Determination of the Electronic Structure and UV–Vis Absorption

Article pubs.acs.org/JPCC

Determination of the Electronic Structure and UV−Vis Absorption Properties of (Na2−xCux)Ta4O11 from First-Principle Calculations Moussab Harb,† Dilshad Masih,† Samy Ould-Chikh,† Philippe Sautet,‡ Jean-Marie Basset,† and Kazuhiro Takanabe*,† †

Division of Physical Sciences and Engineering, KAUST Catalysis Center, King Abdullah University of Science and Technology (KAUST), 4700 KAUST, Thuwal 23955-6900, Saudi Arabia ‡ Université de Lyon, CNRS, Ecole Normale Supérieure de Lyon, Laboratoire de Chimie, 46 allée d’Italie, 69364 Lyon cedex 07, France S Supporting Information *

ABSTRACT: Density functional theory (DFT) and density functional perturbation theory (DFPT) were applied to study the structural, electronic, and optical properties of a (Na2−xCux)Ta4O11 solid solution to accurately calculate the band gap and to predict the optical transitions in these materials using the screened coulomb hybrid (HSE06) exchange-correlation formalism. The calculated density of states showed excellent agreement with UV−vis diffuse reflectance spectra predicting a significant red-shift of the band gap from 4.58 eV (calculated 4.94 eV) to 2.76 eV (calculated 2.60 eV) as copper content increased from 0 to 83.3%. The band gap narrowing in these materials, compared to Na2Ta4O11, results from the incorporation of new occupied electronic states, which are strongly localized on the Cu 3d orbitals, and is located within 2.16−2.34 eV just above the valence band of Na2Ta4O11. These new occupied states, however, possess an electronic character localized on Cu, which makes hole mobility limited in the semiconductor.

1. INTRODUCTION Photocatalytic water splitting using powder semiconductors is an attractive method for the direct conversion of solar energy to chemical energy because of the relatively low capital cost required.1−3 However, extensive conversion of solar energy can only be achieved by harvesting a wide spectrum of light in the visible range. The systematic tuning of semiconductor bands must appropriately adjust the positions of both the conduction and the valence bands relative to water redox potentials under the desired operating conditions. One effective method for synthesizing visible responsive photocatalysts is to make composites with d0-metals (Ti4+, V5+, Nb5+, Ta5+, W6+, etc.) and d10-metals (Cu+, Zn2+, etc.).1 The relatively large band gap of natrotantite (Na2Ta4O11, approximately 4.7 eV) only responds to deep UV light (200−280 nm). 4−6 The incorporation of d10 transition metals into the structure of Na2Ta4O11, such as Cu+ in the Na (p6) sites, is a promising strategy toward improving the optical absorption of the material by introducing new, occupied electronic levels into the gap.7 However, the creation of localized impurity states in the gap is known to limit the photocatalytic activity because the limited mobility of the photogenerated electrons and holes to the catalytic surface leads to charge recombination. Issues relating to charge recombination may be overcome through the creation of strongly delocalized impurity states in the gap, for example, impurity states strongly mixed with the O 2p orbitals governing the valence band of Na2Ta4O11. © 2013 American Chemical Society

An elaborate synthesis study of (Na2−xCux)Ta4O11 was recently reported by Palasyuk et al.7 Their prepared powders revealed enhanced visible light absorption properties compared with Na2Ta4O11, but unfortunately, no photocatalytic activity was observed under visible light irradiation. The electronic origin of the visible light responsive properties in (Na2−xCux)Ta4O11 remains unclear. Using the linear muffin-tin orbital (LMTO) method in the atomic sphere approximation (ASA), Palasyuk and Maggard8 reported the densities of states (DOS) for the limiting compositions Na2Ta4O11 and idealized Cu2Ta4O11. These calculations clearly suggest that the incorporation of Cu+ into Na2Ta4O11, as in Cu2Ta4O11, results in new highest-occupied crystal orbitals. These new occupied orbitals correspond to filled Cu 3d orbitals mixed, to a small extent, with O 2p orbitals. However, the LMTO method used leads to the significant underestimation of the Na2Ta4O11 and Cu2Ta4O11 band gaps. In addition, neither the electronic structure nor the optical absorption spectra of (Na2−xCux)Ta4O11 on the basis of these calculations were reported as a function of Cu concentration, which would enable a more relevant interpretation of the experimental results. In this paper, we report an extended modeling study carried out to provide rational insight into the electronic origin of the Received: June 17, 2013 Revised: July 19, 2013 Published: July 25, 2013 17477

dx.doi.org/10.1021/jp405995w | J. Phys. Chem. C 2013, 117, 17477−17484

The Journal of Physical Chemistry C

Article

TOPAS V4.2 software (Bruker-AXS).9,10 The XRD pattern of Na2Ta2O11 was refined using a trigonal structure (space group R3c (n°167)) taken from card 201714 in the ICSD database.4 The profile parameters included the scale factor, a sample displacement parameter, and a three-term polynomial for the background. The fundamental parameters approach analytically calculates the instrumental contribution to the peak profile. Particle size was calculated from the Lorentzian contribution of this profile. The Rwp, Rbragg, and goodness of fit (GOF) were in the range of 5, 3, and 5, respectively, for all refinements.

visible light responsive (Na2−xCux)Ta4O11 materials. We used an advanced quantum method based on density functional theory (DFT) and density functional perturbation theory (DFPT) using the range-separated hybrid (HSE06) exchangecorrelation formalism to provide an accurate description of the electronic structure and UV−vis optical absorption properties of these materials. We explored two main families of (Na2−xCux)Ta4O11 structures, which differ in the site of Cu+ substitution (Wyckoff position 18d or 12c) into the natrotantite structure (space group R3c (n°167)). Within each structural family, we investigated several compositions by varying the concentrations of Cu (16.6, 50, and 83.3 at. %) to reflect atomic concentrations close to those obtained experimentally. Our method provided an accurate description of the electronic structure and predicted the UV−vis optical absorption of the systems with various Cu/Na compositions. We further analyzed the localized/delocalized character of the gap states created by Cu incorporation in terms of their spatially resolved density distribution. Our calculated results were found to match very well with the recent experimental data obtained in our laboratory.

3. COMPUTATIONAL DETAILS 3.1. Total Energy Calculations. We used spin-polarized periodic DFT within the plane wave (PW) approach, as implemented in the VASP 5.2 quantum simulation code,11−15 to perform the total energy calculations of the (Na2−xCux)Ta4O11 structures. We employed in the first step the generalized gradient approximation (GGA) within the Perdew−Burke−Emzerhof (PBE) exchange-correlation functional16 and the projector-augmented plane wave (PAW) approach to describe the electron−electron and the electron− ion interactions, respectively.11−17 Cutoff energies of 400 and 605.4 eV were used for wave functions and for charge augmentations, respectively. The integration of the band structure energy over the Brillouin zone was performed with the tetrahedron method with Bloch corrections. 3.2. Structural Models. For simulations of the (Na2−xCux)Ta4O11 structures, we considered two families differentiated by the atomic positions of incorporated Cu. For the first family, the structures with various Cu/Na compositions were taken from site-differentiated substitution obtained from the Rietveld refinement (Cu: the 18d Wyckoff position). In the second family, the structures were generated from natrotantite structure by a direct substitution of Na by Cu (Cu: the 12c Wyckoff position). In both structural families, the ion coordinates and lattice parameters of the various generated geometries were fully optimized for all components of the residual forces within 0.01 eV/Å. For the generic (Na12−pCup)Ta24O66 conventional cell, initially containing 102 atoms in total and modified with pCu atoms and pNa vacancies, the atomic concentration of Cu occupying Na sites was defined as (p/12) leading to the corresponding stoichiometry (Na2−xCux)Ta4O11 (x = (p/6)) notation used throughout this manuscript. For p = 2, 6, and 10, we simulated the structures of (Na2−xCux)Ta4O11 with 16.6, 50, and 83.3% Cu or x = 0.33, 1.0, and 1.66, respectively. For p = 2 (16.6% Cu), several Cu positions were examined to determine the most stable configuration. In the various structural models explored in our calculations, the oxidation states of the elements examined were Na+, Cu+, Ta5+, and O2−. The Brillouin zone was sampled with a 5 × 5 × 2 Monkhorst-Pack k-point grid for the various studied systems.18 Constructions of the various systems were performed using the Materials Studio graphical interface.19 3.3. Electronic Structure and UV−Vis Optical Absorption Calculations. Density of states (DOS) calculations of (Na2−xCux)Ta4O11 materials were investigated for the geometries optimized with the PBE functional by employing the range-separated hybrid Heyd−Scuseria−Ernzehof (HSE06) exchange-correlation functional20 as implemented in VASP 5.2.11−15 In this formalism, the correlation part is defined by PBE, whereas a range separation approach is taken for the exchange part. At short range, a mixing of 25% exact Hartree− Fock (HF) and 75% PBE exchange is used, while at long range,

2. EXPERIMENTAL METHODS Cu2O (Aldrich; minimum 99%), anhydrous Na2CO3 (Aldrich; 99.9%), and Ta2O5 (Aldrich; 99.9%) were used as reactant precursors for the syntheses of Cu+ modified natrotantite structures. All the reactants were thoroughly mixed using a mortar and pestle, and the homogeneous mixtures were treated at high temperature under atmospheric pressure in flowing nitrogen gas. The atomic percentage of Cu was varied from 0 to 100% but was always in accordance with a final stoichiometric composition of M2Ta4O11 (M = Cu or Na). The homogeneous precursor mixture was placed in an alumina boat and was heated under a high flow of nitrogen (100 L h−1) in a Nabertherm tube furnace. The optimal synthesis temperatures for phase-pure natrotantite (Na2−xCux)Ta4O11 showed a downward trend with increasing Cu content; samples of 0, 16.6, 50, and 83.3% Cu were heated at 1373, 1373, 1323, and 1273 K, respectively. The temperature was increased at 5 K min−1 to the optimized set point and was held at the desired level for 5 h. After the first treatment, the products were ground to fine powders and were retreated for another 2 h at the same temperatures. The optical properties of the final powder samples were studied by diffuse reflectance ultraviolet visible (DR−UV−vis) spectrometry collected using a JASCO model V-670 spectrophotometer equipped with an integrating sphere. The spectra were scanned from 1100 to 200 nm using halogen and deuterium lamps as light sources. Contributions from scattering were removed using the Kubelka−Munk function. X-ray diffraction (XRD) patterns were collected on a Bruker D8 Advanced A25 diffractometer in the Bragg−Brentano geometry equipped with a Cu tube (Cu−Kα; λ = 0.15418 nm) operating at 40 kV and 40 mA using a linear position sensitive detector (opening 2.9°). The diffractometer was configured with a 0.44° diverging slit, 2.9° antiscattering slit, 2.5° Soller slits, and a nickel filter to attenuate contributions from Cu−Kβ fluorescence. Data sets were acquired in continuous scanning mode (0.004998°/s) over the 2θ range of 10−120°. The integration step size of 0.010° resulted in a counting time of 2 s per step. The XRD data were analyzed by the Rietveld method using the fundamental parameters approach contained within the 17478

dx.doi.org/10.1021/jp405995w | J. Phys. Chem. C 2013, 117, 17477−17484

The Journal of Physical Chemistry C

Article

the standard PBE exchange is maintained. The range-separation parameter was fixed at 0.2 Å. The tetrahedron method with Bloch corrections was also employed for Brillouin zone integration. Recent theoretical work on reference systems indicated that the use of the DFT-HSE06 approach may be expected to more accurately predict the experimental band gap than PBE or other hybrid functionals, such as PBE0 or B3LYP.21,22 UV−vis optical absorption calculations of (Na2−xCux)Ta4O11 materials were performed in the framework of the spinpolarized DFPT, as implemented in VASP 5.2,11−15 by employing the HSE06 functional. We again used the geometries obtained with the PBE functional. Optical properties were calculated with the frequency-dependent complex dielectric function ε(ω) = ε1(ω) + iε2(ω) following a methodology described in the literature.23 The imaginary part ε2(ω) was calculated by summing all the possible transitions from occupied to unoccupied states in the Brillouin zone weighted with the matrix element describing the probability of transition. The real part was given by the Kramers−Kronig relation.24,25 To determine the fraction of the light absorbed by the solid, the optical absorption coefficient α(ω) was calculated using the equation α(ω) = [(4π)/λ]k(ω), where λ and ω are the wavelength and the frequency of the incident light and k(ω) is the imaginary component of the complex refractive index or the extinction coefficient, which is defined by the following expression: k(ω) = {[(ε21 + ε22)1/2 − ε1]/2}1/2.

Figure 1. Powder XRD patterns of (Na2−xCux)Ta4O11 solid solutions with various Cu contents: (a) 0%, (b) 16.6%, (c) 50%, (d) 83.3%, and (e) for Cu5Ta11O30, 100% Cu.

The Cu crystallographic site in the (Na2−xCux)Ta4O11 solid solution (Wyckoff site 18d) is linearly coordinated to oxygen with equivalent Cu−O distances ranging from 1.88 to 1.89 Å over the compositional range between 0 and 83.3% Cu. The Na cations remain in a distorted 7-fold coordinated site (Wyckoff site 12c) with Na−O distances ranging from 2.47−2.70 Å (0% Cu) to 2.58−3.10 Å (83.3% Cu). Both Cu and Na site occupancies exhibited linear compensation reflecting the Cu stoichiometry (Figure 3). As a function of the Cu content, the slopes for the Na and Cu occupancies are −0.96 and 0.63, respectively; the values are very close to the theoretical ones of −1 and 2/3 expected for quantitative substitution. To give more relevant information about the location of Cu in the natrotantite structure, the energetics of various structures were assessed by DFT and were compared with the experimentally observed structures. Figure 4 shows the DFT relaxed unit cell structures of Na2Ta4O11 and (Na2−xCux)Ta4O11 with x = 1.66 (83.3% Cu) either site-differentiated Cu in the 18d Wyckoff position or a direct substitution of Na by Cu occupying the 12c Wyckoff position. All components were relaxed until the residual forces were less than 0.01 eV/Å. For the (Na2−xCux)Ta4O11 structure (x = 1.66 or 83.3% Cu) optimized with site-differentiated Cu in the 18d Wyckoff position, the Cu atoms located in the same layer adopt a pairing configuration at a Cu−Cu distance of 3.09 Å as shown in Figure 4b. Each Cu atom is coordinated with two O atoms at identical Cu−O bond lengths of 1.87 Å. Similar information has been also obtained for systems containing lower Cu contents (16.6 or 50% Cu). For the (Na2−xCux)Ta4O11 structure (x = 1.66 or 83.3% Cu) optimized with directly substituted Cu in the 12c Wyckoff position, the relaxed Cu positions after geometry optimization are shifted up and down along the c-axis with respect to the initial Na positions in Na2Ta4O11 as presented in Figure 4c. In this structure, the Cu atoms are separated by a nearest neighbor Cu−Cu distance of 3.71 Å, and each Cu atom is coordinated with three O atoms at identical Cu−O bond lengths of 2.13 Å. Similar structural information has been also obtained for systems containing lower Cu contents (16.6 or 50% Cu).

4. RESULTS AND DISCUSSION 4.1. Structural Characterization. The first refinement of the structural parameters was performed with pure natrotantite to evaluate the atomic displacement parameters of all atoms assuming site occupation factors of one. Direct substitution of Na+ with Cu+ in the 12c crystallographic site led to mismatches in the intensities of reflections in the Rietveld refinement. Nevertheless, this method of substitution was utilized to generate Fourier difference maps (see Supporting Information, SI1). Visualization of the resultant electron density (Figure SI1.1b) clearly indicates that Cu+ is instead located in the 18d crystallographic site consistent with a previous report by Palasyuk et al. that demonstrated that (Na2−xCux)Ta4O11 is a site-differentiated solid solution.7 The atomic displacement parameters were then fixed to the previously determined values, while the site occupations of Na (12c) and Cu (18d) were refined. The maximum Cu site occupation corresponding to complete Na substitution maintaining charge neutrality is 2/3. The Cu2O−Ta2O5 system is known to have the general formula CuxTa3y+1O8y+3, for example, Cu2Ta4O11, Cu3Ta7O19, Cu5Ta11O30, and Cu7Ta15O41.7,8 To date, only Cu3Ta7O19 and Cu5Ta11O30 have been synthesized in a pure form, while the synthesis of pure Cu2Ta4O11 or Cu7Ta15O41 remains a challenge. In the present study, (Na2−xCux)Ta4O11 solid solutions were synthesized by a solid-state approach using a range of Cu content from 0 to 100%. The XRD patterns in Figure 1 indicate that only the characteristic d-spacings of natrotantite are observed for samples with 0−83.3% Cu. At 83.3% Cu substitution, Cu5Ta11O30 was also present as a small impurity. For the sample with 100% Cu substitution, a pure Cu5Ta11O30 phase was obtained rather than Cu2Ta4O11. The experimental lattice constants and the cell volume of the trigonal unit cell exhibit a linear Vegard law evolution between 0 and 83.3% Cu (see Figure 2). 17479

dx.doi.org/10.1021/jp405995w | J. Phys. Chem. C 2013, 117, 17477−17484

The Journal of Physical Chemistry C

Article

Figure 2. (A) The experimental lattice parameters and (B) volume of the trigonal unit cell as a function of Cu content for (Na2−xCux)Ta4O11 solid solutions.

Figure 3. Evolution of Na and Cu site occupations in (Na2−xCux)Ta4O11 solid solutions as a function of the Cu content. Figure 4. DFT optimized unit cell structures of (a) Na2Ta4O11, (b) (Na2−xCux)Ta4O11 with x = 1.66 (83.3% Cu) with site-differentiated Cu in the 18d Wyckoff position, and (c) same stoichiometry as b with a geometry with a direct-substituted Cu in the 12c Wyckoff position. Color legend: Na in yellow, Cu in blue, Ta in gray, and O in red.

Although the relaxation starting from the structure with Cu in the 12c position led to the metastable structure (Figure 4c), our DFT calculations confirm that the 18d crystallographic position is the energetically favored site for Cu into the natrotantite structure (Figure 4b) in agreement with the experimental data. The refined structures with x = 0.33, 1.0, and 1.66 (or 16.6, 50, and 83.3% of Cu) were found after geometry optimization to be 0.91 (or 0.54), 0.74 (or 0.45), and 0.67 (or 0.33) eV/Cu more stable with PBE (or HSE06) than those with directly substituted Cu. After geometry relaxation, a monoclinic lattice was observed rather than the initial trigonal symmetry. The calculated cell volume also showed a linear increase with increasing Cu content in good agreement with the experimental values (Figure 2B). 4.2. Electronic Structure and UV−Vis Optical Absorption Properties. We investigated the electronic structure and the UV−vis optical absorption properties of the lowest-energy (Na2−xCux)Ta4O11 structural configurations discussed above by calculating their DOS and their optical absorption coefficients with HSE06. By correlating the DOS and optical absorption

results, we will attempt to determine the electronic origin of the band gap narrowing and the enhanced optical absorption observed in (Na2−xCux)Ta4O11 materials. The DR−UV−vis spectra of (Na2−xCux)Ta4O11 (x = 0− 1.66) are shown in Figure 5A. In the absence of Cu, Na2Ta4O11 shows a distinct absorption edge in the UV region (∼270 nm). Upon Cu incorporation, the absorption edge shifted to the visible region. Tauc plots for the direct band gaps corresponding to the obtained spectra are shown in Figure 5B. The measured band gaps were 4.58, 2.94, 2.85, and 2.76 eV for 0, 16.6, 50, and 83.3% Cu substitution, respectively. Increased Cu+ incorporation obviously caused a red-shift of the absorption edge consistent with previous reports.7,8 However, the evolution is not linear with increasing Cu content with a 17480

dx.doi.org/10.1021/jp405995w | J. Phys. Chem. C 2013, 117, 17477−17484

The Journal of Physical Chemistry C

Article

Figure 5. (A) DR−UV−vis spectra and (B) Tauc plots for the direct band gaps of (Na2−xCux)Ta4O11 solid solutions with various Cu contents: (a) 0%, (b) 16.6%, (c) 50%, and (d) 83.3%.

Figure 6. Calculated density of states (DOS) with HSE06 for (Na2−xCux)Ta4O11: (a) 0% Cu, (b) 16.6% Cu, (c) 50% Cu, and (d) 83.3% Cu. Color legend: total DOS in black, DOS projected on Ta in blue, on O in green, and on Cu in red. The top of the valence band EVB is represented by the horizontal dotted line. The energy scale is arbitrary but allows a comparison between the cases.

reveals new occupied electronic states located just above the original valence band of Na2Ta4O11 leading to a narrower optical band gap (2.78 eV) compared with that of Na2Ta4O11 (4.94 eV) as presented in Figure 6b. These new electronic states are mainly composed of Cu 3d orbitals with minor contributions from O 2p orbitals. For Cu concentrations of 50 and 83.3%, similar DOS results are obtained with optical band gaps of 2.70 and 2.60 eV, respectively (Figure 6c, d). Our DFT calculations for systems containing Cu are in very good agreement with the current experimental data within a discrepancy of only ∼0.15 eV. An increase in the Cu concentration in the natrotantite structure leads to higher densities of electronic states located above the valence band of pure Na2Ta4O11 as a result of the stacking of Cu 3d orbitals in the same energy range (Figure 6). In all cases, as expected, the conduction band primarily consists of empty Ta 5d orbitals. The densities of states at the bottom of the conduction band

strong narrowing of the band gap for 16.6% Cu and a further modest reduction for higher Cu amount. As was recently reported in our theoretical studies of reference systems,21,22 the use of the DFPT-HSE06 approach is expected to accurately describe the optical transitions in the UV−vis range as a result of the accurate band structure determination provided by this method. For Na2Ta4O11, our HSE06 calculated DOS gives a band gap of 4.94 eV (Figure 6a) in good agreement with our experimental data (4.58 eV) and showing only a slight overestimation (0.36 eV) of the actual value. Figure 6a also shows that the valence band is dominated by O 2p orbitals, whereas the conduction band is dominated by Ta 5d orbitals. The Na 2p orbitals do not contribute to the valence or conduction band states of this material. If we consider the optimized (Na2−xCux)Ta4O11 structures in their most stable configuration (Cu in the 18d Wyckoff position), the HSE06 calculated DOS for the 16.6% Cu sample 17481

dx.doi.org/10.1021/jp405995w | J. Phys. Chem. C 2013, 117, 17477−17484

The Journal of Physical Chemistry C

Article

gap of Na2Ta4O11 (see Supporting Information SI2 for more detailed information). As a consequence, the calculated absorption coefficient results demonstrate the appearance of new low-intensity resonant bands. We have at 400 nm absorption edges extended up to 480 nm (see Supporting Information SI3 for more detailed information). The Cu 3d band for this metastable direct substitution is narrower than the previous case with Cu in the 18d Wyckoff position implying that the new Cu 3d states are more localized. 4.3. Analysis of the Band States Involved in Excitation under Irradiation with Visible Light. In photocatalysis, it is essential that excited electrons and holes transfer to the surface of the semiconductor, where the relevant redox chemistry takes place.2 Hence, it is important to analyze the hybridization character of these electronic states to understand the photocatalytic behavior of these materials. The energy levels relevant to visible light absorption (