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Computational Design of Perovskite BaSr SnO Alloys as Transparent Conductors and Photocatalysts Zicong Marvin Wong, Hansong Cheng, Shuo-Wang Yang, Teck Leong Tan, and Guoqin Xu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b08681 • Publication Date (Web): 26 Oct 2017 Downloaded from http://pubs.acs.org on October 31, 2017

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The Journal of Physical Chemistry

Computational Design of Perovskite BaxSr1–xSnO3 Alloys as Transparent Conductors and Photocatalysts Zicong Marvin Wong, a,b Hansong Cheng,*c Shuo-Wang Yang,b Teck Leong Tan*b, and Guo Qin Xu,a a

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

b

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

Sustainable Energy Laboratory, Faculty of Material Science and Chemistry, China University of Geosciences, 388 Lumo Road, Wuhan 430074, PR China

ABSTRACT: Using a first-principles based multiscale computational approach involving density functional theory and the cluster expansion method, we produced the structural evolution for the perovskite BaxSr1–xSnO3 system in relation to its Ba:Sr composition from the formation energies of different alloy configurations and demonstrated their use as tunable alloy transparent conductors and photocatalysts via structural, electronic and optical studies. The predicted phase diagram has revealed the transformation of the structure of BaxSr1–xSnO3 from orthorhombic to tetragonal and finally to cubic with increasing x, forming disordered

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solid solutions for 0 < x < 1 that is entropically stabilized from phase segregation. This trend is similarly observed in the published experiments. Special quasirandom structure approach is used to model the disordered solid solutions of the BaxSr1–xSnO3 alloys. Structural analyses have indicated that the decrease in Ba:Sr ratio is associated with the decrease in unit cell volume, and also the increased distortion of the (Ba,Sr)O12 cuboctahedra, while the SnO6 octahedra remained relatively undistorted and underwent tilting to accommodate the smaller Sr atoms. Electronic and optical studies have shown the BaxSr1–xSnO3 alloys to possess transparent conducting and photocatalytic water splitting and CO2-reduction capabilities, which can be tailored via compositional engineering. The results should serve as a guide for the investigations of structure-property relationships of perovskite-based alloys.

INTRODUCTION Among multitudinous classes of compounds, perovskites and perovskite-related structures are one of the most intensely studied materials in solid state chemistry and physics.1 The ideal perovskite structure has ABX3 stoichiometry and cubic Pm3m space group symmetry comprising of three-dimensional corner-sharing network of BX6 octahedra with the A-site cations residing in the cavities formed by the network as AX12 cuboctahedra. Notably, the BX6 octahedra can expand, contract, tilt, or rotate to various degrees to accommodate non-ideal ionic size ratios of the cations and anions. As such, this flexibility allows the accommodation of almost all of the elements in the periodic table,2,3 giving rise to numerous interesting chemical

and

physical

phenomena

such

as

piezoelectricity,4

pyroelectricity,5

ferroelectricity,5,6 multiferroicity,7 ionic conductivity,8 superconductivity,9 photovoltaic effects,10 catalytic activities,11,12 etc. To optimize or tune properties of a perovskite material, it is common to form substitutional alloys in ABX3 systems, e.g. (A,A’)BX3, A(B,B’)X3, or even (A,A’)(B,B’)X3. For instance, the ferroelectric Curie temperature of (Ba,Sr)TiO3


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compounds can be tailored by changing the Ba:Sr ratio to meet various criteria for device applications.13 For (Li,La)TiO3, its ionic conductivity varies greatly with not just the Li:La ratio, but also their A-site configuration in the crystal structure.8 Likewise, high piezoelectric response of Pb(Zr,Ti)O3 is only obtained when Zr:Ti ~ 1:1 and at the rhombohedraltetragonal phase boundary.4 These observations indicate that considerations of ion arrangements and crystal phase are important in the compositional engineering of a perovskite material for functional applications. Despite the many experimental researches and publications regarding alloy perovskite materials, most computational studies are restricted to single-component ABX3 perovskites or perovskites alloys at basic stoichiometric ratios (1:1, 1:2, 1:3) at A- and/or B-sites, largely due to the tractability of using small unit cells of the perovskite system for computational modelling, where all possible arrangements of substitutional elements in the perovskite alloys can be manually worked out.14,15 To model the thermodynamic phase stability of the perovskite alloys, different unit cells of various sizes are needed, so that the stability of many different possible alloy configurations can be evaluated. Relative stabilities between different structures are evaluated via comparison of their formation energies. As we show here, via the use of density functional theory (DFT) calculations with the cluster expansion (CE) method,16-24 one can comprehensively and rapidly evaluate the relative stabilities of 105 structures of alloy perovskites across compositions (0 < x < 1), from which the relationship between alloy composition, phase, and properties are mapped out systematically. For this work, we investigate the alloy of BaSnO3 and SrSnO3, where Ba and Sr can substitute one another. BaSnO3 and SrSnO3 are perovskite alkaline earth stannates that have garnered

interest

in

technological

applications

as

transparent

conductors

and

photocatalysts.25,26 The two perovskites differ in the radii of the A-site cations (Ba2+: 161 pm;



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Sr2+: 144 pm),27 resulting in structural dissimilarities. At room temperature, BaSnO3 has the ideal Pm3 m simple cubic perovskite structure,28-30 while SrSnO3 has the Pnma orthorhombic structure.28,31-33 Moreover, their alloys BaxSr1–xSnO3 have also been found experimentally to have composition-dependent phase transitions, transforming from orthorhombic to tetragonal and finally to cubic with increasing Ba:Sr ratio.28 Combining DFT and CE, we show that the BaxSr1–xSnO3 alloys exist as solid solutions but with compositionally dependent structural distortions that agree with experiments from literature. Using the special quasi-random structure (SQS) approach, we then create BaxSr1–xSnO3 structures that are representative of solid solutions and track their changes in electronic and optical properties across x. From the calculated properties, we suggest potential functional applications for the alloy - BaxSr1– xSnO3.

We show that the calculated bandgaps vary linearly between 2 to 3 eV with x and

given that the predicted bandgaps usually underestimate the experimental ones, BaxSr1–xSnO3 is expected to be transparent to visible light.

COMPUTATIONAL DETAILS The relative stability of BaxSr1–xSnO3 alloy structures at 0 K can be assessed via their formation energies, Ef’s, relative to the ground state constituent perovskites cubic BaSnO3 and orthorhombic SrSnO3, which are calculated by: Ef(BaxSr1–xSnO3, σ) = ET(BaxSr1–xSnO3, σ) – x ET(BaSnO3) – (1 – x) ET(SrSnO3)

(1)

where ET(BaSnO3), ET(SrSnO3), and ET(BaxSr1–xSnO3, σ) are the total energies per atom of cubic BaSnO3, orthorhombic SrSnO3, and a particular alloy configuration (σ) of BaxSr1–xSnO3 respectively. The value of Ef is dependent on the atomic configuration of the BaxSr1–xSnO3 alloys. According to the CE formalism,34-36 we can describe a particular alloy configuration, σ, on a lattice by a set of occupational variables ξαp with ξαp = 1 if the lattice site p is σ

m occupied by an atom of type α and 0 otherwise. If all the sites are occupied, then ∑α α ξαp = 1


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for every site p, where mα is the number of atomic types. For this work, mα = 2, where Ba and Sr form a binary alloy in the A-sites of BaxSr1–xSnO3, with the composition of Sn and O being fixed at 1. The CE Hamiltonian of a given alloy configuration, σ, can be expanded in terms of a set of geometric clusters and is generally written as:37,38 ECE (σ) = Vclusterϕcluster σ

(2)

clusters

where Vcluster is the effective cluster interaction (ECI) and ϕcluster(σ) is the cluster correlation function which is given by: ϕcluster σ =

ξαp

(3)

p∈cluster

In practice, all except a finite number of ECI’s are approximately zero; hence, accurate energies can be predicted from a properly truncated CE Hamiltonian. On the account of symmetry-equivalent ECI’s possessing the same value, only evaluation of the symmetrydistinct ECI’s in the truncated CE is required. The ECI’s are fitted to the DFT energies of a learning set of alloy configurations, σ1 , σ2 , …, σN . A properly truncated CE should not only replicate well the DFT formation energies of the various configurations in the learning set, DFT i.e., ECE (σ) but also be able to predict accurately the formation energies of alloy f (σ) ≈ Ef

configurations not in the learning set. The construction of the CE Hamiltonian and the ground state search are performed via the Thermodynamic Tool-Kit (TTK) code.

16,17,37,39-43

For each of the crystal phase – cubic,

tetragonal, and orthorhombic, an initial CE Hamiltonian is constructed from the DFT calculated energies of ~ 100 structures consisting of up to 40-atom unit cell. A ground state search over 104 possible alloy configurations (σ) with up to 100-atom unit cell is then carried out using the CE energies. CE-predicted ground states are then confirmed by DFT calculations; these new structures and their DFT energies are then added to the learning set to



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generate the next CE Hamiltonian for the ensuing iteration. The iterative process ends when no new ground states are predicted by the CE. First-principles calculations are performed using density functional theory (DFT)44 via the Perdew, Burke, and Ernzerhof (PBE) exchange relation-correlation based on the generalized gradient approximation (GGA)45,46 as implemented in the Vienna ab initio Simulation Package (VASP).47,48 The Projector Augmented Wave (PAW)49 was used to describe the electron-ion interactions. Plane-wave cut-offs are set to 520 eV. All atomic coordinates are fully relaxed until the calculated Hellmann-Feynman force on each atom is less than 0.01 eV/Å. Brillouin zone sampling was performed with Monkhorst-Pack (MP) k-point meshes50 inclusive of the Γ-point. The k-point density of around 20 k-points per Å-1 is sufficient for structural optimizations while a finer k-point mesh of approximately 40 points per Å-1 is implemented in electronic band structure and density of states (DOS) calculations. The PBEGGA and the Heyd-Scuseria-Ernzerhof hybrid functional method (HSE06)51,52 are compared for band gap calculations in BaxSr1–xSnO3 alloys, and in addition, single-shot GW (G0W0)53 for band gaps of BaSnO3 and SrSnO3.

RESULTS AND DISCUSSION Structure-Stability Relationship. To investigate the relationship between structure and stability in detail and hence the electrical and optical properties of stable BaxSr1–xSnO3 alloys, we first establish the ground-state structures of the constituent perovskites SrSnO3 (x = 0) and BaSnO3 (x = 1) predicted from first-principles. The calculated structural features of these perovskites along with their corresponding experimental data obtained from literature are as tabulated in Table 1. For SrSnO3, the orthorhombic structure is more stable than the cubic (tetragonal) case by 48 (12) meV/atom. This is in agreement with experimental observations of orthorhombic SrSnO3 in ambient conditions. 28,31-33 On the other hand, for BaSnO3, it is


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revealed that the orthorhombic, tetragonal, and cubic structures are almost equally stable. Figure 1 shows that the final optimized orthorhombic and tetragonal structures of BaSnO3 (right column) have a much smaller deviation from the cubic structure compared to SrSnO3 (left column). This is further supported by the insignificant deviation of the Sn-O-Sn (< 6%) and O-Sn-O (< 0.3%) bond angles of the optimized orthorhombic and tetragonal BaSnO3 with that of cubic BaSnO3 as indicated in Table 1. This again corresponds well with the experimentally observed cubic BaSnO3 phase under ambient conditions. 28-30 It is to be noted that PBE-GGA calculations tend to overestimate the lattice parameters. Nevertheless, the computed lattice parameters displayed good agreement with the experiments with modest overestimation of less than 1.8%. The simulated X-ray diffractograms of the optimized orthorhombic, tetragonal, and cubic structures (see Figure 2) exhibit almost identical peak positions and intensities for BaSnO3, whereas the diffraction peak positions between the different SrSnO3 structures are more distinct. The Powder Diffraction File (PDF) cards for BaSnO3 (PDF card no. 00-015-0780) and SrSnO3 (PDF card no. 04-010-6354) were also compared to the calculated diffractograms, which show almost similar diffraction patterns to cubic BaSnO3 and orthorhombic SrSnO3 respectively, albeit the positions are shifted marginally due to slight overestimation of PBE-GGA calculated lattice parameters.



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Figure 1. Structures of SrSnO3 (left) and BaSnO3 (right) after optimization using (a) cubic, (b) tetragonal, and (c) orthorhombic as the starting geometry. The Sr and Ba atoms are shown as large green spheres, the Sn atoms as dark grey spheres are located in the centre of the


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translucent grey octahedral, and the O atoms are illustrated as smaller red spheres at the vertices of the octahedra.



Table 1. Calculated and experimental structural parameters for orthorhombic, tetragonal, and cubic structures of SrSnO3 and BaSnO3. Lattice Parameters (Å) SnO6 Octahedra Energy above Ground State PseudoSn-O Sn-O-Sn O-Sn-O Calculated Cubic length (Å) angle (°) angle (°)ⱡ Hull (meV/atom) Orthorhombic a = 5.786 ā = 4.100 2.094 – 2.099 155.7 91.0 0 b = 5.817 156.0 90.7 89.3 c = 8.191 89.0

SrSnO3

Crystal Structure

BaSnO3

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a = 5.743 ā = 4.098 2.081 – 2.087 c = 8.347

154.5 180.0

90.0

+12

a = 4.110 ā = 4.110

180.0

90.0

+48

Experimental a = 5.703 ā = 4.034 2.046 – 2.052 (ortho.)32,33 b = 5.709 c = 8.065

159.6 160.5

92.3 90.8 89.2 87.7

–

Orthorhombic a = 5.922 ā = 4.190 2.096 – 2.099 b = 5.931 c = 8.379

174.4 174.9

90.3 90.2 89.7 89.8

+0.1

a = 5.915 ā = 4.192 2.100 – 2.106 c = 8.422

169.3 180.0

90.0

+0.1

a = 4.193 ā = 4.193

180.0

90.0

0

180.0

90.0

–

Tetragonal Cubic

Tetragonal Cubic

2.055

2.096

Experimental a = 4.124 ā = 4.124 2.055 (cubic)29 ⱡ : Excluding axial 180 ° O-Sn-O of the SnO6 octahedron


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Figure 2. Simulated X-ray diffractograms of (a) SrSnO3 and (b) BaSnO3 with orthorhombic (green), tetragonal (blue), and cubic (red) crystal structures. The experimental peak positions from the Powder Diffraction File (PDF) database are indicated in magenta.



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Figure 3 shows the Ef’s of ~ 105 alloy configurations derived from Equation (1) for different unit cell sizes and crystal systems that were evaluated for BaxSr1–xSnO3 using the effective cluster interactions (ECI’s) constructed from the cluster expansion method. The Ef’s of the ordered alloy structures of BaxSr1–xSnO3 are calculated to be positive regardless of the crystal structures. The finding indicates that the formation of ordered BaxSr1–xSnO3 alloys are energetically unfavourable and phase segregation should occur at sufficiently low temperature. This suggests that Ba and Sr prefer to be in the proximity of similar cation type instead of each other. To account for structural stability at finite temperatures (T > 0 K), the formation free energy, Ff, should be considered. For a disordered solid solution, the free energy at each composition x can be estimated as: Ff(x) = Ef(x) – TS(x)

(4)

where S corresponds to the configurational entropy, which can be estimated by: S(x) = – kB [x ln x + (1 – x) ln (1 – x)] Vibrational entropies are not considered here.


(5)

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Figure 3. Formation energies, Ef’s (evaluated from the cluster expansion method), versus composition plot for BaxSr1–xSnO3 using ~ 105 structures generated from 5 to 100-atom unit cells. Each point represents a particular ordered (ord.) structure whose relative stability is indicated by Ef. Red, blue, and green points indicate alloys derived from cubic (cub.), tetragonal (tetra.), and orthorhombic (orth.) crystal structures respectively. The solid and short-dashed lines indicate the Ef and Ff (the formation free energies at typical processing temperatures of around 1500 K) of the fully disordered BaxSr1–xSnO3 solid solutions (s.s.) respectively.



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Upon inclusion of configurational entropy of the disordered solid solutions of BaxSr1–xSnO3 alloys, the obtained Ff have negative values at typical processing temperatures of around 1500 K (Figure 3), indicating the existence of disordered solid solutions. The relative stability between the cubic, orthorhombic and tetragonal phases changes with x. For x < 0.7, orthorhombic BaxSr1–xSnO3 is the most stable. The tetragonal and the cubic phases are the most stable in the compositional ranges 0.7 < x < 0.9 and x > 0.9 respectively. The phase transition from orthorhombic to tetragonal to cubic phase (with increase x) is in accordance with experimental observation.28 It will be discussed in the following paragraphs that with decreasing Ba:Sr ratio, the average size of A-site cations in BaxSr1–xSnO3 alloys decreases, leading to an increased distortion of the SnO6 octahedra and hence, a higher deviation from the ideal cubic perovskite structure. This shows that the cluster expansion ECI’s are able to reliably evaluate the relative energetics of BaxSr1–xSnO3 alloy structures. BaxSr1–xSnO3 Special Quasirandom Structures (SQS’s). With the understanding of the phase diagram and formation stability of BaxSr1–xSnO3 alloys, we next look into the prediction of various physical and chemical properties of these alloys for functional applications. Since BaxSr1–xSnO3 alloys exist as disordered solid solutions, this implies that the utilization of ordered alloy structures for property calculations is not appropriate here. To this end, we use special quasirandom structures (SQS’s). Generally, SQS configurations aim to recreate specific statistical attributes of random solid solutions like pair correlation functions and orderings in the short-range.54 The SQS approach has already been implemented to semiconductors, metallic alloys and even perovskites.54-56 For this work, the SQS methodology is applied for the BaxSr1–xSnO3 disordered solid solution alloys with x = 0.125, 0.250, 0.375, 0.500, 0.625, 0.750, and 0.875, consisting of 40-atom supercells for practicality in calculations of electrical and optical properties via first-principles. The SQS’s


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are selected from the 106 different structures and configurations generated from the TTK code by comparing the cluster correlations of two- and occasionally three-body interactions that are the closest to those of a random alloy. As such, a total of 15 SQS’s, of which 8, 5, and 2 are derived from the orthorhombic, tetragonal, and cubic crystal structures respectively in relation to the crystal structure changes with x, were used for further investigations of the BaxSr1–xSnO3 disordered solid solution alloys. The structural analyses of the BaxSr1–xSnO3 SQS’s are presented in Figures 4, 5, 6, and 7. There exists a fairly positive linear relationship between the volumes (per unit atom) of the SQS’s with x (Figure 4). The predicted volumetric trend of the versus composition of BaxSr1– xSnO3

solid solutions agree with experimental results,28,29 albeit the overestimation of the

volumes for the PBE-GGA calculations as discussed above. The increase in x means there are more Ba atoms over Sr atoms which occupy more space per unit cell, expanding the volume of the (Ba,Sr)O10 cuboctahedra from 58.3 to 61.4 Å3 as shown in Figure 5. This increase in the (Ba,Sr)O12 cuboctahedra can also be visualized via the lengthening in the average (Ba,Sr)-O bond lengths from 2.922 to 2.965 Å with x as depicted in Figure 6a. The increase in the size of the (Ba,Sr)O10 cuboctahedra, however, does not result in noticeable changes in the volume of the SnO6 octahedra (~ 12.3 Å3) as illustrated in Figure 5 and also from the relatively constant average Sn-O bond length (~ 2.095 Å) in Figure 6b. The variation in the ratio of the volumes of the (Ba,Sr)O12 cuboctahedra to those of the SnO6 octahedra, VA/VB, from 4.75 to 5.00 with increasing x supports the experimentally-observed phase transitions of BaxSr1–xSnO3 from orthorhombic to tetragonal and finally to cubic.28,57 The broad range of the (Ba,Sr)-O bond lengths from 2.5 to 3.5 Å is a consequent to the distortion of the lattice parameters from the uneven distribution of Ba and Sr in the A-sites of the SQS unit cells. A spread in the Sn-O bond lengths is also observed in Figure 6b but to a much smaller extent from about 2.08 to 2.11 Å, inferring that SnO6 octahedra distort less when A-site cations are



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occupied by smaller Sr atoms. To quantify the degree of distortion in the SnO6 octahedra and the (Ba,Sr)O12 cuboctahedra, the following distortion index is utilized:58

|li − lave | 1 Distortion index = n lave n

(6)

i=1

where li is the bond length of the i-th Sn-O or (Ba,Sr)-O bond in the SnO6 octahedron or (Ba,Sr)O12 cuboctahedron; lave is the corresponding average bond length, and n is the number of Sn-O or (Ba,Sr)-O bonds in the SnO6 octahedron (n = 6) or (Ba,Sr)O12 cuboctahedron (n = 12). The distortion indices for both the SnO6 octahedra and the (Ba,Sr)O12 cuboctahedra for the SQS’s are illustrated in Figure 7. It is clear that the distortion in the (Ba,Sr)O12 cuboctahedra (up to 10%) is much more severe than that for the SnO6 octahedra (< 0.7%) upon substitution of Ba with Sr. This supports the inference that SnO6 octahedra are more resistant to distortion by substitution of the A-site cations from Ba to smaller Sr, resulting in the transformation of the overall crystal structure from cubic to tetragonal and then to orthorhombic via tilting of the SnO6 octahedra (deviation of O-Sn-O bond angles from 180 °, Figure 6c) and deformation of the (Ba,Sr)O12 cuboctahedra. Hence, utilizing the fact that for a perfect cubic perovskite, the a parameter can therefore be interpreted as the separation distance between two adjacent Sn atoms. The increase in the average Sn···Sn separation distance from 4.101 to 4.186 Å with x according to the contour plot in Figure 6d is coherent with the expansion of the unit cell with increasing Ba. Certainly, it is to be noted that there is a wide distribution of the actual Sn···Sn separation distance, some with the distance longer than or shorter than average, and the spread being the largest when x = 0.5 (4.103 to 4.199 Å). The longer than (shorter than) average Sn···Sn separation distances are a result of the uneven A-site distribution in the SQS unit cells with regions comprising majority of the larger Ba atoms (smaller Sr atoms). One could note that the general trends in the structural properties of BaxSr1–xSnO3 solid solutions can be predicted via virtual crystal approximation


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approach as implemented in another publication,59 but however, only via SQS methods can one obtain comprehensive structural analyses of the distributions of bond lengths and separations of solid solutions.



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Figure 4. Volume per unit atom versus composition plot for the SQS’s of BaxSr1–xSnO3. The volume obtained for this work is indicated in blue while the experimental volume from literature is labelled in orange.28,29


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Figure 5. Polyhedral volumes of (Ba,Sr)O12 cuboctahedra (VA, green) and SnO6 octahedra (VB, blue) and polyhedral volume ratio (VA/VB, red) versus composition plot for the SQS’s of BaxSr1–xSnO3.



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Figure 6. Contour plots of the distributions of (a) (Ba,Sr)-O and (b) Sn-O bond lengths, c) Sn-O-Sn bond angles, and (d) Sn···Sn separation distance versus composition plots for the SQS’s of BaxSr1–xSnO3. The blue colour signifies negligible frequency of occurrence of the separation distance or bond length while the red colour signifies high frequency of occurrence, along with other colours indicating the frequencies in-between as depicted in the



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legend. Local maxima are indicated by an ‘×’; while the dashed lines are the best-fit lines encompassing the average Sn-O or (Ba,Sr)-O bond lengths, Sn-O-Sn bond angles or Sn···Sn separation distance for each x.


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Figure 7. Distortion index versus composition plot for the SQS’s of BaxSr1–xSnO3. The distortion indices of each SnO6 octahedron and (Ba,Sr)O6 cuboctahedron for a particular SQS are indicated in blue and green respectively. The points with different shades of blue (green) indicate the distortion indices of the SnO6 octahedra ((Ba,Sr)O6 cuboctahedra) of different SQS’s with same x. The dotted lines correspond to the best-fit curves of SnO6 octahedra and (Ba,Sr)O12 cuboctahedra with respect to the variation the distortion indices with x.



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Electronic and Optical Properties. Figure S2 illustrates the electronic band structures, including the partial and total density of states (DOS) of the BaxSr1–xSnO3 SQS’s calculated via PBE-GGA. From the electronic band structures, it is observed that their conduction band minimum (CBM) all lie at the Γ-point while majority of their valence band maximum (VBM) lie at the Γ-point, indicating direct band gap character, with a few at other symmetry points suggesting indirect band gap character, albeit no distinct direct/indirect band transition relation with x. Since the constituent perovskites BaSnO3 and SrSnO3 display indirect band gap characteristics, one can establish the apparent direct band transition of certain BaxSr1– xSnO3

SQS’s to be band artefacts attributed to zone folding arising from the utilization of

supercells for the construction of the SQS’s,60,61 and propose that BaxSr1–xSnO3 solid solution alloys possess indirect band gap characteristics. Notwithstanding, it is evident that the curves near the CBM of the BaxSr1–xSnO3 SQS’s have large dispersion (up to 4 eV), and hence, the excited electrons in the CBM would have high electron mobilities. According to the Drude Model,62,63 the low effective electron masses of the electrons enhance their mobilities, improving the electrical conductivity and reducing the probability of electron-hole recombination. The comparatively parabolic CBM of the BaxSr1–xSnO3 SQS’s permit the obtention of the effective electrons masses by parabolic fitting of the CBM’s curve at selected high symmetry points along certain directions.60 With consideration of the possible anisotropy in the CBM comprising of two transverse (mt1, mt2) and one longitudinal (ml) effective masses for some BaxSr1–xSnO3 SQS’s, the following approach was implemented by summation of the effective masses along the equivalent directions to obtain the resultant effective electron mass, m*, in units of rest mass of a free electron (m0), via the harmonic mean: m* =

3 1 1 1 + + mt1 mt2 ml


(7)

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The relation of these effective electron masses with the Ba composition in BaxSr1–xSnO3 SQS’s is portrayed in Figure 8, where we show that the effective electron masses of BaxSr1– xSnO3

alloys all lie below 0.5 m0, which suggest high electron mobilities. Anisotropy in the

effective electron masses is small with the longitudinal component having a slightly lower effective mass than the transverse components and these components become isotropic at high x where the BaxSr1–xSnO3 alloys tends to be cubic. There is a well-defined trend of decreasing effective electron masses with increasing x down to 0.06 m0 for pure BaSnO3. As a comparison, the calculated effective electron mass of the CBM for In2O3, the TCO host of ITO, using the same method gives a value of 0.17 m0. All these indicate that the BaxSr1–xSnO3 alloys have small enough effective electron masses equable to high electrical conductivity upon n-type doping. The partial DOS (pDOS) for the BaxSr1–xSnO3 SQS’s reveal similar orbital characteristics with the CBM to be comprised mostly of Sn 5s and O 2p orbitals and the VBM to be predominantly O 2p in character. This lead to spatial separation of the negative (electrons) and positive (holes) charges, potentially leading to lower electron-hole recombination rate.39,40 Negligible contribution from Ba and/or Sr is observed.



Orthorhombic

Effective Mass (m0)

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Tetragonal

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Cubic

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

m* mt1

0.1

mt2 ml

0.0 0.0

0.2

0.4

0.6

0.8

0.0 1.0

x in BaxSr1-xSnO3

Figure 8. Effective electron masses versus composition plot for the SQS’s of BaxSr1–xSnO3. The transverse components (mt1, mt2), the longitudinal components (ml), and the resultant (m*) effective electron masses of each SQS’s are indicated as squares, diamonds, circles, and triangles respectively. The dashed line corresponds to the best-fit curve for the effective electron masses.


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A detailed investigation of pDOS of the BaxSr1–xSnO3 SQS’s with respect to x is illustrated in Figure 9. Here, the intensities of selected pDOS of Ba d, Sr d, Sn s, and O p orbitals are amplified to better compare their orbital characteristics and interactions. The valence bands for the BaxSr1–xSnO3 SQS’s appear unchanged with x and almost indistinguishable from each other, except for the varying intensities for Ba and Sr d states with respect to the Ba and Sr composition. On the other hand, for the conduction bands for the BaxSr1–xSnO3 SQS’s, one observes a narrowing of the conduction bandwidths (Sn 5s + O 2p) with increasing Sr composition, widening the band gap albeit similar orbital characteristics to each other. The compression of the conduction bandwidth with increasing Sr composition can be attributed to the increased distortion of the perovskite structure via tilting of the SnO6 octahedra. This in turn results in the decrease in the effective electron masses. The Ba and/or Sr states do not appear to significantly contribute to the valence and conduction bands of the BaxSr1–xSnO3 SQS’s, and only serve as an agent in altering the perovskite octahedral scaffold.



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Figure 9. Selected partial density-of-states (pDOS) versus composition plot for the SQS’s of BaxSr1–xSnO3. The pDOS of the d orbitals of Ba, the d orbitals of Sr, the s orbitals of Sn, and the p orbitals of O are labelled in green, dark green, blue, and red respectively. The widths of the Sn 5s + O 2p orbitals in the conduction band with respect to x are demarcated with thick dashed lines. The Fermi level is set to 0 eV.


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To be an effective transparent conductor or photocatalyst, it is crucial that the band gaps are sufficiently wide and the band edges are appropriately aligned.40,42 Figure 10 shows the band gaps of the BaxSr1–xSnO3 solid solution alloys obtained from this work using the SQS’s and also from the experiments published in literature for thin-film and bulk BaxSr1–xSnO3 solid solution alloys. 64,65 We note that using PBE-GGA functional severely underestimates the band gaps by about 2.5 to 3 eV compared to the experimental data as is commonly known,66-68 although they do provide accurate band shapes and band dispersions which have been reported to match experimental observations.69 Calculations using computationally expensive functionals like HSE06 and single-shot GW (G0W0) calculations produced band gaps that are closer to the experimental ones. Nonetheless, the calculated band gaps, regardless of the functionals implemented, revealed very similar downward sloping trend of almost linearly decreasing band gaps with increasing x as observed in the experiments, indicating reliability in prediction of the band gap trend of disordered alloy solid solutions using SQS’s. If the calculated band gaps are rigidly shifted to match with the experimental ones, they would all lie between 3.1 and 4.1 eV, implying their transparency to visible wavelengths and hence their desirability as transparent conductors and photocatalysts.



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Figure 10. Band gaps, Eg, versus composition plot for BaxSr1–xSnO3 solid solutions. Each point represents the band gap for a specific composition of Ba and Sr obtained via: experimentally-obtained thin film of BaxSr1–xSnO3 (×);64 experimentally-obtained bulk solid solutions of BaxSr1–xSnO3 (+);65 computationally calculated SQS’s of BaxSr1–xSnO3 using PBE-GGA (square) and HSE06 (circle); computationally calculated BaSnO3 and SrSnO3 using G0W0 (triangle).


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Comprehension of the band gaps with Ba:Sn composition allows determination of the band edge potentials for prediction of BaxSr1–xSnO3 alloys’ suitability in photocatalysis. The positions of the CBM and the VBM for BaxSr1–xSnO3 SQS’s were evaluated semi-empirically from the absolute electronegativity of the constituent atoms and the calculated band gaps,70 as tabulated in Table 2 and illustrated in Figure 11, via the following equations: ECB = χBa Sr x

1x SnO3

− 0.5 Eadj. g + E0

(8)

EVB = ECB + Eadj. g

(9) 1

χBa Sr x

1x SnO3

= χBa x · χSr (1x) · χSn · χO 3 5

calc., Bax Sr1x SnO3 BaSnO3 BaSnO3 SrSnO3 Eadj. + x · Eexpt., − Ecalc., + 1 − x·Eexpt., g = Eg g g g

−

SrSnO3 Ecalc., g

(10)

(11)

where χBa, χSr, χSn, and χO are the absolute (Mulliken) electronegativity of constituent atoms Ba, Sr, Sn, and O respectively;71 χBaxSn1-xSnO3 is the electronegativity of the BaxSr1–xSnO3 SQS’s which is the geometric mean of the absolute electronegativities of the component atoms; ECB and EVB are the energy levels of the CBM and VBM respectively; E0 is a scale factor which relates the redox level of the reference electrode to the vacuum level (e.g. E0 = – 4.44 eV for normal hydrogen electrode, NHE); and Egadj. is the calculated band gap that is adjusted to the experimental band gaps of the constituent BaSnO3 (3.1 eV) and SrSnO3 (4.1 eV) assuming linear dependence with x.65 It can be observed from the figure that both the positions of the VBM and CBM for BaxSr1–xSnO3 SQS’s vary rather linearly with x, with the slope of the VBM positions being larger than that of the CBM. An inspection on the various redox potentials reveal that under acidic conditions, the positions of the VBM and the CBM encompass the water reduction and oxidation potential levels, indicating that water splitting to both oxygen and hydrogen can happen. However, under alkaline conditions, only when x < 0.2 would both water reduction and oxidation can occur; beyond x > 0.2, the CBM positions



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fell below the reduction potential of water and hydrogen evolution becomes thermodynamically unfavourable. This means that BaxSr1–xSnO3 alloys are potential water splitting photocatalysts at both low pH for any Ba:Sr ratio and high pH for x < 0.2; and potential oxygen evolution photocatalysts at high pH for x > 0.2. Other than water splitting, the CBM positions for BaxSr1–xSnO3 SQS’s with x < 0.5 lie above various carbon dioxide (CO2) multi-electron reduction potentials,72 which suggest that these alloys can also be used in photocatalytic CO2 reduction applications. It has to be noted that our deductions for this photocatalytic study are based on the intrinsic properties of the BaxSr1–xSnO3 alloys. Influences to the photocatalytic performance arising from the surrounding aqueous medium is not modelled although interfacial interactions of the BaxSr1–xSnO3 alloys’ surfaces with water molecules can potentially screen the photo-induced charges and raise the overpotential for the photocatalytic reactions. Nevertheless, the results can still serve as a guideline for designing and tailoring of photocatalysts for specific reactions.


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Table 2. Electronegativity values and band edge positions of BaxSr1–xSnO3 SQS’s. Conduction Band Position, ECB (eV) –0.95 –0.86 –0.82 –0.81 –0.82 –0.81 –0.76 –0.71 –0.67

Valence Band Position, EVB (eV) 3.14 3.04 2.97 2.97 2.97 2.97 2.90 2.82 2.77

Tetragonal

Orthorhombic

Adjusted Band Crystal Composition,Electronegativity, Gap, Egadjusted Structure x χ (eV) (eV) 0.000 5.54 4.10 65 0.125 5.53 3.90 0.250 5.52 3.79 0.250 5.52 3.78 0.250 5.52 3.79 0.250 5.52 3.78 0.375 5.51 3.66 0.500 5.50 3.52 0.625 5.49 3.43 0.625 0.750 0.750 0.750 0.875

5.49 5.48 5.48 5.48 5.47

3.40 3.28 3.29 3.28 3.18

–0.65 –0.60 –0.61 –0.60 –0.56

2.75 2.68 2.69 2.68 2.62

Cubic

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0.875 0.875 1.000

5.47 5.47 5.46

3.12 3.13 3.10 65

–0.54 –0.54 –0.53

2.59 2.60 2.57



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Figure 11. Electronic band edge positions versus composition plot for the SQS’s of BaxSr1– xSnO3

with respect to NHE and vacuum, using adjusted PBE-GGA bandgaps. The positions

of the CBM and VBM are labelled in blue and red respectively. The potential levels for water reduction and oxidation are indicated in green and magenta to denote acidic and alkaline conditions respectively. The range of potentials for various CO2 reductions is also illustrated as a shaded orange bar.72


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CONCLUSIONS In summary, using a first-principles based multiscale computational approach involving DFT and CE method, we have successfully obtained a phase diagram for the BaxSr1–xSnO3 system comprising of its structural evolution with varying Ba:Sr composition and also provided some insights to selected structure-property relationship. The phase diagram produced from the formation energies of 106 different configurations and crystal structures of BaxSr1–xSnO3 alloys has revealed the transformation of the structure of BaxSr1–xSnO3 from orthorhombic (x < 0.7) to tetragonal (0.7 < x < 0.9) and finally to cubic (x > 0.9) with increasing x, forming disordered solid solutions for 0 < x < 1 that is entropically stabilized from phase segregation. This trend is similarly observed in the experimental syntheses of BaxSr1–xSnO3 alloys. SQS’s were employed to simulate disordered solid solutions of BaxSr1–xSnO3 alloys. Structural analyses indicated the decrease in Ba:Sr ratio is associated with the decrease in unit cell volume, and also increased distortion of the (Ba,Sr)O12 cuboctahedra, while the SnO6 octahedra remained relatively undistorted and underwent tilting to accommodate the smaller Sr atoms. The electronic and optical properties of the BaxSr1–xSnO3 SQS’s were also calculated. Their electronic band structures displayed large dispersion of the conduction bands, producing light effective electron masses, particularly at high Ba compositions. At certain compositions, the light effective masses exceed that of InO3, the well-known TCO host. The pDOS for the BaxSr1–xSnO3 SQS’s reveal similar orbital characteristics with the CBM comprising mostly of Sn 5s and O 2p orbitals and the VBM to be predominantly O 2p in character. The conduction bandwidths are sensitive to the distortion of the perovskite structure caused by variation in Ba:Sr composition, becoming compressed and possessing heavier effective electron masses with increasing distortion. The Ba and/or Sr states do not appear to significantly contribute to



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the valence and conduction bands of the BaxSr1–xSnO3 SQS’s, and only serve as an agent in altering the perovskite octahedral scaffold. The calculated band gaps underestimate experimental results by about 2.5 to 3.0 eV albeit displaying similar trend with x. Adjusting the calculated band gaps to fit the experimental data indicates transparency in the visible wavelengths. This suggests BaxSr1–xSnO3 alloys to have potential as an n-doped transparent conducting material. Using the adjusted positions of the CBM and VBM of BaxSr1–xSnO3 SQS’s, we show their potential as photocatalysts in water splitting redox reactions under acidic conditions for all x and in alkaline conditions for x < 0.2; and oxygen evolution photocatalysts at high pH for x > 0.2. The BaxSr1–xSnO3 SQS’s are also potentially promising for photocatalytic CO2 reductions for x < 0.5. From the above findings, we can see that different alloying compositions can give rise to different crystal structures and properties that are desirable for specific applications. This work showcases the use of DFT with CE method to accurately predict the phase diagrams of perovskite alloys, from which one can tailor material properties via compositional engineering. The results here should serve as a guide in the investigations of structureproperty relationships of perovskite-based alloys.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] *E-mail: [email protected] Notes The authors declare no competing financial interest.


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ACKNOWLEDGEMENTS The authors acknowledge the use of high-performance computing facilities in A*STAR Computational Resource Centre (ACRC) and National Supercomputing Centre (NSCC) in Singapore for the computations performed in this work. The work done in National University of Singapore (NUS) is supported by the Ministry of Education, Singapore (R-143000-636-112). Z. M. Wong would also like to thank Gang Wu and Xue Yong for helpful discussions.

ASSOCIATED CONTENT Supporting Information Plots of structural parameters of the SQS structures of purely orthorhombic BaxSr1–xSnO3, indicating approximate transformation from orthorhombic (x = 0) to cubic (x = 1) (Figure S1); plots of electronic band structures along high symmetry paths and densities-of-states of the SQS structures of BaxSr1–xSnO3 alloys (Figure S2).

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BaxSr1–xSnO3 Increasing Ba, charge mobility x ~ 0.7

Orthorhombic

x ~ 0.9

Tetragonal

Cubic

Increasing Sr, photoredox capability

Table of Contents Graphic


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x

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