J. Phys. Chem. C 2007, 111, 9769-9778
9769
Effect of Grain Boundaries on Semiconducting Properties of TiO2 at Elevated Temperatures† J. Nowotny,* T. Bak, T. Burg, M. K. Nowotny, and L. R. Sheppard Centre for Materials Research in Energy ConVersion, School of Materials Science and Engineering, UniVersity of New South Wales, Sydney, NSW 2052, Australia ReceiVed: NoVember 27, 2006; In Final Form: March 30, 2007
The present work represents the seminal study on the local properties of the grain boundaries of polycrystalline TiO2 at elevated temperatures corresponding to the equilibrium with the gas phase of well-defined oxygen activity. These local properties have been determined from two sets of data obtained in two parallel projects on the determination of the defect-related electrical properties in identical conditions for both polycrystalline and single-crystal TiO2. These properties, which have been determined in the gas/solid equilibrium, are independent of the applied experimental procedure and are determined only by the equilibrium conditions described by temperature and oxygen activity. Therefore, the reported grain boundary properties may be considered as material data. The data considered in this work include the electrical conductivity and thermoelectric power that were determined following the same experimental procedure. The present work also includes the equilibration kinetic data that are considered in terms of the chemical diffusion coefficient. Comparison between these two sets of data indicates that the local defect disorder and the related semiconducting properties of grain boundaries are different from those of the bulk phase. The analysis of the experimental data allows us to make the following conclusions: (1) Grain boundaries of TiO2 act as donors of electrons. This effect seems to be related to the enrichment of the grain boundary layer in donor-type defects, such as oxygen vacancies. (2) The transport mechanisms for electrons and electron holes are the same for both SC-TiO2 and PC-TiO2. This indicates that the transport of electronic charge carriers is not affected by grain boundaries. (3) Grain boundaries exhibit weak links for ionic charge transport across polycrystalline TiO2. (4) The effective band gap for PC-TiO2 is smaller than that for SC-TiO2. This work shows that grain boundaries may be used to tailor semiconducting properties of polycrystalline TiO2 in order to achieve the performance-related properties that are desired for specific applications.
1. Introduction 1.1. Single Crystals versus Polycrystals. Single crystals are considered to be well-defined solids. This perception is determined by the fact that single crystals exhibit a periodic structure that is free of the complications caused by grain boundaries (GBs). Therefore, polycrystalline materials are not the preferred form for examination, especially in respect to the determination of well-defined material-related data. Consequently, the effect of GBs on the properties of polycrystalline solids remains largely unknown because of the studied polycrystalline materials are not well-defined in terms of their microstructure and impurity level. This is the reason that the vast majority of materials data reported in the literature, in relation to, for example, diffusion, charge transport, and surface properties are limited to single crystals. However, most industrial materials, including catalysts, solid electrolytes, and electrodes, are made of polycrystalline materials. Moreover, it becomes increasingly clear that the functional properties of the polycrystalline materials of industrial significance are determined by the local properties of GBs rather than those of the bulk phase. Therefore, there is a need to undertand the effect of GBs on properties, including the functional * Corresponding author. E-mail:
[email protected]. Tel: 6129385.6465. Fax: 612-9385.6467. † This project was performed as part of UNSW R&D program on solar hydrogen.
properties. This understanding may allow to develop the processing of polycrystalline materials with controlled properties through GB engineering. 1.2. Effect of Interfaces on Properties. The effect of interfaces, such as GBs and external surfaces, on properties of polycrystalline solids of nonstoichiometric oxides is substantial.1-7 This effect controls the performance of several functional materials, including the following: (1) Dielectrics. It is well known that properties of dielectrics are determined by the chemical composition of GBs.3 There has been substantial progress in the theory of barrier-layer capacitors based mainly on alkaline earth metal titanates (BaTiO3, CaTiO3, SrTiO3).3 The developed theoretical models allow us to process the dielectric materials with controlled properties through GB engineering. (2) Nonlinear resistors. The properties of the nonlinear resistors are determined by the chemical composition of GBs, which in most cases include intergranular precipitates of other phases.8,9 (3) Ionic conductors. It is well known that the properties of solid electrolytes, such as zirconia, are to a large extent influenced by GBs forming weak links for oxygen transport.2 Therefore, the research on processing zirconia-based oxygen conductors with enhanced properties aims at removal of the GB weak links through GB engineering. (4) Materials for chemical gas sensors. The sensing signal in semiconducting gas sensors and electrochemical gas sensors is generated at external surfaces and interfaces, respectively.
10.1021/jp067869+ CCC: $37.00 © 2007 American Chemical Society Published on Web 06/09/2007
9770 J. Phys. Chem. C, Vol. 111, No. 27, 2007 (5) Catalysts. It is clear that catalytic properties are determined by the local properties of the outermost surface layer. The vast majority of the data on material interfaces, that have been reported so far, are limited to room temperature and some are related to moderate temperatures up to several hundred degrees Celsius. This limitation is dictated by the application conditions. In these conditions, however, the nonstoichiometric compounds are quenched and the interface properties are determined mainly by the applied experimental procedures rather than by specific material properties.1 It is clear that properties of nonstoichiometric oxides are welldefined mainly at elevated temperatures when in equilibrium with the gas phase of controlled oxygen activity. Then these properties, including the properties of interfaces, are determined by the conditions of the equilibrium described by the temperature and the oxygen activity and are independent of the applied experimental procedure. The present study aims at the determination of the effect of GBs on properties in equilibrium. Therefore, the data reported in the present work may be considered as material-related data. Alternatively, these data may differ substantially from those at room temperature. The studies on the effect of cooling on the defect-related properties will be reported later. The present work is focused on titanium dioxide, TiO2, and aims at the determination of its local GB properties at elevated temperatures in the 1073-1298 K range in the gas phase of controlled oxygen activity. The studies are based on the electrical properties for high-purity specimens. The results of this seminal study form a basis of GB defect chemistry of oxide materials in general and TiO2 in particular. So far, little is known on this matter. 1.3. Titanium Dioxide. The interest in titanium dioxide (TiO2) is increasing. This interest has been generated because of its wide range of applications.10-22 TiO2 is a nonstoichiometric compound.23 Titanium dioxide has been generally considered as an n-type semiconductor. The n-type properties have been considered in terms of oxygen vacancies as the predominant defects and titanium interstitials as minority defects.23 However, recent studies have shown that oxidized TiO2 may also exhibit p-type properties owing to the concurrent presence of acceptor-type defects in the form of titanium vacancies.24 Therefore, either formula TiO2-x (reduced specimen) or Ti1-xO2 (oxidized specimen) can be applied. In the latter case, TiO2 exhibits p-type properties.24 The most prominent example of the TiO2 application is its use in photoassisted water electrolysis. The pioneering work of Fujishima and Honda10 described the application of singlecrystal TiO2 as a photoanode. They showed that exposition of TiO2 (immersed in water) to sunlight results in the evolution of oxygen from the anode and hydrogen from the cathode. The report of Fujishima et al.11 resulted in a subsequent and ongoing search for candidates for photoelectrodes.12-21 The discovery of Fujishima and Honda10 was made for single-crystal TiO2 (SCTiO2). However, the commercial photoelectrode is expected to be made of polycrystalline TiO2 (PC-TiO2) because of cost reasons. Besides its photocatalytic properties, TiO2 also exhibits a wide range of other applications that were discussed elsewhere.22-24 The difference between single crystals and polycrystalline materials is that GBs result in the formation of a microstructure, which depends on the distribution of GBs and their local properties. Therefore, the development of high-performance functional materials based on PC-TiO2, including photoelectrodes and photocatalysts, requires an understanding of the effect
Nowotny et al.
Figure 1. Schematic representation of the activity term across the polycrystalline specimen in the gas/solid equilibrium, involving the bulk phase and the grain boundary layer.
of GBs on the key properties, which are essential for performance. Consequently, there is an increasing need to determine the effect of GBs on properties of polycrystalline TiO2. The logical aim of the present study is to address the following question: How can the functional properties of PC-TiO2 be tailored through the imposition of controlled microstructure and, consequently, controlled density of GBs? 2. Aims and Definition of Terms The specific aim of the present study is to characterize the effect of GBs on electrical properties for relatively well-defined PC-TiO2 specimens in well-defined conditions. To achieve this aim, the studies will address the following issues: (1) The PC-TiO2 specimen must be of high purity and, if possible, of high density. (2) The properties must be determined in the gas/solid equilibrium. Then its electrical properties are determined by the conditions of the equilibrium. A schematic representation of the activities of the lattice elements within a high-purity polycrystalline oxide specimen in the gas/solid equilibrium, such as in TiO2, is shown in Figure 1. As seen, the activities of the lattice elements, such as oxygen and Ti ions, are the same within the entire specimen, including the bulk of the grains and the GB layer. The same representation concerns points defects. The picture is entirely different for the specimens that are either contaminated or involve precipitates of another phase within the GB region. Then the activities of both anions and cations exhibit strong gradients of activities that are characteristic of heterogeneous systems, as is shown in Figure 2. The present work does not consider such systems. It is clear that the system shown in Figure 1 is well-defined because its properties are determined by the conditions of the gas/solid equilibrium. Such a system, however, may be achieved when the specimen is of high purity. Alternatively, the presence of contaminations leads to the formation of segregation-induced intergranular precipitates of other phases. These phases are also present in multiphase systems when the GBs of one phase are filled (by diffusion) with another oxide phase, as is the case for nonlinear resistors.8,9 In the latter case, the diffusion concentration gradients within the heterogeneous system, shown schematically in Figure 2, depend largely on the applied experimental procedure. The following section considers the main reasons for the lack of reproducibility of data reported so far for polycrystalline TiO2
Effect of Grain Boundaries on the Properties of TiO2
Figure 2. Schematic representation of the activity terms within the bulk phase and the grain boundary layer for a polycrystalline specimen involving a precipitate of another phase within the grain boundary area.
and outlines the conditions for the processing of well-defined materials. 3. Criteria of Well-Defined Data for Metal Oxides There is a great amount of papers reporting the studies on the electrical properties of TiO2, for both single crystals and polycrystalline specimens. Most of them, however, concern the data determined at room temperature. The literature data on these properties are not overviewed in the present work because of the following reasons: (1) Practically all of the literature data considers the GB properties at room temperature, whereas the present study reports the properties at elevated temperatures. The physical meaning of electrical properties in these conditions are entirely different, and, therefore, (2) most of the data reported at room temperature concern the TiO2 specimens that are not well-defined because of the following reasons: (a) The nonstoichiometry, and the related defect disorder, are unknown. (b) The impurity level is not reported. (c) The microstructure, in terms of grain size and density, is not well-defined. The issue of substantial importance is nonstoichiometry and its effect on properties. The vast majority of data reported for TiO2 have been reported for commercial specimens, which are prepared in conditions that are not well-defined. Then its nonstoichiometry (the Ti/O ratio), which may vary in a large range, is unknown. First, the nonstoichiometry depends on the temperature and the gas-phase composition during processing. Although the most frequently applied gas phase in the high-temperature treatment of TiO2 is air, the temperature of processing is frequently not provided. Most importantly, however, the nonstoichiometry exhibits substantial changes during cooling, and the extent of these changes depends on the rate of cooling. In addition, this aspect of the processing procedure is unknown. This is the reason that there are conflicting reports on the electrical properties of TiO2 at room temperature. There has been an accumulation of several literature reports on the electrical properties of TiO2 at elevated tempertures.25-50 However, the assessment of these literature data does not lead to a clear and uniform picture. As seen in Figure 3, showing the Arrhenius plot on electrical conductivity for undoped TiO2 at 1273 K, these data exhibit a substantial scatter concerning their temperature dependence and the absolute values. As also
J. Phys. Chem. C, Vol. 111, No. 27, 2007 9771 seen, most of these data are consistent with n-type behavior within the entire p(O2) range. However, the most recently reported data for high-purity TiO2 exhibit a clear minimum of the electrical conductivity that is consistent with the n-p transition. The observed discrepancy between the reported data is mainly due to the following reasons:24 (1) Effect of Impurities. Because the electrical properties are very sensitive to the presence of aliovalent ions, present as impurities or deliberately added dopants, it is essential to determine their concentrations and valencies. The information about the impurities is essential in the assessment of material properties. (2) Effect of Oxygen Activity. Properties of nonstoichiometric oxides are determined by oxygen activity, which is imposed at elevated temperatures by the gas phase surrounding the specimen. Knowledge of the oxygen activity during processing is essential to the correct assessment of the defect disorder and the related electrical properties. (3) Departure from the Gas/Solid Equilibrium. Semiconducting properties of metal oxides are well-defined when in the gas/ solid equilibrium. However, the data are frequently determined in the kinetic regime. These data are not well-defined. Therefore, experimental evidence, showing that the equilibrium has been achieved, is essential. (4) Effect of Microstructure. The GBs exhibit properties entirely different from those of the bulk phase.1 Then GBs may be considered as either donors or acceptors depending on their local properties. Knowledge of the microstructure, in terms of the concentration of GBs, is essential in the quantitative assessment of the effect of GBs on properties. In most cases, the information about the above issues has not been reported in the literature. This is also the case for the data shown in Figure 3. Therefore, these data are not welldefined, with a notable exception of the data shown by the thick solid line, which will be discussed below. The aim of the studies reported recently of TiO2 was to determine the data that are free of the shortcomings mentioned above.50-55 The studies involved the determination of electrical properties, including electrical conductivity and thermoelectric power, for two kinds of TiO2 specimens: (1) single-crystal TiO2 (SC-TiO2)50-53 and (2) polycrystalline TiO2 (PC-TiO2).54,55 The studied SC-TiO2 specimen was of high purity.50-53 In the case of PC-TiO2, the system was of high purity and high density.54,55 In both cases, the specimens were equilibrated with the gas phase of controlled oxygen activity. These studies led to the generation of two sets of data that may be used for the assessment of the effect of GBs on properties of TiO2. The assessment of data in terms of the effect of GBs will be preceded by a short overview of interface properties of oxide materials and an outline of the basic relationships describing defect disorder and electrical properties of TiO2. 4. Grain Boundaries of Oxide Materials 4.1. Approach. The main reason for the limited knowledge about GBs is a lack of techniques able to assess their local properties directly. Studies of bicrystals, forming well-defined GBs, is an attempt to address this issue.56 However, GBs may also be assessed through a comparison of data for both single crystals and polycrystalline TiO2. Although there has been an accumulation of data for both SC-TiO2 and PC-TiO2, it was shown above that most of these
9772 J. Phys. Chem. C, Vol. 111, No. 27, 2007 data are not well-defined in terms of the impurity level and experimental conditions. Therefore, these data do not provide a clear picture of the effect of GBs on properties. Consequently, there was a need to generate the data for well-defined specimens that are determined in well-defined experimental conditions. 4.2. Effect of Segregation. The tendency of interfaces to have different chemical compositions from that of the adjoining bulk phase has a strong impact on the properties of solids in general and polycrystalline solids in particular. So far, however, there is only a limited understanding of the local properties of interfaces and the effect of segregation on these properties. Literature reports on segregation in solids have been oriented mainly toward metallic solids,57-59 whereas the progress of research concerning ionic solids of nonstoichiometric compounds is limited.60,61 Therefore, there is an increasing need to understand the effect of interfaces on properties of polycrystalline solids and, specifically, of functional materials based on nonstoichiometric compounds. One of the main reasons for the limited knowledge in this matter is considerable difficulty in studies of interfaces of ionic solids, such as metal oxides, which are the most commonly applied functional materials. Also, application of oxide materials such as photoelectrodes for water splitting using solar energy is expected to be one of the most prominent aims of research.22 Interfaces of metal oxides usually exhibit segregation-induced concentration gradients of extrinsic defects, such as dopants (intentionally introduced foreign ions) and impurities (unintentional dopants).1 Consequently, the local properties of these interfaces are entirely different from those of the bulk phase. So far, however, the experimental assessment of the local properties of interfaces, such as GBs, is difficult. The application of surface-sensitive experimental techniques, based on both electron and ion spectroscopy, have been applied for the determination of the concentration of extrinsic defects.61,62 However, these techniques have limited application to internal surfaces. Their application in studies of GBs requires intergranular breaking. The methods that have been applied for interface analysis includes analytical electron microscopy, which involves scanning transmission electron microscopy (STEM) with energy-dispersive X-ray analysis. Another complication in the assessment of the segregationinduced concentration gradients at interfaces is that they mainly consist of intrinsic defects, such as oxygen, cation vacancies, and interstitials of host lattice cations. Awareness is growing about the fact that the segregation-induced defect disorder of the GB region of metal oxides differs essentially from that of the bulk phase. Moreover, in extreme cases the segregation of intrinsic defects may lead to the formation of low-dimensional interface structures, which exhibit exceptional properties.1 Therefore, there is a need to determine interface properties and assess their effect on the properties of polycrystalline materials. However, most of the experimental techniques for surface and interface analysis are essentially insensitive to the intrinsic defects. An obvious approach in the assessment of the local properties of GBs is to investigate both single-crystal and polycrystalline materials of the same composition and to compare the two sets of data obtained in terms of the specific properties. However, correct assessment of the effects of interfaces on properties using this approach requires one to address several issues, including the following: (1) The chemical composition of the two kinds of specimens, mainly the single crystal and the polycrystalline solid, should be the same.
Nowotny et al. (2) Both specimens should either be free of impurities or their concentrations should be comparable. (3) Studied properties must be determined in identical conditions using the same techniques in order to remove the effects imposed by the specific experimental approaches. (4) The same theoretical framework should be applied for the assessment of data in both cases. The purpose of the present work is to assess the electrical properties of both PC-TiO2 and SC-TiO2 based on two sets of data. The assessment will be preceded by an outline of basic relationships describing the charge transport in oxide semiconductors. 4.3. Strategy of the Present Work. One of the key functional properties of TiO2-based photoelectrodes is charge transport.63,64 Therefore, there is a need to understand the effect of GBs on the charge transport for PC-TiO2. So far, little is known about the local properties of GBs of TiO2, including charge transport. The strategy of the research applied in the present work is based on the assessment of the effect of GBs on the properties of TiO2 that were obtained in two parallel research projects, which aimed at the determination of the same charge-transportrelated quantities for both SC-TiO250-53 and PC-TiO254,55 in the same conditions, following the same experimental procedures and even using the same equipment. Assuming that the main difference between the two studied specimens consists of the presence of GBs in PC-TiO2, forming planar defects, these two sets of data may be considered in terms of the local properties of GBs. The studies determined the charge-transport-related properties, including the following: (1) electrical conductivity and its dependence on temperature and oxygen activity, (2) thermoelectric power and its dependence on temperature and oxygen activity, and (3) the chemical diffusion coefficient. These properties have been examined at elevated temperatures, at which the studied TiO2 specimens are well-defined by the gas/solid equilibrium that is determined by the temperature and oxygen activity. 5. Basic Relationships 5.1. Defect Disorder. TiO2 is an amphoteric semiconductor that exhibits n- and p-type properties, respectively, in low and high oxygen activities, p(O2).50 The semiconducting properties of TiO2 are determined by defect disorder. According to the Kroger-Vink notation, the formation of defects may be represented by the following defect equilibria:50,65,66
1 OO a V••O + 2e′ + O2 2
(1)
2OO + TiTi a Ti••• i + 3e′ + O2
(2)
• O2 a 2OO + V′′′′ Ti + 4h
(3)
nil a e′ + h•
(4)
These defects may be imposed at elevated temperatures by the gas phase of controlled oxygen activity, p(O2). The concentration of both ionic and electronic defects must satisfy the lattice charge neutrality condition, which may be represented in the following form • 2[V••O] + 3[Ti••• i ] + [D ] + p ) n + 4[V′′′′ Ti] + [A′]
(5)
Effect of Grain Boundaries on the Properties of TiO2
J. Phys. Chem. C, Vol. 111, No. 27, 2007 9773
where [D•] and [A′] are the concentrations of singly ionized donor- and acceptor-type foreign ions, respectively, and n and p denotes the concentration of electrons and holes. 5.2. Electrical Properties. Comprehensive considerations of the electrical conductivity for TiO2 requires one to consider all of the components associated with the charge transport, including electrons, electron holes, and ions50
σ ) σn + σp + σi
(6)
where σ is electrical conductivity and the subscripts n, p, and i are related to electrons, electron holes, and ions. It was shown the effect of p(O2) on the electrical conductivity of TiO2 within the n-p transition regime may be expressed by the following respective dependences50
σn ) σ0np(O2)(1/mσ)
(7)
σp ) σ0pp(O2)(1/mσ)
(8)
where σ0 is the parameter independent of p(O2) and the p(O2) exponent, 1/mσ, is related to the defect disorder model. It was shown that 1/mσ in the n- and p-type regime, in the vicinity of the n-p transition, are equal to -1/4 and 1/4, respectively.50 Therefore, eq 6 may be written in the following form:
σ ) σ0np(O2)-(1/4) + σ0pp(O2)(1/4) + σi
(9)
The parameter 1/mσ may be determined from the following dependence:
1 ∂ log σ ) mσ ∂ log p(O2)
(10)
The parameter 1/mσ at the n-p transition point assumes zero. Then
nµn ) pµp
(11)
where n and p denote the concentration of electrons and holes and µn and µp denote their respective mobility. It is well known that thermoelectric power at the p(O2) corresponding to the n-p transition point is assumed to be zero if the kinetic parameters for electrons and holes are the same.67 In this case, we have
n)p
(12)
Therefore, when the mobility of electronic charge carriers are the same, the p(O2) corresponding to conditions 11 and 12 are the same. This effect, named as the effect of symmetry, was observed for BaTiO3.68 The electrical conductivity components may be used for the determination of the respective transference numbers, tn, tp, and ti:
σn tn ) σtot
σp tp ) σtot
σi ti ) σtot
(13)
The activation energy of the electrical conductivity for nonstoichiometric oxides, such as TiO2, has a complex physical meaning because it involves both the concentration and mobility terms65
Eσ )
2 ∆Hf + ∆Hm mσ
(14)
TABLE 1: Main Cation Impurities in the Specimens Studied in the Present Work concentration (ppm) element
SC-TiO2
PC-TiO2
Cu Ni Ag Si Mg Fe Ca As Na total
5 5 5 10 5 2
5
0.2 20 2.5 3.5 31.2
32
where Hf and Hm denote the activation enthalpy of the formation of defects and the activation enthalpy of the mobility of charge carriers, respectively. According to Becker and Frederikse,69 the minimum of the electrical conductivity, which is related to the n-p transition, is the following function of temperature
σmin ) 2e(µnµp NnNp)(1/2) exp
() ( ) E0g β exp 2k 2kBT
(15)
where E0g is the band gap at T ) 0, µ denotes the mobility terms, N is density of states, kB is the Boltzman constant, the subscripts n and p are related to electrons and holes, respectively, T is the absolute temperature, and β is the temperature coefficient of the band gap:69
Eg ) E0g - βT
(16)
Equation 15 may be used for the determination of the band gap from the electrical conductivity data. 5.3. Chemical Diffusion. The distribution of defects within the crystal during oxidation and reduction requires that the new oxygen activity imposed at the gas/solid interface is propagated from the interface into the bulk. The propagation rate is determined by the chemical diffusion coefficient, Dchem.52,53,65 Although Dchem has no effect on properties, its knowledge is essential for the preparation of well-defined oxide specimens. The chemical diffusion coefficient may be monitored by the measurement of the electrical conductivity as a function of time52,53
∆σt ) γ∆σ∞
(17)
where γ is the degree of equilibration and the subscripts t and ∞ refer to the time of measurement (any given moment and after infinite time, i.e., in equilibrium, respectively). The effect of temperature on Dchem may be expressed as
( )
Dchem ) D0chem exp -
ED RT
(18)
where ED is the activation energy of Dchem. The physical meaning of Dchem and ED is outlined elsewhere.65 6. Experimental Section SC-TiO2 was manufactured by ESCETE Holland. XRD studies confirmed the rutile structure.50 PC-TiO2 was precipitated from high-purity Ti-isopropoxide. The powder was cold pressed and sintered at 1423 K for 12 h into pellets that were used for the measurements of both
9774 J. Phys. Chem. C, Vol. 111, No. 27, 2007
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Figure 3. Arrhenius plot of the electrical conductivity data for undoped TiO2 reported in the literature showing the scatter of data.27,31,36,45,46,48-50 Figure 5. Arrhenius plots of the electrical conductivity components associated with the electronic charge carriers, including electrons, σ0n, electron holes, σ0p, and ions, σi, for both PC-TiO254 and SC-TiO2.50
Figure 4. Isothermal changes of the electrical conductivity as a function of oxygen activity, p(O2), for both polycrystalline TiO2 (PC-TiO2)54 and single-crystal TiO2 (SC-TiO2).50
electrical conductivity and thermoelectric power.54,55 The total concentration of cation impurities in PC-TiO2 was
