined.
POLYCRYSTAL EQUILIBRIUM
SINGLE CRYSTAL EQUILIBRIUM
ΔHf [kJ/mol]
400
POLYCRYSTAL HEATING 500 K/h POLYCRYSTAL COOLING 50 K/h
300
Acknowledgements One of us (JS) would like to thank the College of Health and Science, University of Western Sydney, for the opportunity to participate in the advanced science project.
POLYCRYSTAL HEATING 500 K/h
|mσ | = 6
|mσ | = 4
200 POLYCRYSTAL COOLING 50 K/h
References
TiO2 -10
-5
0
5
log p(O2) [p(O2) in Pa] Fig. 9 Enthalpy of defect formation vs oxygen activity for TiO2
1. Fujishima A, Honda K (1972) Nature 238:37 2. Khan SUM, Al-Shahry M, Ingler Jr WB (2002) Science 297:2243 3. Karakitsou KE, Verykios XE (1993) J Phys Chem 97:1184 4. Linsebigler AL, Lu G, Yates JT (1995) Chem Rev 95:735 5. Hoffmann MR, Martin ST, Choi W, Bahnemann DW (1995) Chem Rev 95:69
Ionics (2010) 16:673–679 6. Carp O, Huisman CL, Reller A (2004) Prog Solid State Chem 32:33 7. Lee SK, Mills A (2004) J Ind Eng Chem 10:173 8. Ni M, Leung MKH, Leung DYC, Sumathy K (2007) Renew Sustain Energy Rev 11:401 9. Matsunaga T, Tomoda R, Nakajima T, Wake H (1985) FEMS Microbiol Lett 29:211 10. Lindner M, Theurich J, Bahnemann DW (1997) Water Sci Technol 35:79 11. Yang JC, Kim YC, Shul YG, Shin CH, Lee TK (1997) Appl Surf Sci 121–122:525 12. Nosaka Y, Kishimoto M, Nishino J (1998) J Phys Chem B 102:10279 13. Sakthivel S, Shankar MV, Palanichamy M, Arabindoo B, Bahnemann DW, Murugesan V (2004) Water Res 38:3001 ´ 14. Blanco Galvez J, Malato Rodriguez S (2003) Solar detoxification renewable energies. UNESCO Pub., Paris 15. Nakato Y, Akanuma H, Magari Y, Yae S, Shimizu JI, Mori H (1997) J Phys Chem B 101:4934 16. Nakamura R, Tanaka T, Nakato Y (2004) J Phys Chem B 108:10617 17. Nowotny MK, Sheppard LR, Bak T, Nowotny J (2008) J Phys Chem C 112:5275 18. Nowotny J, Bak T, Nowotny MK, Sheppard LR (2008) J Phys Chem C 112:590 19. Nowotny J, Bak T, Nowotny MK, Sheppard LR (2008) J Phys Chem C 112:602 20. Nowotny MK, Bak T, Nowotny J (2006) J Phys Chem B 110:16270 21. Blumenthal RN, Coburn J, Baukus J, Hirthe WM (1966) J Phys Chem Solids 27:643
679 22. Odier P, Baumard JF, Panis D, Anthony AM (1975) J Solid State Chem 12:324 23. Marucco JF, Gautron J, Lemasson P (1981) J Phys Chem Solids 42:363 24. Balachandran U, Eror NG (1988) J Mater Sci 23:2676 25. Kröger FA (1974) The chemistry of imperfect crystals, vol 3. North Holland, Amsterdam 26. Bak T, Nowotny J, Nowotny MK (2006) J Phys Chem B 110:21560 27. Kofstad P (1972) Nonstoichiometry, diffusion and electrical conductivity in binary metal oxides. Wiley, New York 28. Cronemeyer DC (1952) Phys Rev 87:876 29. Rudolph J (1959) Z Naturforsch, A: Phys Sci 14:727 30. Kofstad P (1962) J Phys Chem Solids 23:1579 31. Yahia J (1963) Phys Rev 130:1711 32. Tannhauser DS (1963) Solid State Commun 1:223 33. Blumenthal RN, Baukus J, Hirthe WM (1967) J Electrochem Soc 114:172 34. Baumard JF (1976) Solid State Commun 20:859 35. Baumard JF, Panis D, Anthony AM (1977) J Solid State Chem 20:43 36. Singheiser L, Auer W (1977) Ber Bunsen Phys Chem 81:1167 37. Tani E, Baumard JF (1980) J Solid State Chem 32:105 38. Kim KH, Oh EJ, Choi JS (1984) J Phys Chem Solids 45:1265 39. Marucco JF, Poumellec B, Gautron J, Lemasson P (1985) J Phys Chem Solids 46:709 40. Millot F (1985) J Mater Sci Lett 4:902 41. Carpentier JL, Lebrun A, Perdu F (1989) J Phys Chem Solids 50:145 42. Fujitsu S, Hamada T (1994) J Am Ceram Soc 77:3281 43. Son J, Yu I (1996) Korean J Ceram 2:131
