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Facet-Dependent Photocatalytic N2 Fixation of Bismuth-Rich Bi5O7I Nanosheets Yang Bai, Liqun Ye, Ting Chen, Li Wang, Xian Shi, Xu Zhang, and Dan Chen ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b08129 • Publication Date (Web): 26 Sep 2016 Downloaded from http://pubs.acs.org on September 27, 2016
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Facet-Dependent Photocatalytic N2 Fixation of Bismuth-Rich Bi5O7I Nanosheets Yang Bai,a,c Liqun Ye,a,b,* Ting Chen,a,d Li Wang,b Xian Shi,a Xu Zhang,e and Dan Chen,f a.
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum
University, Chengdu 610500, China. b.
Key Laboratory of Ecological Security for Water Source Region of Mid-line Project of South-to-
North Water Diversion of Henan Province; Henan Collaborative Innovation Center of Water Security for Water Source Region of Mid-line of South-to-North Diversion Project, Nanyang Normal University, Nanyang 473061, China. c.
School of Oil & Natural Gas Engineering, Southwest Petroleum University, Chengdu 610500 China.
d.
College of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu 610500,
China. e.
College of Oil Engineering, Chongqing University of Science and Technology, Chongqing 401331,
China. f.
Institute of Tarim Oilfield Company, Kuerle 841000, China.
Corresponding author: Nanyang Normal University; Southwest Petroleum University E-mail:
[email protected]; (L. Ye)
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Abstract: Bismuth-rich bismuth oxyhalides (Bi–O–X; X = Cl, Br, I) display a high photocatalytic reduction activity due to the promoting conduction band potential. In this work, two Bi5O7I nanosheets with different dominant facets were synthesized using either molecular precursor hydrolysis or calcination. Crystal structure characterizations, included X-ray diffraction patterns (XRD), field emission electron microscopy and fast fourier transformation (FFT) images, showed that hydrolysis and calcination resulted in the dominant exposure of {100} and {001} facets, respectively. Photocatalytic data revealed that Bi5O7I–001 had a higher activity than Bi5O7I–100 for N2 fixation and dye degradation. Photoelectrochemical data revealed that Bi5O7I–001 had higher photo-induced carrier separation efficiency than Bi5O7I–100. The band structure analysis also used to explain the underlying photocatalytic mechanism based on the different conduction band position. This work presents the first report about the facet-dependent photocatalytic performance of bismuth-rich Bi–O–X photocatalysts. Key Words: Bi5O7I, Bismuth-rich, Facet, N2 fixation, Photocatalysis.
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Introduction The surface atom configuration strongly affects the exposure of action sites and the electronic structure of crystalline photocatalytic materials.1–4 Since Cheng et al. reported the facet engineering of anatase TiO2 for photocatalysis in 2008,5 more research has been published about the facet effects of photocatalysts for environmental applications and/or energy photocatalysis. For example, the exposure of reactive facets, facet-dependent photocatalytic activity, and mechanisms of oxide-based (brookite TiO2, ZnO, CeO2, WO3, and Cu2O),6–11 silverbased (AgPO4, AgBr, and AgI),12–14 and bismuth-based (BiVO4, (BiO)2CO3, and BiOX; X = Cl, Br, and I)15–18 semiconductor all have been researched. Recently, we found based on our previous research that a high percentage of exposed facets (ideally > 80%) and identical morphologies are very important for studying the facet-dependent photocatalytic performance of crystalline photocatalysts,19,20 because facets synergies and morphology effects need to be eliminated.21–24 Therefore, the ideal samples for facet-dependent research possess the same morphologies and high percentages of exposed facets. To the best of our knowledge, the facet-dependent photoactivity of bismuth-rich Bi–O–X (X = Cl, Br, I) photocatalysts (defined as BixOyXz) has not been reported to date due to limitations in the exposure of facets. At present, pH adjustment is used as standard method for exposing the facets of bismuth-based photocatalysts. For instance, the {010} and {110} facets of BiOV425–27 and the {001} and {100} facets of BiOCl and BiOBr were exposed at different pH values.16,17,28–30 However, also the main procedure for the synthesis of BixOyXz photocatalysts is performed pH controlled. For example, Bi3O4Cl,31
Bi3O4Br,32
Bi4O5Br2,33
Bi4O5I2,34
Bi5O7Br,35
Bi5O7I,36
Bi12O17Cl2,37
Bi12O17Br2,38
Bi24O31Cl10,39 and Bi24O31Br1040 were synthesized by changing the pH values. Therefore, the facets exposure of above BixOyXz photocatalysts is impossible by pH adjustment. Recently, our group developed a new molecular precursor process for the synthesis of BixOyXz photocatalysts. By 3 ACS Paragon Plus Environment
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changing the molecular precursor, BiOCl–001 nanosheets with different thicknesses could be synthesized.41 Different BixOyXz materials could be obtained by changing the post-processing method.42 In this paper, the molecular precursor process was also used to synthesize Bi5O7I nanosheets, as shown Scheme 1. Bi5O7I–001 and Bi5O7I–100 with more than 80% facet exposure were synthesized by molecular precursor hydrolysis and calcination, respectively.
Scheme 1. Synthesis process of Bi5O7I–100 and Bi5O7I–001 via different methods processing molecular precursors.
The most promising applications of photocatalysis for solar fuel generation and N2 fixation involve reduction reactions. However, in the past ten years, most studies about Bi–O–X photocatalysts dealt with organic pollutant degradation rather than solar fuel generation, as the holes of Bi–O–X photocatalysts exhibit a high photocatalytic oxidation activity.43,44 Since two years, our group has been reporting photocatalytic solar fuel generation over Bi–O–X photocatalysts,18,42,45–48 whereas Zhang et al. reported the light induced N2 fixation of Bi-O-X.49,50 In our work, we researched the facet-dependent photoactivity of Bi5O7I nanosheets using photocatalytic N2 fixation. We found that Bi5O7I–001 displays the highest activity among the studied photocatalysts and its facet-dependent photocatalytic mechanism was elucidated based on experimental evidences.
Results and Discussion
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Figure 1. XRD patterns of Bi5O7I–100 and Bi5O7I–001.
The X-ray diffraction patterns (XRD) patterns of Bi5O7I–100 and Bi5O7I–001 (Figure 1) reveal four main peaks (001), (312), (001), and (204) at 2θ = 7.72°, 28.08°, 31.09°, and 33.03°, respectively. All XRD peaks of Bi5O7I–100 and Bi5O7I–001 displayed the orthorhombic Bi5O7I (JCPDS file No. 00–40–0548; a = 1.6267 nm, b = 0.5356 nm, c = 1.1503 nm; α = β = γ = 90°). The absence of any characteristic peaks related to impurities (such as BiOI, Bi4O5I2, or Bi2O3) indicates that both samples only contained pure Bi5O7I. More importantly, we found that the intensity of (001) peak of Bi5O7I–001 was much higher than that of Bi5O7I–100 with a 001/200 intensity ratio of 4.9 for Bi5O7I–001 and only 0.7 for Bi5O7I–100. This implies that Bi5O7I–001 exposes more {001} facets, whereas Bi5O7I–100 exposes more {100} facets. For confirming this inference, Field emission electron microscopy and fast fourier transformation (FFT) analysis have been performed, as shown in the following.
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Figure 2. Characterization of Bi5O7I–001. (a) FESEM image; (b) TEM image; (c) top view HRTEM image; (d) enlarged red range of Figure 2c; (e) FFT pattern corresponding to Figure 2c; (f) side view HRTEM image (the inset picture is the enlarged red range); (g) crystal growth direction of the nanosheets; (h) atomic structure of {001} facets with side view; and (i) atomic structure of {001} facets with top view.
Field emission scanning electron microscopy (FESEM) and transmission electron microscopy (TEM) (Figure 2a-b and Figure S1) reveal that Bi5O7I–001 consists of nanosheets of a size of about 100–200 nm × 10–20 nm and exhibits a Brunauer-Emmett-Teller (BET) surface area of 6.7 m2 g–1 (Figure S2). Figure 2c shows the high-resolution transmission electron microscopy (HRTEM) image with [001] orientation (top view). The enlarged red range of Figure 2c and the corresponding fast fourier transformation pattern are shown in Figure 2d and 2e, respectively. They reveal clear lattice spacing of 0.27 nm, indexed to the {020} (theoretical value: 0.267 nm) and {600} facets (theoretical value: 0.271 nm). The FFT patterns show that the angles of {020}/{600} and {620}/{600} are 89.9° and 45.3°, respectively. These values are same with 6 ACS Paragon Plus Environment
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theoretical angles (90.0° for {020}/{600} and 45.4° for {620}/{600}). Figure 2f shows the HRTEM image with side view, which reveals lattice spacing of 0.58 nm, which indexed to the {002} facets (theoretical value: 0.58 nm). Based on the above analysis, it proved that the two facets (top and bottom surface) of Bi5O7I–001 nanosheets are {001} facets (Figure 2g). Figure 2g and 2h display the atomic structure of {001} facets in top and side views. This reveals the hackly surface of the {001} facets and that all atoms (including Bi, O, and I) appear on the {001} facets.
Figure 3. Characterization of Bi5O7I–100. (a) SEM image; (b) TEM image; (c) top view HRTEM image; (d) enlarged red range of Figure 3c; (e) FFT pattern corresponding to Figure 3c; (f) side view HRTEM image (the inset picture is the enlarged red range); (g) crystal growth direction of the nanosheets; (h) atomic structure of {100} facets with side view; and (i) atomic structure of {100} facets with top view.
FESEM and TEM images (Figure 3a-b and Figure S3) reveal that Bi5O7I–100 consists of nanosheets of a size of about 200 nm × 15–20 nm and exhibits a BET surface area of 6.9 m2 g–1
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(Figure S2). Figure 3c shows the HRTEM image of the [100] orientation (top view). The enlarged red range of Figure 3c and the corresponding FFT patterns are shown in Figure 3d and 3e, respectively. They reveal two clear lattice spacing of 0.27 and 0.29 nm, which indexed to that of the {020} (theoretical value: 0.267 nm) and {004} facets (theoretical value: 0.288 nm), respectively. The FFT patterns reveal that the angles of {020}/{004} and {024}/{004} are 90.2° and 46.9°, respectively. These values are same with the theoretical angles (90.0° for {020}/{004} and 47.0° for {020}/{004}). The HRTEM image with side view is shown in Figure 3f, which reveals lattice spacing of 0.80 nm, which indexed to that of the {200} facets (theoretical value: 0.813 nm). Based on the above analysis, it proved that the two square facets (top and bottom surface) of the Bi5O7I–100 nanosheets are {100} facets (Figure 3g). Figure 3g and 3h display the atomic structure of the {100} facets in top and side views. They reveal the smooth surface of the {100} facets and that only Bi and O atoms appear on the {100} facets. The different surface atom configurations of the {001} and {100} facets may result in different surface adsorption properties and energy band structures, which may lead to different photocatalytic performances. Figure 4 show the X-ray photoelectron spectrometer (XPS) spectra of Bi5O7I–100 and Bi5O7I–001. Survey spectra show the same elements (Bi, I, O, and contaminative C) for Bi5O7I–100 and Bi5O7I–001 (Figure 4a). Figure 4b shows two Bi 4f signals for Bi5O7I–001 at 159.1 and 164.4 eV, which were indexed to Bi 4f7/2 and Bi 4f5/2, respectively. The corresponding binding energies of Bi 4f7/2 and Bi 4f5/2 increased for Bi5O7I–100 to 159.5 and 164.8 eV, respectively. Figure 4c shows the deconvolution of the O 1s signal into 530.0 eV (or 530.3 eV) and 531.3 eV. The first peak (530.0 or 530.3 eV) was assigned to O2– in the Bi–O bond,42,51 whereas the peak at 531.3 eV should be attributed to surface hydroxyl groups. Bi5O7I– 001 reveals two peaks at 619.0 and 630.5 eV, which indexed to I 3d5/2 and I 3d3/2, respectively. The corresponding binding energies of I 3d5/2 and I 3d3/2 of Bi5O7I–100 increased to 619.3 and 630.8 eV, respectively. The different binding energies of B i4f, O 1s, and I 3d imply that Bi5O7I–100 and Bi5O7I–001 8 ACS Paragon Plus Environment
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exhibit different surface atom configurations. On the other hand, XPS revealed for Bi5O7I–001 and Bi5O7I–100 different molar ratios of Bi:O:I = 5:7:1 and 5:7:0.5, respectively. The lower I 3d intensity of Bi5O7I–100 may reflect the absence of I atoms on the {100} facets, as shown in Figure 3h. The XPS depth was detected to be about 2 nm,52 which is close to the value of cell parameter a (a = d100 = 1.6267 nm). Therefore, fewer I atoms are detected on Bi5O7I–100 by XPS. More importantly, the ICP data exhibited a bulk molar ratio of Bi:O:I = 5:7:1 for Bi5O7I–100 and Bi5O7I–001. This confirms that the intensity difference of I 3d results from the absence of I atoms on {100} facets.
Figure 4. XPS spectra of Bi5O7I–100 and Bi5O7I–001. (a) Survey, (b) Bi 4f, (c) O1s, and (d) I3d.
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Figure 5. (a) DRS spectra and (b) plots of (ahv)1/2 vs photon energy (hv) of Bi5O7I–100 and Bi5O7I–001.
UV-Vis diffuse reflectance spectra (DRS) revealed different absorption edges for Bi5O7I–100 and Bi5O7I–001 of about 422 and 410 nm, respectively (Figure 5a).53,54 Based on the plots of (ahv)1/2 vs photon energy (hv), the band gap energies (Eg) of Bi5O7I–100 and Bi5O7I–001 were calculated to be 2.78, and 2.88 eV, respectively. These data are in good agreement with our previous theoretically calculated results.51
Figure 6. Photocatalytic activities of Bi5O7I–100 and Bi5O7I–001 for RhB degradation upon 300 W Xe lamp irradiation.
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Figure 7. Photocatalytic NH3 (a) and NO3- (b) generation rates of Bi5O7I–100 (a) and Bi5O7I–001 under 300 W Xe lamp irradiation; (c) cyclic experiment over Bi5O7I–100 and Bi5O7I–001 with 100 min per cycle.
The activity of photocatalysts can be easily evaluated by photocatalytic dye degradation. As shown in Figure 6, Bi5O7I–001 displays a higher photocatalytic activity than Bi5O7I–100 for RhB degradation upon 300 W Xe lamp irradiation. After 120 min irradiation of Bi5O7I–001 and Bi5O7I– 100, about 67% and 29% RhB, respectively, has been removed. Obviously, Bi5O7I cannot be used for efficient environmental remediation, which may be due to its non-layered crystal structure. In comparison with other layered bismuth-based photocatalysts, Bi5O7I exhibits a lower separation efficiency of photo-induced carriers. Therefore, the photocatalytic N2 fixation of Bi5O7I was performed with 20% CH3OH as sacrifice reagent. Photocatalytic N2 fixation is a novel application of photocatalysis. It has been reported that bismuth oxyhalides, diamond, g-C3N4, and TiO2 have been used for photocatalytic N2 fixation (Table S1).10–18,37 Figure 7 demonstrates the photocatalytic activities of Bi5O7I–100 and Bi5O7I–001 for N2 fixation. Without light irradiation (dark control) and in the absence of N2 gas without pholocatalyst (light control), 11 ACS Paragon Plus Environment
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neither NH3 nor NO3– has been detected. Bi5O7I–001 shows a higher photocatalytic NH3 generation rate (111.5 μmol L–1 h–1) than Bi5O7I–100 (47.6 μmol L–1 h–1). And the turnover frequency (TOF) was calculated as 49.23 h-1 and 21.02 h-1 for Bi5O7I-100 and Bi5O7I-001, respectively. Figure 7b implies that NO3– was not the main product of the photocatalytic N2 fixation over Bi5O7I. Our photocatalytic N2 fixation system is oxygen-free condition. It indicated that O2•− cannot generate from the e- in CB of photocatalyst. And in our previous works, it has been revealed that the •OH cannot be generated from the h+ in VB of Bi5O7I.51 Therefore, there no reactive oxygen species (ROS) to react with N2 to generate NO3-. So, it reveals that less than 0.26 μmol L–1 h–1 of NO3– was photocatalytically detected for Bi5O7I–001. Recently, I have found that N2H4 and H2 were reported as reduction products from Bi-O-X photocatalysts.50 We also have detected N2H4 and H2 using para-(dimethylamino) benzaldehyde and gas chromatography, respectively. However, no N2H4 and H2 were detected. The apparent quantum efficiency (AQE) was calculated for a precise quantification of the photocatalytic N2 fixation activity. This revealed that the AQE of Bi5O7I–001 (5.1%) was about 2.2 times larger than that of Bi5O7I–100 (2.3%) upon irradiation with 365 nm monochromatic light. Figure 7c displays the cyclic experiment over Bi5O7I–100 and Bi5O7I–001. After five cycles (100 min per cycle), the photocatalytic NH3 generation rate of Bi5O7I–001 decreased slightly about 2% from 195.2 to 191.8 μmol L–1. The photocatalytic NH3 generation rate of Bi5O7I–100 decreased about 5% from 85.2 to 81.1 μmol L–1 (Figure 7c). On the other hand, after catalysis, the XRD patterns of Bi5O7I–100 and Bi5O7I–001 did not change. They imply that Bi5O7I–001 as well as Bi5O7I–100 possess good stabilities for photocatalytic N2 fixation.
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Figure 8. Mott–Schottky plots of Bi5O7I–100 (a) and Bi5O7I–001 (b) Bi5O7I electrodes in an aqueous solution of Na2SO4 (0.1 M) with frequencies of 1000 and 2000 Hz; (c) valence band XPS spectra of Bi5O7I–100 and Bi5O7I–001; and (d) band diagram of Bi5O7I–100 and Bi5O7I–001.
In order to analyse the photocatalytic reduction power of Bi5O7I with different degrees of exposed facets, the band gaps (Eg), conduction band (CB), and valence band (VB) positions of Bi5O7I–100 and Bi5O7I–001 were examined. Figure 8 shows the Mott–Schottky (MS) plots of Bi5O7I–001 (Figure 8a) and Bi5O7I–100 (Figure 8b) electrodes at frequencies of 1000 and 2000 Hz. The flat band potentials of Bi5O7I–001 and Bi5O7I–100 were –0.54 and –0.63 V, respectively, versus the Ag/AgCl electrode, which corresponds to –0.32 and –0.41 V versus the normal hydrogen electrode (NHE).55,56 Figure 8c shows the VB-XPS spectra of Bi5O7I–001 and Bi5O7I–100. It reveal that the energy gap between Fermi level (Evf) and valence band were 2.34 and 1.75 V for Bi5O7I–100 and Bi5O7I–001, respectively.57 It has been reported that the flat band potential of n-type semiconductor equals the Fermi level.57–59 So, VB positions could be calculated for Bi5O7I– 100 and Bi5O7I–001 to be 1.93 and 1.43 V, respectively. The CB positions of Bi5O7I–100 and Bi5O7I–001 were calculated based on the band gaps to be –0.85 and –1.45 V, respectively. It can 13 ACS Paragon Plus Environment
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be seen that the CB positions of Bi5O7I samples are higher than E0(N2/NH3 = -0.28 V vs NHE).60 It indicates that Bi5O7I can reduce N2 to NH3 based on thermodynamics. Figure 8d shows the band diagrams of Bi5O7I–100 and Bi5O7I–001. Negative CB positions are correlated with a high reduction power, which indicates that Bi5O7I–001 has a higher reduction activity for N2 fixation than Bi5O7I–100.
Figure 9. (a) Photocurrent response spectra and (b) EIS of Bi5O7I–100 and Bi5O7I–001.
As we known that the photoactivity of semiconductor is usually affected by the photo-induced carrier separation efficiency. For comparing the photoactivity of Bi5O7I–100 and Bi5O7I–001, electrochemical impedance spectra (EIS) and photocurrent response spectra are shown in Figure
9. They reveal a much higher photocurrent for Bi5O7I–001 upon irradiation than for Bi5O7I–100 (Figure 9a). Furthermore, Bi5O7I–001 exhibited a semicircle arc with a smaller diameter than Bi5O7I–100 (Figure 9b), which indicates that Bi5O7I–001 has a lower resistance value for electrontransfer. So, the separation efficiency and mobility of the photo-induced carriers of Bi5O7I was
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effectively improved after exposure of {001} facets.61 Finally, Bi5O7I–001 shows a higher activity for N2 fixation than Bi5O7I–100.
Conclusions In this work, two samples of Bi5O7I nanosheets with {100} or {001} facets exposure were synthesized via molecular precursor hydrolysis and calcination, respectively. They were characterized by XRD, BET, FESEM, TEM, HRTEM, FFT, and XPS. Photocatalytic results revealed that Bi5O7I–001 has a higher activity than Bi5O7I–100 for N2 fixation and dye degradation. Upon irradiation with 365 nm monochromatic light, the AQE of Bi5O7I–001 (5.1%) was about 2.2 times larger than that of Bi5O7I–100 (2.3%). DRS, MS, and VB-XPS displayed the more negative CB position of Bi5O7I–001 with a higher reduction power. Photoelectrochemical data proved the higher efficiency of Bi5O7I–001 for photo-induced carrier separation. These results revealed that the photocatalytic performance depends on the exposure of the {001} facets. This finding expands the occurrence of the facet effect from Bi-O-X (X = Cl, Br, I) to bismuth-rich Bi–O–X photocatalysts.
Experimental Section Synthesis Complex precursor: The complex precursor was prepared according to our previously reported procedure.42,46 Bi5O7I–100: The 0.5 g precursor was dispersed in 100 mL deionized (DI) water with pH = 9. Then, by a simple hydrolytic process, Bi5O7I–100 was obtained. Finally, Bi5O7I–100 was dried at 80 °C and subjected to a thermal treatment for 3 h at 400 °C.
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Bi5O7I–001: The complex precursor (0.5 g) was calcinated directly at 400 °C for 3 h. Then, Bi5O7I– 001 was obtained. Photocatalytic N2 Fixation Photocatalytic N2 fixation was carried out in a sealed reactor. In the first step, 0.05 g photocatalyst was added in 100 mL DI water containing 20% CH3OH as sacrifice reagent. In the second step, the reaction system was sealed and to remove the air thorough vacuum treated. In the third step, N2 gas was injected into the reactor to build up pressure of 1 atm. After above preparation, a 300 W high-pressure xenon lamp (PLS-SXE300, Beijing Perfectlight Technology Co., Ltd., China. Wavelength range: 280 nm-800 nm; Power density on their solution: 2.36 W/cm2) was used as light source, and the reaction temperature was maintained at 20 °C using a low-temperature thermostat bath (DC–0506, Shanghai Sunny Hengping Scientific Instrument Co., Ltd., China). Every 20 min, 5 mL solution was taken out from the reaction to detect NH3 by UV-Vis spectrometry using Nessler's reagent as a chromogenic agent at 420 nm. The apparent quantum efficiency (AQE) was measured with the same reaction conditions, except that 365 nm monochromatic light (300 W high-pressure xenon lamp and 365 nm band filter) was used as incident light. The NH3 yields were measured after 1 h irradiation, and the AQE was calculated as the following equation: AQE (%) = (number of reacted electrons/number of incident photons) × 100% This equation is based on the following main reaction: N2 + 2H2O + 6H+ + 6e– = 2NH3•H2O (E0(N2/NH3) = –0.276 V vs NHE) 60
AQE =
N 6 × the number of evolved NH molecules = × 100% N
the number of incident photons
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=
6 × N# × M %&'( )*
where Na is Avogadro's constant; MNH3 is the mole number of generated NH3; P is the optical density; S is the light irradiation area; t is the light irradiation time; λ is wavelength of monochromatic light; h is the Planck’s constant; and c is the speed of light.
Acknowledgments This work was supported by Open Fund (PLN201615) of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University), National Natural Science Foundation of China (No. 51502146, U1404506), Natural Science Foundation of Henan Department of Science & Technology (No. 142102210477), Natural Science Foundation of Henan Department of Education (No. 14A150021), Natural Science Foundation of Nanyang Normal University (No. ZX2014039), Scientific Research Starting Project of SWPU (No.2015QHZ001), and Young Scholars Development Fund of SWPU (No.201499010100).
ASSOCIATED CONTENT Supporting Information Available: [xxxxx] This material is available free of charge via the Internet at http://pubs.acs.org.
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TOC
Bi5O7I nanosheets samples with {100} or {001} facets exposure were synthesized via molecular precursor hydrolysis and calcination, respectively. Bi5O7I-001 had higher activity than Bi5O7I-100 for N2 fixation.
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