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Mechanism of enhancing visible-light photocatalytic activity of BiVO4 via hybridization of graphene based on a first-principles study

The interface properties of the hybrid graphene/BiVO4(001) heterojunction were investigated by first-principle calculations incorporating semiempirical dispersion-correction schemes to correctly describe van der Waals interactions. The results indicate that graphene and BiVO4 are in contact and form a stable heterojunction. After equilibration of the graphene/BiVO4 interface, their energy levels are adjusted with the shift of their Fermi levels based on calculated work functions. In addition, electrons in the upper valence band of BiVO4 can be excited to the conduction band under irradiation, and then arrive at the C pz orbital of graphene, in which the electrons cannot migrate back to BiVO4 and thus are trapped in graphene. Thus, substantial holes are accumulated in the BiVO4(001) surface, facilitating the separation of photogenerated e−/h+ pairs. The calculated charge density difference unravels that the charge redistribution drives the interlayer charge transfer from graphene to the BiVO4(001) surface. It is identified that the hybridization between the two components induces an increase of optical absorption of BiVO4 in the visible-light region. A deep understanding of the microcosmic mechanisms of interface interaction and charge transfer in this system would be helpful for fabricating BiVO4-based heterojunction photocatalysts.


Introduction
Bismuth vanadate (BiVO 4 ) is one of the most promising photocatalytic materials for O 2 evolution from water-splitting, and the degradation of organics under visible-light irradiation. 1,2 It is well known that BiVO 4 has three main crystalline phases: scheelite-monoclinic (sm-BiVO 4 ), scheelite-tetragonal (st-BiVO 4 ) and zircon-tetragonal (zt-BiVO 4 ). 1 Among them, sm-BiVO 4 with a band gap of 2.4 eV and a valence band (VB) edge at approximately 2.5 V vs. NHE is the most common phase under ambient conditions and exhibits the highest photocatalytic activity under visible-light irradiation. [3][4][5][6] Various successful modications have been made to improve the photocatalytic and photoelectrochemical activity of BiVO 4 using the following techniques: controlling morphologies, 7-9 doping, 10,11 and coupling with metal oxide semiconductors 12,13 or carbon materials. 14 Among the above mentioned strategies, coupling with a different semiconductor or metal to match their energy levels is an effective method to separate charges using internal polarization and charged surfaces, but the importance of these phenomena in BiVO 4 have not yet been fully explored. 15,16 In the reported systems of heterostructured photocatalysts, it is accepted that interface properties of heterojunctions are critical for determining the nal photocatalytic activity of the systems. [17][18][19] Interface properties can be attributed to two important aspects: one is the lattice match between the two components, which is the prerequisite for fabricating heterojunctions; the other is the suitable conduction band (CB) and/or VB levels, considered to be the prime and fundamental requirement for charge transfer and separation in heterostructured interfaces. It is well known that graphene is an electron collector and transporter, and may be used to boost the performance of various energy conversion and storage devices, 20,21 or to be a dispersible carrier for catalysts. 22 The uniqueness of this two-dimensional crystal, i.e., high carrier mobility, make it a dopant with the purpose of manipulating the electronic structure of BiVO 4 , and thus facilitates the enhancement of the carrier mobility, namely, metal-like electroconductivity.
The graphene/BiVO 4 systems successfully prepared via a onestep hydrothermal method without the use of any surfactants show superior photoactivity in the degradation of MB, RhB, MO and active black BLG under visible-light irradiation. 14 Considering the large specic surface area, the combination of BiVO 4 and graphene effectively inhibits the aggregation of these nanoparticles and consequently gives rise to a higher photocatalytic performance. 14,23 It is noted that sm-BiVO 4 nanoplates (space group: I2/b) with exposed (001) facets exhibit greatly enhanced photocatalytic activity 9,24,25 and the rate of oxygen evolution increases with the area of the (001) surface under visible-light irradiation. 24 A higher dri velocity of carriers in the (001) direction would bring more of the majority carrier to the (001) surface and promote reduction. 25 However, compared with the progress in experimental fabrication of graphene/BiVO 4 (001) heterojunctions, its underlying characteristics of the interaction from a theoretical point of view are still far from being explained. Thus, complementary to previous experimental results, in this work, much effort was made to study the basic mechanisms of interface interaction, charge transfer and separation, and optical properties through density functional theory (DFT) calculations. We nally present a coherent picture of the interface properties, which provides a necessary reference for further optimizing the performance of heterojunctions.

Calculation methods
All calculations were performed using the ultraso pseudopotentials (USP) with the exchange and correlation in the Perdew-Burke-Ernzerhof (PBE) 26 and Ceperley-Alder (CA) 27 formalisms of density functional theory as implemented in the CASTEP code. In USP calculations, a pragmatic method to correctly describe van der Waals (vdW) interactions resulting from dynamical correlations between uctuating charge distributions was taken by the Grimme method. 28 And a hybrid semiempirical solution from Ortmann, Bechstedt and Schmidt (OBS) was also given to introduce damped atom pair wise dispersion corrections of the form C 6 R 6À in the DFT formalism. 29 The total energy (E total ) is represented as: where E KS-DFT is the conventional Kohn-Sham DFT energy and E vdW is the dispersion correction. The semiempirical approach provides the best compromise between the cost of rstprinciples evaluation of the dispersion terms and the need to improve non-bonding interactions in the standard DFT description. The valence atomic congurations are 6s 2 6p 3 for Bi, 3s 2 3p 6 3d 3 4s 2 for V, 2s 2 2p 4 for O, and 2s 2 2p 2 for C, respectively. A cutoff energy of 450 eV and a Monkhorst-Pack k-mesh of 3 Â 8 Â 2 are used. 30 All calculations with the denser meshes ensure that the results are fully converged. Geometry optimizations were done before single point energy calculation, and the self-consistent convergence accuracy was set at 2 Â 10 À6 eV per atom. The convergence criterion for the maximal force on atoms is 0.03 eVÅ À1 . The maximum displacement is 2 Â 10 À4Å , and the stress is less than 0.03 GPa.

Structural stability
Before exploring the properties of the graphene/BiVO 4 heterojunction, we rst investigated the crystal structures of single-layer graphene, bulk BiVO 4 , and the BiVO 4 (001) surface. Our optimized lattice parameters for graphene (a ¼ b ¼ 2.458Å, a ¼ 90.013 ) and bulk BiVO 4 (space group: I2/b, a ¼ 5.182Å, b ¼ 5.139Å, c ¼ 11.757Å, a ¼ 89.876 ) are in agreement with experimental values. 31 It is worthwhile to mention that the I/2b space group can be converted to C2/c. 15 Since both I2/b and C2/c space groups, which have different unit cell choices and crystallographic axes, are commonly used to describe the scheelitemonoclinic structure of BiVO 4 , it is necessary to clarify the space group used when referring to specic atomic planes or crystal directions as well as the hkl indices of X-ray diffraction peaks in order to prevent any possible confusion. In fact, it can be inferred clearly that the (001) surface for the I2/b space group is equivalent to the (010) surface for the C2/c space group. 15 Depending on where the surface is sliced, there are two different structures of the BiVO 4 (001) surface with the same number of surface dangling bonds (1 Â 1 slab with four dangling bonds), as shown in Fig. 1a. It is well known that the number of ionic layers and the width of vacuum space play crucial roles in the accuracy of the calculations of the atomic relaxation and the electronic properties. A vacuum layer of 10Å is used to isolate the slab as the boundary condition, which according to other previous work, is good enough to make interactions between neighbouring slabs negligible. Dependence of surface energies on slab thickness presents an oscillating odd-even behavior, as shown in Fig. 1b. The surface energies of slabs with an odd number of layers (model 2) are higher because they have an additional symmetry plane at the slab center, so the atomic displacements on both sides of the slab are mirrored and tend to reinforce each other. It is found that the slabs of the BiVO 4 (001) surface with an even number of layers (model 1) are energetically more favorable than those with an odd number of layers within the GGA-PBE or LDA-CA formalism. Thus, it can be inferred from Fig. 1 that the ideal 1 Â 1 slab of the BiVO 4 (001) surface exposes two 2-fold undercoordinated O atoms, a 6-fold undercoordinated Bi atom and a fully 4-fold coordinated V atom. Comparing with our nal value of surface energy, the surface energies of the 6-layer slab only result in an error of À4.5%. So the model of the 6-layer slab is sufficient to present the geometry structure and electronic properties of the BiVO 4 (001) surface.
To further examine the interaction between graphene and BiVO 4 (001), based on the TEM and SEM result of graphene/ BiVO 4 heterojunctions, 32 the graphene/BiVO 4 (001) interface is modeled by using a supercell slab, in which the geometry structure contains parallel graphene and BiVO 4 (001) sheets. A 2 Â 5 (following the conventional denition of the zigzag/ armchair nanoribbon) graphene layer containing 40 carbon atoms was chosen as the substrate to support a 1 Â 4 BiVO 4 (001) surface containing 8Bi, 8V and 32O atoms, as shown in Fig. 2. The whole system contained 88 atoms with 496 valence electrons. The mismatch of initial lattice parameters between the optimized graphene and BiVO 4 (001) sheets is only 1.6% using the Grimme scheme and 1.8% using the OBS scheme, which are larger than that of the graphene@MoSe 2 interface 33 and slightly smaller than that of the graphene@diamond interface. 34 In subsequent work, the Grimme schemes are taken to deal with the vdW interactions in the graphene/BiVO 4 (001) interface.
To investigate the thermodynamic stability of the graphene/ BiVO 4 (001) heterojunction, the interface adhesion energy was obtained according to the following equation: [33][34][35] where E(hetero), E(graphene) and E(BiVO 4 (001)) represent the total energies of the relaxed graphene/BiVO 4 (001) heterojunction, pure graphene, and the pure BiVO 4 (001) sheet, respectively. The calculated interface adhesion energy of the graphene/BiVO 4 (001) heterojunction is À16.02 eV (À0.151 eV A À2 ), which indicates that the interface is stable. In fact, the interface cohesive energies of the graphene/BiVO 4 (001) heterojunction contain a lattice mismatch energy, DE mismatch , and other interactions (vdW force) between graphene and the BiVO 4 (001) surface. Here, the lattice mismatch energy, DE mismatch , of the graphene/BiVO 4 (001) interface from the strain-driven interaction can be estimated as follows: where E(BiVO 4 (001)) a 0 and E(graphene) a 0 are the total energies of the isolated BiVO 4 (001) sheet and isolated graphene with the equilibrium lattice constant a 0 of the graphene/BiVO 4 (001) interface, respectively. E(BiVO 4 (001)) a1 and E(graphene) a2 represent the total energies of the isolated BiVO 4 (001) sheet and graphene aer all free geometry relaxation, respectively. Our calculated lattice mismatch energy is about À11.37 eV, so the vdW interaction is no more than 4.65 eV (0.044 eVÅ À2 ). Aer geometric optimization, it is also found that the equilibrium distance between the top of the BiVO 4 (001) surface and graphene layer is about 2.99Å, which is very similar to the results observed for graphene/g-C 3 N 4 heterojunctions (3.1Å). 35 It is nicely matched to the traditional vdW interaction distance, which is a typical vdW equilibrium spacing. [33][34][35] There is no obvious distortion aer geometry optimization, and the shortest distances between the C and Bi/O are 3.034 and 4.019Å, respectively. It should be noted that when graphene adsorbs onto the BiVO 4 (001) surface, only physical adsorption occurs; no chemical adsorption is observed. The close but nondestructive contact between graphene and the BiVO 4 (001) surface may be a unique characteristic for applications as photocatalysts and in solar cells.

Electronic structure
To understand the effect of the orbital hybridization on electronic structure of the interface, we calculated the energy band structures of the graphene/BiVO 4 (001) heterojunction using the GGA-PBE method. For the purposes of comparison, the energy bands of isolated graphene, bulk BiVO 4 and the BiVO 4 (001) surface were also calculated. The energy band structures, drawn along high symmetry lines of the Brillouin zone, are shown in Fig. 3. The calculated results show that the graphene is a gapless semiconductor, the (bonding) p bands and (antibonding) p* bands cross only at the corners of the hexagonal Brillouin zone of the system, the so-called K points. A direct band gap of 2.17 eV for bulk BiVO 4 is 0.23 eV smaller than the experimental value previously reported by Li et al., 5 due to the well-known limitation in DFT calculations. However, it is noted that the band gap of the BiVO 4 (001) sheet was calculated to be 2.52 eV, which is very close to the experimental measurement of 2.54 eV using UV-vis absorbance spectroscopy for BiVO 4 (001) nanoplates. 9 For the graphene/BiVO 4 (001) interface, it is found that by comparing Fig. 3a and c, the energy band structures can almost be divided into two groups (from the BiVO 4 (001) layer or from graphene), due to the weak vdW force between interlayers. This phenomenon is similar to that previously reported by Du et al. for a g-C 3 N 4 /graphene heterobilayer, 35 in which the energy bands near the Fermi level can almost be divided into two groups (from g-C 3 N 4 or from graphene) as a result of the relatively weak interlayer coupling. It is noted that the typical conical structures of the p and p* bands of graphene in the vicinity of the Fermi level are split into double parts (two lines), which is different from those of the isolated graphene. In the graphene/BiVO 4 (001) interface with the equilibrium interlayer distance d ¼ 2.99Å, it can be seen that the p and p* linear dispersion bands separate from each other near the Fermi level at the K point, forming a small band gap of 0.14 eV, as shown in Fig. 3d. Thus, graphene adsorbed on the BiVO 4 (001) surface is no longer a metallic material with massless electrons, but a semiconductor with a direct narrow fundamental band gap. Unfortunately, for the BiVO 4 -graphene system, the band gap energy is difficult to estimate experimentally from the UV-vis diffuse reectance spectra data. 14 Furthermore, we calculated their density of states (DOS) and corresponding partial density of states (PDOS) with the equilibrium interlayer distance d ¼ 2.99Å between À15 eV and 10 eV, as shown in Fig. 4a. For BiVO 4 , the VB is composed of hybrid orbitals of Bi 6s and O 2p, whereas the CB is composed of V 3d orbitals. 36 For the graphene/BiVO 4 (001) heterojunction, the new VB maximum and CB minimum are mainly contributed to by the p z orbital of the C atoms in the graphene layer. It is noted that the O 2p and V 3d states of the BiVO 4 (001) layer in the interface extend so that they are neighbouring the Fermi level from the two directions of the VB and CB. Thus, the hybridization between the BiVO 4 (001) surface and graphene results in a serious decrease of the band gap of BiVO 4 in the interface. And the charge transfer is supposed to take place from Bi 6s and O 2p hybrid orbitals to V 3d orbitals upon photoexcitation. As a consequence of this, the introduced states neighbouring the Fermi level greatly enhance the carrier mobility, thus promoting the separation of photogenerated e À /h + pairs.
To further investigate the charge transfer between the BiVO 4 (001) surface and graphene, the charge density difference was investigated and Milliken analysis was performed to reveal the interlayer charge transfer between graphene and BiVO 4 . The charge density difference, r graphene/BiVO 4 (001) ¼ r graphene + r BiVO 4 (001) , can be obtained by subtracting the electronic charge of the graphene/BiVO 4 (001) interface from that of the corresponding isolated graphene and BiVO 4 (001) surfaces. Fig. 4b and c clearly show that the charge density is redistributed by forming electron-rich and hole-rich regions within the graphene/BiVO 4 (001) interface. Through Milliken analysis, there is an average charge transfer of 0.04|e| from every top Bi atom to graphene when graphene adsorbs on the BiVO 4 (001) surface. In the meantime, the charge transfer of 0.02|e| happens from graphene to every top O atom. This fact implies that the inhomogeneous onsite energy between the interlayers is induced not only by the inhomogeneous charge redistribution between the interlayers caused by graphene, but also by the charge transfer between the BiVO 4 (001) surface and graphene. As a consequence, the hybridization between graphene and the BiVO 4 (001) surface disrupts the degeneracy of the p and p* bands of graphene at the K point, resulting in its semiconducting character.

Band edge potentials
To investigate the energy level match between the two components for charge transfer and separation in the heterostructured interface, the band edge energies of the CB and VB of BiVO 4 were estimated from the absolute electronegativity of the atoms and the band gap as follows: 37,38  where c(A), c(B), and c(C) are the absolute electronegativities of atoms A, B and C, respectively; E C , E V and E g are the band edge energies of the CB and VB and the band gap of semiconductor, respectively; E 0 is the scale factor relating the reference electrode redox level to the absolute vacuum scale (AVS) (E 0 ¼ À4.5 eV for normal hydrogen electrode (NHE)). The average electronegativity, c ¼ (c(A) a + c(B) b + c(C) c ) 1/(a+b+c) , of BiVO 4 is 6.04. According to eqn (4) and (5), the CB and VB edge potentials of BiVO 4 are about 0.34 and 2.74 V vs. NHE at pH ¼ pH ZPC (corresponding to that in aqueous solution, the net adsorbed charge of the sample obtained in an electrolyte is zero) with a band gap of 2.4 eV, respectively. It is close to the experimental measurement (0.31 V) carried out using MB solution as a probe material with an initial concentration of 2 mmol dm À3 . 39 The work function of a material is a critical parameter commonly used as an intrinsic reference for band alignment. Here, the work function is calculated and the corresponding energy level lineup diagrams for BiVO 4 and graphene before and aer equilibrium are plotted, as shown in Fig. 5. The work function is dened as follows: 40 where E vac is the energy of a stationary electron in the vacuum near the surface. E F is the Fermi level. The calculated electrostatic potentials for graphene, the BiVO 4 (001) sheet, and the graphene/BiVO 4 (001) interface are demonstrated in Fig. 5a-c. The calculated work function of BiVO 4 (6.68 eV) is larger than that of graphene (4.5 eV). Along with the formation of the graphene/BiVO 4 contact, the electrons in graphene with a low work function ow into BiVO 4 with a high work function, which thereby levels up the potential energy surface at the interface and eventually builds up an n-type-like Schottky barrier ($0.96 V, see Fig. 5d). As a result, the work function of the graphene/BiVO 4 heterojunction is 5.72 eV. It can be inferred that the BiVO 4 layer will accumulate negative charges. In the meantime, the graphene layer will gather positive charges. This result is in great agreement with the charge density difference and Mulliken charge analysis.
As an n-type photocatalyst, the good hole conductivity of BiVO 4 is highly favorable for hole transfer, which is critical for both photocatalytic and photoanodic water oxidation. 15,41 The Fermi level of BiVO 4 is located under the CB and is slightly more positive than that of graphene. Aer equilibration of the graphene/BiVO 4 (001) interface, the Fermi levels shi in the negative direction for BiVO 4 and the positive direction for graphene, respectively, until they are equal. At this time, the CB and VB of BiVO 4 are pulled in the negative direction a little, and then form a slightly downward band bending close to the interface between BiVO 4 and graphene. It is reasonable to say that under visible-light irradiation, the electrons receiving photon energy in the BiVO 4 layer transit from the VB to the CB, then continuously ow into graphene via a percolation mechanism, 42 through which the electrons in graphene cannot migrate back to BiVO 4 and thus are trapped in graphene. The n-type-like Schottky junction thus boosts the ow of electrons from BiVO 4 to graphene and leaves holes in BiVO 4 , facilitating the separation of photogenerated carriers. 43 In effect, these electrons on the surface of graphene sheets can be captured easily by the adsorbed O 2 molecules to produce superoxide radical anions, cO 2 À , because the standard redox potential of O 2 /cO 2 À (À0.28 V vs. NHE) is more negative than the CB potential of graphene in the interface. 44 In this case, the VB potential (1.77 V vs. NHE) of the BiVO 4 layer is less positive than the standard redox potential of cOH/OH À (1.99 V vs. NHE), indicating that the photogenerated holes in the VB of the BiVO 4 layer could not oxidize OH À into cOH free radicals with a very strong oxidation capacity. Of course, the VB edge is more positive than the redox potential of RhB (1.43 V). 45 This ascertains, for example, that in the system, direct photogenerated hole oxidation is energetically possible and will photodegrade RhB. 46,47 So the superoxide radical anions, cO 2 À , and photogenerated holes are responsible for the degradation of RhB.

Optical absorption
To examine the effect of graphene combination on the photocatalytic efficiency of BiVO 4 , the optical spectra were investigated by calculating the imaginary part of the complex dielectric function using the GGA-PBE method. It is well known that the allowed transitions are determined by the nonzero matrix elements of the position operator. Here, the optical calculations are achieved using plane polarization with the specied polarization direction where the E eld vector is parallel to the x, y or z axes (marked as Ekx, Eky, Ekz) and the "polycrystalline" polarization where the E eld vector is an isotropic average over all directions. In the optical spectra analysis, a small smearing of 0.2 eV is used to greatly distinguish the absorption peaks. Fig. 6 shows the polycrystalline and polarized optical absorption coefficient spectra of the isolated BiVO 4 layer and graphene/BiVO 4 interface. For the isolated BiVO 4 layer, in the polarization direction of Ekx and Eky, it is noted that the optical properties are almost the same prominent peaks between 500 and 550 nm, while a different curve is obtained along the polarization direction of Ekz, as shown in Fig. 6c, which indicates that the BiVO 4 layer has strong optical anisotropy. The similarity of the absorption coefficient spectra under Ekx and Eky is certainly reasonable since the symmetry of the absorption coefficient spectra corresponds to the symmetry of the lattice structure in the plane directions. In fact, the previous results show clearly that the absorption edge of pure BiVO 4 , corresponding to the largest wavelength, is about 520 nm, which indicates that BiVO 4 is a visible-light semiconductor photocatalyst. 3,47 However, the absorption intensity of pure BiVO 4 is so weak in the visible-light region that the optical absorption isn't enough to contribute to the high photocatalytic activity of BiVO 4 .
It can be seen from the polycrystalline curve of the optical absorption coefficient spectra of the graphene/BiVO 4 (001) heterojunction in Fig. 6a that the absorption edges extend to more than 950 nm. In addition, Fig. 6b shows that the absorption coefficient spectra of the graphene/BiVO 4 (001) heterojunction have certain anisotropy in the long wavelength region. By analyzing Fig. 6b, it is found that the two prominent peaks (I and II) in Fig. 6a are mainly contributed to by the absorption coefficient spectra under Ekx and Eky. It is noteworthy that peak I at 610 nm is mainly contributed to by the effect of the graphene layer on the BiVO 4 (001) surface, namely, the inhomogeneous charge redistribution between interlayers caused by graphene. Further, it is noted that the absorption coefficient spectrum under Ekx has much stronger signals than those under Eky and Ekz in the visible-light region, which is attributed to a delocalized electron transition, and is not related to the crystal structure. It is inferred that peak II at 440 nm corresponds to a phototransition energy of about 2.82 eV, from the top of the VB to V 3d levels in the CB of the BiVO 4 layer, or Bi 6s and O 2p levels in the VB of the BiVO 4 layer to the bottom of the CB. Compared with the results for pure BiVO 4 , the absorption intensity of the graphene/BiVO 4 (001) heterojunction increases a lot in the visible-light region due to the large distribution of C 2p states near the new bottom of the CB and the new top of the VB. In fact, Fu et al. also reported that the UV-vis diffuse reectance spectra of pure BiVO 4 and BiVO 4 -graphene photocatalysts show that there is no signicant absorption in the region of 520-850 nm for pure BiVO 4 , while the absorption of BiVO 4 -graphene is much stronger than that of pure BiVO 4 particles covering the whole visible-light region due to the presence of graphene. 14 It is reasonable to consider that the hybridization between BiVO 4 layers and graphene induces an increase in the optical absorption range and intensity of BiVO 4 in the visible-light region, 14,23,47 and thus their visible-light absorption is enough to contribute to the high photocatalytic activity of heterostructured systems.

Conclusions
The microscopic mechanisms of interface interactions, charge transfer and separation, as well as their inuence on the photocatalytic activity of graphene/BiVO 4 (001) heterojunctions have been studied by rst-principles calculations incorporating semiempirical dispersion-correction schemes to correctly describe vdW interactions. The mismatch of initial lattice parameters between the optimized graphene and BiVO 4 (001) layers is only 1.6-1.8%, and the results indicate that the BiVO 4 (001) surface and graphene are in contact and form a vdW heterostructured interface. By analyzing the energy level based on our calculated work function between the two components, it can be found aer equilibration of the graphene/BiVO 4 (001) interface that the electrons receiving photon energy in the BiVO 4 (001) layer continuously ow into the C p z orbital of graphene under visible-light irradiation, in which the electrons cannot migrate back to BiVO 4 and thus are trapped in graphene, facilitating the separation of photogenerated carriers. It is further indicated that the hybridization between the two components induces an increase of optical absorption of BiVO 4 in the visible-light region. In short, the incorporation of graphene into BiVO 4 facilitates the separation of photogenerated e À /h + pairs and the enhancement of visible-light absorption. The present investigation is useful in the wider development of new BiVO 4 -based heterojunction photocatalysts.