Supporting Information

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1 Supporting Information Controlled Growth of Ceria Nanoarrays on Anatase Titania Powder: A Bottom-up Physical Picture Hyun You Kim 1, Mark S. Hybertsen 2*, and Ping Liu 2* 1 Department of Materials Science and Engineering, Chungnam National University, 99- Daehakro, Daejeon 34134, Republic of Korea 2 Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA *To whom correspondence should be addressed: mhyberts@bnl.gov, pingliu3@bnl.gov Contents: Computational methods Model for the formation energy of CeO 2 NPs on A-TiO 2 (112) Tables S1 and S2 Figures S1 S10 References 1

2 Computational methods We performed GGA-level spin-polarized DFT calculations with the VASP code 1, 2 and the PW91 functional. 3 To appropriately treat the Ti d-orbitals and Ce f-orbitals, DFT+U with U eff = 4.5 ev was applied for Ti and Ce ions. 4 The reliability of the U eff value was experimentally verified by the XPS/UPS spectra in the CeO x supported on the Rutile TiO 2 (110) system. 5 The interaction between the ionic core and the valence electrons was described by the projector augmented wave method, 6 and the valence electrons were treated with a plane wave basis up to an energy cutoff 400 ev. The Brillouin zone was sampled at the Γ-point. The convergence criteria for the electronic structure and the geometry were 10-4 ev and 0.02 ev/å, respectively. We used the Gaussian smearing method with a finite temperature width of 0.05 ev in order to improve convergence of states near the Fermi level. Several Anatase (A)-TiO 2 slab models were implemented to describe A-TiO 2 (101) and A-TiO 2 (112) surfaces. Most of calculations on A-TiO 2 (101) was done with a diagonal (surface vectors of [1-1 -1] and [0 1 0]) 3 4 and a rectangular 5 6 slab models with three or two layers of TiO 2, respectively. A rectangular 3 4, a 4 3, and a diagonal 6 4 model with three layers were used for long chains. Depending on the size of targeted structure of ceria, three slab models, a 3 3 slab with four TiO 2 layers, a 4 4 slab with three layers, and a 6 6 slab with three layers were used to describe A-TiO 2 (112) surface. As described in the text and in Figure 2, structures with partially oxidized Ce were not found to be the most stable. The most stable structures fundamentally consisted of CeO 2 monomers, on both A-TiO 2 (101) and A-TiO 2 (112), with a Ce atom that was fully coordinated with four oxygen atoms: two surface bridging oxygen atoms of TiO 2 and two additional oxygen atoms from a gas phase oxygen source (Figure 2, S1, S2, S3). Such adsorbed monomers were used as building blocks for the construction of larger ceria arrays. 2

3 To estimate the driving force of the formation of ceria arrays on A-TiO 2 surface, we calculated the formation energy, E form, the energy released upon the formation of a ceria array from gasphase CeO 2 monomers. For instance, the E form of Ce 14 O 28 -NP was calculated as follows to yield the energy per monomer: E form (Ce 14 O 28 -NP) = (E(Ce 14 O 28 -NP) E(TiO 2 ))/14 E(CeO 2 ). (1) Here, E(Ce 14 O 28 -NP), E(TiO 2 ), and E(CeO 2 ) represents the DFT calculated total energy of A- TiO 2 supported Ce 14 O 28 -NP, A-TiO 2 support, and a gas-phase CeO 2 monomer, respectively. As formulated, negative E form indicates relative stability of the product state. Model for the formation energy of CeO 2 NPs on A-TiO 2 (112) The size and shape of CeO 2 NPs on A-TiO 2 (112) are key to determine E form (Figure 4b). Growth of the CeO 2 NPs leads to more negative E form and therefore increased stability. With the same size, a rectangular CeO 2 NP (e.g. Ce 8 O 16 and Ce 40 O 80, Figure 4b) with two larger (111) facets is more preferential on A-TiO 2 (112) than the square NP (e.g. Ce 5 O 10 and Ce 55 O 110, Figure 4b) with four equivalent (111) facets. To gain insight into the origin of CeO 2 NP growth on A-TiO 2 (112) and project trends, we decompose E form into two terms (Figure S8): the energy gain upon the formation of a CeO 2 NP in gas phase (E NP ) and that associated with ceria-titania interaction at the interface (E Int ). E form = E NP + E Int (2) Three physical effects are considered for E NP : bulk cohesive energy of CeO 2 (E bulk ), surface energy of CeO 2 (E surf ) and the energy associated with the formation of low coordinated atoms at the edges and the corners of the NP (E LC ) 7, 8. This is expressed as the energy per CeO 2 unit: E NP = E bulk + (E surf-(111) Area (111) + E surf-(100) Area (100) + E LC N LC )/N (3) 3

4 Here N is the number of CeO 2 units in the NP, N LC is the number of low coordinated sites. In the calculation of the surface contributions, the area for each facet is determined by edges set to be d/2 from the final Ce atom center, where d is the Ce-Ce distance in the facet. With reference to Figure S8, the interface energy E Int is the net gain upon binding the preformed NP to the A- TiO 2 (112). This consists of three contributions, the intrinsic adhesion energy (E bind ), the bulk cost in elastic energy necessary to strain the free NP to conform to the constraint of matching the interface lattice and contribution that scales as the perimeter of the contact area representing the energy gain due to non-uniform relief of strain at the edge of a finite, strained epitaxial NP: E Int = (E bind Area (100) )/N + E str + E perim N perim /N (4) The quantitative analysis of this model based on the specific clusters studied here using DFT is summarized in Table S2. First, the free NPs were analyzed. DFT calculations were performed for each of the NPs that was stabile on the A-TiO 2 (112) support. Large, free NPs, Ce 20 O 40, Ce 30 O 60, Ce 40 O 80, and Ce 55 O 110, were fully relaxed. Small, free NPs, Ce 5 O 10, Ce 8 O 16, and Ce 14 O 28 were partially relaxed, releasing only the bottom layer, to preserve shape. Using the computed values for the bulk formation energy (-6.53 ev/ceo 2 cluster) and the surface energies of CeO 2 (Table S1), the model consistently over-binds the free NPs. The discrepancy was assumed to be associated with the E LC (Table S2). We assigned an average value to E LC (0.405 ev/ce atom). The larger ceria NPs, those consisting of more than one Ce atom with bulk-like coordination (Ce 20 O 40, Ce 30 O 60, Ce 40 O 80, and Ce 55 O 110 ), were used for the estimation of the E LC with the result shown in Table S2, where the model is converging to the DFT results for the largest NPs. We used the same set of NPs to estimate the average binding energy of ceria NPs on A- TiO 2 (112). The raw binding energy includes the effect of strain to match the support lattice (E str ). 4

5 We use an auxiliary calculation for a 4 ML CeO 2 film to estimate the volume strain energy and the interface adhesion energy. The structure is visualized in Fig. S7e. The energy change required to constrain a ceria film to the in-plane lattice parameters while allowing for relaxation in the perpendicular direction is E str = ev/ Å 2 for 4 ML (0.077 ev/ce atom). Then the adhesion energy gain upon bonding this strained film to the TiO 2 surface, allowing for further relaxation, is E Int = ev/å 2. Finally, just as for the average energy assigned per low coordinated atom, based on the average binding energy of the largest NPs, we fit the value for E perim = ev/ce atom. With the additional terms, the model for the formation energy of the NPs can be tested. As shown in Table S2, the model reproduces the calculated E form from DFT even for NPs as small as Ce 14 O 28 (d=1.64 nm) surprisingly well. Higher accuracy is achieved with an increasing size, where the properties of CeO 2 NPs approach more closely to the bulk values employed in the model (Table S2, Figure S9a). The model captures the main energy difference observed for the rectangular base NPs compared to those with square base. Those with rectangular base are more stable than the average of the neighboring size NPs with square base (N=20 versus N=14 and 30, N=40 versus N=30 and 55). However, the DFT calculations show a larger stabilization. Note that this effect is on a very subtle energy scale (order 0.05 ev) for the larger clusters studied. The size dependence of the individual model contributions is shown in Figure S9b. In the formation of the free NPs, the E surf-(100) is much larger per unit area than the E surf-(111). This clearly favors the formation of the pyramidal NPs over flat plates that would correspond to thin film epitaxy, but leave the high energy (100) facet of CeO 2 exposed. On the TiO 2 (112) support, the adhesion energy is larger than E surf-(100) and the additional strain relief at the edges, captured here by the perimeter term rough cancels the undercoordinated atom penalty. In this size range, 5

6 the volume strain term is less significant, but it eventually drives the formation of interface defects and strain relief at larger particle sizes (outside the scope of this study). Table S1. Calculated surface energy of representative A-TiO 2 and CeO 2 facets. Surface energy, E surf, (ev/å 2 ) E surf (112)-(101) (ev/å 2 ) b A-TiO 2 (101) A-TiO 2 (100) A-TiO 2 (112) CeO 2 (111) CeO 2 (100) (0.0350) a (0.0463) a (0.0563) a (0.0213) a a : Ref 9 b : Surface energy difference between the A-TiO 2 (112) and A-TiO 2 (101) facets 6

7 Table S2. Modelling the energy of formation of ceria nanoparticles on A-TiO 2 (112). For each cluster considered, the model for the free NP is first considered in comparison to DFT results. Then the model including effects of adhesion to the support is compared to the DFT results. For the formation energies, the value in parenthesis represents the percentage deviation. ev/ceo 2 monomer E NP (DFT) E NP (Model w/o E LC ) E NP (Model with E LC ) E form (DFT) E form (Model) Ce 5 O 10 (Square) (7.0%) Ce 8 O 16 (Rectangular) (1.3%) Ce 14 O 28 (Square) (2.4%) Ce 20 O 40 (Rectangular) (0.2%) Ce 30 O 60 (Square) (0.6%) Ce 40 O 80 (Rectangular) (0.6%) Ce 55 O 110 (Square) (<0.1%) 7

8 Figure S1. Comparison of the formation energy of three different Ce 2 O 4 diclusters from two separated CeO 2 clusters. 8

9 Figure S2. Optimized structures and corresponding E form of ceria arrays on A-TiO 2 (101): a CeO 2 clusters, b Ce 2 O 2 clusters plus O 2 gas phase, c diagonal chains, d chains grown along the 101 direction of A-TiO 2, e plate formation, and f Ce 10 O 20 NPs. The value of E form relative to CeO 2 monomers in vacuum. Red arrows show the preferred growth direction. 9

10 Figure S3. Optimized structures and corresponding E form of ceria arrays on A-TiO 2 (112): a diagonal chains and plates, b vertical chains and plates, c diagonal basal-plane plates, and d NPs. The value of E form of structure is shown relative to CeO 2 monomers in vacuum. 10

11 Figure S4. Partial density of states (PDOS) for the Ce ions in CeO x /TiO 2 : a CeO 2 plate/tio 2 (101) and b Ce 14 O 28 -NP/TiO 2 (112). 11

12 Figure S5. CeO x plates on A-TiO 2 (101) constructed from diagonal chains. These are offstoichiometric and suffer from severe distortion upon formation. Figure S6. Optimized structure of Ce 14 O 28 NP on when transferred from A-TiO 2 (112) to A- TiO 2 (101). Top and side views of the whole NP (left) and the bottom layer (right) show that the TiO 2 -ceria interface cannot be stabilized on A-TiO 2 (101). 12

13 Figure S7. Structural motifs for a A-TiO 2 (112) and b CeO 2 (100), based on structure optimization with DFT. Selected overlayer structures illustrating changes of the Ce-Ce bonds, including percentage change referenced to the bulk values: c Ce 4 O 8 plate, d CeO 2 monolayer, and e CeO 2 quadlayer. 13

14 Figure S8. Structural factors that control the growth of CeO 2 NPs on TiO 2 (112). a Schematic process of the growth of CeO 2 -NPs on TiO 2 (112). E form of CeO 2 NPs on TiO 2 (112) was decomposed into basic thermodynamic steps: formation of bulk-like CeO 2 crystallite from individual CeO 2 clusters, formation of (100) and (111) surfaces, and the CeO 2 (100)-TiO 2 (112) interface formation. Energies associated to each step were calculated to build a model for E form. b Side view of Ce 55 O 110 -NP on TiO 2 (112) and the morphology of the structural unit of ideal CeO 2 (100) and TiO 2 (112). The location of adjacent cations of CeO 2 (100) and TiO 2 (112) along the direction a fits well whereas Ce ions are little more closely-packed along the direction b. The central cation of the ab square unit of CeO 2 (100) is located at the exact center of the ab unit due to the linear repeating arrangement of oxygen ions while the central Ti ion is displaced and associated to a zigzag oxygen ion arrangement. Not only is there a lattice mismatch between the cells (distortion of 0.2% and 1.3% needed for CeO 2 relative to TiO 2 along a and b respectively, here from bulk DFT-based calculations), but there is also a change in atomic organization. 14

15 Figure S9. a Size and morphology dependency in the E form of seven DFT-studied ceria NPs. Area-to-volume ratio of ceria NPs closely represents the trend in the E form. S and R represent the square and rectangular morphology of NPs, respectively. b Contributions to each term in the model to E form for square base NPs versus number of CeO 2 units in the NP. 15

16 Figures S10. Morphology of CeO 2 plates and nanoparticle on A-TiO 2 (112). a Top and side views of relaxed 1, 2 and 4 ML CeO 2 films. b Top view of 4 ML structure showing successive planes, starting from the first layer at the TiO 2 -CeO 2 interface and followed by the second, third and top layer. c Top view of the,ce 30 O 60 NP showing successive planes, starting from first layer at the TiO 2 -CeO 2 interface and followed by the second, third and NP apex. 16

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