Point Defects in 3D and 1D Nanomaterials: The Model Case of Titanium Dioxide

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1 IP Conference Series: Materials Science and Engineering Point Defects in 3D and 1D Nanomaterials: The Model Case of tanium Dioxide To cite this article: Philippe Knauth 2010 IP Conf. Ser.: Mater. Sci. Eng Related content - Solid State Ionics: from Michael Faraday to green energy the European dimension Klaus Funke - ptical and X-ray absorption spectroscopy in lead doped lithium fluoride crystals F Somma, P Aloe, F d'acapito et al. - 2 a prototypical memristive material K Szot, M Rogala, W Speier et al. View the article online for updates and enhancements. Recent citations - Development of a microwave sintered 2 reinforced Sn 0.7wt%Cu 0.05wt%Ni alloy M.A.A. Mohd Salleh et al This content was downloaded from IP address on 01/11/2018 at 12:35

2 Point Defects in 3D and 1D Nanomaterials: The Model Case of tanium Dioxide Philippe Knauth Aix-Marseille University-CNRS: Laboratoire Chimie Provence, Marseille, France Abstract. tanium dioxide is one of the most important oxides for applications in energy and environment, such as solar cells, photocatalysis, lithium-ion batteries. In recent years, new forms of titanium dioxide with unusual structure and/or morphology have been developed, including nanocrystals, nanotubes or nanowires. We have studied in detail the point defect chemistry in nanocrystalline 2 powders and ceramics. There can be a change from predominant Frenkel to Schottky disorder, depending on the experimental conditions, e.g. temperature and oxygen partial pressure. We have also studied the local environment of various dopants with similar ion radius, but different ion charge (Zn 2+, Y 3+, Sn 4+, Zr 4+, Nb 5+ ) in 2 nanopowders and nanoceramics by Extended X-Ray Absorption Fine Structure (EXAFS) Spectroscopy. Interfacial segregation of acceptors was demonstrated, but donors and isovalent ions do not segregate. An electrostatic space charge segregation model is applied, which explains well the observed phenomena. 1. Introduction tanium dioxide is a model binary oxide for fundamental studies that presents many of the exciting properties of electroceramics, including variations of oxygen stoichiometry and ranges of ionic or electronic conductivity. It can also be readily doped with acceptor or donor dopants, i.e. solutes with negative or positive effective charge, respectively. 2 has a multitude of applications: it has been a grand-scale white pigment for many years and is currently under investigation for advanced technological and environmental applications, such as solid state gas sensors, photovoltaic cells, photocatalysis, lithium-ion battery anodes and many more. The metastable Anatase modification presents better characteristics for photo-electrochemistry. Concerning the defect properties of 2, there is still ongoing debate as to whether Schottky or cation Frenkel disorder is predominant. In fact, Schottky and cation Frenkel defect concentrations seem to be rather similar, so that variation of temperature or chemical potential can change the predominant defect type. Fundamental studies on the electrical properties of the Anatase modification are seldom, given that ceramic preparation and long-time measurements at elevated temperature generally lead to grain growth and a partial phase transition into Rutile. Knauth and Tuller first succeeded to study the electrical properties of dense nanocrystalline Anatase as function of temperature and oxygen partial pressure. [1] Reference 2 reports ac electrical measurements of dense, phase-pure Anatase ceramics over the largest oxygen partial pressure range ever investigated. [2] The defect and solute distribution near grain boundaries influences many properties of polycrystalline materials, including grain boundary energy, grain growth, fracture and deformation, and transport properties, such as diffusion along or conductivity across grain boundaries. This c 2010 Ltd 1

3 influence can become particularly important for properties of materials with reduced dimensions, such as very thin films, nanocrystalline or nanocomposite solids, which are currently rapidly developing in the framework of nanotechnology. [3] Two modes of boundary segregation are encountered in ionic materials. The first one is common with metallic systems and is due to ionic radius misfit between host and solute ion. The second one is particular to semiconductors and ionic compounds: it is the possibility of existence of space charge regions, which are a consequence of the symmetry break at boundaries leading to a break of local electroneutrality. Redistribution of charged defects occurs between a charged boundary core and adjacent space charge regions, which bear the counter-charge. This phenomenon was first discussed for free surfaces, but occurs at all other interfaces, including grain and phase boundaries. An important technique for studying the nature of grain boundaries and the position of dopant atoms in nanocrystalline oxides is Extended X-ray Absorption Fine Structure (EXAFS) spectroscopy. [4] Major advantages of this method are its non-destructive nature, its sensitivity to low atomic concentrations, and the ability to provide quantitative information on the local environment of atoms, such as radial distances or co-ordination numbers, without the necessity of long-range order. However, the intensity of EXAFS oscillations depends on the mass of the backscattering atom and the technique is more appropriate for heavy elements. We compared in reference 5 grain boundary segregation in nanocrystalline anatase 2 for a series of solutes with ionic radii quite similar to the host 4+ ions (0.68 Å), but increasing ion charge, thus having different electrical behaviour: acceptor dopants, Zn 2+ and Y 3+, isovalent dopants, Sn 4+ and Zr 4+, and a donor dopant Nb 5+. The strategy is to reduce the mechanical driving force for boundary segregation in order to observe unambiguously the electrostatic driving force. [5] The tabulated ionic radii for octahedral environment (Pauling radii) are: Zn 2+ (0.74 Å), Y 3+ (0.87 Å), Sn 4+ (0.71 Å), Zr 4+ (0.79 Å) and Nb 5+ (0.69 Å) (1) ther ion valences, such as 3+ or Nb 4+, are only relevant under strongly reducing conditions, not encountered in our study. Furthermore, all these dopants have a sufficiently high mass to be easily observable by EXAFS. 2. Experimental 2.1. Sample preparation Pure Anatase nanopowders were obtained by precipitation from sulfuric acid solutions by heating to C. ( sulfate route ). [6] Subsequent neutralisation and washing resulted in removal of most sulphate down to ca. 1% S 4 / 2. For doping, between 0.1 and 1 mol% dopant precursor (Zn: ZnS 4. 7H 2, Y: YCl 3, Sn: SnCl 2. 2H 2, Zr: ZrCl 2. 8H 2, Nb: NbCl 5 ) was added and precipitated onto the Anatase nanomaterial using NH 3. The 2 /dopant precipitates were thoroughly washed, dried and calcined for 1 h at 300 or 600 C. Residual impurities were found to be low, e.g. sulphate <0.3% or sodium ca. 0.01%. Chemical analysis of the metal content was performed by ICP. The average crystallite size was estimated on the basis of BET data assuming spherical particles or using Scherrer s equation from the width at half maximum of X-ray diffraction peaks (X-Ray Diffractometer Siemens D5000). We have recently compared the most usual techniques for determination of average crystallite size and size distribution, specifically for the case of nanocrystalline materials. [7] Similar size ( 20 nm) was deduced from the reflections of different (hkl) values, suggesting that the crystallites were of a regular shape. Nanocrystalline anatase ceramics were made by hot-pressing the powders calcined at 600 C. In this procedure [8,9], the powder was introduced in pure alumina dyes, compressed under 4500 bar in pure alumina dies and then subjected to a fixed heating rate of 5 K/min up to a plateau temperature of 500 C, where it was kept for two hours, before releasing pressure and cooling with the intrinsic cooling rate of the hot-press (Cyberstar, Grenoble). The density of the nanocrystalline ceramics was determined from mass and geometrical dimensions and confirmed by dilatometric experiments and 2

4 mercury porosimetry. Densities of (92±1) % of theory, based on the density of pure Anatase, were obtained under these conditions EXAFS spectroscopy The EXAFS experiments were performed at the Daresbury Synchrotron Radiation Source (elements, Zn and Nb [10]) and Hamburg Synchrotron facility (Hasylab, DESY, elements Y, Sn [11], Zr [12]). The Daresbury synchrotron has electron energy of 2 GeV and the average current during the measurements was 150 ma. K-edge EXAFS spectra were recorded in transmission mode at room temperature. Anatase 2 powders were pressed into pellets with non-absorbing polyethene as diluent. For the nanocrystalline Anatase ceramics, EXAFS spectra were obtained in fluorescence mode at station 9.3. This mode was also used to collect K-edge EXAFS data for the dopant elements, Zn and Nb. The spectra were recorded at room temperature. The Hamburg synchrotron has positron energy of 4.45 GeV and the average current during the measurements was 100 ma. Fluorescence Y, Sn [11] and Zr [12] K edge spectra were recorded at room temperature at station X1. The nanoceramic sample was used as-pressed (4 mm diameter 1 mm thickness). The doped powder samples were prepared by pressing into pellets with polyethene as binder Impedance spectroscopy Impedance measurements were made at open circuit potential in a frequency domain between 10-1 and Hz using a frequency response analyzer Solartron SI Three samples could be studied at the same time. Reproducibility of our results was checked on two pellets. The signal amplitude was optimized in each experiment in order to maintain a linear response with the best quality spectrum. Sputtered gold or platinum electrodes with approximate thickness 200 nm were used to analyze the electrode reaction, but they gave comparable results at high P( 2 ). The signal stabilization after change of oxygen partial pressure took between 2 and 5 h. Measurement campaigns were always realized from oxidizing to reducing conditions, starting with pure oxygen (P( 2 )=10 5 Pa) and going to the most reducing H 2 /H 2 mixture (P( 2 ) Pa). The standard free enthalpy of reaction (2) is: (3) Reproducibility was checked after a complete run at maximum temperature (700 C) to confirm the absence of major sample modifications, by grain growth or phase transition. [2] 3. Point Defects in Nanocrystalline Anatase The electrical conductivity of Anatase is plotted in a double logarithmic plot versus oxygen partial pressure in Figure 1. ver more than 30 decades of P( 2 ), one notices linear dependencies, but the pressure dependence is not identical and the slope is lower below 580 C (-1/6) than above 650 C (- 1/5). For example, at 579 and 701 C, we determined by linear regression slope values of and , very close to -1/6 and -1 /5 and with very satisfactory correlation coefficients ( and , respectively). The observed partial pressure and temperature dependencies indicate a change of defect reaction and can be nicely interpreted by point defect chemistry Intrinsic ionic and electronic defect equilibria There are contradictions in literature on the disorder type in titanium dioxide, with reports of either Schottky or Frenkel cation type. The respective intrinsic defect chemical reactions are written in Kröger nomenclature [13]: 3

5 Figure 1. Electrical conductivity of Anatase Nanoceramics (D = 70 nm) Schottky disorder: Pairs of titanium ion vacancy V 4 and oxide ion vacancy V are formed: Frenkel disorder: Pairs of titanium ion vacancy V 4 and titanium interstitial i 4 are formed: In the equilibrium constants K S and K F, the brackets represent the molar fractions of point defects and G is the standard free enthalpy of the corresponding defect reaction. Fully ionized defects can be assumed, because the ionization energies are relatively small in 2 [9]. The intrinsic formation of electronic defects can be written: h and e represent an electron hole and an excess electron with respective concentrations p and n; Nc and Nv are the density of states and Eg the band gap energy, which depends on particle size, and has for the Anatase structure an average value: Eg=(3.3±0.1) ev 3.2. Extrinsic disorder: non-stoichiometry The reduction of 2 at low oxygen partial pressures can be described by different reactions, depending on the assumed predominant disorder type (Schottky or cation Frenkel). For predominant Schottky disorder, the reduction reaction involves formation of oxygen vacancies: 4

6 G red V 2 is the standard Gibbs free enthalpy of reduction of 2 with formation of oxygen vacancies. Using Brouwer s approximation for the electroneutrality condition, n =2 [V 2 ], one obtains: For predominant Frenkel cation disorder, the reduction reaction involves titanium interstitials. nly fully ionized titanium interstitials are considered, given the low ionization energies: G red i 4 is the standard Gibbs free enthalpy of reduction with titanium interstitial formation. Using the Brouwer approximation, n =4 [ i 4 ], one can write: 3.3. Conductivity data below 580 C The total conductivity of a solid can be written as the sum of electronic and ionic contributions: µ is the charge carrier mobility. Under reducing conditions, the electronic conductivity is much larger and the other contributions can be neglected. In this domain, conductivity can be expressed using Eqs. (13) and (17) and the Gibbs Helmholtz equation G = H -T S : The observed slope of -1/6 is characteristic of oxygen vacancy formation (Eq. (13)), showing that below 580 C Schottky disorder is predominant in 2 Anatase. In this temperature domain, the activation energy is (1.3±0.1) ev. The standard enthalpy of reduction can be calculated according to Eq. (18): H red V 2 = (3.9±0.3) ev. ur result is consistent with reduction of 2 at reduced temperature with oxygen vacancy formation. The reduction equilibrium constant can be obtained from the intercept (corresponding to P( 2 )=10 5 Pa) of the straight line at constant temperature. The electron mobility is assumed to be independent of temperature above 300 K, as in the Rutile phase, and equal to 0.1 cm 2 V -1 s -1. This assumption is later justified by the similar electrical behaviour of the two 5

7 phases. Using the experimental data reported in Fig. 1, we obtain at 557 C: K V 2 (557-C)= The molar fraction of oxygen vacancies [V 2 ] can then be calculated at P( 2 )=10 5 Pa using Eq. (11) and the electroneutrality condition (n =2 [V 2 ]). ne obtains: [V 2 ]=(K V 2 /4) 1/3 = Conductivity data above 650 C In this domain, the conductivity can be written using Eqs.(16) and (17): The slope of -1/5 is characteristic of titanium interstitial formation (Eq. (16)), indicating that at high temperature Frenkel cation disorder is predominant in Anatase. The activation energy determined from the Arrhenius plot at higher temperature is (2.2±0.2) ev. Using Eq. (19), we can calculate the standard reduction enthalpy: H red i 4 =(11±1) ev, consistent with literature data. A similar calculation as the previous one using Eq.(19) gives at P( 2 )=10 5 Pa, but higher temperature (T=700 C): K i 4 (700 C)= The molar fraction of titanium interstitials is obtained using Eq. (15): [ i 4 ] = (K i 4 /16) 1/5 = However, these values were measured at much higher temperature on Rutile, where interstitial formation is observed only above 1100 C and under 10-1 Pa oxygen pressure. In the case of Anatase, this transition appears already around 600 C. The calculated oxygen deficiencies are small, because they correspond to high oxygen partial pressure (pure oxygen). Furthermore, the concentrations of titanium interstitials and oxygen vacancies are quite near and one can imagine that the predominance of one defect type over the other can be tuned by relatively small changes of experimental conditions. A change of majority point defect type is here observed from V 2 at reduced temperature to i 4 at high temperature. The transition is observed between 600 and 620 C under Pa. This behaviour was previously observed for Rutile, but at a distinctly higher temperature, between 800 and 1100 C, around Pa at 800 C and around 10-1 Pa at 1100 C. Very recent work by Lee and Yoo on Rutile indicates also that Schottky and Frenkel defect concentrations are very similar. The formation of titanium interstitials appears more favourable in Anatase in comparison to Rutile, because Anatase has a 10% lower density than Rutile and the crystal lattice is more open. Considering the two reduction Eqs. (10) and (14), one can write: The calculation gives H =(3.2±1.6) ev, this reaction is endothermic and according to the Le Chatelier principle, a temperature increase, as well as an increase of the oxygen vacancy concentration, are favourable to the formation of titanium interstitials. This result is in very good agreement with our experimental observations. Finally, the energy of formation of a point defect may be approximated in the Born model as z 2 e 2 /(εε 0 r d ) where z is the charge number, e the electronic charge, εε 0 the permittivity of the solid and r d is the defect radius. Considering only the charge numbers (i.e. ignoring the difference in radius between an oxygen vacancy and a titanium interstitial), the energy of formation of an interstitial titanium is approximately four times that of an oxygen vacancy. This qualitative argument for an easier creation of oxygen vacancies is in good agreement with the experiment. 6

8 4. Point Defects near Interfaces: Dopant Segregation at the Nanoscale Let us recall the basic driving forces for boundary segregation of dopants. Basically two segregation mechanisms can be discussed: one is due to ion radius mismatch (mechanical driving force) and the other to ion charge difference between dopant and host ions (electrostatic driving force). First, ion radius mismatch creates compressive or tensile strains around a dopant ion that can be reduced if the dopant leaves the regular lattice and segregates to a boundary, where the free volume is normally different from that in the bulk. The corresponding segregation isotherm can usually be described by the McLean-Guggenheim equation, similar to the one derived for metallic systems. However, this equation assumes electroneutral segregation, which is often not a good postulate in ionic systems. The segregation energy for solute ions larger or smaller than the host ion can be estimated from the elastic energy for a misfitting elastic inclusion in a continuous elastic matrix. Taking into account the temperature dependence of the elastic constants, this energy U can be expressed for 2 by the following equation: U / ev r = r 2 T r is the radius of 4+ ions, r is the size difference between solute and host ions and T the absolute temperature. The calculated elastic energy is well below 0.1 ev for all ions except for Y. (U/eV: Zn , Y , Sn , Zr , Nb ). This mode of segregation is therefore clearly not relevant except for Y. Second, electrostatic interactions between intrinsic point defects and ionized dopants lead to space charge segregation. In this case, the segregation isotherm must be written introducing explicitly an electrical boundary potential φ(0). This electrostatic driving force is much more relevant for our problem. It is well known that the boundary potential of most undoped oxides, such as 2, is positive, corresponding to a positive boundary charge with formation of an oxygen deficiency at the boundary core. The relevance of an oxygen deficiency for most nanocrystalline oxide surfaces has been shown in several recent investigations and positive boundary potentials were reported for various oxides, including Ce 2 and Zr 2. The experimental EXAFS spectra for dopants in nanocrystalline Anatase powders and ceramics can be found in the original publications [5, 10, 11, 12] 4.1. Intrinsic boundary segregation: oxide ion vacancies In the case of nominally undoped Anatase and considering predominant Schottky disorder, a positive boundary charge corresponds fundamentally to the lower energy of formation of a two-times charged oxide ion vacancy in comparison with a four-times charged titanium ion vacancy. In other words, we have a point defect segregation process, sometimes also called intrinsic boundary segregation, written: V = V,B (21) µ(v,b ) µ (V ) = - 2Fφ (0) (22) Ιn this equation, µ represents the chemical potential and F is Faraday s constant (for molar quantities). φ (0) is the electrical potential at the boundary core. By definition, the bulk potential is taken as zero. As one can easily recognize, the boundary potential φ(0) depends decisively on the difference between the chemical potentials of oxide ion vacancies in the bulk and at interfaces. The corresponding mass action law can be obtained assuming local thermodynamic defect equilibrium. The intrinsic segregation constant can be written, using the definition of standard chemical potentials: (20) K seg ( V [ V ) = [ V, B φ B ] G ( V ) + 2F = exp ] RT (0) (23) 7

9 G B (V ) = µ (V,B ) - µ (V ) (24) R is the gas constant and T the absolute temperature. verall charge neutrality in the system implies that negatively charged counter defects of the positive boundary charge, i.e. titanium vacancies and electrons, are accumulated in the space charge regions adjacent to the boundary Extrinsic boundary co-segregation: oxide ion vacancies and dopant ions In doped systems, co-segregation of point defects and dopants can occur, corresponding for example for niobium- yttrium- and zinc-doped samples to the following reactions. In these equations, boundary sites are written using a subscript B. Niobium donors [10]: Nb + V = Nb B + V,B (25). B B. [ NbB ][ V, ] G V + G Nb + F B ( ) ( ) 3 φ(0) K seg ( Nb) = = exp. [ Nb V RT ][ ] (26) G B (Nb. ) = µ (NbB. ) - µ (Nb. ) (27) Yttrium acceptors Y + V = Y B + V,B (28) B B [ YB '][ V, ] G V + G Y + F B ( ) ( ') φ(0) K seg ( Y ) = = exp [ Y V RT '][ ] (29) G B (Y ) = µ (Y B ) - µ (Y ) (30) Zinc acceptors [10]: Zn + V = Zn B + V,B (31) B B [ ZnB ''][ V, ] G V + G Zn B ( ) ( '') K seg ( Zn) = = exp [ Zn V RT ''][ ] (32) G B (Zn ) = µ (Zn B ) - µ (Zn ) (33) ne might expect a small difference between standard chemical potentials for dopant ions at bulk and interface sites, given the small difference between host and dopant ion radii: G B (Nb. ) = G B (Y ) = G B (Zn ) 0. This approximation is rougher for Y ions. ne can further reasonably assume that at dopant concentrations below 1 mol% considered here, the standard chemical potential of oxide ion vacancies is independent of the nature of the dopant, i.e. G B (V ) is constant. Given that the boundary potential φ(0) is considered positive, one obtains then by comparison of eq. (26), (29) and (32) immediately the relation: K seg (Zn) > K seg (Y) > K seg (Nb). (34) This relation is in qualitative agreement with the experiment and explains why acceptor ions segregate to boundaries and donor ions do not. For a quantitative comparison, more thermodynamic data on defect formation in the bulk and at boundaries in Anatase are needed. From defect thermodynamics data, Ikeda and Chiang calculated a space charge potential of about 0.2 V in reduced 2. Assuming 8

10 a similar value of 0.2 V also in the case of doped 2, the segregation constant at 600 C would be nearly 200 times larger for Y than for Nb. The outlined space charge segregation model explains the boundary segregation of acceptor ions according to an electrostatic driving force. In the Y case, the driving force for boundary segregation includes an elastic term. The model explains also the remarkable absence of donor Nb 5+ segregation in Anatase samples at low temperature, observed by us and other authors. According to our electrostatic model, this is not a kinetic effect, due e.g. to insufficient thermal activation for Nb migration, but a thermodynamic effect. References [1] P. Knauth, H. L. Tuller, 1999 J. Appl. Phys., 85, 897 [2] A. Weibel, R. Bouchet, P. Knauth, 2006 Solid State Ionics, 177, 229 [3] P. Knauth, 2006 Solid State Ionics, 177, [4] G. E. Rush and A. V. Chadwick 2002 Nanocrystalline Metals and xides: Selected Properties and Applications, ed P. Knauth, J. Schoonman (Kluwer Academic, Boston) [5] P. Knauth, A. V. Chadwick, P. Lippens, G. Auer, 2009 ChemPhysChem, 10, 1238 [6] P. Knauth, R. Bouchet,. Schäf, A. Weibel, G. Auer, 2002 Synthesis, Functionalization and Surface Treatments of Nanoparticles, ed M.-I. Baraton (American Science Publ., Stevenson) [7] A. Weibel, R. Bouchet, F. Boulc h, P. Knauth, 2005 Chem. Mater., 17, [8] A. Weibel, R. Bouchet, R. Denoyel, P. Knauth, 2007 J. Europ. Ceram. Soc., 27, [9] A. Weibel, R. Bouchet, P. Bouvier, P. Knauth, 2006 Acta Mater., 54, [10] R. Bouchet, A. Weibel, P. Knauth, G. Mountjoy, A. V. Chadwick, 2003 Chem. Mater., 15, [11] A. Weibel, R. Bouchet, S. L. P. Savin, A. V. Chadwick, P. E. Lippens, M. Womes, P. Knauth, 2006 ChemPhysChem, 7, [12] P. E. Lippens, A. V. Chadwick, A. Weibel, R. Bouchet, P. Knauth, 2008 J. Phys. Chem. C, 112, [13] P. Knauth, H. L. Tuller, 2002 J. Am. Ceram. Soc., 85,