Supporting Information

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1 Supporting Information Thermal Stability of Metal Nanocrystals: An Investigation of the Surface and Bulk Reconstructions of Pd Concave Icosahedra Kyle D. Gilroy, a,ϯ Ahmed O. Elnabawy, b,ϯ Tung-Han Yang, a,ϯ Luke T. Roling, b Jane Howe, c Manos Mavrikakis, b,* Younan Xia a,d,* a The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, Georgia 30332, United States b Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States c Hitachi High-Technologies Canada, Toronto, Ontario M9W 6A4, Canada d School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States ( Ϯ signifies equal contribution) * Corresponding authors: manos@engr.wisc.edu (for computation) and younan.xia@bme.gatech.edu (for synthesis and characterization) 1

2 Methods. Synthesis of Pd icosahedra to be used as the seeds. The Pd regular icosahedra with an average size of 13 nm were synthesized using a previously reported protocol. 1 Typically, 80 mg PVP was dissolved in 2 ml diethylene glycol (DEG, hosted in a 20-mL vial), and then heated at 130 C for 10 min. At the same time, 15.5 mg Na2PdCl4 was dissolved in 1 ml DEG and the solution was injected in one shot into the pre-heated solution. The reaction was maintained at 130 C for 3 h under magnetic stirring. The product was collected by centrifugation, washed once with acetone and twice with deionized water, and finally dispersed in deionized water for further use. Seed-mediated growth of Pd concave icosahedra. In a standard synthesis, 2.0 ml of aqueous PdBr4 2 (i.e., 1 mg of Na2PdCl4 and 16.2 mg of KBr) precursor was injected in one shot into a 20- ml glass vial containing an 8 ml aqueous suspension of 0.36 mg of the Pd regular icosahedra, 60 mg of AA, and 100 mg of PVP under magnetic stirring. The reaction was then capped and maintained at room temperature for 5 h. Afterwards, the product was collected by centrifugation at 55,000 rpm for 60 min and washed three times with deionized water. Electron microscopy with heating capability. The TEM images shown in Figure 1 and S1 were captured using the Hitachi HT7700 TEM operating at 120 kv. All heating experiments were conducted in situ using an aberration-corrected Hitachi HD2700 STEM operated at 200 kv. The nanoparticles were supported on a Norcada TEM heating chip model: X (HTN-0101) with a membrane thickness of 30 nm, which were manufactured by Norcada Inc. in Edmonton, Canada. The temperature was controlled through the applied voltage, and calibration curves were derived from melting studies of ultra-pure metal powders. All experiments were performed using the Hitachi Blaze heating holder manufactured by Hitachi High Technologies Canada Inc. 2

3 DFT calculations. All calculations are performed using the Vienna ab initio Simulation Package (VASP), 1 a density functional theory (DFT) code. 2 The properties of core electrons are estimated with the projector augmented wave (PAW) potentials, 3-5 in which the electron density is described using the GGA-PW91 exchange correlation functional. 6 Plane waves with a kinetic energy cutoff of 400 ev are used to expand the electron wave function. Pd is calculated to have a lattice constant of 3.95 Å, in good agreement with the experimental value of 3.89 Å. 7 A 2.5% expansive strain is imposed on all extended surfaces, to model the presence of the twin boundary of an icosahedron. Extended surfaces of (111), (100), and (110) facets of Pd are modeled using 4 4 unit cells, repeated periodically, with at least 18 Å of vacuum. The (111) and (100) surfaces are constructed with four metal layers (excluding the incomplete layer that represents a step), with the bottom two layers fixed at their bulk positions, while the top two are allowed to fully relax. The (110) surface slab is constructed with five metal layers (excluding the incomplete layer that represents a step), with the bottom two layers fixed at their bulk positions, while the top two are allowed to fully relax. In all cases, atoms moving via the substitution mechanism are not nearest-neighbors to atoms in the fixed layers. The surface Brillouin zone is sampled with a Monkhorst-Pack k-point mesh, 8 and atoms are relaxed to 0.02 ev/å of Hellmann-Feynman forces. Pd adatoms are made to diffuse along one face of the metal slab, applying appropriate dipole corrections to the electrostatic potential. 9,10 The edge model was constructed of three complete metal layers (with the bottom layer fixed), and two incomplete metal layers to model steps. In particular, the atomic stacking of the icosahedral structure was modeled according to the structure originally proposed by Mackay 11 and confirmed to be assumed to Pd icosahedra by Chuvilin and coworkers. 12 From this stacking, we constructed a model (Figure S2) of the edge (where a twin boundary is present) joining two Pd(111)-like facets present in a regular icosahedron. Two incomplete layers were then added at 3

4 the icosahedral edge to represent the concave nature of the larger nanoparticles. Vacuum separating periodic images in the z-direction is at least approximately 13 Å, and the Monkhorst- Pack k-point mesh is divided into a grid. Activation energy barriers of the various diffusion events are calculated using the climbing-image nudged elastic band (CI-NEB) method. 13 Initial and final states of each diffusion process are interpolated with seven intermediate images, each converged to a maximum force of 0.1 ev/å. Calculations converged with respect to all parameters. Calculation Details of Figure 4. The reference state is calculated to be the average energy of a single Pd atom, when a monolayer of Pd is added to the strained surface (at 2.5% expansive strain) of Pd(111), according equation (1): E Ref = E E (1) where, E is the total energy of a five-layered Pd slab in a 4 4 unit cell, whereas E is the corresponding energy for a four-layered slab. The difference between these two structures is 16 Pd atoms, and therefore, this difference is divided by 16, to yield an average energy for a single Pd atom as it resides in a complete surface layer. Energy of a given configuration (or stage) n in Figure 4 by equation (2): Energy = (n 1)E Ref E 1 E n 4 (2) where, E n is the total energy of configuration n and E 1 is the total energy of the starting configuration of a concave icosahedron. As depicted in Figure S3, each row is 4 atoms wide. Therefore, stages proceed in increments of 4 Pd atoms, hence the division by 4 in the formula above. Finally, this averaged difference is subtracted from the corresponding number of Pd atoms in their reference state. Table S2 explains the calculation details of the energy values of the 4

5 different stages as they appear in Figure 4, using Stage 2, Stage 6, and Stage 15 as illustrative examples. 5

6 Figure S1. Histogram showing the size-distribution of icosahedral seeds. The insets show a typical TEM image (Scale bar = 50 nm) of the as-synthesized seeds and an illustration for how the size of an individual icosahedron was measured. 6

7 Figure S2. HAADF-STEM image of an individual Pd concave icosahedron outlined with redlines to illustrate how the angle measurements were made. The scale bar is 5 nm. 7

8 Figure S3. Graphical representation of the edge model. To the left is the concave edge model, with two additional incomplete layers, creating an edge (pale blue spheres) and two steps on each side of the edge (orange spheres). Upon surface reconstruction to regular icosahedron, the two additional layers are removed to yield the regular icosahedron edge model to the right. Pd atoms of the substrate are represented by teal spheres. 8

9 Figure S4. (a) HAADF-STEM image of the Pd concave icosahedra heated at 400 C. The red box marks a particle that lost its decahedral cap during heating, while the green box indicates a structure reminiscent of a decahedral cap. (b) HRTEM image of a particle with the missing of its decahedral cap. The scale bars in (a) and (b) are 50 and 5 nm, respectively. 9

10 Table S1. Successive ejection of edge atoms from a single step edge of the edge model. Colored rows of the table highlight elementary steps in the most favorable path for the elimination of step edge atoms. Within each row, the numbers of each column are relative to those of the initial states. The numbers for the transition states represent the activation energy barrier, while the numbers for the final states represent the energy of the process. In the insets, the diffusing (i.e., ejected) atom is in yellow, step edge atoms are in orange, edge atoms of the concave edge model are in pale blue, and the Pd substrate is composed of teal spheres. All numbers are in ev. Process Initial State Transition State Final State The first step-edge atom (yellow) is ejected to a terrace A second step-edge atom (yellow) is ejected to a terrace A second step-edge atom (yellow) is ejected to a terrace A third step-edge atom (yellow) is ejected to a terrace A third step-edge atom (yellow) is ejected to a terrace The fourth step-edge atom (yellow) is ejected to a terrace

11 Table S2. Illustration of calculation details for Figure 4, as explained for Stage 2, Stage 6, and Stage 15. All insets represent configurations of the corresponding energies that appear in equations (1) and (2). _ E Ref = = 16 This is the average energy of a single Pd atom (the teal sphere in the rightmost configuration) as it resides in a complete surface layer of an extended (111) facet, which resembles the face of a regular icosahedron. White spheres represent Pd atoms that are made absent, either by subtracting them out as for the bottom four layers, or averaging them as for the top layer. Stage 2 (n=2) The difference between the two edge structures are 4 Pd atoms (marked in red). When divided by 4, this yields an average energy for a single Pd atom as it resides in the removed atomic row (the red row). This energy is subtracted from the energy of a single Pd atom in the reference state, thus giving us the energy gained (or lost) when a Pd atom leaves the red row in the concave icosahedron and diffuses to reside in a surface layer of an extended (111) face of a regular icosahedron. Stage 6 (n=6) The difference between the two edge structures are 20 Pd atoms (marked in red). When divided by 4, this yields an average energy for 5 Pd atoms as they reside in the removed atomic rows (the red rows). This energy is subtracted from the energy of 5 Pd atoms in the reference state, thus giving us the energy gained (or lost) when these Pd atoms leave the red rows in the concave icosahedron and diffuse to reside in a surface layer of an extended (111) face of a regular icosahedron. Stage 15 (n=15) The difference between the two edge structures are 56 Pd atoms (marked in red). When divided by 4, this yields an average energy for 14 Pd atoms as they reside in the removed atomic rows (the red rows). This energy is subtracted from the energy of 14 Pd atoms in the reference state, thus giving us the energy gained (or lost) when these Pd atoms leave the red rows in the concave icosahedron and diffuse to reside in a surface layer of an extended (111) face of a regular icosahedron. Energy = Energy = Energy =

12 Table S3. Substitution of an adatom into a step by replacing a step edge atom. Within each row, the numbers of each column are relative to those of the initial states. For the (111) facet, the adatom lies on an hcp hollow site. The numbers for the transition states represent the activation energy barrier, while the numbers for the final states represent the energy of the process. In the insets, the step atoms are represented by orange spheres, the adatom is represented by a yellow sphere, the step edge atom being substituted is represented by a red sphere, the edge atoms of the concave edge model are represented by pale blue spheres, while the Pd substrate is composed of teal spheres. All numbers are in ev. Model Initial State Transition State Final State Edge (111) (100) (110)

13 Table S4. Hopping of an adatom down a step edge. Within each row, the numbers of each column are relative to those of the initial states. For the (111) facet, the adatom lies on an hcp hollow site. The numbers for the transition states represent the activation energy barrier, while the numbers for the final states represent the energy of the process. In the insets, the step atoms are represented by orange spheres, the adatom is represented by a yellow sphere, the edge atoms of the concave edge model are represented by pale blue spheres, while the Pd substrate is composed of teal spheres. All numbers are in ev. Model Initial State Transition State Final State Edge (111) (100) (110)

14 Table S5. Successive ejection of atomic rows from the topmost incomplete layer of the concave edge model. Colored rows of the table highlight energetics found in the most favorable path for the elimination of the atomic rows. Within each row, the activation energy barrier is the transition state energy relative to the initial state, while the process energy is the final state energy relative to the initial state energy. In the inset, atomic rows of the topmost layer are numbered from 1 to 5. Each row consists of four atoms. Step edge atoms are orange, edge atoms of the concave edge model are pale blue, and the Pd substrate is composed of teal spheres. All numbers are in ev Process Activation Energy Barrier Process Energy An atom is ejected from atomic row 1; rows 2, 3, 4, and 5 are present. An atom is ejected from atomic row 2; rows 3, 4, and 5 are present; row 1 is absent. An atom is ejected from atomic row 3; rows 4 and 5 are present; rows 1 and 2 are absent. An atom is ejected from atomic row 4; row 5 is present; rows 1, 2 and 3 are absent. An atom is ejected from atomic row 5; row 4 is present; rows 1, 2 and 3 are absent. An atom is ejected from atomic row 5 onto the edge; rows 1, 2, 3 and 4 are absent. An atom is ejected from atomic row 5 onto the terrace; rows 1, 2, 3 and 4 are absent. An atom is ejected from atomic row 4 onto the terrace; rows 1, 2, 3 and 5 are absent

15 Table S6. Deformation of steps by ejecting a step edge atom out of the step by means of hopping or substitution, whichever is easier for each surface. Within each row, the numbers of each column are relative to those of the initial states. The numbers for the transition states represent the activation energy barrier, while the numbers for the final states represent the energy of the process. In the insets, the step atoms are represented by orange spheres, the moving atom is represented by a yellow sphere, the substrate atom substituted by the step atom is represented by a red sphere, the edge atoms of the concave edge model are represented by pale blue spheres, while the Pd substrate is composed of teal spheres. All numbers are in ev. Model Initial State Transition State Final State Edge (111) (100) (110)

16 Table S7. Diffusion of an adatom on a pristine slab by hopping. Within each row, the numbers of each column are relative to those of the initial states. The numbers for the transition states represent the activation energy barrier, while the numbers for the final states represent the energy of the process. In the insets, the diffusing atom is in yellow, while the Pd substrate is composed of teal spheres. For the (111) facet, the adatom diffuses from the fcc hollow site (the most stable adsorption state) to the hcp hollow site. All numbers are in ev. Model Initial State Transition State Final State (111) (100) (110)

17 Table S8. Diffusion of an adatom on a pristine slab by substitution. Within each row, the numbers of each column are relative to those of the initial states. The numbers for the transition states represent the activation energy barrier, while the numbers for the final states represent the energy of the process. In the insets, the diffusing adatom is in yellow, the moving substrate atom is in red, while the Pd substrate is composed of teal spheres. For the (111) facet, the adatom at the fcc hollow site (the most stable adsorption state) pushes a substrate atom to the hcp hollow site. All numbers are in ev. Model Initial State Transition State Final State (111) (100) (110)

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