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Electronic band structure, optical absorption and photocatalytic activity of anatase doped with bismuth or carbon
Journal of Alloys and Compounds 548 (2013) 46–51
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Electronic band structure, optical absorption and photocatalytic activity of anatase doped with bismuth or carbon V.P. Zhukov ⇑, I.R. Shein, V.M. Zainullina Institute of Solid-State Chemistry, Ural Branch of RAS, GSP-145, 620990 Ekaterinburg, Russia
a r t i c l e
i n f o
Article history: Received 31 May 2012 Received in revised form 14 August 2012 Accepted 15 August 2012 Available online 26 August 2012 Keywords: Oxide materials Semiconductors Electronic band structure Optical properties Catalysis Computer simulations
a b s t r a c t The electronic band structure, frequency-dependent dielectric function and absorption spectra of the anatase containing oxygen vacancy or doped with bismuth or carbon have been calculated with the aid of the pseudopotential plane-wave method. Basing on the calculated data, the available experimental data on the visible light absorption are discussed. The main conclusion is that the Bi3+ ions cannot replace the Ti4+ ions in the structure of anatase. The conclusion is confirmed by the calculations of the energy of the defect formation. The visible light absorption can be explained by the presence of the carbon impurities or additional phases, probably Bi2O3 or Bi4Ti3O12. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Titanium dioxide in the anatase structure is probably the most promising compound for photocatalytic applications, in particular for cleaning the environment from pathogenic bacteria or chemical contaminants. It possesses a high photocatalytic activity (PCA) in the UV part of spectra, so in many works the attempts have been carried out to extend its PCA to the visible part of spectra, see e.g. the review of Carp et al. [1]. The main aim of such studies was to obtain the photocatalysts that effectively absorb the visible sunlight and have sufficiently long time of the electron–hole recombination. One of the used techniques was the doping of anatase with simple or transition elements. It was doped with the elements of the second period, with transition elements of the fourth and fifth periods, see [2,3]. A number of papers has been also devoted to the doping with the elements of the fifth period, see [4–8], and sixth period, see [9]. Of such works promising seem to be the researches on the doping of anatase with bismuth, see [10–15]. The authors of these papers studied the PCA, crystal structure, morphology, XPS spectra, Raman spectra, optical absorption and reflectance spectra depending on the content of Bi and the temperature of calcination that was an essential stage of the synthesis. The change of the crystal structure, from anatase to rutile, with the rise of the calcination temperature has been demonstrated. An essential increase of the ⇑ Corresponding author. Tel.: +7 953 382 36 84. E-mail addresses: [email protected] (V.P. Zhukov), [email protected] (I.R. Shein), [email protected] (V.M. Zainullina). 0925-8388/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2012.08.072
PCA in comparison with that of the standard anatase photocatalysts has been shown. Xin et al. [10], Whang et al. [11], Yu et al. [12]have demonstrated also an enhancement of the PCA with the rise of the calcination temperature and an extremal change of the PCA depending on the content of Bi. However, the papers on Bi-doping have a number of uncertainties and contradictions. Xin et al. [10] evaluated the content of Bi corresponding to the maximum of the PCA as equal to about 1.5% whereas according to the data of Yu et al. [12] it is near 3% but according to the data of Whang et al. [11] it is near 5%. The authors demonstrated also an increase of the size of nano-particles of the doped anatase with the rise of the calcination temperature. This leads to a decrease of the surface area that is incompatible with the enhancement of the PCA. In different papers different ways of explaining the photocatalytic properties of the Bi-doped anatase were proposed. Xin et al. [10] associated the change of PCA depending on the Bi-content with the changes of the electron–hole recombination time. Whang et al. [11] affirmed that the enhancement of the PCA was induced by the presence of the islands of the Bi4Ti3O12 phase that can serve as electron traps retarding the recombination. Yu et al. [12] associated the improvement of the PCA with the reduction of the band gap that supposedly takes place with Bi-doping. Li et al. [13] affirmed that the incorporation of Bi induced an emergence of the Bi4+ species that can serve as the traps of electrons prolonging the recombination time. In particular contradictive are the data on optical properties of the Bi-doped anatase. Whang et al. [11] did not find any light absorption in visible region; Yu et al. [12] also did not find absorption in this
V.P. Zhukov et al. / Journal of Alloys and Compounds 548 (2013) 46–51
region, but, in a strange way, they found a sharp increase of absorption at 6.1 eV. On the contrary, Li et al. [13] found a noticeable absorption in visible region that they associated with a presumable presence of oxygen vacancies. Later Ji et al. [14] again did not find an absorption in visible region, but Xu et al. [15] anew have shown the presence of such absorption. Hence, new researches on the properties of the Bi-doped anatase are desirable in order to resolve the mentioned contradictions. A certain help can be provided by the modern first-principle methods of the electronic band structure calculations. Some of them are capable to calculate the optical properties of the crystals taking into account the crystal lattice distortions near the doping atoms. So we have undertaken a first-principle research of the band structure and optical absorption of anatase containing several defects that can presumably emerge in the course of the Bi-doping. First of such defects is naturally the Bi atom that, as it was proposed in the works of Whang et al. [11] and Li et al. [13], presumably can replace Ti atom. Important is also the oxygen vacancy in anatase that can emerge in high concentration if the synthesis is carried out in a deficit of oxygen. It was supposed in the work of Li et al. [13] that the visible light absorption in the Bi-doped anatase is induced mainly by the presence of the oxygen vacancies. Since in the sol–gel syntheses of the Bi-doped anatase various kinds of hydrocarbons are normally involved, one more possible defect is the carbon atom replacing the oxygen atom of anatase. Such defect can be found if the calcination of the Bi-doped samples is not sufficient to evaporate all the hydrocarbons involved, see e.g. [16]. 2. Method of calculation In Fig. 1 we show the tetragonal extended unit cell that contains the main structural elements of anatase. The nearest surrounding of the titanium atoms is a distorted octahedron of eight oxygen atoms whereas the nearest surrounding of the oxygen atom is a triangle that consists of titanium atoms. The simulation of defects is performed by the replacement of one of the Ti atom with Bi atom, removal of one oxygen atom or substitution of such an atom with carbon atom. The 2 2 2 super-cell is employed in our calculations that is obtained by the 2-fold repetition of the primitive Ti2O4-cell along all the three crystallographic axes. This corresponds to the 6.25% concentration of the mentioned defects. Previous calculations
have demonstrated that with such a size of the super-cell the interactions between the impurity atoms in the adjacent neighbor super-cells are negligible in the sense that neither positions of the impurity bands inside the band gap no widths of these bands do not change with a further increase of the cell, see [17,18]. The electronic band structure calculations were performed by using the pseudopotential plane wave method realized in the VASP program version 5.2 code, see [19]. The projector augmented wave approach was employed in the calculations and the pseudopotentials provided by the VASP code, with 4 valence electrons for Ti, 6 for O and 4 for C atoms. The generalized gradient approximation (GGA) was approved for the exchange–correlation functional. A plane-wave cutoff energy of 500 eV was accepted and an augmentation charge cutoff was equal to 330 eV. The relaxation of volume of cells and atomic positions were performed for the 2 2 2 super-cell of pure and doped anatase. The final variation of the total energy with respect to the changes of atomic coordinates were less than 0.001 eV, and the final forces acting on atoms were no more than 0.05 eV/Å. All the calculations, including the evaluations of densities of states, were performed with 18 k-points in the irreducible part of the Brillouin zone. A typical error of the density functional theory is the underestimation of the value of the band gap. In our case the calculated band gap of the pure anatase was 2.1 eV, too small in comparison with experimental data, 3.2 eV. More correct description of the electronic band structure of the transition metal oxides is achieved in the methods with the account of on-site Coulomb correlations. In such methods the correction of the band gap is performed by applying to the partly localized states, here to the 3d Ti states, a screened Hartree–Fock-like interactions which depend on the parameter U of Coulomb and J of exchange interactions. We employed the version of the method proposed by Dudarev et al. [20]. An advantage of this approach in comparison with the earlier versions of the GGA + U approach of Anisimov et al. [21] is that, with the precision no worse than in the earlier method, the on-site correlations in this approach depend only on the U J difference. A general problem of the GGA + U approach is that the methods of evaluating the U-value are not strictly established. Although the ways of non-empirical evaluation of this value exist, Anisimov et al. [21], often it is considered to be an adjustable parameter. The range of this value for the 3d Ti states is rather broad: 2, 3, 4 eV in the Ref. of Finazzi et al. [22], 4 eV (with U-corrections also applied to oxygen atoms!) in the Ref. of Mattioli et al. [23], 5 eV in the Ref. of Spadavecchia et al. [24] and 6.2 eV in the Ref. of Korotin et al. [25]. A good theoretical description of optical properties requires that at least experimental data on the band gap value of anatase have to be reproduced. We found that with the Dudarev’s formulations this occurs when the value U–J mounts to 7.2 eV. More arguments in favor of this value are provided by the data on the non-stoichiometric anatase. It is semiconducting with activation energy from 0.6 to 1.2 eV, [26]. The UP spectra demonstrate also that the band of oxygen vacancies has the maximum at the energy about 1 eV below the bottom of the conduction band. These data are reproduced with the U J = 7.2 eV while the calculations with more typical value U = 3.2 eV predict that the non-stoichiometric anatase is semi-metallic, see the data in the next section. Nevertheless, in the following we demonstrate the data on the band structure and absorption coefficient calculated with both these U J-values, 3.2 and 7.2 eV, in order to confirm that the change of properties with changing U–J is not drastic and the main conclusions do not depend on the specific choice of the U J value. As far as the 2p oxygen states and 6s Bi states are concerned, we omit the U,J-corrections for these states. The work of [27] where the XPS spectra of the compound BiVO4 have been measured and the (VASP) densities of electronic states have been calculated, provides a justification for such a simplification. These calculations have been done without the U,J-corrections, but the accordance to experimental data of the distance between the 6s Bi band and the bottom of the 2pO band is almost perfect; also in the calculations the experimental width of the 2p O band is well reproduced. Our evaluation of the optical properties started from the calculations of the imaginary and real part of the frequency-dependent dielectric function. These calculations have been performed neglecting the local-fields effects. Within this approximation the imaginary part of the dielectric function is a tensor value that is expressed as [28]
a2b ðxÞ ¼
Fig. 1. The tetragonal unit cell of anatase.
47
4e2 p2
X
lim q!0
1X 2wk d ck vk hx huckþea q juvk ihuckþeb q juvk i q2 k;c;v
ð1Þ
Here summation is carried out over all the wave-vectors k inside the irreducible part of the Brillouin zone whose weights are wk. The imaginary part of the dielectric function includes contributions of all the excitations from the valence band states (v) with the energies vk to conduction band states (c) with the energies ck . The matrix elements huckþea q juvk i are the overlap integrals of the cell-periodic parts of the pseudo-wave-functions of the mentioned states. The limit limq?0 means that the wavevector of the applied electric field (e.g. that of sunlight) is neglected. The real components of the dielectric functions were calculated via the Kramers–Kronig transform, Gajdoš et al. [28]. In the case of anatase the calculated in such a way non-diagonal elements of the dielectric tensor are negligibly small in comparison with the diagonal elements, so calculating angle-averaged dielectric function 1 + i2 we neglected them. It is then an easy task to calculate the frequency-dependent absorption and reflection coefficients of the crystals, see [29]. In particular, the absorption coefficient is calculated as
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n o1=2 KðxÞ ¼ 2x ½21 ðxÞ þ 22 ðxÞ1=2 1 ðxÞ =c
ð2Þ
3. Results and discussion In Fig. 2 we show the total densities of states of the studied objects near the fundamental band gap. In the case of the pure anatase the states of the bands between 2 and 3 eV are composed mainly of the 2p oxygen states; above the band gap the conduction band states are located that near the bottom of the band are composed mainly of the 3d Ti states. At U J = 3.2 eV the value of the band gap, 2.5 eV, is too small in comparison to experimental data. The enlargement of the U–J value of the 3d Ti states to 7.2 eV causes a rise of the valence and conduction bands, respectively, by 0.3 and 1 eV, so the band gap increases up to 3.2 eV. The similar effect takes place for the rest of compounds. With the emergence of the Bi atom two new bands arise. One of them, located below the valence band, is composed of the valence Bi 6s state hybridized with the 2p states of the oxygen atoms nearest to the bismuth atom; this band contains two electrons. The second band is located near the middle of the band gap, at about 2.9 and 3.3 eV when U J = 3.2 eV, 7.2 eV, respectively, and the Fermi level is just at the top of this band. This is the band of hybridized states composed mainly of the 2p oxygen orbitals and additions of the 6s Bi valence orbitals. It can be regarded as an anti-bonding counterpart of the 6s
A
B
C
D
Fig. 2. Total densities of states (per super-cell) for the pure anatase (A), doped with bismuth (B), containing oxygen vacancy (C) and doped with carbon (D). Solid lines are for the U J value equal to 3.2 eV, dashed lines are for U J = 7.2 eV. With arrows the positions of the Fermi level are shown.
Bi band. (Notice that the nature of this band is analogous to that of the states on top of the 2p oxygen band in the BiVO4 compound, Payne et al. [27]!) The 6p Bi orbitals do not form separate bands; they manifest themselves as admixtures to the 2p oxygen and 6s Bi bands. Since the band inside the fundamental band gap is preferably the band of oxygen states, it follows that Bi atom is formally in the 3+ oxidation state. When anatase ‘‘is doped’’ with oxygen vacancy, one new band emerges inside the band gap near the bottom of the conduction band. Although the states of this band are generally referred to as the oxygen vacancy states, they are composed of the 3d states of the Ti atoms nearest to the vacancy. These states drop from the conduction band when the hybridization between the titanium and oxygen states breaks, see [30]. The band contains 2 electrons, so it represents the F0 impurity center. When U J = 3.2 eV this band intersects with the conduction band. So such calculations predict that the non-stoichiometric anatase should be semi-metallic that contradicts to the experimental data of [26]. When U J = 7.2 eV the vacancy band is separated from the conduction band by 0.35 eV that corresponds to the semi-conductivity of the non-stoichiometric anatase. When anatase is doped with carbon, three new band emerge inside the lower part of the band gap. The states of these bands are composed mainly of the 2p carbon orbitals; the nature of the states and the energy intervals between them are in agreement with the results of the previous calculation performed with the TB-LMTO method by Zhukov et al. [31] and Zainullina et al. [32]. In the Fig. 3 the calculated absorption coefficient is shown for all the discussed objects. The comparison with the absorption coefficient of the pure anatase demonstrates that with all the kinds of doping the edge of fundamental absorption does not practically change. Noteworthy is the similarity of absorption of anatase doped with bismuth and carbon. Both for U J = 3.2 eV and 7.2 eV it covers the whole region of visible light. Very different is the absorption of the vacancy-containing anatase. Due to the position of the vacancy states near the bottom of the conduction band the absorption takes place at much less photon energy, that is at markedly higher wavelengths, also both for U J = 3.2 eV and 7.2 eV. In Fig. 4 the experimental absorption data on the Bi-doped anatase are given according to the papers of Yu et al. [12], Li et al. [13], Ji et al. [14], Xu et al. [15]. Of the data submitted in these papers only those are shown that correspond to the Bi content maximally close to 6.25% studied in our research. The only exception is the data of Li et al. [13] obtained only for much lower content of Bi. The inconsistency of the data attracts attention. Obscure are the data of Yu et al. [12]; according to them the onset of fundamental absorption should be at about 250 nm (5 eV), so these data probably contain a technical error. Contradictory are the data of Li et al. [13] and Ji et al. [14]: the first of them definitely demonstrate an absorption in visible region at 1% Bi content whereas the second show the absence of absorption at 5% content of Bi. Also contradictory are the ideas of the authors on the physical nature of absorption in the Bi-doped anatase. It is affirmed in the paper Yu et al. [12] that, because of a big differences in radii, the ions Bi3+ cannot replace the ions Ti4+ in the structure of anatase and instead with Bi doping the phase Bi4Ti3O12 is formed. On the contrary, Li et al. [13] affirm that such replacement is possible, but the absorption in visible region occurs because of the presence of oxygen vacancies. In the work of Ji et al. [14] it is proposed that the ions Bi3+ mainly exist near the surface of anatase. However, the authors do not explain the observed in their work small red shift of absorption edge, in comparison with that of the pure anatase. Xu et al. [15] affirm that the oxidation state of the titanium ions does not change with Bi doping, so the most probable reason of the absorption in visible region in the emergence of the Bi2O3 phase.
V.P. Zhukov et al. / Journal of Alloys and Compounds 548 (2013) 46–51
49
Fig. 3. The calculated absorption coefficient for pure anatase (solid line), anatase doped with Bi (dashed line), containing oxygen vacancy (dotted line) and doped with carbon (dash-dotted line). The left panel is for U J = 7.2 eV and the right panel is for U J = 3.2 eV.
In order to elucidate the causes impeding the incorporation of the Bi atoms into the structure of anatase a thermodynamic analysis of such process is desirable. Normally such incorporation is carried out by the methods of ‘‘wet chemistry’’. The final step of such complicated processes consists in the calcination of the dried gels whose composition and crystal structure are not known, so the first-principle thermodynamic analysis of such processes is now not possible. We carried out therefore more simple evaluations, namely the calculations of the defect formation energy (DFE) for the replacement of Ti atom with Bi atom. We follow the method proposed in the papers of Erhart et al. [33], Janotti et al. [34] and Xin-guo et al. [35] that was employed for the evaluation of the energy of the native defect formation in ZnO and vacancy formation in rutile. An analogous approach has been applied to the thermodynamics of the doping of anatase with carbon by DiValentin et al. [36]. Following the approach developed in these works the formation energy for the Ti replacement with Bi can be written as þn
Ef ðBi Þ ¼ ½Ec ðTi15 BiO32 Þ þ lðTiÞ ð3 nÞle ½Ec ðTi16 O32 Þ Fig. 4. The experimental absorption coefficient of the Bi-doped anatase. Solid line represents the data of Yu et al. [12] for 5% Bi doping; dashed line are the data of Ji et al. [13] for 1% of doping; dotted line are the data of Ji et al. [14] for 5% doping, and dash-dotted line are the data of Xu et al. [15] for 4% Bi doping.
Comparing our calculated absorption spectra with experimental data one can come to some definite conclusions. Since the very small absorption above 400 nm observed in the works of Yu et al. [12] and Ji et al. [14] is not compatible with our calculated absorption in the Bi-doped anatase, one may conclude that the Bi3+ ions do not enter in sufficient amount in the structure of anatase. This conclusion is in consent with the speculations of Yu et al. [12] and Xu et al. [15] on the role of accompanying phases that can be formed in the process of synthesis. The most probable such phases are Bi2O3 and Bi4Ti3O12. Xu et al. [15] observed a red shift of the fundamental absorption edge in the Bi-doped anatase. This corresponds to a lesser value of the band gap of monoclinic Bi2O3, 2.8 eV, in comparison with that of the pure anatase. One more conclusion that follows from the comparison of the calculated data with experiments is that the absorption in visible region observed in the work of Li et al. [13] is hardly explained by the presence of oxygen vacancies. Moreover, the rather high absorption in visible region observed by Li et al. [13] is incompatible with low content of Bi, about 1%. Taking into account the following from our calculations similarity of the absorption in the Bi-doped and C-doped anatase, the absorption observed by Li et al. [13] can probably be associated with the carbon impurity that can be present if the calcination in the course of synthesis is not sufficiently long.
þ lðBiÞ;
ð3Þ
In the left square bracket of this equation the value Ec(Ti15BiO32) is the energy of the super-cell containing the defect, l(Ti) is the chemical potential of the Ti atom withdrawn to reservoir, and (3 n)le is the chemical potential of the electrons transferred to (or received from) the reservoir if the Bi-defect is charged. In the second square bracket Ec(Ti16O32) is the energy of the super-cell without defect, and l(Bi) is the chemical potential of the Bi atom inside the reservoir. We assume that the formation of the Bi2O3 phase is possible in the course of synthesis, since this reaction is expected to be exothermic with big negative energy of formation that according to our calculations is equal to 6.27 eV per formula unit. The formation of the TiO2 and Bi2O3 phases impose restrictions on the values of the chemical potentials of Bi and Ti in reservoir. The restrictions depend on the conditions of synthesis, first of all on the content of oxygen. The highest limit of the chemical potential of oxygen lh(O) corresponds to the condensation of oxygen molecules (that can occur at very high pressures). One can take for it lh(O) = 1/2E(O2) where E(O2) = 9.84 eV is the ground state energy of the oxygen molecule with spin polarization taken into account. Following the work of [36], we assume that the chemical potential of oxygen is equal to l(O) = lh(O) 0.7 = 5.62 eV, since this value corresponds to atmospheric pressure and temperature of 700 K, close to the conditions of synthesis of the Bi-containing anatase. The imposed restriction follow from the considerations of the thermodynamic cycles corresponding to the formation of oxides,
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see [37]. For the reaction of anatase synthesis one can write the Gibbs free energy balance as
GðTiO2 Þ ¼ lðTiÞ þ 2lðOÞ þ DGðTiO2 Þ
ð4Þ
where DG is the oxide formation energy. One can evaluate approximately this energy from the DFT calculations as
DGðTiO2 Þ ffi EðTiO2 Þ EðTiÞ EðO2 Þ:
ð5Þ
Here E(TiO2) and E(Ti) are the ground state energies per formula units. It follows then that
lðTiÞ ¼ EðTiÞ þ EðO2 Þ 2lðOÞ:
ð6Þ
By analogy, from the Gibbs free energy balance for the formation of Bi2O3 from metallic Bi and oxygen one can obtain for the chemical potential of Bi
lðBiÞ ¼
1 3 2EðBiÞ þ EðO2 Þ 3lðOÞ 2 2
ð7Þ
The values of the potentials calculated in such a way applying the VASP code are l(Ti) = 6.49 eV and l(Bi) = 2.82 eV. Then the calculated EDF of the Ef(Bi+3) defect is equal to 14.54 eV. Since according to our calculations the 2pO,6sBi-band is halffilled, one can suppose that additionally two charged Bi-defects also may emerge in the course of synthesis, the Bi+4 defect with 1 electron withdrawn to reservoir or Bi2+ with 1 electron accepted from reservoir. The value of the electronic chemical potential in reservoir le is not strictly defined. However, its lower limit lle should be equal to the top of the valence band and the higher limit lhe to the bottom of the conduction band, otherwise the condition of equilibrium between the defect-containing system and reservoir cannot be satisfied. Our calculated values of lle and lhe are 2.6 eV and 5.8 eV, respectively. The addition of one electron to the 2pO,6sBi-band rises the Ec(Ti15BiO32) by 5.35 eV, but reduces it at the score of the chemical potential of the electron in reservoir. The removing of one electron from the Bi-level leads to a reduction of the Ec(Ti15BiO32) value by 0.75 eV, that is compensated by the increase of the energy of electrons in reservoir. At lle the EDF for Bi4+ and Bi2+ become equal, respectively, to 16.40 and 16.52 eV, where at lh these values are 19.60 and 13.32 eV. Hence, the EDF-values for all the three kinds of Bi-defects are too high in order the formation of such defects in presence of the phases TiO2 and Bi2O3 were possible. Since the phase Bi2O3 has a rather big negative formation energy, this is an evidence in favor of formation of the islands of this phase inside the Bi-containing anatase. The presence of this phase in the Bi-containing anatase was observed by means of the high-resolution XPS measurements of Xu et al. [15]. Two factors responsible for the instability of the Bi-defects are the anti-bonding interaction between the Bi atom and the nearest oxygen atoms and the size factor. The impurity state is formed in this case via hybridization of the oxygen 2p states and Bi 6s states, but it has the energy about 1.5 eV higher than the top valence band states. This value can be regarded as the contribution of anti-bonding to the destabilization of the defect. The second factor, more important, is associated with the great difference of ionic radii, 0.096 nm for Bi3+ and 0.068 nm for Ti4+. We notice also that the character of this state, anti-bonding and formed preferably by the oxygen 2p-states, is in disagreement with the opinion of Yu et al. [12] who supposed that this is the 6s Bi state. 4. Conclusions The necessity of new studies on the Bi-doped anatase is motivated by the existence of a number of contradictions in the results of previously performed experimental works on its photo-catalytic
properties. The essential contradictions also concern the interpretation of the absorption spectra of the Bi-doped anatase. We calculated therefore the electronic band structure and optical absorption spectra of anatase containing some defects that presumably can arise in the course of doping; they are Bi-atoms replacing titanium atoms, oxygen vacancies or carbon atoms replacing oxygen atoms. The calculations demonstrate that the Bi-atoms replacing the Ti atoms have to be in the 3+ oxidation state. However, comparing our calculated absorption spectra with experimental data we find that the replacement of titanium by bismuth with the formation of the Bi3+ is hardly probable. Also the optical absorption of the Bi-doped anatase cannot be explained by the presence of the oxygen vacancies. Instead, the calculated absorption spectra of the anatase doped with carbon has a similarity with some of the experimental spectra, so the presence of such type of defects in the studied specimens is possible. This is, probably, the case of the absorption observed in the experiments of Li et al. [13] and Xu et al. [15]. The absence of the visible range absorption in the Bi-doped anatase registered in some experiments, see [12,14], can be explained by the presence of bismuth only inside the islands of accompanying phases; Bi2O3 or Bi4Ti3O12 can be such phases. We also have carried out the calculation of the energy formation of the Bi-defects. The calculations confirm that the occurrence of the Bi-ions replacing Ti in anatase is hardly probable. The conclusion on the nature of enhanced photocatalytic activity of the Bi-doped anatase is that it hardly is associated with the visible light absorption of the Bi embedded into anatase. Instead it can be explained by the electron–hole separation induced by the presence of the accompanying phases and, probably, by the visible range absorption of the carbon impurities. Notice also that the accompanying phases, Bi2O3 and Bi4Ti3O12, possess themselves a high photocatalytic activity, see [38–40], as also some of the composites containing these phases, see [41,42]. Acknowledgments This work was supported in part by a grant of Prezidium of the Urals Branch of the Russian Academy of Sciences. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
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V.P. Zhukov et al. / Journal of Alloys and Compounds 548 (2013) 46–51 [23] G. Mattioli, P. Alippi, F. Filippone, R. Caminiti, A.A. Bonapasta, J. Phys. Chem. C 114 (2010) 21694. [24] F. Spadavecchia, G. Cappelletti, S. Ardizzone, M. Ceotto, L. Falciola, J. Phys. Chem. C 115 (2011) 6381. [25] M.A. Korotin, I.S. Elfimov, V.I. Anisimov, M. Troyer, D.I. Khomskii, Phys. Rev. Lett. 83 (1999) 1387. [26] A. Pura, K. Rubenis, D. Stepanovs, L. Berzina-Cimdina, J. Ozolins, Process. Appl. Ceram. 6 (2012) 91. [27] D.J. Payne, M.D.M. Robinson, R.G. Egdell, A. Walsh, J. McNulty, K. Smith, L. Piper, Appl. Phys. Lett. 98 (2011) 212110. [28] M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, F. Bechstedt, Phys. Rev. B 73 (2006) 045112-1–045112-9. [29] J. Ziman, Principles of the Theory of Solids, University Press, Cambridge, 1972. [30] V. Zainullina, M. Korotin, V. Zhukov, Physica B 405 (2010) 2110–2117. [31] V. Zhukov, V. Zainullina, E. Chulkov, Int. J. Mod. Phys. 24 (2010) 6049–6067. [32] V. Zainullina, V. Zhukov, V. Krasilnikov, M. Ianchenko, L.I. Buldakova, E. Poliakov, Fizika Tverdogo Tela 52 (2010) 253–261.
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Electronic band structure, optical absorption and photocatalytic activity of anatase doped with bismuth or carbon V.P. Zhukov ⇑, I.R. Shein, V.M. Zainullina Institute of Solid-State Chemistry, Ural Branch of RAS, GSP-145, 620990 Ekaterinburg, Russia
a r t i c l e
i n f o
Article history: Received 31 May 2012 Received in revised form 14 August 2012 Accepted 15 August 2012 Available online 26 August 2012 Keywords: Oxide materials Semiconductors Electronic band structure Optical properties Catalysis Computer simulations
a b s t r a c t The electronic band structure, frequency-dependent dielectric function and absorption spectra of the anatase containing oxygen vacancy or doped with bismuth or carbon have been calculated with the aid of the pseudopotential plane-wave method. Basing on the calculated data, the available experimental data on the visible light absorption are discussed. The main conclusion is that the Bi3+ ions cannot replace the Ti4+ ions in the structure of anatase. The conclusion is confirmed by the calculations of the energy of the defect formation. The visible light absorption can be explained by the presence of the carbon impurities or additional phases, probably Bi2O3 or Bi4Ti3O12. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Titanium dioxide in the anatase structure is probably the most promising compound for photocatalytic applications, in particular for cleaning the environment from pathogenic bacteria or chemical contaminants. It possesses a high photocatalytic activity (PCA) in the UV part of spectra, so in many works the attempts have been carried out to extend its PCA to the visible part of spectra, see e.g. the review of Carp et al. [1]. The main aim of such studies was to obtain the photocatalysts that effectively absorb the visible sunlight and have sufficiently long time of the electron–hole recombination. One of the used techniques was the doping of anatase with simple or transition elements. It was doped with the elements of the second period, with transition elements of the fourth and fifth periods, see [2,3]. A number of papers has been also devoted to the doping with the elements of the fifth period, see [4–8], and sixth period, see [9]. Of such works promising seem to be the researches on the doping of anatase with bismuth, see [10–15]. The authors of these papers studied the PCA, crystal structure, morphology, XPS spectra, Raman spectra, optical absorption and reflectance spectra depending on the content of Bi and the temperature of calcination that was an essential stage of the synthesis. The change of the crystal structure, from anatase to rutile, with the rise of the calcination temperature has been demonstrated. An essential increase of the ⇑ Corresponding author. Tel.: +7 953 382 36 84. E-mail addresses: [email protected] (V.P. Zhukov), [email protected] (I.R. Shein), [email protected] (V.M. Zainullina). 0925-8388/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2012.08.072
PCA in comparison with that of the standard anatase photocatalysts has been shown. Xin et al. [10], Whang et al. [11], Yu et al. [12]have demonstrated also an enhancement of the PCA with the rise of the calcination temperature and an extremal change of the PCA depending on the content of Bi. However, the papers on Bi-doping have a number of uncertainties and contradictions. Xin et al. [10] evaluated the content of Bi corresponding to the maximum of the PCA as equal to about 1.5% whereas according to the data of Yu et al. [12] it is near 3% but according to the data of Whang et al. [11] it is near 5%. The authors demonstrated also an increase of the size of nano-particles of the doped anatase with the rise of the calcination temperature. This leads to a decrease of the surface area that is incompatible with the enhancement of the PCA. In different papers different ways of explaining the photocatalytic properties of the Bi-doped anatase were proposed. Xin et al. [10] associated the change of PCA depending on the Bi-content with the changes of the electron–hole recombination time. Whang et al. [11] affirmed that the enhancement of the PCA was induced by the presence of the islands of the Bi4Ti3O12 phase that can serve as electron traps retarding the recombination. Yu et al. [12] associated the improvement of the PCA with the reduction of the band gap that supposedly takes place with Bi-doping. Li et al. [13] affirmed that the incorporation of Bi induced an emergence of the Bi4+ species that can serve as the traps of electrons prolonging the recombination time. In particular contradictive are the data on optical properties of the Bi-doped anatase. Whang et al. [11] did not find any light absorption in visible region; Yu et al. [12] also did not find absorption in this
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region, but, in a strange way, they found a sharp increase of absorption at 6.1 eV. On the contrary, Li et al. [13] found a noticeable absorption in visible region that they associated with a presumable presence of oxygen vacancies. Later Ji et al. [14] again did not find an absorption in visible region, but Xu et al. [15] anew have shown the presence of such absorption. Hence, new researches on the properties of the Bi-doped anatase are desirable in order to resolve the mentioned contradictions. A certain help can be provided by the modern first-principle methods of the electronic band structure calculations. Some of them are capable to calculate the optical properties of the crystals taking into account the crystal lattice distortions near the doping atoms. So we have undertaken a first-principle research of the band structure and optical absorption of anatase containing several defects that can presumably emerge in the course of the Bi-doping. First of such defects is naturally the Bi atom that, as it was proposed in the works of Whang et al. [11] and Li et al. [13], presumably can replace Ti atom. Important is also the oxygen vacancy in anatase that can emerge in high concentration if the synthesis is carried out in a deficit of oxygen. It was supposed in the work of Li et al. [13] that the visible light absorption in the Bi-doped anatase is induced mainly by the presence of the oxygen vacancies. Since in the sol–gel syntheses of the Bi-doped anatase various kinds of hydrocarbons are normally involved, one more possible defect is the carbon atom replacing the oxygen atom of anatase. Such defect can be found if the calcination of the Bi-doped samples is not sufficient to evaporate all the hydrocarbons involved, see e.g. [16]. 2. Method of calculation In Fig. 1 we show the tetragonal extended unit cell that contains the main structural elements of anatase. The nearest surrounding of the titanium atoms is a distorted octahedron of eight oxygen atoms whereas the nearest surrounding of the oxygen atom is a triangle that consists of titanium atoms. The simulation of defects is performed by the replacement of one of the Ti atom with Bi atom, removal of one oxygen atom or substitution of such an atom with carbon atom. The 2 2 2 super-cell is employed in our calculations that is obtained by the 2-fold repetition of the primitive Ti2O4-cell along all the three crystallographic axes. This corresponds to the 6.25% concentration of the mentioned defects. Previous calculations
have demonstrated that with such a size of the super-cell the interactions between the impurity atoms in the adjacent neighbor super-cells are negligible in the sense that neither positions of the impurity bands inside the band gap no widths of these bands do not change with a further increase of the cell, see [17,18]. The electronic band structure calculations were performed by using the pseudopotential plane wave method realized in the VASP program version 5.2 code, see [19]. The projector augmented wave approach was employed in the calculations and the pseudopotentials provided by the VASP code, with 4 valence electrons for Ti, 6 for O and 4 for C atoms. The generalized gradient approximation (GGA) was approved for the exchange–correlation functional. A plane-wave cutoff energy of 500 eV was accepted and an augmentation charge cutoff was equal to 330 eV. The relaxation of volume of cells and atomic positions were performed for the 2 2 2 super-cell of pure and doped anatase. The final variation of the total energy with respect to the changes of atomic coordinates were less than 0.001 eV, and the final forces acting on atoms were no more than 0.05 eV/Å. All the calculations, including the evaluations of densities of states, were performed with 18 k-points in the irreducible part of the Brillouin zone. A typical error of the density functional theory is the underestimation of the value of the band gap. In our case the calculated band gap of the pure anatase was 2.1 eV, too small in comparison with experimental data, 3.2 eV. More correct description of the electronic band structure of the transition metal oxides is achieved in the methods with the account of on-site Coulomb correlations. In such methods the correction of the band gap is performed by applying to the partly localized states, here to the 3d Ti states, a screened Hartree–Fock-like interactions which depend on the parameter U of Coulomb and J of exchange interactions. We employed the version of the method proposed by Dudarev et al. [20]. An advantage of this approach in comparison with the earlier versions of the GGA + U approach of Anisimov et al. [21] is that, with the precision no worse than in the earlier method, the on-site correlations in this approach depend only on the U J difference. A general problem of the GGA + U approach is that the methods of evaluating the U-value are not strictly established. Although the ways of non-empirical evaluation of this value exist, Anisimov et al. [21], often it is considered to be an adjustable parameter. The range of this value for the 3d Ti states is rather broad: 2, 3, 4 eV in the Ref. of Finazzi et al. [22], 4 eV (with U-corrections also applied to oxygen atoms!) in the Ref. of Mattioli et al. [23], 5 eV in the Ref. of Spadavecchia et al. [24] and 6.2 eV in the Ref. of Korotin et al. [25]. A good theoretical description of optical properties requires that at least experimental data on the band gap value of anatase have to be reproduced. We found that with the Dudarev’s formulations this occurs when the value U–J mounts to 7.2 eV. More arguments in favor of this value are provided by the data on the non-stoichiometric anatase. It is semiconducting with activation energy from 0.6 to 1.2 eV, [26]. The UP spectra demonstrate also that the band of oxygen vacancies has the maximum at the energy about 1 eV below the bottom of the conduction band. These data are reproduced with the U J = 7.2 eV while the calculations with more typical value U = 3.2 eV predict that the non-stoichiometric anatase is semi-metallic, see the data in the next section. Nevertheless, in the following we demonstrate the data on the band structure and absorption coefficient calculated with both these U J-values, 3.2 and 7.2 eV, in order to confirm that the change of properties with changing U–J is not drastic and the main conclusions do not depend on the specific choice of the U J value. As far as the 2p oxygen states and 6s Bi states are concerned, we omit the U,J-corrections for these states. The work of [27] where the XPS spectra of the compound BiVO4 have been measured and the (VASP) densities of electronic states have been calculated, provides a justification for such a simplification. These calculations have been done without the U,J-corrections, but the accordance to experimental data of the distance between the 6s Bi band and the bottom of the 2pO band is almost perfect; also in the calculations the experimental width of the 2p O band is well reproduced. Our evaluation of the optical properties started from the calculations of the imaginary and real part of the frequency-dependent dielectric function. These calculations have been performed neglecting the local-fields effects. Within this approximation the imaginary part of the dielectric function is a tensor value that is expressed as [28]
a2b ðxÞ ¼
Fig. 1. The tetragonal unit cell of anatase.
47
4e2 p2
X
lim q!0
1X 2wk d ck vk hx huckþea q juvk ihuckþeb q juvk i q2 k;c;v
ð1Þ
Here summation is carried out over all the wave-vectors k inside the irreducible part of the Brillouin zone whose weights are wk. The imaginary part of the dielectric function includes contributions of all the excitations from the valence band states (v) with the energies vk to conduction band states (c) with the energies ck . The matrix elements huckþea q juvk i are the overlap integrals of the cell-periodic parts of the pseudo-wave-functions of the mentioned states. The limit limq?0 means that the wavevector of the applied electric field (e.g. that of sunlight) is neglected. The real components of the dielectric functions were calculated via the Kramers–Kronig transform, Gajdoš et al. [28]. In the case of anatase the calculated in such a way non-diagonal elements of the dielectric tensor are negligibly small in comparison with the diagonal elements, so calculating angle-averaged dielectric function 1 + i2 we neglected them. It is then an easy task to calculate the frequency-dependent absorption and reflection coefficients of the crystals, see [29]. In particular, the absorption coefficient is calculated as
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n o1=2 KðxÞ ¼ 2x ½21 ðxÞ þ 22 ðxÞ1=2 1 ðxÞ =c
ð2Þ
3. Results and discussion In Fig. 2 we show the total densities of states of the studied objects near the fundamental band gap. In the case of the pure anatase the states of the bands between 2 and 3 eV are composed mainly of the 2p oxygen states; above the band gap the conduction band states are located that near the bottom of the band are composed mainly of the 3d Ti states. At U J = 3.2 eV the value of the band gap, 2.5 eV, is too small in comparison to experimental data. The enlargement of the U–J value of the 3d Ti states to 7.2 eV causes a rise of the valence and conduction bands, respectively, by 0.3 and 1 eV, so the band gap increases up to 3.2 eV. The similar effect takes place for the rest of compounds. With the emergence of the Bi atom two new bands arise. One of them, located below the valence band, is composed of the valence Bi 6s state hybridized with the 2p states of the oxygen atoms nearest to the bismuth atom; this band contains two electrons. The second band is located near the middle of the band gap, at about 2.9 and 3.3 eV when U J = 3.2 eV, 7.2 eV, respectively, and the Fermi level is just at the top of this band. This is the band of hybridized states composed mainly of the 2p oxygen orbitals and additions of the 6s Bi valence orbitals. It can be regarded as an anti-bonding counterpart of the 6s
A
B
C
D
Fig. 2. Total densities of states (per super-cell) for the pure anatase (A), doped with bismuth (B), containing oxygen vacancy (C) and doped with carbon (D). Solid lines are for the U J value equal to 3.2 eV, dashed lines are for U J = 7.2 eV. With arrows the positions of the Fermi level are shown.
Bi band. (Notice that the nature of this band is analogous to that of the states on top of the 2p oxygen band in the BiVO4 compound, Payne et al. [27]!) The 6p Bi orbitals do not form separate bands; they manifest themselves as admixtures to the 2p oxygen and 6s Bi bands. Since the band inside the fundamental band gap is preferably the band of oxygen states, it follows that Bi atom is formally in the 3+ oxidation state. When anatase ‘‘is doped’’ with oxygen vacancy, one new band emerges inside the band gap near the bottom of the conduction band. Although the states of this band are generally referred to as the oxygen vacancy states, they are composed of the 3d states of the Ti atoms nearest to the vacancy. These states drop from the conduction band when the hybridization between the titanium and oxygen states breaks, see [30]. The band contains 2 electrons, so it represents the F0 impurity center. When U J = 3.2 eV this band intersects with the conduction band. So such calculations predict that the non-stoichiometric anatase should be semi-metallic that contradicts to the experimental data of [26]. When U J = 7.2 eV the vacancy band is separated from the conduction band by 0.35 eV that corresponds to the semi-conductivity of the non-stoichiometric anatase. When anatase is doped with carbon, three new band emerge inside the lower part of the band gap. The states of these bands are composed mainly of the 2p carbon orbitals; the nature of the states and the energy intervals between them are in agreement with the results of the previous calculation performed with the TB-LMTO method by Zhukov et al. [31] and Zainullina et al. [32]. In the Fig. 3 the calculated absorption coefficient is shown for all the discussed objects. The comparison with the absorption coefficient of the pure anatase demonstrates that with all the kinds of doping the edge of fundamental absorption does not practically change. Noteworthy is the similarity of absorption of anatase doped with bismuth and carbon. Both for U J = 3.2 eV and 7.2 eV it covers the whole region of visible light. Very different is the absorption of the vacancy-containing anatase. Due to the position of the vacancy states near the bottom of the conduction band the absorption takes place at much less photon energy, that is at markedly higher wavelengths, also both for U J = 3.2 eV and 7.2 eV. In Fig. 4 the experimental absorption data on the Bi-doped anatase are given according to the papers of Yu et al. [12], Li et al. [13], Ji et al. [14], Xu et al. [15]. Of the data submitted in these papers only those are shown that correspond to the Bi content maximally close to 6.25% studied in our research. The only exception is the data of Li et al. [13] obtained only for much lower content of Bi. The inconsistency of the data attracts attention. Obscure are the data of Yu et al. [12]; according to them the onset of fundamental absorption should be at about 250 nm (5 eV), so these data probably contain a technical error. Contradictory are the data of Li et al. [13] and Ji et al. [14]: the first of them definitely demonstrate an absorption in visible region at 1% Bi content whereas the second show the absence of absorption at 5% content of Bi. Also contradictory are the ideas of the authors on the physical nature of absorption in the Bi-doped anatase. It is affirmed in the paper Yu et al. [12] that, because of a big differences in radii, the ions Bi3+ cannot replace the ions Ti4+ in the structure of anatase and instead with Bi doping the phase Bi4Ti3O12 is formed. On the contrary, Li et al. [13] affirm that such replacement is possible, but the absorption in visible region occurs because of the presence of oxygen vacancies. In the work of Ji et al. [14] it is proposed that the ions Bi3+ mainly exist near the surface of anatase. However, the authors do not explain the observed in their work small red shift of absorption edge, in comparison with that of the pure anatase. Xu et al. [15] affirm that the oxidation state of the titanium ions does not change with Bi doping, so the most probable reason of the absorption in visible region in the emergence of the Bi2O3 phase.
V.P. Zhukov et al. / Journal of Alloys and Compounds 548 (2013) 46–51
49
Fig. 3. The calculated absorption coefficient for pure anatase (solid line), anatase doped with Bi (dashed line), containing oxygen vacancy (dotted line) and doped with carbon (dash-dotted line). The left panel is for U J = 7.2 eV and the right panel is for U J = 3.2 eV.
In order to elucidate the causes impeding the incorporation of the Bi atoms into the structure of anatase a thermodynamic analysis of such process is desirable. Normally such incorporation is carried out by the methods of ‘‘wet chemistry’’. The final step of such complicated processes consists in the calcination of the dried gels whose composition and crystal structure are not known, so the first-principle thermodynamic analysis of such processes is now not possible. We carried out therefore more simple evaluations, namely the calculations of the defect formation energy (DFE) for the replacement of Ti atom with Bi atom. We follow the method proposed in the papers of Erhart et al. [33], Janotti et al. [34] and Xin-guo et al. [35] that was employed for the evaluation of the energy of the native defect formation in ZnO and vacancy formation in rutile. An analogous approach has been applied to the thermodynamics of the doping of anatase with carbon by DiValentin et al. [36]. Following the approach developed in these works the formation energy for the Ti replacement with Bi can be written as þn
Ef ðBi Þ ¼ ½Ec ðTi15 BiO32 Þ þ lðTiÞ ð3 nÞle ½Ec ðTi16 O32 Þ Fig. 4. The experimental absorption coefficient of the Bi-doped anatase. Solid line represents the data of Yu et al. [12] for 5% Bi doping; dashed line are the data of Ji et al. [13] for 1% of doping; dotted line are the data of Ji et al. [14] for 5% doping, and dash-dotted line are the data of Xu et al. [15] for 4% Bi doping.
Comparing our calculated absorption spectra with experimental data one can come to some definite conclusions. Since the very small absorption above 400 nm observed in the works of Yu et al. [12] and Ji et al. [14] is not compatible with our calculated absorption in the Bi-doped anatase, one may conclude that the Bi3+ ions do not enter in sufficient amount in the structure of anatase. This conclusion is in consent with the speculations of Yu et al. [12] and Xu et al. [15] on the role of accompanying phases that can be formed in the process of synthesis. The most probable such phases are Bi2O3 and Bi4Ti3O12. Xu et al. [15] observed a red shift of the fundamental absorption edge in the Bi-doped anatase. This corresponds to a lesser value of the band gap of monoclinic Bi2O3, 2.8 eV, in comparison with that of the pure anatase. One more conclusion that follows from the comparison of the calculated data with experiments is that the absorption in visible region observed in the work of Li et al. [13] is hardly explained by the presence of oxygen vacancies. Moreover, the rather high absorption in visible region observed by Li et al. [13] is incompatible with low content of Bi, about 1%. Taking into account the following from our calculations similarity of the absorption in the Bi-doped and C-doped anatase, the absorption observed by Li et al. [13] can probably be associated with the carbon impurity that can be present if the calcination in the course of synthesis is not sufficiently long.
þ lðBiÞ;
ð3Þ
In the left square bracket of this equation the value Ec(Ti15BiO32) is the energy of the super-cell containing the defect, l(Ti) is the chemical potential of the Ti atom withdrawn to reservoir, and (3 n)le is the chemical potential of the electrons transferred to (or received from) the reservoir if the Bi-defect is charged. In the second square bracket Ec(Ti16O32) is the energy of the super-cell without defect, and l(Bi) is the chemical potential of the Bi atom inside the reservoir. We assume that the formation of the Bi2O3 phase is possible in the course of synthesis, since this reaction is expected to be exothermic with big negative energy of formation that according to our calculations is equal to 6.27 eV per formula unit. The formation of the TiO2 and Bi2O3 phases impose restrictions on the values of the chemical potentials of Bi and Ti in reservoir. The restrictions depend on the conditions of synthesis, first of all on the content of oxygen. The highest limit of the chemical potential of oxygen lh(O) corresponds to the condensation of oxygen molecules (that can occur at very high pressures). One can take for it lh(O) = 1/2E(O2) where E(O2) = 9.84 eV is the ground state energy of the oxygen molecule with spin polarization taken into account. Following the work of [36], we assume that the chemical potential of oxygen is equal to l(O) = lh(O) 0.7 = 5.62 eV, since this value corresponds to atmospheric pressure and temperature of 700 K, close to the conditions of synthesis of the Bi-containing anatase. The imposed restriction follow from the considerations of the thermodynamic cycles corresponding to the formation of oxides,
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see [37]. For the reaction of anatase synthesis one can write the Gibbs free energy balance as
GðTiO2 Þ ¼ lðTiÞ þ 2lðOÞ þ DGðTiO2 Þ
ð4Þ
where DG is the oxide formation energy. One can evaluate approximately this energy from the DFT calculations as
DGðTiO2 Þ ffi EðTiO2 Þ EðTiÞ EðO2 Þ:
ð5Þ
Here E(TiO2) and E(Ti) are the ground state energies per formula units. It follows then that
lðTiÞ ¼ EðTiÞ þ EðO2 Þ 2lðOÞ:
ð6Þ
By analogy, from the Gibbs free energy balance for the formation of Bi2O3 from metallic Bi and oxygen one can obtain for the chemical potential of Bi
lðBiÞ ¼
1 3 2EðBiÞ þ EðO2 Þ 3lðOÞ 2 2
ð7Þ
The values of the potentials calculated in such a way applying the VASP code are l(Ti) = 6.49 eV and l(Bi) = 2.82 eV. Then the calculated EDF of the Ef(Bi+3) defect is equal to 14.54 eV. Since according to our calculations the 2pO,6sBi-band is halffilled, one can suppose that additionally two charged Bi-defects also may emerge in the course of synthesis, the Bi+4 defect with 1 electron withdrawn to reservoir or Bi2+ with 1 electron accepted from reservoir. The value of the electronic chemical potential in reservoir le is not strictly defined. However, its lower limit lle should be equal to the top of the valence band and the higher limit lhe to the bottom of the conduction band, otherwise the condition of equilibrium between the defect-containing system and reservoir cannot be satisfied. Our calculated values of lle and lhe are 2.6 eV and 5.8 eV, respectively. The addition of one electron to the 2pO,6sBi-band rises the Ec(Ti15BiO32) by 5.35 eV, but reduces it at the score of the chemical potential of the electron in reservoir. The removing of one electron from the Bi-level leads to a reduction of the Ec(Ti15BiO32) value by 0.75 eV, that is compensated by the increase of the energy of electrons in reservoir. At lle the EDF for Bi4+ and Bi2+ become equal, respectively, to 16.40 and 16.52 eV, where at lh these values are 19.60 and 13.32 eV. Hence, the EDF-values for all the three kinds of Bi-defects are too high in order the formation of such defects in presence of the phases TiO2 and Bi2O3 were possible. Since the phase Bi2O3 has a rather big negative formation energy, this is an evidence in favor of formation of the islands of this phase inside the Bi-containing anatase. The presence of this phase in the Bi-containing anatase was observed by means of the high-resolution XPS measurements of Xu et al. [15]. Two factors responsible for the instability of the Bi-defects are the anti-bonding interaction between the Bi atom and the nearest oxygen atoms and the size factor. The impurity state is formed in this case via hybridization of the oxygen 2p states and Bi 6s states, but it has the energy about 1.5 eV higher than the top valence band states. This value can be regarded as the contribution of anti-bonding to the destabilization of the defect. The second factor, more important, is associated with the great difference of ionic radii, 0.096 nm for Bi3+ and 0.068 nm for Ti4+. We notice also that the character of this state, anti-bonding and formed preferably by the oxygen 2p-states, is in disagreement with the opinion of Yu et al. [12] who supposed that this is the 6s Bi state. 4. Conclusions The necessity of new studies on the Bi-doped anatase is motivated by the existence of a number of contradictions in the results of previously performed experimental works on its photo-catalytic
properties. The essential contradictions also concern the interpretation of the absorption spectra of the Bi-doped anatase. We calculated therefore the electronic band structure and optical absorption spectra of anatase containing some defects that presumably can arise in the course of doping; they are Bi-atoms replacing titanium atoms, oxygen vacancies or carbon atoms replacing oxygen atoms. The calculations demonstrate that the Bi-atoms replacing the Ti atoms have to be in the 3+ oxidation state. However, comparing our calculated absorption spectra with experimental data we find that the replacement of titanium by bismuth with the formation of the Bi3+ is hardly probable. Also the optical absorption of the Bi-doped anatase cannot be explained by the presence of the oxygen vacancies. Instead, the calculated absorption spectra of the anatase doped with carbon has a similarity with some of the experimental spectra, so the presence of such type of defects in the studied specimens is possible. This is, probably, the case of the absorption observed in the experiments of Li et al. [13] and Xu et al. [15]. The absence of the visible range absorption in the Bi-doped anatase registered in some experiments, see [12,14], can be explained by the presence of bismuth only inside the islands of accompanying phases; Bi2O3 or Bi4Ti3O12 can be such phases. We also have carried out the calculation of the energy formation of the Bi-defects. The calculations confirm that the occurrence of the Bi-ions replacing Ti in anatase is hardly probable. The conclusion on the nature of enhanced photocatalytic activity of the Bi-doped anatase is that it hardly is associated with the visible light absorption of the Bi embedded into anatase. Instead it can be explained by the electron–hole separation induced by the presence of the accompanying phases and, probably, by the visible range absorption of the carbon impurities. Notice also that the accompanying phases, Bi2O3 and Bi4Ti3O12, possess themselves a high photocatalytic activity, see [38–40], as also some of the composites containing these phases, see [41,42]. Acknowledgments This work was supported in part by a grant of Prezidium of the Urals Branch of the Russian Academy of Sciences. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
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