Enhancing the Photocatalytic Performance of MXenes via

Subscriber access provided by University of Sunderland

Functional Inorganic Materials and Devices

Enhancing the Photocatalytic Performance of MXenes via Stoichiometry Engineering of their Electronic and Optical Properties Zicong Marvin Wong, Teck Leong Tan, Shuo-Wang Yang, and Guoqin Xu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b14325 • Publication Date (Web): 24 Oct 2018 Downloaded from http://pubs.acs.org on October 25, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Applied Materials & Interfaces

Enhancing the Photocatalytic Performance of MXenes via Stoichiometry Engineering of their Electronic and Optical Properties

Zicong Marvin Wong,a,b Teck Leong Tan,*b Shuo-Wang Yang,b and Guo Qin Xu*a

aDepartment

of Chemistry, National University of Singapore, 3 Science Drive 3, Singapore 117543

bInstitute

of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632

Keywords MXenes, Two-Dimensional Material, Density Functional Theory, Cluster Expansion, Alloy, Photocatalyst

0. Abstract Combining both density functional theory and the cluster expansion method, we investigate 3 binary MXene alloy systems of semiconducting Ti2CO2, Zr2CO2, and Hf2CO2, where the transition metals substitute one another (i.e., Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xC O2). We show that this group of MXene alloys forms the solid-solution phase across all composition. Special quasirandom structures are generated to model the solid-solution phase of these alloys, using which, we demonstrate how their structural, mechanical, electronic, and optical

ACS Paragon Plus Environment

ACS Applied Materials & Interfaces 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

properties are tuned via stoichiometry engineering. These alloys exhibit outstanding mechanical strength and stability. They possess indirect band gaps of 1.25 to 1.80 eV. For Ti2(1 - x)Zr2xCO2 and Ti2(1 - x)Hf2xCO2, they display higher absorbance in the solar spectrum than their constituent Zr2C O2 and Hf2CO2 respectively. Most of the MXene alloys also show appropriately aligned band edges for water-splitting. We predict that the Ti2(1 - x)Zr2xCO2 alloy with x = 0.2778 to be the most promising water-splitting photocatalyst among the MXenes studied here, outperforming its constituents, Ti2CO2 and Zr2CO2, when solar absorbance performance and band edge alignments are simultaneously considered. This work demonstrates that alloying can be used to effectively tune photocatalytic performance.

1. Introduction The discovery of graphene and its exceptional properties and achievements in the recent years1 have garnered immense research motivations to uncover and isolate more of such twodimensional (2D) materials,2-4 among which a few prominent examples are transition metal dichalcogenides (TMDs), single-layer boron nitrides, and complex oxides.5-6 More recently, the discovery of MXenes has created a new family of 2D materials.7-8 MXenes are 2D layered transition metal carbides, nitrides, and carbonitrides that are usually produced via the selective etching of the A-element layers (mostly from groups IIIA and IVA) from their parent MAX phases.9 Derivations from other parent laminated phases and direct syntheses via chemical vapor deposition (CVD) are also possible pathways to obtain MXenes.10-11 Being mostly electrically conductive and hydrophilic,12 MXenes have been extensively studied in a wide range of applications including energy-related ones: Li-ion batteries,13 supercapacitors,14 electrocatalysts


Page 2 of 39

Page 3 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


for hydrogen evolution reaction,15 etc. The rich chemistry of MXenes exhibits impressive versatility in material properties design.7 Ti2CO2, Zr2CO2, and Hf2CO2 are group IVB transition metal carbide MXenes that possess semiconducting properties and have been studied for potential photocatalytic applications.16-17 To be a practical water-splitting photocatalyst, the material should possess a band gap larger than 1.23 eV, suitable band edges which straddle the water redox potentials, efficient absorption of photons in the solar spectrum, and low hole-electron recombination rate.18 Being 2D materials, MXenes exhibit high specific surface area for photocatalytic reactions. The two-dimensionality also minimizes the migration distances of the photogenerated holes and electrons to the reaction interface, lowering the possibility of hole-electron recombination which potentially improves the photocatalytic performance. However, the band edges of Ti2CO2 are misaligned while the absorption of the Zr2CO2 and Hf2CO2 within the solar spectrum are weak,17 which compromise their desirability as efficient photocatalysts. Therefore, it is imperative to tune and optimize these MXenes for enhanced photocatalytic performance. Fortunately, there exists 2 general approaches for property modification of MXenes: (1) surface functionalization and (2) alloying.19-21 Here, we investigate the engineering of the properties of three binary MXene alloy systems of Ti2CO2, Zr2CO2, and Hf2CO2, where the transition metals substitute one another (i.e., Ti2(1 - x) Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2). Combining density functional theory (DFT) calculations and the cluster expansion (CE) method,22-27 we rapidly and comprehensively access and evaluate the relative stabilities of more than 3 million different alloy structures across all compositions (0 < x < 1) for each system in order to systematically establish the relationship between alloy composition, configuration, and properties. We found that the Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 MXene alloys do not have thermodynamically stable



ordered structures but instead exist as entropically-stabilized disordered solid solutions. By applying the special quasirandom structure (SQS) approach,28 we recreate Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 structures that are representative of the disordered solidsolutions and demonstrate how their structural, mechanical, electronic, and optical properties can be tuned via stoichiometry engineering. These alloys exhibit outstanding mechanical strength and stability, and they possess (indirect) band gaps of 1.25 to 1.80 eV, above the minimum 1.23 eV band gap requirement for photo water-splitting. Especially for Ti2(1 - x)Zr2xCO2 and Ti2(1 - x)Hf2xC O2 MXene alloys, they display enhanced absorbance in the solar spectrum as compared to their constituent Zr2CO2 and Hf2CO2 MXenes. Most of the MXene alloys also have favorably aligned band edges for thermodynamically feasible water redox processes. Above all, we propose that the Ti2(1 - x)Zr2xCO2 alloy with x = 0.2778 to be the best performing water-splitting photocatalyst among the MXenes studied here, with an optimal band gap, large difference in effective masses of the holes and electrons, appropriate band positions, and high absorbed photon flux. Considering that Ti2CO2 is a good solar absorber but misaligned band edges (w.r.t. water-splitting), while Zr2C O2 and Hf2CO2 absorb solar photons weakly albeit suitably aligned band positions, our work demonstrates substitutional alloying as an avenue to assimilate the desired properties from the constituents to produce better photocatalytic performance.

2. Computational Details 2.1 Cluster Expansion (CE) Method For a given substitutional alloy, the Hamiltonian of a particular alloy configuration, σ, can be represented by the cluster expansion (CE) formalism,29-31 where the atom species occupying a lattice site p can be described via a set of occupational variables {ξαp}σ, such that ξαp = 1 if p is


Page 4 of 39

Page 5 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


m

occupied by an atom of type α and 0 otherwise. If the sites are fully occupied, then ∑α αξαp = 1 for every site p, where mα is the number of alloying atomic species. For our work, mα = 2, whereby binary M2(1 - x)M'2xCO2 substitutional MXene alloys (also denoted as (M,M')2CO2) are formed with (M,M') = (Ti,Zr), (Ti,Hf), and (Zr,Hf), while the composition of C and O are fixed. For an alloy, both the composition and the configuration of the M and M' atoms on the lattice sites can influence properties. The formation energy, Ef, which is associated with the stability of the alloy at 0 K, is one such property. For a particular alloy configuration, σ, of a composition x, the Ef relative to its constituent MXenes M2CO2 and M'2CO2 is calculated by Ef(M2(1 - x)M'2xCO2, σ) = E(M1 - xM'xCO2, σ) ― (1 ― x)E(M2CO2) ― xE(M'2CO2)

(1)

where E(M2CO2), E(M'2CO2), and E(M2(1 - x)M'2xCO2, σ) are the total energies per atom of M2CO2 , M'2CO2, and the given alloy configuration (σ) of M2(1 - x)M'2xCO2 respectively. The Ef of the given alloy configuration can be described by the CE Hamiltonian, which can be expanded in terms of a set of geometric clusters 32-33 ECE(σ) =

∑V

clusterϕcluster(σ)

clusters

(2)

where Vcluster and ϕcluster(σ) are called the effective cluster interaction (ECI) and the cluster correlation function. The latter is expressed as ϕcluster(σ) =

∏

ξαp

(3)

p ∈ cluster

The construction of the CE Hamiltonian and the ground state search are performed via the Thermodynamic Tool-Kit (TTK) code.20, 22-23, 31-37 In practice, all except a finite number of ECIs are assumed to be approximately zero; as such, accurate energies can be predicted from a properly truncated CE Hamiltonian. The clusters are grouped according to symmetry and only ECIs of symmetry-unique clusters are evaluated. For each alloy, we construct the initial CE Hamiltonian



by fitting the ECIs to a learning set of formation energies computed via DFT, involving ~100 alloy configurations, {σ1, σ2, …, σ100}, comprising of up to 20-atom M2(1 - x)M'2xCO2 MXene supercells. Then, we implement a ground state search of over three million alloy structures with unique configurations (up to 70-atom supercells) to obtain their corresponding CE energies (see Equation (2)). Configurations that possess formation energies close to or at the ground-state hull would have their DFT energies validated and added to the learning set to produce an updated CE Hamiltonian for the proceeding iteration. Usually, the iterative process ends when no new ground-states are predicted and/or CE formation energies are reproduced accurately to a reasonable extent. Via TTK, we obtain properly truncated ECIs (Figure S1) and hence CE 31 which replicates the DFT formation DFT energies in the learning set, i.e., ECE (σ), and has a low cross-validation error (Table f (σ) ≈ Ef

S1).

2.3 First-Principles Calculations We performed first-principles calculations using density functional theory (DFT)38 via the Perdew, Burke, and Ernzerhof (PBE) exchange correlation based on the generalized gradient approximation (GGA)39-40 as implemented in the Vienna ab initio Simulation Package (VASP).4142

The projector augmented wave (PAW)43 was used to describe the electron-ion interactions.

Plane-wave cutoffs are set to 500 eV. All atomic coordinates were fully relaxed until the calculated Hellmann-Feynman force on each atom was less than 0.01 eV/Å. During structural relaxation, the volume of the cells was kept fixed while their shape was allowed to change. A vacuum space of more than 15 Å was applied along the z-direction to minimize spurious interactions between periodic images. Spin-polarized calculations were carried out even though the magnetic moments were found to be negligible. Brillouin zone sampling was performed with Monkhorst-Pack (MP)44


Page 6 of 39

Page 7 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


k-point meshes inclusive of the Γ-point with a k-point density of approximately 40 k-points per Å -1 for structural optimizations, while a finer mesh of 160 k-points per Å -1 was implemented for highly detailed electronic densities-of-states (DOSs) and band structure calculations. To obtain more accurate band gaps and band edge positions for the alloys, the Heyd-Scuseria-Ernzerhof hybrid functional method (HSE06)45-46 was used. The determination of the elastic tensor for each structure were performed by six finite distortions of the lattices to derive the elastic constant from the stress-strain relationship.47 Both rigid- and relaxed-ion approaches are used in the estimation of the elastic tensor. The ionic contributions are evaluated from the inversion of the ionic Hessian matrix, calculated from finite differences and multiplied with the internal strain tensor.48 Rescaling ∆z

of the elastic constants is carried out by multiplying with t , where ∆z is the length of the cell in the z-direction and t is the effective thickness of the MXene monolayer, to avoid the forces being averaged over the entire simulation cell which includes the vacuum space.49

3. Results and Discussion 3.1 Structure-Stability Relationship Before investigating the relationship between the structure and stability of the M2(1 - x)M'2x CO2 alloys, we first establish the ground state structures of the constituent Ti2CO2, Zr2CO2, and Hf2CO2 MXenes from first-principles. A fully O-terminated MXene surface can adopt 3 possible geometries of O atoms: fcc, hcp, or mixed (fcc on one surface and hcp on the other) (Figure S2). Their structural parameters and energies are compared in Table S2 while their phonon dispersions are shown in Figure S3. These results concur with literature.16, 21, 50 For Ti2CO2, Zr2CO2, and Hf2C O2, we observe the fcc geometry to be dynamically stable and energetically more stable than the



Page 8 of 39

hcp and mixed geometries by at least 0.18 eV per atom. Therefore, we shall consider fcc Oterminated MXene structures. Figure 1 shows the formation energies, Ef’s, of more than three million different alloy configurations derived from Equation (1) for Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xC O2 alloy MXenes, using the ECIs constructed from the CE method. For all the 3 alloy systems, it is evident that the Ef’s of the ordered alloy structures are all positive, implying the formation of ordered Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 alloy MXenes to be energetically unfavorable. The range of Ef values are large for both Ti2(1 - x)Zr2xCO2 and Ti2(1 - x)Hf2xCO2, and much smaller for Zr2(1 - x)Hf2xCO2. Interestingly, this observation appears to correlate with the size difference between two alloyants in each system, in which |rTi(IV) ― rZr(IV)| ~ |rTi(IV) ― rHf(IV)| >

|rZr(IV) ― rHf(IV)|, where rTi(IV), rZr(IV), and rHf(IV) correspond to the ionic radii of six-coordinated Ti(IV), Zr(IV), and Hf(IV) of 0.61, 0.72, and 0.71 Å respectively.51 The size differences lead to structural distortions, as we shall see later, which can cause some instability to the alloy. Despite these, to account for the structural stability at finite temperatures (T > 0 K), the formation free energy, Ff, should be considered. For a perfectly disordered solid solution, the free energy at each composition x can be evaluated from the Gibbs free energy equation: (4)

Ff(x) = Ef(x) ― TS(x) where S corresponds to the configurational entropy which can be estimated by S(x) = ― kB[xln x + (1 ― x)ln (1 ― x)]

(5)

with kB being the Boltzmann constant. Upon inclusion of the configurational entropy for the disordered solid solution alloy MXenes, the derived Ff’s possess negative values beyond temperatures of 1500 K, 1000 K, and 300 K for Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 alloys respectively, indicating


Page 9 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


their thermodynamic stability above these temperatures. As Equation (5) corresponds to fully disordered alloys at infinite temperature and may result in overestimation of the configurational entropy, we performed semi-grand canonical Monte Carlo simulations to these alloy systems (Figure S4). As observed, the formation of Ti2(1 - x)Zr2xCO2 and Ti2(1 - x)Hf2xCO2 alloys are thermodynamically favorable at temperatures beyond 1300 K and 1000 K, respectively; while Zr2(1 - x)Hf2xCO2 alloys are already stable at 300 K. These temperatures agree rather well with Figure 1 and are lower than the typical fabricating temperatures of the parent MAX phases (1600 to 1900 K)52-53 and comparable to that from direct MXene synthesis via CVD (~1400 K).11 We note that vibrational entropies are not considered here and therefore the actual thermodynamic stable temperatures could be even lower. Furthermore, Ti, Zr, and Hf are in the same group IVB with similar d4 configuration and electronegativity (ΧTi = 1.54, ΧZr = 1.33, and ΧHf = 1.30),54 and comparable ionic sizes, which validate the Hume-Rothery rules in favoring the formation of substitutional solid solutions.55 Hence, the experimental realization of disordered solid solution Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 MXene alloys are highly attainable, perhaps even more so than their constituent MXenes due to the additional stability bestowed from the configurational entropy.

3.2 M2(1 - x)M'2xCO2 Special Quasirandom Structures (SQSs) To supplement our understanding of the phase diagrams and formation stabilities of Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 MXene alloys, we investigate various physical and chemical properties of these alloys for potential functional applications. As these MXene alloys are predicted to exist as disordered solid solutions, we create special quasirandom structures (SQSs) for further evaluation of their properties. In general, SQS configurations seek to



recreate specific statistical attributes of fully random solid solutions like 2-body or 3-body cluster correlation functions.28 For a perfectly disordered alloy, the occupational variable at a given site p in Equation (3) can be considered as lattice-averaged composition, i.e., ξαp = 〈ξa〉p = x, and Equation (3) hence reduces to ϕdisordered = xn, where n is the number of sites in the cluster. An cluster ideal SQS of a particular configuration, σSQS, would possess similar cluster correlations as that of the fully random solid solutions, ϕcluster(σSQS) ≅ ϕdisordered . Therefore, from our truncated clusters, cluster we identified configurations with lowest accumulated deviation from the correlation functions of the perfectly disordered alloys, also denoted as accumulated structural deviation index (ASDI), 2

| (Table S3). Accordingly, we construct SQSs of the i.e., ASDI = ∑clusters|ϕcluster(σ) ― ϕdisordered cluster MXene alloys at x = 0, 0.0556, 0.1111, 0.1667, 0.2222, … 0.9444, and 1. Nineteen SQSs consisting of 45 atoms (9 times of MXene primitive unit cell) are generated for further investigations of their properties via first-principles. Structural analyses of the Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 MXene SQSs are presented in Figures 2 and 3. Linear relationships versus x are observed between both the lattice constants a (normalized to per MXene primitive unit cell) and MXene monolayer thickness for all the alloys with x (Figure 2), obeying the Vegard’s law. Since the ionic radii increases in the order: Ti < Hf ~ Zr; the increase in composition x for Ti2(1 - x)Zr2xCO2 and Ti2(1 - x) Hf2xCO2 would mean more Zr or Hf than Ti which occupy more space per unit cell, expanding both the lateral plane and the thickness of the MXene monolayer, and vice versa. For Zr2(1 - x)Hf2xC O2, as x increases, there is more Hf than Zr, leading to shrinkages in the in-plane lattice parameters and thickness of the MXene monolayer. Similar trend is also observed for the averages of both the (M,M')-C and (M,M')-O bond lengths in Figure 3. Moreover, here we can distinctly perceive the effect of ionic size differences of the metals with respect to the distribution of the bond lengths.


Page 10 of 39

Page 11 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


We can distinguish two groups of bond lengths in each plot, one relating to M-C/O, while the other to M'-C/O. The occurrence of M-C/O (M'-C/O) decreases (increases) with x. In addition, for both Ti2(1 - x)Zr2xCO2 and Ti2(1 - x)Hf2xCO2, since the ionic radii of Zr and Hf are about 18% and 16% respectively larger than that of Ti, structural distortions in the alloy MXene lattice, where the bond length distribution are observed as spreading (up to approximately ±0.2 Å) for both (M,M')-C and (M,M')-O bonds. On the other hand, the ionic radii similarity between Zr and Hf leads to a very narrow spread in the (Zr,Hf)-C and (Zr,Hf)-O bond lengths in Zr2(1 - x)Hf2xCO2, implying a very small degree of distortion of the MXene lattice. These structural observations appears to correlate with the magnitude of formation energies, Ef’s, of these MXene alloys, with Ti2(1 - x)Zr2xCO2 and Ti2(1 - x)Hf2xCO2 having higher degree of structural distortions possessing more positive formation energies than Zr2(1 - x)Hf2xCO2 with the least distortions having the least positive formation energies. Notwithstanding, similar to the constituents, the phonon dispersion curves of these alloys in Figure S6 display no imaginary (negative) frequencies, indicating dynamic stability.

3.3 Elastic Constants of Solid-Solution M2(1 - x)M'2xCO2 For (hexagonal) 2D MXenes, there are at most 3 independent non-zero elastic constants: C11, C12, and C66. To analyze the mechanical properties of the Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 MXene SQSs, their elastic constants and related parameters such as the inplane Young’s modulus, Ys, and Poisson’s ratio, ν, which are obtained according to the following relationships:56-57 Ys =

C211 ― C212 C11

and ν =

C12 C11

; are illustrated in Figure 4. Our calculation of the

elastic constants shows all the MXene SQSs to satisfy the Born stability criteria according to BornHuang’s lattice dynamical theory for 2D hexagonal structures:58-59 C11 > 0, C11 ― C12 > 0, and



C66 =

C11 ― C12 2

. This implies that Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 MXene

alloys are stable from thermodynamic (from the formation free energies) and mechanical (from the elastic constants) perspectives. The in-plane Young’s moduli, Ys’s for the constituent MXenes have indicated Hf2CO2 to be the stiffest (582 GPa), followed by Ti2CO2 (550 GPa) and Zr2CO2 (523 GPa) not very far behind, implying these MXenes to be very strong and resistant to deformation. The Ti2(1 - x)Zr2xCO2 and Ti2(1 - x)Hf2xCO2 MXene alloys display downward bowing of Ys with x, indicating a reduction in the stiffness. Interestingly, the degree of bowing seems to relate with the degree of structural distortion. Ti2(1 - x)Zr2xCO2 alloys with the highest distortions have the most bowing while Zr2(1 - x)Hf2xCO2 alloys (least distortions) exhibit negligible bowing. The structural distortions could slightly weaken the interactions within the MXene layer and result in the reduction in stiffness. However, we do note that the Ys’s for all the MXene SQSs range from 500 to 590 GPa, much higher than that of monolayer TMDs MoS2 and WS2 (264 ± 18 and 272 ± 18 GPa) and 50% to that of graphene (1025 ± 35 GPa),60 which illustrate their remarkable strength and deformation resistance. As the Poisson’s ratio, ν, provides insights into the brittleness and ductility of a material, we observe the ν’s of the MXene alloys to lie within the range from 0.26 to 0.33, suggesting their low brittleness, and the upward bowings imply their increased ductility as compared to their constituent MXenes Hence, from our mechanical investigations, the Ti2(1 - x)Zr2x CO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 MXene alloys are mechanically stable and strong materials that are stiff, resistant to deformation, and ductile.

3.4 Band Structure Characteristics of Solid-Solution M2(1 - x)M'2xCO2 Figure S7, S8, and S9 illustrate the electronic band structures and the densities-of-states (DOS) of the Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 MXene SQSs respectively.


Page 12 of 39

Page 13 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The electronic band structures possess band gaps which indicate that all of these MXene alloys are semiconductors like their constituents Ti2CO2, Zr2CO2, and Hf2CO2 MXenes. Even though there exists band folding from the usage of supercells for the SQSs, all their valence band maxima (VBM) are found to be located at the Γ-point (0 0 0); while the conduction band minima (CBM) 11

lie at the K-point (3 3 0), denoting indirect band gap character. Although a thicker absorption layer is typically required for indirect band gap semiconductor, the indirect band gap character is still desirable especially for photocatalysis since the electron-hole recombination rate is impeded increasing the probability for the electrons and holes to participate in the redox reactions.61 Next, we derive the effective electron and hole masses, by implementation of the parabolic fitting to the VBM and CBM respectively, using the MXene SQSs at selected high symmetry kpoints.62 Possible anisotropies of the VBM and CBM comprising of perpendicular in-plane effective hole (mh1 and mh2) electron (me1 and me2) masses were considered for the MXene SQSs; and therefore, the resultant effective hole and electron masses, mh* and me* respectively (in units of rest mass of a free electron, m0 ≈ 9.109 × 10 -31 kg), are determined from the harmonic mean of the respective effective masses along the perpendicular directions: * mh/e =

2 1 mh1/e1

+

1 (6)

mh2/e2

The anisotropy comparisons between the perpendicular in-plane components of the effective hole and electron masses and the resultant effective hole and electron masses with x for the Ti2(1 - x)Zr2x CO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 MXene alloys are illustrated in Figure 5. Essentially, their effective hole masses, regardless of the directions, are all lighter than that of the effective electron masses, suggesting the holes to have higher mobilities. While the effective hole masses are almost perfectly isotropic, the effective electron masses are instead highly anisotropic, with



one direction possessing up to an order of magnitude heavier. These observations are in general agreement with previously published results for the constituent Ti2CO2, Zr2CO2, and Hf2CO2 MXenes.16-17, 50, 63 In addition, for the Ti2(1 - x)Zr2xCO2 and Ti2(1 - x)Hf2xCO2 MXene alloys, we see upward bowing of the electron effective masses with respect to composition x (∆me* ~ +0.1 m0), implying some reduction in the electron mobility for the alloys; while the effective hole masses varies in a rather linear manner to a much smaller extent (∆mh* ~ +0.04 m0), i.e., no significant changes in the hole mobilities. This observation can be traced back to the electronic DOSs of the MXene alloys (Figures S7, S8, and S9). The CBMs are dominated mostly by the transition metal d-orbitals while the VBMs are comprised of majority C and O p-orbitals. Hence, variations in the composition x of M and M' will exhibit a greater effect towards the CBMs and almost negligible changes to the VBMs. In fact, the projected DOSs of C and O atoms appear to be nearly identical for all the alloys regardless of x. The anisotropy and the reduction in the electron mobilities accompanied with the isotropy and higher hole mobilities can potentially improve the effective spatial separation of these charges, decreasing the probability of hole-electron recombination.34-35 On the other hand, for the Zr2(1 - x)Hf2xCO2 MXene alloy, both the effective electron and hole masses decrease monotonously with Hf, probably due to the similar ionic radii and electronegativity of Zr and Hf, resulting in similar electronic properties. Nevertheless, the above observation shows that with suitable alloying, one can improve the effective separation of the electron-hole pairs and further enhance the redox capability as compared to their constituent MXenes.

3.5 Band Alignment of Solid-Solution M2(1 - x)M'2xCO2


Page 14 of 39

Page 15 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


To be an effective photocatalyst for practical applications, other than possessing effective separation of photogenerated hole-electron pairs, the MXene alloys should also have sufficiently wide band gaps and properly aligned band edges.35-36, 64 Figure 6 shows the band gaps, Eg’s, of the Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 MXene SQSs obtained via the HSE06 functional, which vary from 1.25 to 1.80 eV, signifying a wide band gap tuning range from alloying. All these band gaps are larger than 1.23 eV, which is the minimum value required for photocatalytic water-splitting. Moreover, we see that the band gaps increase with x with partial upward bowing and curving (although their linear regression R2 values are still above 0.95). The band edge positions, ECBM and EVBM, of the MXene SQSs relative to the vacuum level are determined according to the method by Toroker et al.:65 1 ECBM = EBGC + Eg 2

(7a)

1 EVBM = EBGC ― Eg 2

(7b)

where EBGC is the energy of the band gap center which is located halfway between the CBM and VBM. The reduction and oxidation capabilities of the MXenes SQSs are illustrated in Figure 7. The positions of the CBM are also shown to increase at a larger extent than that of the VBM positions with x for Ti2(1 - x)Zr2xCO2 and Ti2(1 - x)Hf2xCO2, suggesting the reduction capabilities to be more sensitive to changes in x than the oxidation capabilities. In addition, the constituent Ti2C O2 (Hf2CO2) MXene shows the most negative (positive) VBM (CBM) with respect to vacuum among the MXenes studied in this work, thus, Ti2CO2 (Hf2CO2) possesses the highest oxidizing (reducing) capability. However, we also notice that not all of the alloy MXenes have appropriate band edges that encompass the water redox potentials even with favorable band gaps. For Ti2(1 - x) Zr2xCO2 and Ti2(1 - x)Hf2xCO2 alloy MXenes, only when x > 0.2778 and 0.3333 respectively can



Page 16 of 39

both water oxidation and reduction processes become thermodynamically feasible. Below these compositions, since the positions of the VBM is low enough, they can still be useful for water oxidation process in a z-scheme photocatalysis.66 The band positions of the Zr2(1 - x)Hf2xCO2 remains constant versus x, probably due to the similar band gaps of its constituents, as discussed above, and all of them are suitably aligned for both water oxidation and reduction processes. In addition to photocatalytic water-splitting, the band edges of the MXene alloys are suited for CO2 reduction, especially for Ti2(1 - x)Zr2xCO2 (x > 0.5556), Ti2(1 - x)Hf2xCO2 (x > 0.6667), and Zr2(1 - x) Hf2xCO2 (for all x).

3.6 Solar Absorption Efficiency of Solid-Solution M2(1 - x)M'2xCO2 An effective photocatalyst should efficiently absorb solar energy in order to promote a high hole-electron pair generation rate. We explore the solar absorbance of Ti2(1 - x)Zr2xCO2, Ti2(1 - x) Hf2xCO2, and Zr2(1 - x)Hf2xCO2 SQSs via the imaginary part of the dielectric functions, ε2, (Figure S10, with HSE06 functional) and optical absorbance spectra (Figure 8) of the Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 MXene SQSs. The optical absorbance spectra, A(ω), are derived from ε2 according to the following relation based on the Taylor expansion of absorbance relation at small thicknesses:36, 67-68 A(ω) =

ω ε2(ω)∆z c

(8)

where ω, c, and ∆z correspond to the photon frequency, speed of light, and the length of the simulation cell in the z-direction respectively. Generally, similar to their constituent MXenes, the ε2 of the MXene alloys are isotropic in the in-plane directions, and the relative magnitude of the ε2 in the out-of-plane direction appear to be much weaker and contribute negligibly to the absorption properties. For these reasons, our analyses of the optical absorbance spectra would be based on the


Page 17 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


in-plane x-direction. Both the ε2 and the optical absorbance spectra of the MXene alloys are observed to be blue-shifted versus x, consistent with the increase in band gaps. For the Zr2(1 - x)Hf2x CO2 MXene alloys, the peaks near the ultraviolet-visible boundary (~ 375 to 400 nm) are narrow and pronounced; while those for Ti2(1 - x)Zr2xCO2 and Ti2(1 - x)Hf2xCO2 are broader and the wavelengths overlap to a greater extent in the regions with significant solar photon flux, suggesting that Ti2(1 - x)Zr2xCO2 and Ti2(1 - x)Hf2xCO2 are better solar absorbers. A metric that could be used to distinguish the solar absorbance of the alloy MXenes is the maximum short-circuit current under solar irradiation, Jabs:36, 67 λEg

∫A(λ) J (λ) dλ

Jabs = e

p

0

where λEg corresponds to the band gap’s equivalent wavelength (λEg (nm) =

(9) 1240 eV nm ) Eg (eV)

of the

MXene alloys, while A(λ) and Jp(λ) are respectively the absorbance (in terms of wavelength) and the incident photon flux (no. of photons per unit time per unit area per unit wavelength) according to the AM1.5G solar spectrum69 at a given wavelength λ. The multiplication of the elementary charge e to the integral assumes the ideal case where every absorbed photon is converted to a charge carrier.67 As such, Jabs sets the upper bound of the short-circuit current generated from the MXene alloys under solar irradiation. Figure 9 plots the Jabs values versus x for Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2. With increasing composition x, the absorbed photon fluxes generally decrease, with Ti2(1 - x)Hf2xCO2 MXenes decreasing most steeply, followed by Ti2(1 - x) Zr2xCO2 and Zr2(1 - x)Hf2xCO2 MXene alloys; this is related to the constituent Ti2CO2 MXene possessing the highest Jabs of 4.5 mA cm -2, followed by Zr2CO2 (1.6 mA cm -2) and Hf2CO2 (0.9 mA cm -2). We would note that the absorbed photon fluxes of the MXene alloys are much higher than typical photovoltaic materials like Si, GaAs, and P3HT of 0.1, 0.3, and 0.2 mA cm -2



respectively and are comparable to those of other 2D materials, including graphene, and TMDs like MoS2 and WS2 (2.0, 3.9, and 2.3 mA cm -2 respectively),67 suggesting potential applications as photovoltaics. In addition, we remark that since our calculations are based on the independent particle picture which usually underestimates the absorbance at wavelengths near the onset of optical absorption, this would ensure a conservative estimate of Jabs values. Comparing Jabs, the band positions and the likelihood of electron-hole recombination among the MXene alloys, we identify Ti2(1 - x)Zr2xCO2 alloy with x ~ 0.2778 to be potentially the best performing water-splitting photocatalyst; it has a sufficiently broad band gap (Eg = 1.48 eV) along with properly aligned band positions (ECBM = -0.02 eV vs. NHE; EVBM = +1.45 eV vs. NHE) for water-splitting, a large difference in effective masses of the holes and electrons (mh* = 0.18 m0; me* = 0.80 m0) to impede electron-hole recombination, and high absorbed photon flux (Jabs = 3.0 mA cm -2; ~ 200% of Zr2CO2). Inasmuch as Ti2CO2 being a good solar absorber (highest Jabs) but with improperly aligned band positions, while Zr2CO2 and Hf2CO2 to absorb solar photons weakly albeit suitably aligned band positions, this work demonstrates the importance of alloying to bring out and enhance the desired properties from the constituents which allow the material to possess better photocatalytic performance.

4. Conclusions In conclusion, through the systematic implementation of a first-principles-based multiscale computational approach involving both DFT and CE methods, we determined the phase stability of different alloy structures of Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 via the evaluation of the formation energies of more than three million different configurations for each of the MXene alloy systems, showing that these alloys tend to form disordered solid-solutions.


Page 18 of 39

Page 19 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


To model the random distribution of alloyants, we constructed special quasirandom structures (SQSs) for subsequent evaluation of structural and band structure-related properties. Structural analyses revealed that the lattice parameters obey the Vegard’s law, i.e., changes linearly versus composition. Further investigation shows correlations between ionic size differences of the alloyants, the distortion of the bond lengths of the alloys, and the formation energies. Evaluated elastic constants show these solid-solution alloys to be mechanically stable and possess high elastic stiffness and resistance to deformation. Generally, this group of alloy MXenes’ electronic band structures and DOSs exhibit similar features; they are indirect band gap semiconductors with the VBM comprising of predominantly C and O p-orbitals while the CBM possessing transition metal d-orbital characters. Their band gaps range from 1.25 to 1.80 eV, above 1.23 eV necessary for photocatalytic water-splitting. Their effective electron masses displayed significant anisotropy; while their effective hole masses are essentially isotropic and with a lighter effective mass than the electrons. The Ti2(1 - x)Zr2xCO2 and Ti2(1 - x)Hf2xCO2 alloy MXenes demonstrated increased differences between the effective hole and electron masses relative to their constituent MXenes. This indirect band nature and the dissimilarity between the effective hole and electron masses of the alloy MXenes further promote spatial separation of the holes and electrons for enhanced photocatalytic performance. Comparing the CBM and VBM positions relative to the NHE showed that the band edges are properly aligned for water-splitting photocatalysts except for alloys high in Ti (x < 0.2222 for Ti2(1 - x)Zr2xCO2 and x < 0.27778 for Ti2(1 - x)Hf2xCO2). From the dielectric and the solar absorbance calculations, we find these alloy MXenes to possess higher absorbed photon fluxes than typical photovoltaic materials like Si, GaAs, P3HT, graphene, and even TMDs MoS2 and WS2, indicating their potential application in photovoltaics too.



From the inspection of our findings, we predict that Ti2(1 - x)Zr2xCO2 alloy with x ~ 0.2778 to be a promising water-splitting photocatalyst with appropriate band gap, large electron-hole mass difference to reduce recombination rate, appropriate band positions, and high absorbed photon flux. Considering the fact that, Ti2CO2 has decent solar absorption but improperly aligned band positions, while Zr2CO2 and Hf2CO2 absorb solar photons weakly albeit suitably aligned band positions, our results demonstrates the importance of alloying of the MXenes to tune, optimize, and enhance the desired functional properties for better photocatalytic performance.

Supporting Information ECIs for the MXene alloys; Structures of different geometries of O-functionalized MXenes; Phonon dispersion curves and DOSs of the constituents MXenes; Semi-grand canonical MC simulation plots for the MXene alloys; Structures of SQSs; Phonon dispersion curves of selected SQSs; Electronic band structure along 2-D hexagonal high symmetry paths and total and projected DOS plots for the SQSs; Contour plots of the imaginary part of the dielectric function for the SQSs; Table of the least-squares fitting and leave-one-out cross validation errors of the cluster expansion set for the MXene alloys.

Author Information Corresponding Authors *E-mail: [email protected] *E-mail: [email protected]


Page 20 of 39

Page 21 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ORCID Zicong Marvin Wong: 0000-0003-1530-0340 Teck Leong Tan: 0000-0002-7089-8966 Guo Qin Xu: 0000-0003-4671-7923 Notes The authors declare no competing financial interest.

Acknowledgement The authors acknowledge the use of high-performance computing facilities in A*STAR Computational Resource Centre (ACRC) and the National Supercomputing Centre (NSCC) in Singapore for the computational calculations implemented in this work. The work done in the National University of Singapore is supported by the Ministry of Education, Singapore (Grant No. R-143-000-636-112).

References 1. Geim, A. K.; Novoselov, K. S., The Rise of Graphene. Nat. Mater. 2007, 6, 183. 2. Tang, Q.; Zhou, Z., Graphene-Analogous Low-Dimensional Materials. Prog. Mater. Sci. 2013, 58 (8), 1244-1315. 3. Tang, Q.; Zhou, Z.; Chen, Z., Innovation and Discovery of Graphene‐like Materials via Density‐Functional Theory Computations. WIRES Comput. Mol. Sci. 2015, 5 (5), 360-379. 4. Zhao, M.; Zhang, R., Two-Dimensional Topological Insulators with Binary Honeycomb Lattices: SiC3 Siligraphene and its Analogs. Phys. Rev. B 2014, 89 (19), 195427. 5. Chhowalla, M.; Shin, H. S.; Eda, G.; Li, L.-J.; Loh, K. P.; Zhang, H., The Chemistry of Two-Dimensional Layered Transition Metal Dichalcogenide Nanosheets. Nat. Chem. 2013, 5, 263. 6. Chen, Y.; Xi, J.; Dumcenco, D. O.; Liu, Z.; Suenaga, K.; Wang, D.; Shuai, Z.; Huang, Y.S.; Xie, L., Tunable Band Gap Photoluminescence from Atomically Thin Transition-Metal Dichalcogenide Alloys. ACS Nano 2013, 7 (5), 4610-4616. 7. Anasori, B.; Lukatskaya, M. R.; Gogotsi, Y., 2D Metal Carbides and Nitrides (MXenes) for Energy Storage. Nat. Rev. Mater. 2017, 2, 16098.



8. Zhang, X.; Zhang, Z.; Zhou, Z., MXene-based Materials for Electrochemical Energy Storage. J. Energy Chem. 2018, 27 (1), 73-85. 9. Mashtalir, O.; Naguib, M.; Mochalin, V. N.; Dall’Agnese, Y.; Heon, M.; Barsoum, M. W.; Gogotsi, Y., Intercalation and Delamination of Layered Carbides and Carbonitrides. Nat. Commun. 2013, 4, 1716. 10. Zhou, J.; Zha, X.; Chen Fan, Y.; Ye, Q.; Eklund, P.; Du, S.; Huang, Q., A Two‐Dimensional Zirconium Carbide by Selective Etching of Al3C3 from Nanolaminated Zr3Al3C5. Angew. Chem. Int. Ed. 2016, 55 (16), 5008-5013. 11. Gogotsi, Y., Transition Metal Carbides go 2D. Nat. Mater. 2015, 14, 1079. 12. Naguib, M.; Mashtalir, O.; Carle, J.; Presser, V.; Lu, J.; Hultman, L.; Gogotsi, Y.; Barsoum, M. W., Two-Dimensional Transition Metal Carbides. ACS Nano 2012, 6 (2), 1322-1331. 13. Naguib, M.; Come, J.; Dyatkin, B.; Presser, V.; Taberna, P.-L.; Simon, P.; Barsoum, M. W.; Gogotsi, Y., MXene: A Promising Transition Metal Carbide Anode for Lithium-Ion Batteries. Electrochem. Commun. 2012, 16 (1), 61-64. 14. Er, D.; Li, J.; Naguib, M.; Gogotsi, Y.; Shenoy, V. B., Ti3C2 MXene as a High Capacity Electrode Material for Metal (Li, Na, K, Ca) Ion Batteries. ACS Appl. Mater. Interfaces 2014, 6 (14), 11173-11179. 15. Seh, Z. W.; Fredrickson, K. D.; Anasori, B.; Kibsgaard, J.; Strickler, A. L.; Lukatskaya, M. R.; Gogotsi, Y.; Jaramillo, T. F.; Vojvodic, A., Two-Dimensional Molybdenum Carbide (MXene) as an Efficient Electrocatalyst for Hydrogen Evolution. ACS Energy Lett. 2016, 1 (3), 589-594. 16. Guo, Z.; Zhou, J.; Zhu, L.; Sun, Z., MXene: A Promising Photocatalyst for Water Splitting. J. Mater. Chem. A 2016, 4 (29), 11446-11452. 17. Zhang, H.; Yang, G.; Zuo, X.; Tang, H.; Yang, Q.; Li, G., Computational Studies on the Structural, Electronic and Optical Properties Of Graphene-like MXenes (M2CT2, M = Ti, Zr, Hf; T = O, F, OH) and Their Potential Applications as Visible-Light Driven Photocatalysts. J. Mater. Chem. A 2016, 4 (33), 12913-12920. 18. Singh, A. K.; Mathew, K.; Zhuang, H. L.; Hennig, R. G., Computational Screening of 2D Materials for Photocatalysis. J. Phys. Chem. Lett. 2015, 6 (6), 1087-1098. 19. Anasori, B.; Xie, Y.; Beidaghi, M.; Lu, J.; Hosler, B. C.; Hultman, L.; Kent, P. R. C.; Gogotsi, Y.; Barsoum, M. W., Two-Dimensional, Ordered, Double Transition Metals Carbides (MXenes). ACS Nano 2015, 9 (10), 9507-9516. 20. Tan, T. L.; Jin, H. M.; Sullivan, M. B.; Anasori, B.; Gogotsi, Y., High-Throughput Survey of Ordering Configurations in MXene Alloys Across Compositions and Temperatures. ACS Nano 2017, 11 (5), 4407-4418. 21. Khazaei, M.; Arai, M.; Sasaki, T.; Chung, C. Y.; Venkataramanan Natarajan, S.; Estili, M.; Sakka, Y.; Kawazoe, Y., Novel Electronic and Magnetic Properties of Two‐Dimensional Transition Metal Carbides and Nitrides. Adv. Funct. Mater. 2012, 23 (17), 2185-2192. 22. Zarkevich, N. A.; Tan, T. L.; Johnson, D. D., First-Principles Prediction of PhaseSegregating Alloy Phase Diagrams and a Rapid Design Estimate of Their Transition Temperatures. Phys. Rev. B 2007, 75 (10), 104203. 23. Zarkevich, N. A.; Tan, T. L.; Wang, L. L.; Johnson, D. D., Low-Energy Antiphase Boundaries, Degenerate Superstructures, And Phase Stability in Frustrated fcc Ising Model and Ag-Au Alloys. Phys. Rev. B 2008, 77 (14), 144208. 24. Ceder, G.; Garbulsky, G. D.; Tepesch, P. D., Convergent Real-Space Cluster Expansion for Configurational Disorder in Ionic Systems. Phys. Rev. B 1995, 51 (17), 11257-11261.


Page 22 of 39

Page 23 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


25. Ceder, G.; Ven, A. V. D.; Marianetti, C.; Morgan, D., First-Principles Alloy Theory in Oxides. Model. Simul. Mat. Sci. Eng. 2000, 8 (3), 311. 26. Chen, W.; Schmidt, D.; Schneider, W. F.; Wolverton, C., First-Principles Cluster Expansion Study of Missing-Row Reconstructions of fcc (110) Surfaces. Phys. Rev. B 2011, 83 (7), 075415. 27. Herder, L. M.; Bray, J. M.; Schneider, W. F., Comparison of Cluster Expansion Fitting Algorithms for Interactions at Surfaces. Surf. Sci. 2015, 640, 104-111. 28. Zunger, A.; Wei, S. H.; Ferreira, L. G.; Bernard, J. E., Special Quasirandom Structures. Phys. Rev. Lett. 1990, 65 (3), 353-356. 29. Connolly, J. W. D.; Williams, A. R., Density-Functional Theory Applied to Phase Transformations in Transition-Metal Alloys. Phys. Rev. B 1983, 27 (8), 5169-5172. 30. Sanchez, J. M.; Ducastelle, F.; Gratias, D., Generalized Cluster Description of Multicomponent Systems. Physica A 1984, 128 (1), 334-350. 31. Zarkevich, N. A.; Johnson, D. D., Reliable First-Principles Alloy Thermodynamics via Truncated Cluster Expansions. Phys. Rev. Lett. 2004, 92 (25), 255702. 32. Tan, T. L.; Wang, L.-L.; Johnson, D. D.; Bai, K., A Comprehensive Search for Stable Pt– Pd Nanoalloy Configurations and their Use as Tunable Catalysts. Nano Lett. 2012, 12 (9), 48754880. 33. Tan, T. L.; Wang, L.-L.; Zhang, J.; Johnson, D. D.; Bai, K., Platinum Nanoparticle during Electrochemical Hydrogen Evolution: Adsorbate Distribution, Active Reaction Species, and Size Effect. ACS Catal. 2015, 5 (4), 2376-2383. 34. Ng, M.-F.; Tan, T. L., Unveiling Stable Group IV Alloy Nanowires via a Comprehensive Search and their Electronic Band Characteristics. Nano Lett. 2013, 13 (10), 4951-4956. 35. Tan, T. L.; Ng, M.-F., Computational Screening for Effective Ge1-xSix Nanowire Photocatalyst. Phys. Chem. Chem. Phys. 2015, 17 (31), 20391-20397. 36. Tan, T. L.; Ng, M.-F.; Eda, G., Stable Monolayer Transition Metal Dichalcogenide Ordered Alloys with Tunable Electronic Properties. J. Phys. Chem. C 2016, 120 (5), 2501-2508. 37. Wong, Z. M.; Cheng, H.; Yang, S.-W.; Tan, T. L.; Xu, G. Q., Computational Design of Perovskite BaxSr1–xSnO3 Alloys as Transparent Conductors and Photocatalysts. J. Phys. Chem. C 2017, 121 (47), 26446-26456. 38. Kohn, W.; Sham, L. J., Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140 (4A), A1133-A1138. 39. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77 (18), 3865-3868. 40. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]. Phys. Rev. Lett. 1997, 78 (7), 1396-1396. 41. Kresse, G.; Furthmüller, J., Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6 (1), 15-50. 42. Kresse, G.; Furthmüller, J., Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54 (16), 11169-11186. 43. Blöchl, P. E., Projector Augmented-Wave Method. Phys. Rev. B 1994, 50 (24), 1795317979. 44. Monkhorst, H. J.; Pack, J. D., Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13 (12), 5188-5192. 45. Heyd, J.; Scuseria, G. E.; Ernzerhof, M., Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2003, 118 (18), 8207-8215.



46. Heyd, J.; Scuseria, G. E.; Ernzerhof, M., Erratum: “Hybrid Functionals Based on a Screened Coulomb Potential” [J. Chem. Phys. 118, 8207 (2003)]. J. Chem. Phys. 2006, 124 (21), 219906. 47. Le Page, Y.; Saxe, P., Symmetry-General Least-Squares Extraction of Elastic Data for Strained Materials from Ab Initio Calculations of Stress. Phys. Rev. B 2002, 65 (10), 104104. 48. Wu, X.; Vanderbilt, D.; Hamann, D. R., Systematic Treatment of Displacements, Strains, and Electric Fields in Density-Functional Perturbation Theory. Phys. Rev. B 2005, 72 (3), 035105. 49. Kurtoglu, M.; Naguib, M.; Gogotsi, Y.; Barsoum, M. W., First Principles Study of TwoDimensional Early Transition Metal Carbides. MRS Commun. 2012, 2 (4), 133-137. 50. Zha, X.-H.; Huang, Q.; He, J.; He, H.; Zhai, J.; Francisco, J. S.; Du, S., The Thermal and Electrical Properties of the Promising Semiconductor Mxene Hf2CO2. Sci. Rep. 2016, 6, 27971. 51. Shannon, R., Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides. Acta Cryst. A 1976, 32 (5), 751-767. 52. Sun, Z. M., Progress in Research and Development on MAX Phases: A Family of Layered Ternary Compounds. Int. Mater. Rev. 2011, 56 (3), 143-166. 53. Naguib, M.; Kurtoglu, M.; Presser, V.; Lu, J.; Niu, J.; Heon, M.; Hultman, L.; Gogotsi, Y.; Barsoum Michel, W., Two-Dimensional Nanocrystals Produced by Exfoliation of Ti3AlC2. Adv. Mater. 2011, 23 (37), 4248-4253. 54. Allred, A. L., Electronegativity Values from Thermochemical Data. J. Inorg. Nucl. Chem. 1961, 17 (3), 215-221. 55. Hume-Rothery, W.; Haworth, C. W.; Smallman, R. E., The Structure of Metals and Alloys. Institute of Metals and the Institution of Metallurgists: London, 1969. 56. Wei, X.; Fragneaud, B.; Marianetti, C. A.; Kysar, J. W., Nonlinear Elastic Behavior of Graphene: Ab Initio Calculations to Continuum Description. Phys. Rev. B 2009, 80 (20), 205407. 57. Zhou, J.; Huang, R., Internal Lattice Relaxation of Single-Layer Graphene under In-Plane Deformation. J. Mech. Phys. Solids 2008, 56 (4), 1609-1623. 58. Born, M.; Huang, K., Dynamical Theory of Crystal Lattices. Clarendon Press: Oxford,1954. 59. John, R.; Merlin, B., Theoretical Investigation of Structural, Electronic, and Mechanical Properties of Two Dimensional C, Si, Ge, Sn. Cryst. Struct. Theory Appl. 2016, 5 (3), 13. 60. Liu, K.; Yan, Q.; Chen, M.; Fan, W.; Sun, Y.; Suh, J.; Fu, D.; Lee, S.; Zhou, J.; Tongay, S.; Ji, J.; Neaton, J. B.; Wu, J., Elastic Properties of Chemical-Vapor-Deposited Monolayer MoS2, WS2, and their Bilayer Heterostructures. Nano Lett. 2014, 14 (9), 5097-5103. 61. Luttrell, T.; Halpegamage, S.; Tao, J.; Kramer, A.; Sutter, E.; Batzill, M., Why is Anatase a Better Photocatalyst Than Rutile? - Model Studies on Epitaxial TiO2 Films. Sci. Rep. 2014, 4, 4043. 62. Hamaguchi, C., Wannier Function and Effective Mass Approximation. In Basic Semiconductor Physics, Hamaguchi, C., Ed. Springer International Publishing: Cham, 2017; 125151. 63. Zhang, X.; Zhao, X.; Wu, D.; Jing, Y.; Zhou, Z., High and Anisotropic Carrier Mobility in Experimentally Possible Ti2CO2 (MXene) Monolayers and Nanoribbons. Nanoscale 2015, 7 (38), 16020-16025. 64. Zhang, X.; Zhang, Z.; Wu, D.; Zhang, X.; Zhao, X.; Zhou, Z., Computational Screening of 2D Materials and Rational Design of Heterojunctions for Water Splitting Photocatalysts. Small Methods 2018, 2 (5), 1700359.


Page 24 of 39

Page 25 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


65. Toroker, M. C.; Kanan, D. K.; Alidoust, N.; Isseroff, L. Y.; Liao, P.; Carter, E. A., First Principles Scheme to Evaluate Band Edge Positions in Potential Transition Metal Oxide Photocatalysts and Photoelectrodes. Phys. Chem. Chem. Phys. 2011, 13 (37), 16644-16654. 66. Tada, H.; Mitsui, T.; Kiyonaga, T.; Akita, T.; Tanaka, K., All-Solid-State Z-Scheme in CdS–Au–TiO2 Three-Component Nanojunction System. Nat. Mater. 2006, 5, 782. 67. Bernardi, M.; Palummo, M.; Grossman, J. C., Extraordinary Sunlight Absorption and One Nanometer Thick Photovoltaics Using Two-Dimensional Monolayer Materials. Nano Lett. 2013, 13 (8), 3664-3670. 68. Yang, L.; Deslippe, J.; Park, C.-H.; Cohen, M. L.; Louie, S. G., Excitonic Effects on the Optical Response of Graphene and Bilayer Graphene. Phys. Rev. Lett. 2009, 103 (18), 186802. 69. Renewable Resource Data Center – National Renewable Energy Laboratory. Reference Solar Spectral Irradiance: Air Mass 1.5. https://rredc.nrel.gov/solar/spectra/am1.5/ (accessed July 13, 2018). 70. White, J. L.; Baruch, M. F.; Pander, J. E.; Hu, Y.; Fortmeyer, I. C.; Park, J. E.; Zhang, T.; Liao, K.; Gu, J.; Yan, Y.; Shaw, T. W.; Abelev, E.; Bocarsly, A. B., Light-Driven Heterogeneous Reduction of Carbon Dioxide: Photocatalysts and Photoelectrodes. Chem. Rev. 2015, 115 (23), 12888-12935.



(a)

(b)


Page 26 of 39

Page 27 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(c)

Figure 1. Formation energies, Ef’s (evaluated from CE), versus composition plots for (a) Ti2(1 - x) Zr2xCO2, (b) Ti2(1 - x)Hf2xCO2, and (c) Zr2(1 - x)Hf2xCO2 alloy MXenes using more than 3 million alloy configurations for each system generated from 5- to 70-atom supercells. Each point represents a particular ordered alloy structure whose relative stability is indicated by its formation energy w.r.t. that of the constituent MXenes. The green curve indicates the formation enthalpy of the perfectly disordered solid solution, while the pink, blue, violet, and purple curves correspond to the formation free energies of the perfectly disordered solid solution (formation enthalpy with configurational entropy) at temperatures of 300 K, 500 K, 1000 K, and 1500 K respectively.



(a)

(b)

Figure 2. Plots of (a) lattice constant a per primitive cell, pc, and (b) thickness of the MXene monolayer versus composition for the SQSs of M2(1 - x)M'2xCO2. The points in blue, red, and green


Page 28 of 39

Page 29 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


along with their linear fittings correspond to the Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x) Hf2xCO2 MXene SQSs respectively.



(a)

(b)

(c)

(Ti,Zr)-C

(Ti,Zr)-O

(Ti,Hf)-C

(Ti,Hf)-O

(Zr,Hf)-C

(Zr,Hf)-O

Figure 3. Contour plots of the distributions of (M,M')-C (left) and (M,M')-O (right) bond lengths for (a) Ti2(1 - x)Zr2xCO2, (b) Ti2(1 - x)Hf2xCO2, and (c) Zr2(1 - x)Hf2xCO2 MXene SQSs. Blue represents negligible frequency of occurrence of the bond length, bond angle, or separation


Page 30 of 39

Page 31 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


distance; while red color represents high frequency of occurrence, along with other colors indicating the frequencies in between as shown in the legend. The average values for the frequencies of occurrence are indicated as thick dashed lines.



(a)

(b)

(c)

(d)

Figure 4. Plots of the elastic constants (a) C11, (b) C12 and C66, (c) in-plane Young’s modulus, Ys, and (d) Poisson’s ratio, ν, versus composition for the SQSs of M2(1 - x)M'2xCO2. The points in blue, red, and green along with their best-fit curves correspond to Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 respectively.


Page 32 of 39

Page 33 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

Figure 5. Plots of (a) resultant effective electron and hole masses versus composition and (b) anisotropy comparisons of effective mass of electron and hole along two perpendicular components for the SQSs of M2(1 - x)M'2xCO2. The points in blue, red, and green along with their best-fit curves and the points in dark blue, dark red, and dark green correspond to the effective



electron and hole masses of Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 respectively. The dashed line in (b) indicates isotropy, i.e., the effective mass is equal in both directions.

Figure 6. Band gaps, Eg’s, obtained via HSE06 functional versus composition plot for the various M2(1 - x)M'2xCO2. The points in blue, red, and green correspond to the Ti2(1 - x)Zr2xCO2, Ti2(1 - x)Hf2x CO2, and Zr2(1 - x)Hf2xCO2 MXene SQSs respectively. The dashed lines are best-fit lines for each alloy systems and are guide for the eyes.


Page 34 of 39

Page 35 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)



(c)

Figure 7. Electronic band edge positions versus composition for the SQSs of (a) Ti2(1 - x)Zr2xCO2, (b) Ti2(1 - x)Hf2xCO2, and (c) Zr2(1 - x)Hf2xCO2 with respect to the normal hydrogen electrode (NHE) and vacuum. The positions of the CBM and VBM are labeled in blue and red respectively. The water reduction and oxidation potential levels at pH = 0 are indicated in purple; while the range of potentials for various CO2 reductions70 are within the orange shaded region.


Page 36 of 39

Page 37 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 8. Contour plots of the optical absorbance along the in-plane x-direction versus wavelength and composition x for the (a) Ti2(1 - x)Zr2xCO2, (b) Ti2(1 - x)Hf2xCO2, and (c) Zr2(1 - x)Hf2xCO2 MXene SQSs as derived from Equation (8). The magnitudes are as shown in the scale bar with red representing strong absorbance and blue color representing negligible absorbance, along with other colors indicating magnitudes in between. The photon flux of AM1.5G solar spectrum69 is shown as a contour plot above the MXene SQSs (AM: air mass; G: global).



Figure 9. Plot of absorbed photon flux, Jabs, versus composition for the SQSs of M2(1 - x)M'2xCO2. The points in blue, red, and green along with their best-fit curves correspond to the Ti2(1 - x)Zr2xCO2 , Ti2(1 - x)Hf2xCO2, and Zr2(1 - x)Hf2xCO2 MXene SQSs respectively.


Page 38 of 39

Page 39 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic @ x = ??? e--h+ separation Band alignment

x=0

Absorbance

x

Semiconducting

M'2(1–x)M''2xCO2 MXenes

x=1

Ti2(1–x)Zr2xCO2, Ti2(1–x)Hf2xCO2, Zr2(1–x)Hf2xCO2


Enhancing the Photocatalytic Performance of MXenes via

Recommend Documents