Muamer Kadic
email: muamer.kadic@femto-st.fr

Changguo

Qingxiang Ji

Zhiming Xue

Zaoxu Zhang

Zhanbo Cui

Changguo Wang
email: wangcg@hit.edu.cn

Interlayer Torsional Sliding and Strain Localization in Bilayer Graphene

Keywords: Computational mechanics, Computational physics, Materials science Twisted bilayer graphene, Van der Waals interaction, Torsional deformation, Strain localization

Twisted bilayer graphene can demonstrate extraordinary optical and electrical characteristics due to its interlayer interactions. The strong coupling of normal and tangential van der Waals interactions at the interface results in inhomogeneous interlayer deformations and further changes the bilayer graphene's physical properties. Herein, theoretical and numerical models are established to study the torsional deformation behavior of twisting a graphene flake over a rigid graphene substrate. It is found that in-plane deformations have significant influences on the interlayer potential energy density of AA stacking, but seldom affect other stacked domains. The deformation process is thus approximated by first twisting the graphene flake rigidly, and then relaxing the rigid constraints. The bilayer graphene system minimizes its energy by reducing (enlarging) the size of highenergy (low-energy) domains through additional rotations. The additional angles of the graphene flake are derived analytically based on a mechanical model following the principle of minimum potential energy. Results show that the influences of graphene film deformations get significant at small-twistangles (typically less than 2 • ). This work reveals the torsional deformation evolution mechanism of bilayer graphene and provides beneficial guidance on achieving intriguing physical properties.

Introduction

Graphene has recently drawn increasing attention for their extraordinary properties in hyper elasticity [START_REF] Kumar | On the hyperelastic softening and elastic instabilities in graphene[END_REF][START_REF] Wang | Super-elasticity and deformation mechanism of three-dimensional pillared graphene network structures[END_REF], piezoelectricity [START_REF] Wu | Tuning electromechanics of dynamic ripple pattern in graphene monolayer[END_REF][START_REF] Zhong | Graphene-piezoelectric material heterostructure for harvesting energy from water flow[END_REF], frictional characteristics [START_REF] Li | Micromechanics of friction: effects of nanometre-scale roughness[END_REF][START_REF] Zheng | Robust ultra-low-friction state of graphene via moiré superlattice confinement[END_REF][START_REF] Sun | Anisotropic vacancy-defect-induced fracture strength loss of graphene[END_REF], optical properties [START_REF] Ooi | Nonlinear graphene plasmonics[END_REF][START_REF] Zinenko | Terahertz range resonances of metasurface formed by double-layer grating of microsize graphene strips inside dielectric slab[END_REF][START_REF] Farhat | Exciting graphene surface plasmon polaritons through light and sound interplay[END_REF][START_REF] Alaee | A perfect absorber made of a graphene microribbon metamaterial[END_REF][START_REF] Amin | An ultra-broadband multilayered graphene absorber[END_REF][START_REF] Christensen | Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons[END_REF] and so on. In particular, bilayer structures or van der Waals materials that feature more tunability in physical characteristics are formed by stacking graphene on top of one another. Twisted bilayer graphene (TBG) with a specific twist angle (magic-angle) can demonstrate intriguing properties, i.e., insulator characteristics, superconductivity and anomalous quantum hall effect [START_REF] Andrei | Graphene bilayers with a twist[END_REF][START_REF] Cao | Unconventional superconductivity in magic-angle graphene superlattices[END_REF][START_REF] Cao | Correlated insulator behaviour at half-filling in magic-angle graphene superlattices[END_REF][START_REF] Zhang | Abnormal conductivity in low-angle twisted bilayer graphene[END_REF]. Indeed, the twisting of graphene layers will lead to direction mismatch and result in a periodic Moiré pattern, which significantly changes electronic structures, transport, disorder and interactions of the TBG system [START_REF] Andrei | Graphene bilayers with a twist[END_REF][START_REF] Nimbalkar | Opportunities and challenges in twisted bilayer graphene: a review[END_REF]. Due to the unique structure of graphene lattices, the twist angle becomes a key controlled degree of freedom to regulate electronic and optical properties of TBGs [START_REF] Cao | Tunable correlated states and spin-polarized phases in twisted bilayer-bilayer graphene[END_REF][START_REF] Santos | Graphene bilayer with a twist: electronic structure[END_REF]. It is important to fully understand the torsional behavior of TBGs with variance of the twist angle. In some ways, graphene posses many extraordinary properties like metamaterials which are an alternative way to stucture the matter at bigger scale with the quest of properties beyond those of the constituents [START_REF] Christensen | Vibrant times for mechanical metamaterials[END_REF][START_REF] Kadic | Hall-effect sign-inversion in a realizable 3d metamaterial[END_REF][START_REF] Kern | Experimental evidence for sign reversal of the hall coefficient in three-dimensional metamaterials[END_REF][START_REF] Chen | Light-weight shell-lattice metamaterials for mechanical shock absorption[END_REF][START_REF] Kadic | 3d metamaterials[END_REF]. Recently, elastic metamaterials took a similar direction based on quasi-crystals [START_REF] Chen | Isotropic chiral acoustic phonons in 3d quasicrystalline metamaterials[END_REF] and higher order interactions [START_REF] Chen | Roton-like acoustical dispersion relations in 3d metamaterials[END_REF][START_REF] Iglesias Martínez | Experimental observation of roton-like dispersion relations in metamaterials[END_REF][START_REF] Wang | Nonlocal interaction engineering of 2d roton-like dispersion relations in acoustic and mechanical metamaterials[END_REF].

So far, researchers have mostly focused on TBG's rigid twisting behavior without considering any deformations. However, the interlayer van de Waals forces will inevitably result in both inplane and out-of-plane deformations. These slight deformations can further change the electronic bands of the TBG system, i.e., the deformations require that the TBG reduces AA stacked domains and increases AB stacked domains. Alden et al. [START_REF] Alden | Strain solitons and topological defects in bilayer graphene[END_REF] found that AB stacking is the dominated manner in Moiré pattern. Zhang et al. [START_REF] Zhang | Structural and electron diffraction scaling of twisted graphene bilayers[END_REF] revealed local rotating and shrinking mechanism of the AA stacked domains in twisted graphene films: the local rotation angle is first invariant (then linear-correlated) with the interlayer twist angle, as the latter is within (beyond) the critical value. Kazmierczak et al. [START_REF] Kazmierczak | Strain fields in twisted bilayer graphene[END_REF] experimentally demonstrated the nanoscale deformation of TBG and found that relative stacking order domains varied differently as the interlayer twist angle reached 0.5 • .

Though the influences of deformations on TBG's physical properties are explored, the deformation evolution mechanism and strain characteristics still remain unclear. In this work we have studied the scaling law of interlayer potential energy density (IED) during the rigid twisting process. The deformation and strain characteristics of the graphene film is then presented considering released rigid constraints. We establish the strain potential energy function of deformed graphene films, and theoretically analyze the evolution mechanism of both in-plane and out-of-plane deformations following the principle of minimum potential energy. This work is of great significance in understanding the deformation mechanism of TBG and achieving more intriguing phenomenon.

Numerical study on torsional sliding of bilayer graphene

We have built a numerical model of TBG, where the graphene substrate is defined as a rigid that generates interlayer interaction without any deformation. In case of rigid twisting, Moiré pattern diameter λ, namely the distance between nearby AA stacked points, can be determined by [START_REF] Hermann | Periodic overlayers and moiré patterns: theoretical studies of geometric properties[END_REF]

λ = √ 3a 2sin( θ 2 ) (2.1)
where θ is the twist angle and a = 0.142 nm denotes carbon-carbon bond length of the graphene lattices. It is observed from Fig. 1a that λ decreases first sharply and then slowly with the increment of θ, which indicates that the structural size should be large enough so that relative small twist angles can result in Moiré pattern. In addition, we define shell element size as 0.2 nm. A circular-shaped graphene model is employed to suppress the edge effects, and all degrees of freedom are constrained for the substrate graphene (see the insets in Fig. 1b). We plot the IED as a function of relative displacement along y-axis, where interlayer energy density was normalized as U N = [U (ux, uy, uz) -U 0 (uz = 0)] /U 1 (uz = 0). Initially, the graphene film is in AA stacking order relative to the substrate, which corresponds to the minimum interlayer potential energy state. AB stacking switches to AA stacking in case of film gliding distance a and further switches to BA stacking with the film gliding distance 2a. Due to geometrical symmetry, AB stacking and BA stacking corresponds to the same potential energy state. For simplicity, we name the two modes both as AB stacking. Note that the interlayer potential energy of Saddle Point (SP) stacking is larger than AB stacking but far less than AA stacking. The TBG demonstrates extraordinary physical properties, i.e., insulator behavior and superconductivity, mainly at its initial twisted stage [START_REF] Cao | Unconventional superconductivity in magic-angle graphene superlattices[END_REF][START_REF] Cao | Correlated insulator behaviour at half-filling in magic-angle graphene superlattices[END_REF][START_REF] Kazmierczak | Strain fields in twisted bilayer graphene[END_REF]. Therefore, we focus on the deformation behavior of the TBG with small twist angles. In Fig. 2 we show at different twist angles the out-of-plane displacement uz, IED, Strain energy density (SED), distortion energy density (DED) and effective shear strain ε i . It is observed that AA stacked domains first appear in the edges and gradually evolves to the inner domain. The distribution of out-of-plane displacement uz agrees well with those of IED, corresponding to maximum interlayer potential energy state. The stripes that connect different AA stacked domains are SP stacked domains. Amplitudes of uz and IED are invariant with the increment of twist angles, as shown in Fig. 3. By contrast, shear strain and SED in SP stacked domains decrease gradually as the twist angle increases. Indeed, the maximum strain is about 0.1% as the twist angle reaches 2 • , demonstrating that the strain energy is negligible and the twisting behavior tends to be a rigid one. Besides, the in-plane strain disappears when the twist angle reaches 60 • , indicating that the film relative to the substrate recovers to AB stacking order. We should note that the deformation and strain are significant in case of small twist angles (smaller than 2 • ), which will result in structural variations of the lattices and further lead to different physical properties.

We define quantitatively the AA (SP) stacked domain in Fig. 4, and plot the geometrical diameters as functions of the twist angle. For rigid twisting, we have

d AA = a θ , w SP = a 2θ . (2.2)
It is observed in Fig. 4 that the deformations have few influences on the Moiré pattern diameter λ, but significantly reduces the AA stacking diameter and SP stacking width, especially at smalltwist-angles. Besides, local AB stacked domain turns around by a small angle, which is indicated by the difference between the dotted line and red points in Fig. 4e. Generally, AA stacking point is not affected by the deformations, and can be modeled as rigid rotation during the bilayer graphene twisting process. We define a triangular unit cell characterized by three AA stacking points and show the variations of AA/AB/SP stacking domains within each unit cell in Fig. 4f. With the increment of twist angles, SP (AB) stacking domains increase (decrease) linearly until the twist angle reaches around 0.75 • , then both the SP and AB stacking domains decrease by a rate far less than their initial variation rates. AA stacking domain increases with the twist angles, but the increasing rate drops a bit when the twist angle goes beyond 0.75 • .

Theoretical analysis on deformation characteristics of twisted bilayer graphene (a) Rigid twisting behavior of the graphene film

For a rigid twisted graphene film with constrained normal displacement uz, the relative displacement field can be expressed as

     ux = r[cos(θ 0 + θ) -cos(θ 0 )] uy = r[sin(θ 0 + θ) -sin(θ 0 )], uz = 0 . (3.1)
where θ 0 (θ) is the angle between x-axis and the direction of the point before (after) twisting, as shown in Fig. 5a. The mean IED can be expressed as

U Iave = R 0 2π 0 U (ux, uy, uz)rdrdθ 0 πR 2 , (3.2)
where R is the radius of the graphene film and U (ux, uy, uz) is the interlayer potential energy (per unit area) determined by [START_REF] Kumar | Elastic deformations in 2d van der waals heterostructures and their impact on optoelectronic properties: predictions from a multiscale computational approach[END_REF][START_REF] Kumar | Limits of coherency and strain transfer in flexible 2d van der waals heterostructures: formation of strain solitons and interlayer debonding[END_REF] U (ux, uy, uz) = U 0 (Uz) + U 1 (Uz) f (ux, uy).

(3.3)
On the right-hand side of Eq. (3.3), the first term describes the dependence of the interaction potential energy on the normal separation uz in a commensurate AB stacking order ux = uy = 0 and takes the form [START_REF] Zhang | Energy and moiré patterns in 2d bilayers in translation and rotation: A study using an efficient discrete-continuum interlayer potential[END_REF] U

0 (Uz) = ε 0 A 0 - 5 3
z 0 z 0 + uz 4 + 2 3
z 0 z 0 + uz 10 . (3.4)
where z 0 = 0.334 nm is the equilibrium separation, ε 0 = 0.0411 eV, A 0 = 3 √ 3 4 a 2 with a = 0.142 nm denotes the carbon-carbon bond length in the graphene. The adhesion energy for the commensurate AB stacking order is thus obtained as ε 0 /A 0 = 0.25 J/m 2 . The second term on the right-hand side quantifies the periodic corrugation of the potential energy with respect to in-plane displacements ux and uy, from the commensurate stacking with

f (ux, uy) = 3 2 + cos(G 1 (uy -a)) + 2 cos G 1 (uy -a) 2 cos √ 3G 1 ux 2 , (3.5)
and

U 1 (Uz) = ε 1 A 0 - z 0 z 0 + uz 4 + β z 0 z 0 + uz 10 . (3.6)
where G 1 = 1.33π/a, ε 1 = 1.33 × 10 -4 eV, β = 28.7; the values of ε 1 and β are obtained by fitting to atomistic calculations [START_REF] Xue | Peeling and sliding of graphene nanoribbons with periodic van der waals interactions[END_REF].

The mean IED value U Iave increases gradually to its maximum value as the twist angle reaches the critical value θcr, as shown in Fig. 5b. Note that initially the graphene film is in AB stacking order relative to the substrate, and corresponding IED is ε 0 /A 0 = 0.25J/m 2 . Here we define the state when the film is completely stripped from the substrate as zero point of the potential energy density. After the twist angle reaches its critical value, the mean value U Iave decreases gradually to its minimum value and then fluctuates around a constant value -U 0 (uz = 0) + U 1 (uz = 0)f (ux = uy = 0). Besides, the oscillation period is reversely related to the film radius. In Fig. 5 we plot the critical twist angle θcr and first oscillation period θ λ as functions of the radius of the graphene film disk. Now we turn to analyze the underlying mechanism that results in the oscillation behavior. We study the unit cell shown in Fig. 6a and find that the relative displacement field meets following constraint:

√ 3λ 3 - √ 3λ 6 √ 3 3 ( √ 3λ 3 -x) √ 3 3 (x- √ 3λ
3 )

f (ux, uy) -

3 2 dydx = 0. (3.7)
If we fix the out-of-plane displacements during the twisting process as uz = c, we can obtain following relationship for any twist angle θ:

√ 3λ 3 - √ 3λ 6 √ 3 3 ( √ 3λ 3 -x) √ 3 3 (x- √ 3λ
3 )

U (ux(θ), uy(θ))dydx

A 0 = U 0 (c) + 3 2 U 1 (c). (3.8)
where the Moiré pattern diameter is λ = √ 3a/ 2(1 -cos(θ)), the unit cell area is

A 0 = √ 3
4 λ 2 denotes interlayer potential energy and the in-plane displacements are expressed by

   ux(θ) = x 2 + y 2 cos(tan -1 ( y x ) + θ) -cos(tan -1 ( y x )) uy(θ) = x 2 + y 2 sin(tan -1 ( y x ) + θ) -sin(tan -1 ( y x )) . (3.9)
We observe from Eq. (3.9) that the mean interlayer potential energy of a unit cell is invariant with the twist angle, indicating that the oscillation behavior is induced by edge effects. In the initial twisting stage of the graphene film, the deformations result in a drop of interlayer potential energy and a rise of strain energy, which makes the total energy smaller than that of the rigid counterpart. As the strain increases, the strain energy gradually decreases, and the total energy difference between the deformed twisting behavior and rigid twisting behavior was reduced correspondingly.

(b) Deformable twisting behavior of the graphene film

We show in Fig. 7 the Interlayer potential energy density of a graphene in rigid twisting (IEDr) and in deformable twisting (IED d ) and the difference between the two terms (∆ IED ), in case of the twist angle θ = 0.6 • and the displacement uz = 0. It is observed that in-plane deformations have significant influences on the IED of AA stacked domains, but have few influences on AB stacked domains and SP stacked domains. Besides, in-plane deformations (shear deformations) mainly exist in SP stacked domains. The film strain distributes uniformly in SP stacked domains with quasi-rectangular shapes, which denotes that displacements of contrary directions are generated on the edges of such quasi-rectangular shapes and results in uniformly distributed shear strain. Note that the IED of SP stacked domains are less than that of AA stacked domains. Then we can describe the deformation behavior in following ways: we first conduct rigid twisting by a twist angle θ, then releases the rigid constraints; AA stacked domains continue to twist in the same direction by an angle α while AB stacked domains twist in the opposite direction by an angle β.

The work done by AB stacked domains to overcome the interlayer reactions is expressed by

W AB (θ) = √ 3λ 6 - √ 3λ 12 √ 3 3 ( √ 3λ 6 -x) √ 3 3 (x- √ 3λ 6 ) [U (ux(θ), uy(θ)) -U (ux = uy = 0)] dydx ≈ U 1 λ 2 5 . ( 3
W AB (θ -β) = √ 3λ 6 - √ 3λ 12 √ 3 3 ( √ 3λ 6 -x) √ 3 3 (x- √ 3λ
6 )

[U (ux(θ -β), uy(θ -β)) -U (ux = uy = 0)] dydx. (3.11) The work can be approximated by

W AB (θ -β) ≈ U 1 λ 2 5 (k 2 -2k + 1). (3.12)
where

k = 1 -β/θ, U 1 (uz) = (β -1)ε 1 /A 0 , λ = √ 3a/ 2(1 -cos(θ)).
In the interval k ∈ [0, 1] the approximated solution and accurate solution from Eq. (3.11) show good agreement, as depicted in Fig. 8a.

As mentioned before, the film deformation are mainly shear deformations existing in the SP stacked domains, as shown in Fig. 7d. We can obtain the shear strain of a unit cell as

W S = 3t(λ -2R A )w P Gγ 2 2 . (3.13)
where the coefficient "3" is applied due to the fact that three SP stacked domains exist in each unit cell, t is the film thickness, G is the shear modulus, w P is half-width of SP stacked domains, γ the shear strain energy of SP stacked domains determined by

γ = ∂uy ∂x + ∂ux ∂y = β + α √ 3 2 r λ 2 - √ 3 2 r = α θ θ + 2α + 1 . (3.14)
Note that film strain energy in AB stacked domains is far less than that in SP stacked domains. Therefore, we safely ignore the deformations in AB stacked domains and view them as rigid twisting. From geometrical compatibility, we have

a 2 sin(θ + α) α = a 2 sin(θ -α) β. (3.15)
As α and β are small, Eq. (3.15) can be simplified as

β = θα θ + 2α . (3.16)
Then we have

W P = a 4 sin(θ + β) ≈ a 4(θ + β) ; (3.17)
R A = a 2 sin(θ + α) ≈ a 2(θ + α) . (3.18)
Substituting Eqs. (3.14) (3.18) into Eq. (3.13), we can express the shear strain energy of a unit cell as

W S = 3Gta 8 λ - a θ + α (θ + 2α)α 2 θ 2 + 3θα θ θ + 2α + 1 2 . (3.19)
Now we turn to the interlayer potential energy of AA stacked domains. For a graphene film/substrate system in AA stacking order, the interlayer potential energy is

U AA = U 0 + U 1 3 2 + cos(G 1 uy) + 2 cos G 1 uy 2 cos √ 3G 1 ux 2 , (3.20)
The work needed to twist a graphene film disk by an angle θ is expressed as If we increase the twist angle to θ + α, the stored energy becomes

W θ = r 0 √ r 2 -x 2 - √ r 2 -x 2 [U AA (ux(θ), uy(θ)) -U AA (ux = uy = 0)] dydx ≈ - √ 3 + 1 2 U 1 π a 2θ 2 . ( 3
W θ+α = r 0 √ r 2 -x 2 - √ r 2 -x 2 [U AA (ux(θ + α), uy(θ + α)) -U AA (ux = uy = 0)] dydx, (3.22)
which can be approximated by

W θ+α ≈ √ 3 + 1 2 U 1 π a 2θ 2 √ 3 + 1 4 α 2 θ 2 - 2α θ -1 . (3.23)
In the case α/θ < 2, the approximated solution and accurate solution from Eq. (3.22) are in good agreement, as shown in Fig. 8b. For the studied unit cell, the total energy variations induced by film deformations can be obtained by

U relaxed = W S + (W AB (θ -β) -W AB (θ)) + 1 2 (W θ+α -W θ ) . (3.24)
Combining Eq. (3.8), we obtain the total energy of a unit cell of the twisted graphene film as U relaxed + U 0 + 3U 1 /2. Using minimum energy principle, we get

∂ ∂α (U relaxed + U 0 + 3U 1 /2) = 0. ( 3
3Gta 8 λ + a (θ + α) 2 (θ + 2α)α 2 θ 2 + 3θα θ θ + 2α + 1 2 + U 1 λ 2 5 2β θ 2 θ 2 (θ + 2α) 2 + 3Gta 8 λ - a θ + α 2αθ 3 + 9α 2 θ 2 + 12α 3 θ (θ 2 + 3αθ) 2 2α θ θ + 2α + 1 2 - 3Gta 8 λ - a θ + α (θ + 2α)α 2 θ 2 + 3αθ 2 θ θ + 2α + 1 2θ (θ + 2α) 2 - √ 3 + 1 4 U 1 π a 2θ 2 2 θ - √ 3 + 1 2 α θ 2 = 0 (3.26)
Given a twist angle θ, we can obtain the additional twist angle α of AA stacked domains from Eq. (3.26), and further get the additional twist angle β of AB stacked domains from Eq. (3.15), and finally obtain SP stacked domain width w P and AA stacked domain radius R A from Eq. (3.17) and Eq. (3.18), respectively. We observe in Fig. 9a the relation α/θ < 1.5, β/θ < 0.5 during the small-angle-twisting process, indicating that the approximated solutions from Eq. (3.12) and Eq. (3.23) are valid. Besides, the theoretical predictions agree well with the finite element analysis when the twist angle reaches 0.75 • , demonstrating the accuracy of our proposed analytical model. When the twist angle is beyond 2 • , the influences of graphene film deformations can be neglected and the bilayer graphene can be viewed as rigid twisting. However, we notice some differences between theoretical results and simulations when the twist angle is very small. This difference may imply different deformation mechanism, which will be our further consideration.

Conclusion

The torsional deformation behavior and strain localization of TBG has been studied numerically and analytically. It is found that the periodicity and symmetry of interlayer van der Waals force makes the mean strain energy density invariant during the rigid twisting process. Both in-plane and out-of-plane deformations are observed after releasing the rigid twisting constraints, due to the strong coupling of in-plane and out-of-plane displacements. Out-of-plane deformations agree well with the IED distributions, and have invariant amplitudes with increasing twist angles. Compared with rigid twisting, the in-plane deformations are mainly observed in the inner domain of the unit cells, while the shapes and sizes of the edges are invariant. Following this phenomenon, we derived the total strain potential energy function of the deformable system, and further obtained the film deformations as functions of the twist angles. Results show that the shear strain distributes uniformly in SP stacked domains and decreases sharply with the increment of twist angles. The influences of graphene film deformations is significant when the twist angle is less than 2 • .

Figure 1 .

 1 Figure 1. (a) Schematic of Moiré Pattern and its periode λ function of the twist angle for TBG films (as inset, an example is depicted); (b) interlayer potential energy density is depicted as a function of relative displacements uy/a.

  rspa.royalsocietypublishing.org Proc R Soc A 0000000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 21 )

 21 rspa.royalsocietypublishing.org Proc R Soc A 0000000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 25 )

 25 Substituting Eqs. (3.4) (3.6) (3.24) into Eq. (3.25), we can obtain the relation between α and θ as

Figure 2 .

 2 Figure 2. (a, b, c) Out-of-plane displacements component uz, (d, e, f) IED, (g, h, i) SED, (j, k, l) DED, and (m, n, o) equivalent strain distribution at different twist angles 0.3 • , 0.5 • , and 1 • , respectively.

  rspa.royalsocietypublishing.org Proc R Soc A 0000000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3 .

 3 Figure 3. (a) The out-of-plane displacement uz, (c) IED, and (e) the distribution of SED as the twist angle θ = 0.5 • ; (b, d, f) the corresponding maximum value as functions of the twist angle.

Figure 4 .

 4 Figure 4. (a) Schematic of different stacking domains; functions of the twist angle for: (b) the size of moiré pattern, (c) the AA stacking diameter, (d) the width of SP stacking, (e) the twist angle of AB stacking and (f) relative stacking order domains.

Figure 5 .

 5 Figure 5. (a) Schematic of relative displacements; (b) the IED as a function of twist angles; (c) the critical twist angle and (d) the first oscillation period as functions of the graphene disk diameter.

Figure 6 .

 6 Figure 6. (a) Contour of the IED for rigid twisting bilayer graphene; (b) the energy densities as a function of twist angles for a graphene disk with diameter of 50 nm.

Figure 7 .

 7 Figure 7. The IED of (a) rigid twisting and (b) deformable twisting; (c) the difference of IED between rigid and deformable twisting; (d) SED of the graphene film. All the results are considered for the twist angle θ = 0.6 • and the displacement uz = 0.

Figure 8 .

 8 Figure 8. The interlayer potential energy of (a) AB stacked domain and (b) AA stacked domain as functions of additional twist angles.

  rspa.royalsocietypublishing.org Proc R Soc A 0000000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  .10) rspa.royalsocietypublishing.org Proc R Soc A 0000000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Similarly, the work done by AB stacked domains to turn back by an angle β is expressed by

Acknowledgements. Z.M.X. thanks Dr. Rui Huang at the University of Texas at Austin for many valuable discussions.

Funding. This work was supported by the National Natural Science foundation of China [grant numbers 12172102, 11872160].

Data Accessibility. This article does not contain any additional data. Authors' Contributions. Q.X.J: Formal analysis, Writing original draft, Investigation and Project administration. Z.M.X.: Conceptualization, Formal analysis, Editing. Z.X.Z: Formal analysis. Z.B.C.: Methodology, Data curation. M.K.: Supervision, Validation, Review and editing. C.G.W.: Supervision, Validation, Project administration, Review and editing.

Competing Interests. We declare we have no competing interests.


S Barlemont

G Colas

P-H Cornuault

P Laffont

R Daudin

A Lenain

PERFORMANCE ET FIABILITE DES ALLIAGES METALLIQUES AMORPHES BASE CU-ZR POUR DES APPLICATIONS TRIBOLOGIQUES

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Performance et fiabilité des alliages métalliques amorphes base Cu-ZR pour des applications tribologiques

INTRODUCTION

Les alliages métalliques amorphes (AMA) sont des alliages métalliques de composition complexe fabriqués par un processus de refroidissement rapide depuis l'état liquide, de manière à obtenir un matériau à l'état solide qui présente la structure d'un verre. Les AMA ont un fort potentiel d'applications industrielles en micromécanique en raison de leurs excellentes propriétés mécaniques [START_REF] Greer | Metallic Glasses… On the threshold[END_REF] (en particulier une limite élastique et une déformation élastique élevées), combinées à un très faible retrait et une excellente résistance à la corrosion. Un certain nombre d'études s'intéressent en particulier à la fabrication de micro-engrenages en AMA [START_REF] Inoue | Fabrication, properties and applications of bulk glassy alloys in late transition metal-based systems[END_REF]. Cependant, les domaines micromécaniques ciblés requièrent des considérations tribologiques, en raison du rôle important du frottement et de l'usure aux micro-échelles.

MATERIAUX ET METHODES

La présente étude vise à étudier les performances des AMA en matière de frottement et d'usure en vue d'applications industrielles futures dans le domaine des micro-mécanismes. Des AMA base Cu-Zr ont été choisis pour la combinaison de leur bonne formabilité (Glass Forming Ability, GFA) et de leurs bonnes propriétés mécaniques, en particulier leur ductilité. Diverses configurations expérimentales ont été exploitées afin d'explorer le comportement tribologique des AMA base Cu-Zr de manière représentative à l'échelle macroscopique. Tout d'abord, des configurations de glissement et de roulement ont été utilisées avec des conditions de contact variables. De plus, les conditions environnementales ont été prises en compte et plus particulièrement l'impact de l'humidité relative (RH). Enfin, des frotteurs de matériaux différents (laiton, bronze, aciers) ont été utilisés pendant les essais, afin d'analyser l'impact de la nature de la contreface et d'identifier les contre-matériaux prometteurs d'un point de vue tribologique.

Pendant les essais de frottement, le coefficient de frottement (COF) a été calculé en considérant l'énergie dissipée par cycle de frottement, et les volumes d'usure ont été mesurés après frottement sur les deux contrefaces à l'aide d'un microscope optique à focale variable. Une compréhension approfondie des mécanismes d'usure et des réactions tribochimiques a été élaborée par rugosimétrie 3D, microscopies optique et électronique à balayage (MEB), analyses EDS et XPS.

RESULTATS ET DISCUSSION

Les résultats mettent en évidence une grande répétabilité des essais de frottement réalisés avec les AMA, ainsi qu'une large gamme de COF et de taux d'usure qui dépendent fortement du contrematériau et des conditions de contact.

Contrairement à une majorité de matériaux (dont les métaux traditionnels et les céramiques), la dureté n'a pas un rôle prépondérant sur l'usure des AMA, comme le suppose la loi d'Archard. En revanche, cette étude montre un impact déterminant des réactions tribochimiques sur le comportement tribologique des AMA. Le COF et l'usure sont le résultat de phénomènes de transferts de matière, résultant en l'établissement d'un troisième corps dans le contact. La présente étude montre que ce transfert de matière est fortement dépendant du film d'oxydes natifs à la surface de l'AMA (majoritairement composé de ZrO2 et CuO), et des oxydes provenant de la contreface (par exemple le Fe2O3 pour une contreface en acier AISI 52100, ou le ZnO pour une contreface en laiton) (Figure 1a) [START_REF] Barlemont | Effect of the countermaterial on the tribological behavior of Cu45Zr46Al7Nb2 bulk metallic glass[END_REF]. Un second résultat majeur de cette étude concerne l'importance de l'humidité relative (RH) de l'air ambiant sur le contact tribologique [START_REF] Barlemont | Strong dependency of the tribological behavior of CuZr-based bulk metallic glasses on relative humidity in ambiant air[END_REF]. En effet, le COF diminue de 0,95 à 0,55 pour une RH passant de 20% à 80% lors d'essais de frottement de plaques en AMA contre des billes en acier AISI 52100 (Figure 1b). Cette dépendance à l'humidité s'explique par des changements de morphologie du 3 ème corps issu de la bille en acier par transfert de matière : en environnement sec, le 3 ème corps est rugueux et éparse, tandis qu'en environnement humide, le 3 ème corps est lisse et compact. La résistance à l'usure de l'AMA est ainsi améliorée lorsque RH est élevée.

Cette étude met donc en évidence la possibilité d'optimiser le comportement tribologique des AMA pour une application spécifique en fonction du matériau antagoniste et des conditions environnementales.

  Stoens, Guillaume Colas, Pierre-Henri Cornuault, Paul Laffont, Rémi Daudin, Alexis Lenain To cite this version: Solène Stoens, Guillaume Colas, Pierre-Henri Cornuault, Paul Laffont, Rémi Daudin, et al.. Performance et fiabilité des alliages métalliques amorphes base Cu-ZR pour des applications tribologiques. 34èmes Journées Internationales Francophones de Tribologie, May 2023, Villeneuve d'Ascq, France. hal-04233192

Figure 1 :

 1 Figure 1 : Taux d'usure et COF pour des essais de glissement bille-plan impliquant des plaques en AMA Cu45Zr46Al7Nb2 et des billes de différents matériaux (identifiés sur le graphe), avec indication de la composition du 3 ème corps dans la trace d'usure de la plaque (a). Evolution du COF en fonction de l'humidité relative de l'air ambiant pour différents AMA frottant contre des billes en AISI 52100 (b).


Siavash Bakhtiarnia

Saeed Sheibani
email: ssheibani@ut.ac.ir

Abbas Nadi

Eric Aubry

Hui Sun

Pascal Briois

Mohammad Arab Pour Yazdi

Keywords: Photocatalyst, BiVO 4, Cu doping, Thin film, Sputtering, Nanoporous

come

Preparation of sputter-deposited Cu-doped BiVO 4 nanoporous thin films comprised of amorphous/crystalline heterostructure as enhanced visible-light photocatalyst

Introduction

Water scarcity is a serious concern heavily affecting the world. Preserving precious water resources is of great importance. In recent years, photocatalysis as a sustainable solution has been proposed for wastewater treatment applications employing semiconductors with high photoactivity under solar light as an unlimited source of energy [START_REF] Rueda-Marquez | A critical review on application of photocatalysis for toxicity reduction of real wastewaters[END_REF]. A variety of semiconductor categories were employed and studied as photocatalysts such as nonmetallics (e.g. g-C 3 N 4 and black phosphorous), metal calcogenides (e.g. CdS and CdTe), metal oxides (e.g. TiO 2 , WO 3 and Cu 2 O), metal-organic and covalent organic frameworks known as MOFs and COFs, transition metal carbides and nitrides (e.g. Ti 3 C 2 T x ), and bismuth-based materials (e.g. BiVO 4 and Bi 2 WO 6 ) [START_REF] Feng | Surface Modification of 2D Photocatalysts for Solar Energy Conversion[END_REF][START_REF] Feng | A novel sulfur-assisted annealing method of g-C3N4 nanosheet compensates for the loss of light absorption with further promoted charge transfer for photocatalytic production of H2 and H2O2[END_REF]. TiO 2 is the most adopted semiconductor in the field [START_REF] Akhavan | Protein degradation and RNA efflux of viruses photocatalyzed by graphene-tungsten oxide composite under visible light irradiation[END_REF][START_REF] Ahadi | Characteristics and photocatalytic behavior of Fe and Cu doped TiO2 prepared by combined sol-gel and mechanical alloying[END_REF][START_REF] Montakhab | Modification and photocatalytic activity of open channel TiO2 nanotubes array synthesized by anodization process[END_REF], though many drawbacks, including the lack of photoactivity under visible light on account of its wide bandgap (~3.2 eV) [START_REF] Nakhate | Hydrothermally derived nanosized Ni-doped TiO2: A visible light driven photocatalyst for methylene blue degradation[END_REF], lead the researchers to try developing alternative photocatalysts capable of harnessing a wider range of the solar spectrum [START_REF] Wang | Photocatalytic activity of novel Ag4V2O7 photocatalyst under visible light irradiation[END_REF]. BiVO 4 with a ~2.4 eV bandgap concerning the monoclinic scheelite crystal structure, received lots of attention as a visible-light-active semiconductor, along with advantages such as cost-efficiency, stability, high photoactivity under visible light and versatility in forming various morphology [START_REF] Venkatesan | Nanostructured bismuth vanadate (BiVO4) thin films for efficient visible light photocatalysis[END_REF][START_REF] Bakhtiarnia | Enhanced photocatalytic activity of sputter-deposited nanoporous BiVO4 thin films by controlling film thickness[END_REF].

While BiVO 4 thin films have gained much interest as photoanodes for water-splitting applications [START_REF] Zhou | Enhanced photoelectrochemical water splitting using a cobalt-sulfide-decorated BiVO4 photoanode[END_REF][START_REF] Bai | Fabrication of Zn-MOF decorated BiVO4 photoanode for water splitting[END_REF], researchers showed a preference for the nanopowder form in photocatalysis due to some advantages namely facile synthesis, high specific surface and morphology control [START_REF] Fan | Highly selective deethylation of rhodamine B on TiO2 prepared in supercritical fluids[END_REF][START_REF] Abbad | Effect of silver doping on the photocatalytic activity of TiO2 nanopowders synthesized by the solgel route[END_REF], but their nanometric size is problematic for their recyclability and reusability in industrial wastewater treatment [START_REF] Valadez-Renteria | Flexible CuS/TiO2 based composites made with recycled bags and polystyrene for the efficient removal of the 4-CP pesticide from drinking water[END_REF][START_REF] Choi | Photocatalytic TiO2 films and membranes for the development of efficient wastewater treatment and reuse systems[END_REF]. Therefore, BiVO 4 thin-film photocatalysts enhanced with nanoporous morphology could be a great candidate to substitute nanopowder photocatalysts raising the cost efficiency of photocatalytic water treatment [START_REF] Bakhtiarnia | Deposition of nanoporous BiVO4 thin-film photocatalyst by reactive magnetron sputtering: Effect of total pressure and substrate[END_REF].

Despite the advantages, BiVO 4 suffers some flaws including charge carrier mobility, recombination and low specific surface [START_REF] Li | Hydrothermal synthesis and enhanced photocatalytic activity of hierarchical flower-like Fe-doped BiVO 4[END_REF][START_REF] Chen | Mo-Doped BiVO 4 Photoanodes Synthesized by Reactive Sputtering[END_REF][START_REF] Fakhravar | Excellent performance of a novel dual Zscheme Cu2S/Ag2S/BiVO4 heterostructure in metronidazole degradation in batch and continuous systems: Immobilization of catalytic particles on α-Al2O3 fiber[END_REF]. Certain solutions have been proposed to enhance the photoactivity of semiconductors. Our team has implemented Ag incorporation into pristine BiVO 4 thin films in previous research [START_REF] Bakhtiarnia | One-step preparation of Ag-incorporated BiVO4 thin films: plasmon-heterostructure effect in photocatalytic activity enhancement[END_REF], and the results were promising with a 99 % visiblelight photodegradation of RhB at neutral pH thanks to the charge separation of photogenerated electrons and holes due to BiVO 4 /Ag 4 V 2 O 7 heterostructure, as well as the plasmonic effect of Ag nanoparticles improving the light absorption. In another research [START_REF] Razi | Photocatalytic activity enhancement by composition control of mechano-thermally synthesized BiVO 4 -Cu 2 O nanocomposite[END_REF], BiVO 4 /Cu 2 O nanocomposite with the p-n junction structure was prepared by mechanochemical synthesis, and the photocatalytic results showed 97 % MB photodegradation. The heterojunction between BiVO 4

(n-type) and Cu 2 O (p-type) was proposed to be responsible for effective charge separation and reduction of recombination rate, as well as bandgap optimization (2.18 eV). Other solutions have also been explored, e.g., heterojunctions including p-n junction [START_REF] Xiang | Heterojunctions of β-AgVO3/BiVO4 composites for enhanced visible-light-driven photocatalytic antibacterial activity[END_REF] and z-scheme [START_REF] Ju | In-situ green topotactic synthesis of a novel Z-scheme Ag@AgVO3/BiVO4 heterostructure with highly enhanced visible-light photocatalytic activity[END_REF], plasmonic sensitization [START_REF] Zhao | Study the photocatalytic mechanism of the novel Ag/p-Ag2O/n-BiVO4 plasmonic photocatalyst for the simultaneous removal of BPA and chromium(VI)[END_REF], facet engineering [START_REF] Li | Spatial separation of photogenerated electrons and holes among {010} and {110} crystal facets of BiVO 4[END_REF] and the incorporation of transition metals [START_REF] Ge | Novel Pd/BiVO4 composite photocatalysts for efficient degradation of methyl orange under visible light irradiation[END_REF]. Cu incorporation is considered to be a suitable candidate thanks to being inexpensive compared to noble metals, nontoxicity, antimicrobial properties and acting as electron traps [START_REF] Razi | Photocatalytic activity enhancement by composition control of mechano-thermally synthesized BiVO 4 -Cu 2 O nanocomposite[END_REF][START_REF] Chen | Microwave assisted synthesis of sheet-like Cu/BiVO4 and its activities of various photocatalytic conditions[END_REF][START_REF] Regmi | Understanding the multifunctionality in Cu-doped BiVO4 semiconductor photocatalyst[END_REF]. The synthesis of BiVO 4 and metal incorporation both in powder or thin-film forms have been implemented by many methods such as hydrothermal [START_REF] Geng | Synthesis of Co doped BiVO4 with enhanced visiblelight photocatalytic activities[END_REF], electrodeposition [START_REF] Kong | Ni-Doped BiVO4 with V4+ Species and Oxygen Vacancies for Efficient Photoelectrochemical Water Splitting[END_REF], sol-gel [START_REF] Wang | Effective visible light-active nitrogen and samarium co-doped BiVO4 for the degradation of organic pollutants[END_REF] and high energy ball milling [START_REF] Razi | Photocatalytic activity enhancement by composition control of mechano-thermally synthesized BiVO 4 -Cu 2 O nanocomposite[END_REF], though vapor phase techniques did not receive proper attention. Few researchers selected the sputtering method to produce BiVO 4 thin films, and despite advantages like uniform products, versatility, scalable and affordable production [START_REF] Thalluri | Chemically induced porosity on BiVO4 films produced by double magnetron sputtering to enhance the photo-electrochemical response[END_REF], publications on Cuincorporated BiVO 4 using the sputtering technique are scarce in the literature [START_REF] Venkatesan | Nanostructured bismuth vanadate (BiVO4) thin films for efficient visible light photocatalysis[END_REF][START_REF] Ju | Structured BiVO4Photoanode Fabricated via Sputtering for Large Areas and Enhanced Photoelectrochemical Performance[END_REF].

This research aims to implement Cu incorporation into nanoporous BiVO 4 thin films employing reactive magnetron sputtering in a single step, which is unprecedented to the best of our knowledge. Further, to conduct a comparative analysis of the Cu content effect on the structural, microstructural and optical properties of the thin films through various characterization methods, as well as to investigate photocatalytic activity towards various dye pollutions at acidic, basic and neutral pH conditions. The mechanism of photodegradation using scavengers as the trapping agents of reactive species could help to have a deeper understanding of the Cuincorporated thin films' photocatalytic function, and the recyclability experiment could ensure the suitable stability of the thin films which is critical for industrial applications. The results of this research contribute to making industrial photocatalytic wastewater treatment more practical and efficient, thus preserving the precious and scarce water resources more effectively.

Experimental procedure

Thin film deposition

Reactive magnetron sputtering as an environment-friendly technique was employed to synthesize the Cu-incorporated BiVO 4 thin films. Metallic cylindrical targets of Bi, V and Cu (50

× 3 mm 2 )
were utilized with a purity of 99.9 at. %. A turbomolecular pump provided the necessary vacuum below 10 -4 Pa in the sputtering reactor (90 L cylinder, Alcatel) which utilizes four watercooled magnetron sputtering sources. The Ar and O 2 gas flow rates were controlled and measured using flowmeters (Brooks). The working pressure of the device was measured with a Baratron gauge (MKS). The discharge power was provided with a pulsed DC dual generator (Advanced Energy Pinnacle+) for Bi and V sources and a DC generator for Cu (Advanced Energy MDX 500).

Adjusting the discharge power applied on each target allows to control of the chemical composition of the films (see Fig. S1 of the supplementary file). The films were deposited at room temperature on single crystal Si and fused silica (76 × 26 × 1 mm 3 ) substrates, which were cleaned before deposition and attached to a rotating holder kept parallel to the cathodes at a 60 mm distance to preserve any microstructural lateral gradient [START_REF] Aubry | Microstructural and photocatalytic properties distribution of TiO2 coatings reactively sputtered as a function of the substrate position relatively to the Ti target[END_REF]. The thickness of the films was around 1 µm.

The films underwent a post-annealing treatment at 450 ℃ for 2 h in the air atmosphere to crystallize the samples. The deposition parameters are provided in Table . 1.

Characterization methods

XRD using a cobalt X-ray tube (Co Kα1 + α2 radiations λ α1 = 0.178897 nm and λ α2 = 0.179278 nm) was performed for crystallographic analysis (Bruker). The film's thickness was measured by a step method with an Altysurf Profilometer (Altisurf 500) manufactured by Altimet society.

Before each measurement, the calibration of the device was performed with a reference sample number 787569 accredited by the CETIM organization. Ultraviolet-visible-near infrared (UV-Vis-NIR) spectrophotometer (UV-3600, Shimadzu) equipped with an integration sphere (ISR-3100) was used for measuring the total reflectance and transmittance spectra of the thin films (220-2600 nm). A standard BaSO 4 reference was used for the baseline. The absorbance spectra were then calculated based on Eq. 1 [START_REF] Sarkar | Optical constants, dispersion energy parameters and dielectric properties of ultra-smooth nanocrystalline BiVO4 thin films prepared by rfmagnetron sputtering[END_REF]. Using the absorbance and Eq. 2 [START_REF] Sarkar | Optical constants, dispersion energy parameters and dielectric properties of ultra-smooth nanocrystalline BiVO4 thin films prepared by rfmagnetron sputtering[END_REF] the Tauc plots were illustrated to evaluate the bandgaps of the samples.

α λ = 1 t ln 1 -R λ T λ (Eq. 1) αhν . / = A hν -E 2 (Eq. 2)
Where α(λ) (cm -1 ), T(λ) (%) and R(λ) (%) are absorption, transmission and reflection, respectively, as a function of wavelength. t, A, h and ν represent the film thickness (cm), a constant, Planck constant and photon frequency, respectively. E g is the bandgap energy of the semiconductor and n depends on the direct (n = 0.5) or indirect (n = 2) nature of the bandgap. The direct bandgap nature of the BiVO 4 semiconductor was reported in the literature [START_REF] Walsh | Band Edge Electronic Structure of BiVO 4 : Elucidating the Role of the Bi s and V d Orbitals[END_REF].

The microscopic top surface and brittle-fracture cross-section observation of the carboncoated samples were implemented with FESEM (JEOL JSM-7800F). The chemical composition of the thin films was measured by Energy-Dispersive X-ray Spectroscopy (EDS, Bruker). Since the EDS method does not provide accuracy for oxygen, only the metallic elements were measured and the Cu contents reported in this work are the at. % ratio of Cu over Bi + V + Cu. TEM observations were also performed by JEOL JEM-2100 200 kV with 0.19 nm resolution equipped with EDS. Focused Ion Beam (FIB, Hitachi NX2000) was also employed in sample preparation stage. The interplanar spacings were calculated by the Fast Fourier Transform (FFT) method using high-resolution TEM (HR-TEM) images. Selected area electron diffraction (SAED) patterns were also provided to further analyze the crystallographic structure.

The chemical oxidation state of the elements on the surface was analyzed by X-ray photoelectron spectroscopy (XPS) using ESCALAB 250 Xi (Thermo Fisher) equipped with monochromatic Al Kα X-rays. The Shirley background was adjusted for the spectra and the Lorentzian -Gaussian function was employed as the spectral shape line in peak deconvolutions.

Valence band XPS (VB-XPS) was also employed to measure the valence band edge potential of the semiconductors. C 1s spectra of the samples were used for charge correction against the standard value of 284.8 eV and the carbon fermi level (0.3 V vs RHE) [START_REF] Guo | Experimental and DFT insights of the Zn-doping effects on the visible-light photocatalytic water splitting and dye decomposition over Zn-doped BiOBr photocatalysts[END_REF] is used as a reference for calculating band edge potentials. The photoluminescence (PL) spectra were measured using

Varian Cary Eclipse Fluorescence Spectrophotometer with an excitation wavelength of 270 nm.

Photocatalytic experiment

Photocatalytic activity of the Cu-incorporated thin films was assessed under visible light (Metal halide 400 W, λ > 400 nm) using RhB, MB and MO dye solutions (5 mg/L) as sources of organic pollutions at various pH (3, 7 and 10) in a water-cooled homemade setup. Hydrochloric acid and ammonia were used to adjust the pH, and the samples were fixed at a 15 cm distance from the light source. The thin films were immersed in the dye solution (photocatalyst surface over dye solution volume: 0.1 cm 2 /mL) 45 min before the illumination to ensure an adsorption-desorption equilibrium. Once the photocatalyst film was illuminated, 2 mL of the solution was collected every hour to measure the dye solution absorption using a UV-Vis spectrophotometer at the maximum wavelength of 464, 554 and 664 nm corresponding to MO, RhB and MB, respectively. The concentration was then calculated based on the Beer-Lambert law. The recycling experiment was implemented for evaluating the stability of the films in 3 × 7 h consecutive cycles. To identify the reactive species involved in the photocatalytic mechanism, ethylenediaminetetraacetic acid disodium salt (EDTA, 10 mM), p-benzoquinone (p-BQ, 2 mM), cupric nitrate (CN, 10 mM) and methanol (10 mM) were used as the trapping agents of the photogenerated hole (h + ), superoxide

( • O 2 ̅
), electron (e ̅ ) and hydroxyl radicals ( • OH), respectively. The kinetics of the photocatalytic processes involving low concentrations of organic dyes is well accepted to be correspondent with the pseudo-first-order model following Eq. 3 [START_REF] Kumar | Langmuir-Hinshelwood kinetics -A theoretical study[END_REF].

ln 3 4 3 = k′t (Eq. 3)
Where t is time (min), C 0 and C correspond to the initial concentration (g/L) and the concentration at t, respectively, as kʹ represents the rate constant (min -1 ).

Results and discussion

Structural and microstructural properties

According to the relatively high working pressure used in this study, the as-deposited thin films were amorphous, and therefore a post-annealing treatment for 2 h at 450 ℃ under air was necessary to crystallize the photoactive monoclinic BiVO 4 structure. The XRD pattern of the pristine sample provided in Fig. is between 500 and 550 ℃ [START_REF] Cao | Sol-gel synthesis and electrochemical properties of CuV2O6 cathode material[END_REF]. The crystallization of a 2 nd phase from 17 at. % Cu corresponding to BiCu 2 VO 6 (JCPDS No: 089-7016, space group: P2 1 /n) in small quantities also emerged. In the sample with 23 at. % Cu, the crystallization of the tetragonal BiVO 4 phase (t-BiVO 4 , JCPDS 14-0133, space group: I4 1 /amd) prevailed on the monoclinic structure. The effect of Cu on the BiVO 4 structure was already observed and reported in the literature [START_REF] Regmi | Understanding the multifunctionality in Cu-doped BiVO4 semiconductor photocatalyst[END_REF]. The introduction of dopants favors the stabilization of the tetragonal phase [START_REF] Jo | Phase transition-induced band edge engineering of BiVO 4 to split pure water under visible light[END_REF].

A finer observation of the XRD patterns reveals a slight and progressive decrease of the a and b cell parameters and almost constant c parameter by the increase of the Cu content in the film.

This would be the result of the Cu introduction in the monoclinic cell of BiVO 4 (in agreement with the lower radius of Cu compared to Bi and V atoms). The calculated cell parameters are provided in Table . S1. The relatively small amplitude of the deviation (less than 1 % at 17 at.% Cu) would also be explained by the limited solubility and the formation of an amorphous phase composed of Cu. The top surface FESEM observations of the samples along with the corresponding elemental mappings were provided in Fig. 3 to investigate the morphology of the thin films, as well as the distribution of the elements. The pristine BiVO 4 thin film shown in Fig. 3 (a) demonstrates a uniform surface with the presence of cracks, which tend to disappear in the Cu-incorporated thin films. The formation of these cracks was previously reported [START_REF] Bakhtiarnia | Deposition of nanoporous BiVO4 thin-film photocatalyst by reactive magnetron sputtering: Effect of total pressure and substrate[END_REF] as a result of the difference in the linear expansion coefficient of the film and the substrate coupled with the crystallization. Thus, Cu incorporation seems to decrease the crack density of the BiVO 4 thin films and mitigate the crack formation problem. In a higher magnification image shown in Fig. S2, nanometric black dots on the film surface could be seen, which represents a nanoporous morphology. These nanopores were caused by the presence of Bi as a low melting element. This phenomena was discussed in previous works [START_REF] Bakhtiarnia | Enhanced photocatalytic activity of sputter-deposited nanoporous BiVO4 thin films by controlling film thickness[END_REF][START_REF] Bakhtiarnia | Deposition of nanoporous BiVO4 thin-film photocatalyst by reactive magnetron sputtering: Effect of total pressure and substrate[END_REF]. The thin film with a 2 at. % Cu shown in Fig. 3 (b) depicts finer grain size compared to the pristine BiVO 4 sample. It also shows shard-like nodules on the surface based on Cu and V elements. The formation of the shards being clearly distinct from the BiVO 4 films would be related to a 2 nd amorphous phase as supposed from the analyses of XRD.

The shards on the sample with a 3 at. % Cu, shown in Fig. 3 (c), are smaller in size and more numerous on the film surface, while the BiVO 4 grains are coarser. The shards on the thin film with a 4 at. % Cu, demonstrated in Fig. 3 (d), seem to conform more to spherical shapes with a degree of porosity in the BiVO 4 phase (black holes). The sample with a 6 at. % Cu shown in Fig. 3 (e) demonstrates a uniform distribution of the Cu element, which also conforms to the FESEM and elemental mapping observations of the thin films with an 11 and 17 at. % Cu, shown in Fig. 3 (f) and (g). The thin film with a 23 at. % Cu depicted in Fig. 3 (h) appears to have a higher porosity and surface roughness compared to other samples with less Cu content. The shard-like nodules seem to disappear in the thin films with higher than 4 at. % Cu, which could be due to the increased deposition rate as the result of raising the discharge power of the Cu target, leaving less time for the coalescence of the sputtered atoms on the substrate to form shard-like nodules. In a higher magnification shown in Fig. S2, it is observable that the thin films enjoy a nanoporous morphology. The brittle fracture cross-section images shown in Fig. S2 demonstrate the thickness of the films to be in the range of 1 -1.2 µm. The chemical states of the film surfaces were investigated using the XPS method. The survey spectra of the samples are depicted in Fig. S3 showing the presence of Bi, V, Cu, O and C elements on the films' surfaces. The Cu 2p peaks in the spectra become more intense with the rise of Cu at. %. Fig. 4 (a) exhibits the Cu 2p core levels with peak values at around 933 and 953 eV corresponding to Cu 2p 3/2 and Cu 2p 1/2 , respectively. The peaks around 942 and 962 with the shakeup satellite structure were also observed in all the samples which is the characteristic of Cu 2+ [START_REF] Biesinger | Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Sc, Ti, V, Cu and Zn[END_REF][START_REF] Behjati | Photodegradation of dyes in batch and continuous reactors by Cu2O-CuO nano-photocatalyst on Cu foils prepared by chemicalthermal oxidation[END_REF]. Since the Cu 2p 3/2 peak in the samples with Cu is not unimodal, they could be deconvoluted to multiple components with the maximum at around 932, 934 and 935 eV corresponding to Cu + , Cu 2+ (oxide) and Cu 2+ (hydroxide) [START_REF] Biesinger | Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Sc, Ti, V, Cu and Zn[END_REF], respectively. The reproduced curve in the deconvolution process is shown in a dotted line. It could be concluded that all the samples are composed of Cu 2+ /Cu + species with a higher proportion of Cu 2+ . It is mentioned by Biesinger [START_REF] Biesinger | Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Sc, Ti, V, Cu and Zn[END_REF][START_REF] Biesinger | Advanced analysis of copper X-ray photoelectron spectra[END_REF] that the shape of the shake-up satellite structure could be used to qualitatively identify the Cu 2+ species. The shape of the shake-up structure corresponding to the sample with 23 at. % Cu conforms to that of oxide Cu 2+ which could be verified by the prominent peak at 934 eV. The shake-up structure of the samples with a 17 and 6 at. % Cu resembles that of hydroxide Cu +2 presented in the report. The peak intensity at 935 eV was also developed compared to the peak at 934 eV, which verifies that the share of the hydroxide Cu 2+ rose. It is noteworthy that the Cu 2+ proportion increases more than that of Cu + with the Cu introduction. It is also possible that Cu 0 species exist in the samples, but since its peak is very close to that of Cu + [START_REF] Biesinger | Advanced analysis of copper X-ray photoelectron spectra[END_REF], it is indistinguishable by the XPS technique, however its probability is very low due to the formation of the 2 nd phase based on Cu, V and O as observed by EDS. The Bi 4f core-level spectra are shown in Fig. 4 (b) with peaks at around 164.5 and 159.3 eV ascribed to Bi 4f 5/2 and Bi 4f 7/2 , respectively.

It shows the existence of the Bi 3+ oxidation state associated with the BiVO 4 structure. A slight peak shift to lower binding energies was observed in the Bi 4f spectra by the rise of Cu content. It has been suggested in the literature [START_REF] Sengar | Size and alloying induced shift in core and valence bands of Pd-Ag and Pd-Cu nanoparticles[END_REF] that the charge transfer and hybridization effect as a result of the penetration of the dopant elements into the crystal could cause a shift in the core level spectra, confirming the Cu introduction into the monoclinic BiVO 4 phase as observed from the XRD observations. V 2p 1/2 and V 2p 3/2 peaks at around 524.6 and 516.9 eV are demonstrated in Fig. 4 (c). It has been reported [START_REF] Wang | Effects of Cu dopants on the structures and photocatalytic performance of cocoon-like Cu-BiVO4 prepared via ethylene glycol solvothermal method[END_REF] that V 5+ and V 4+ could co-exist in the BiVO 4 structure, therefore V 2p 3/2 was deconvoluted to its component peaks at around 516.3 and 516.9-517.1 eV corresponding to V 4+ and V 5+ , respectively, which is in agreement with the literature [START_REF] Biesinger | Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Sc, Ti, V, Cu and Zn[END_REF][START_REF] Silversmit | Determination of the V2p XPS binding energies for different vanadium oxidation states (V5+ to V0+)[END_REF]. The O 1s peak corresponding to lattice oxygen at around 530 eV could be observed in Fig. 4 (d). A slight shift is seen in the O 1s spectra probably as a result of Cu incorporation as well. In some samples, a small shoulder at around 533 eV is also noticed which could be ascribed to adsorbed hydroxyl groups [START_REF] Landoulsi | Organic adlayer on inorganic materials: XPS analysis selectivity to cope with adventitious contamination[END_REF].

Optical properties

The absorbance spectra depicted in Fig. 7 (a) were calculated based on Eq. 1 using transmittance and reflectance spectra measured by UV-Vis spectrophotometry (see Fig. S4). The absorbance spectra show the absorption edge of the pristine BiVO 4 at around 490 nm, which agrees with the literature data [START_REF] Xue | An interesting Eu,F-codoped BiVO4 microsphere with enhanced photocatalytic performance[END_REF][START_REF] Khan | Sonochemical assisted hydrothermal synthesis of pseudo-flower shaped Bismuth vanadate (BiVO4) and their solar-driven water splitting application[END_REF]. The spectra corresponding to Cu-incorporated thin films are also in close range with that of the pristine BiVO 4 , except for the film with 23 % at. Cu exhibiting a lower absorption coefficient below 500 nm. The bandgap of the samples calculated by the Tauc plot method is illustrated in Fig. 7 (b), and the bandgap values versus Cu contents of the thin films are shown in Fig. 7 (c). The bandgap of the pristine BiVO 4 thin film is calculated to be 2.5 eV and those of the Cu-incorporated samples are in the range of 2.5-2.6 eV. The variation of the bandgaps could stem from the Cu doping or emerging of the 2 nd phase. The sample with a 23 at. % Cu showed a lower bandgap (2.46 eV) due to the crystallization of the BiCu 2 VO 6 secondary phase with a lower bandgap value of 2.1 eV [START_REF] Ding | A polymeric complex method to nanocrystalline BiCu2VO6 with visible light photocatalytic activity[END_REF]. It also exhibits a secondary absorption edge around 450 nm that could well be ascribed to the t-BiVO 4 phase with bandgap value of 2.9 eV [START_REF] Pattengale | The effect of Mo doping on the charge separation dynamics and photocurrent performance of BiVO4 photoanodes[END_REF]. The change in the morphology and porosity of the thin films increased the reflectance around 600 nm, shown in Fig. S4 (b) by increasing the diffuse reflectance component.

Photocatalytic activity

The visible-light-driven photocatalytic activity of the Cu-incorporated thin films was investigated through the RhB photodegradation experiments at neutral pH [START_REF] Nakhate | Hydrothermally derived nanosized Ni-doped TiO2: A visible light driven photocatalyst for methylene blue degradation[END_REF], and the results are illustrated in Fig. 8 (a). The kinetics results based on the pseudo-first-order model given by Eq. 3 are provided in Fig. S5 (a), and the rate constants representing the photocatalytic potential in the corresponding photoreaction are demonstrated in the inset graph of Fig. 8 (a). The blank experiment was conducted to separate the photolysis effect. The dark experiment for each sample was performed for 60 min and the solutions were sampled at 15 min intervals to ensure the system has reached the adsorption-desorption equilibrium. The system reached an equilibrium between 15 to 45 min in all the experiments, and the concentration remained constant after 45 min. Based on these results, the dark section of the photocatalytic experiments in the next stages was performed for 45 min. Herein, the highest photoactivity among the samples is ascribed to the sample with the least amount of Cu content (2 at. %) with a 72 % RhB photodegradation (kʹ = 0.19 h -1 ). A further increase of the Cu content leads to a progressive decrease of photodegradation. The thin films containing less or equal to 6 at. % Cu performed higher activities (59-72 % RhB photodegradation, kʹ = 0.13-17 h -1 ) compared to the pristine BiVO 4 (54 % RhB photodegradation, kʹ = 0.11 h -1 ), while the samples with higher than 6 at. % Cu contents showed poorer performance.

The photocatalytic performance of the thin films with less than 2 at. % Cu is currently unknown since reaching a composition with a lower amount of Cu using the sputtering machine in this research is challenging. The photocatalytic enhancement could be the result of Cu doping that was verified by the XPS and XRD results, as well as the heterostructure of the crystalline m-BiVO 4 and amorphous Cu-O-V phase exhibited in TEM observations, which acts through charge carrier separation inhibiting the fast recombination of photogenerated electrons and holes. The benefits of employing amorphous materials in the crystalline/amorphous heterostructure have been previously reported [START_REF] Deng | Progress in design of new amorphous alloy catalysts[END_REF] owing to providing a more uniform dispersion of active sites, as well as enjoying high unsaturated sites that facilitate the adsorption and surface reactions. Gue et al.

reported similar photocatalytic improvement for the mixture of crystalline/amorphous heterostructure of TiO 2 /ZnO in 2 production due to a superior electrical charge separation [START_REF] Guo | Structurally controlled ZnO/TiO2 heterostructures as efficient photocatalysts for hydrogen generation from water without noble metals: The role of microporous amorphous/crystalline composite structure[END_REF].

Indeed Cu doping could increase the charge carrier concentration, though, the higher amount of Cu incorporation results in fewer active sites on the film surface, subsequently less photoactivity due to the presence of less active phase. The PL results of the Cu-incorporated BiVO 4 (2 at. % Cu) and the pristine sample are shown in Fig. 8 (b). The intensity of the PL spectra could be associated with the recombination rate of the photogenerated electrons and holes [START_REF] Regmi | Fabrication of Nidoped BiVO4 semiconductors with enhanced visible-light photocatalytic performances for wastewater treatment[END_REF]. The PL results verified that less recombination occurs in the thin film with a 2 at. % Cu compared to the pristine sample.

Cu dopants could function as electron traps by creating electronic states below conduction band and receiving electrons changing their oxidation states from Cu 2+ to Cu + and Cu + to Cu 0 [START_REF] Zhang | In-situ FTIR-DRS investigation on shallow trap state of Cu-doped TiO2 photocatalyst[END_REF], hence inhibiting the recombination and providing more time for photogenerated charge carriers to participate in the redox reactions to destroy organic pollution.

The scavengers experiment using trapping agents of reactive species could help to study the photocatalytic mechanism by identifying the reactive agents acting the main role in the RhB photodegradation process under visible light by Cu-incorporated BiVO 4 thin films. The RhB photodegradation results involving the scavengers, using the sample with the highest photocatalytic activity (2 at. % Cu) from the previous section, are illustrated in Fig. 8 (c). The photodegradation versus time and the kinetics study are provided in Fig. S5 (b). The experiment with p-BQ as the trapping agent of superoxide ( • O 2 ¯) showed a moderate decrease in the performance by 11 %, while the performance concerning the CN experiment as the electron scavenger experienced a distinctly more decrease of 26 %. This could mean that a significant part of the electrons separately participated in the direct photoreduction of RhB. This phenomenon has been reported in the literature [START_REF] Park | Photodegradation of organic dyes via competitive direct reduction/indirect oxidation on InSnS2 under visible light[END_REF] and also observed by our team [START_REF] Bakhtiarnia | Enhanced photocatalytic activity of sputter-deposited nanoporous BiVO4 thin films by controlling film thickness[END_REF] regarding the photocatalytic degradation of RhB by pristine BiVO 4 thin films. The contribution of electrons in pristine BiVO 4 is lower than that implied in the Cu-doped BiVO 4 film, probably resulting from a direct effect of Cu doping on the electron charge carrier concentration. Electrons could also contribute to photodegradation through the reduction of superoxide radicals producing hydrogen peroxide (H 2 O 2 ) through Eq. 7 [START_REF] Nosaka | Generation and Detection of Reactive Oxygen Species in Photocatalysis[END_REF]. The results of EDTA (36 %) and Methanol (44 %) experiments as the scavengers of the photogenerated holes (h + ) and hydroxyl radicals ( • OH), respectively demonstrate the vital role of these reactive agents. This is in agreement with the electron paramagnetic resonance results published in the literature for Cu-doped BiVO 4 photocatalyst with 0.75 % Cu incorporation showing the production of • OH radicals and its importance in the photodegradation of organic pollutants [START_REF] Kanigaridou | Solar photocatalytic degradation of bisphenol A with CuO x /BiVO 4 : Insights into the unexpectedly favorable effect of bicarbonates[END_REF]. Based on the collective results in this part, it could be stated that a part of the hydroxyl radicals involved in the photodegradation process was produced by the oxidation of hydroxide ions (OH‾) through Eq. 5 and the rest were produced through the reduction of superoxides described by Eq. 6 -8. The Haber-Weiss reaction (Eq. 8) is a well-known path for producing hydroxyl radicals in photocatalysis [START_REF] Nosaka | Generation and Detection of Reactive Oxygen Species in Photocatalysis[END_REF]. Based on the results illustrated in Fig. 8 (c), it could be concluded that the photogenerated holes have a crucial role in the RhB photodegradation mechanism, as well as the hydroxyl radicals. BiVO 4 thin film with a 2 at. % Cu showed higher photoactivity in all cases with 72 % (kʹ = 0.19 h -1 ), 85 % (kʹ = 0.28 h -1 ) and 51 % (kʹ = 0.1 h -1 ) for RhB, MB and MO, respectively, compared to the pristine sample with 54 % (kʹ = 0.11 h -1 ), 61 % (kʹ = 0.13 h -1 ) and 28 % (kʹ = 0.05 h -1 ) photodegradation, exhibiting the superior photocatalytic performance of Cu-incorporated BiVO 4 towards the photodegradation of organic dye pollutions. The photodegradation towards MB was performed with highest efficiency followed by RhB and MO. One reason could be the cationic/anionic nature of the dyes. The photocatalytic degradation of organic dye pollutions occurs stepwise. Firstly, the dye molecules are adsorbed on the surface of the photocatalyst, and secondly, the degradation happens on the surface through the redox reactions previously discussed.

Therefore, the adsorption property of the photocatalyst is of great importance. It is reported in the literature that the point of zero charges (pH pzc ) of BiVO 4 is around 2.5 [START_REF] Obregón | On the different photocatalytic performance of BiVO4 catalysts for Methylene Blue and Rhodamine B degradation[END_REF]. Thus, assuming the small amount of Cu content (2 at. %) has a negligible impact on the PZC shift, the surface of the thin film is negatively charged at pH = 7, and therefore, due to electrostatic charges, has a stronger attraction towards a cationic dye (MB) rather than an anionic dye (MO) or a dye with a neutral charge at pH = 7 (RhB). The adsorption values concerning each dye in the dark experiment, depicted in Fig. S7, also support this with a 5.1 % decrease in the concentration for MB compared to 3 and 2 % for MO and RhB, respectively at pH = 7. The lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) of the dyes are provided in Fig. 10 (c), as well as the band edge position of the Cu-incoporated BiVO 4 photocatalyst gathered from VB-XPS shown in Fig. 5 (b), and the spectrophotometry analysis. The LUMO of RhB (0.54 V vs RHE) [START_REF] Lebedev | Rational design of visible-light-sensitive Ag-BiVO4 oxides by matching redox potentials of catalyst, dyes, and reactive oxygen species towards more efficient photocatalytic degradation[END_REF] is more positive than that of MO (-0.036 V vs RHE) [START_REF] Lebedev | Rational design of visible-light-sensitive Ag-BiVO4 oxides by matching redox potentials of catalyst, dyes, and reactive oxygen species towards more efficient photocatalytic degradation[END_REF] and MB (0.065 V vs RHE) [START_REF] Lebedev | Rational design of visible-light-sensitive Ag-BiVO4 oxides by matching redox potentials of catalyst, dyes, and reactive oxygen species towards more efficient photocatalytic degradation[END_REF], hence, in addition to the previous argument regarding the surface adsorption, it should be noted that the photo-oxidation of the RhB dyes could be more difficult compared to other dyes.

Plus, since the reduction potential of H 2 O 2 (0.32 V) [START_REF] Krumova | Chapter 1. Overview of Reactive Oxygen Species[END_REF] produced during redox reactions (Eq. 7)

is lower than RhB LUMO but more positive than that of MB, it could photodegrade MB but not RhB, therefore, it could be considered as another reason for the higher performance of photocatalytic degradation towards MB.

In previous sections, the photocatalytic performance of the samples at neutral pH was investigated. Examining the samples' photoactivity in acidic and basic conditions is also helpful.

Therefore, the experiments at pH = 3 and 10 were also conducted. The order of photodegradation efficiency towards different dyes at acidic and basic pH conditions shown in Fig. 10 (b) along with kinetics studies in Fig. S6 (c) and (d), are also coherent with that of neutral pH, though, higher photocatalytic activities have been achieved with 100 % (kʹ = 0.87 h -1 ) and 99 % (kʹ = 0.72 h -1 )

respectively by the thin film with a 2 at. % Cu. As mentioned before, the pH pzc of BiVO 4 is around 2.5, and therefore, at pH = 3 it is negatively charged, while the dye molecules are protonated due to excessive H + concentration of the solution, thus more electrostatic attractions could lead to better adsorption of the dye molecules on the photocatalyst surface, where the photoreaction takes place.

Moreover, the extra H + could result in higher production of the reactive species such as hydrogen peroxide and hydroxyl radical through Eq. 7 and 8 and enhance the photocatalytic performance [START_REF] Fakhravar | Excellent performance of a novel dual Zscheme Cu2S/Ag2S/BiVO4 heterostructure in metronidazole degradation in batch and continuous systems: Immobilization of catalytic particles on α-Al2O3 fiber[END_REF]. This is also true for the presence of extra OH -in the basic solution to produce other types of reactive agents through redox reactions based on Eq. 5 -8.

Conclusions

• Cu incorporation was successfully implemented into nanoporous BiVO 4 thin films using reactive magnetron sputtering resulting in enhanced visible-light-driven photocatalytic activity with 100, 99 and 63 % photodegradation of MB, RhB and MO, respectively.

• Cu incorporation affected the preferential orientation of the thin film's crystal with a tendency along [002] and [011], particularly concerning the thin film with a 2 at. % Cu. It was observed in HRTEM images that the crystal orientation of the (002) plane is significant. Cu incorporation also affected the cell volume which was progressively decreased and consistent with the lower ion radius of Cu compared to V and Bi.

• Amorphous shard-like Cu-O-V nodules were formed on the Cu-incorporated thin film with a 2 at. % Cu, which were also observed in HRTEM images. They might also promote an effective separation of charge carriers, which was verified by the PL results showing less recombination rate after the Cu incorporation.

• Cu-incorporated BiVO 4 with a 2 at. % Cu had a bandgap of 2.5 eV and the XPS results

showed the presence of Cu + and Cu 2+ species. XPS also showed the rise of V 4+ /V 5+ by increasing Cu content and verified the penetration of Cu ions into the BiVO 4 crystal.

• Hydroxyl radical and photogenerated electrons were identified as the main reactive species driving the RhB photodegradation by the Cu-incorporated BiVO 4 thin films under visible light.

• Recyclability experiment with three consecutive cycles proved the films' suitable stability, which will contribute to an effective, cost-efficient and economically viable solution for the industrial water treatment application.

  Preparation of sputter-deposited Cu-doped BiVO4 nanoporous thin films comprised of amorphous/crystalline heterostructure as enhanced visible-light photocatalyst Siavash Bakhtiarnia, Saeed Sheibani, Abbas Nadi, Eric Aubry, Hui Sun, Pascal Briois, Mohammad Arab Pour Yazdi To cite this version: Siavash Bakhtiarnia, Saeed Sheibani, Abbas Nadi, Eric Aubry, Hui Sun, et al.. Preparation of sputterdeposited Cu-doped BiVO4 nanoporous thin films comprised of amorphous/crystalline heterostructure as enhanced visible-light photocatalyst. Applied Surface Science, 2023, 608, pp.155248. hal-04233200

Fig. 1 4 )

 14 Fig. 1 XRD patterns of the pristine BiVO 4 and Cu-incorporated samples.

Fig. 2

 2 Fig. 2 texture grades of the samples corresponding to (011), (121), (040) and (002) planes.

Fig. 3 .

 3 Fig. 3. FESEM and elemental mappings of (a) the pristine BiVO 4 sample, and the thin films with

Fig. 4 .

 4 Fig. 4. High-resolution XPS spectra of (a) Cu, (b) Bi, (c) V, (d) O core levels

Fig. 5 .Fig. 6 .

 56 Fig. 5. (a) V 4+ :V 5+ versus Cu content and (b) Valence band XPS spectra of pristine BiVO 4 and

Fig. 6 .

 6 Fig. 6. (a), (b) TEM and HRTEM images of BiVO 4 thin film with 2 at. % Cu incorporation with

Fig. 7 .

 7 Fig. 7. (a) Absorbance spectra of the thin films with various Cu content (b) Tauc plots of the

OHFig. 8

 8 Fig. 8 (a) RhB photodegradation experiments of Cu-incorporated samples at pH = 7 and the inset

Fig. 9

 9 Fig. 9 (a) recycling experiment in three consecutive cycles of RhB photodegradation by the thin

Fig. 10 . 2 .

 102 Fig. 10. Visible-light-driven photodegradation of RhB, MB and MO (a) by the pristine BiVO 4

Table 1 .

 1 The sputtering parameters for the deposition of thin films.

	Ar flow rate (sccm)	200 Targets	Bi	V	Cu
	O 2 flow rate (sccm)	20 Intensity (A)	0.08 0.67 0.004 → 0.016
	Total pressure (Pa)	4.5 Power (W)	10	255	1 → 5
	Runtime (min)	205 Frequency (kHz)	70	50	-

Drawing distance (mm) 60 T off (µs) 4 4 -

Table . 2

 . . Summary of BiVO 4 photocatalysts' performance towards photodegradation of organic pollutants.

	Photocatalyst	Form	Pollutant	Light source	Degradation efficiency (%)	Ref.
	Cu/BiVO 4	Powder	MB, 50 mg/L	400 W Xenon	50	[28]
	Cu/BiVO 4	Powder	RhB, 15 mg/L	250 W Halogen	96	[48]
	Cu/BiVO 4	Powder	MO, 10 mg/L	54 W LED	86	[65]
	BiVO 4	Thin Film	Bisphenol-A, 10 mg/L	150 W Xenon	10	[66]
	Y/BiVO 4	Thin Film	RhB, 0.2 mg/L	300 W Xenon	18	[67]
	Ag, Ni, Co/BiVO 4	Powder	MB, 10 mg/L	500 W Xenon	90	[68]
	Cu/BiVO 4	Thin Film	RhB, MB, MO, 5 mg/L	400 W Metal Halide	RhB=95, MO=63 MB=100,	This work

Acknowledgments

The authors would like to acknowledge the support of this study by the Iran National Science Foundation (project No: 98001285), Pays de Montbéliard Agglomération, and the Iran Nanotechnology Initiative Council for the support of this work.

Conflict of interest

The authors declare that they have no conflict of interest.