Supporting Information:

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1 Supporting Information: Competing Interactions between Various Entropic Forces towards Assembly of Pt 3 Ni Octahedra into a Body-Centered- Cubic Superlattice Ruipeng Li, Jun Zhang, Rui Tan, # Frauke Gerdes, Zhiping Luo, Hongwu Xu, Jennifer A. Hollingsworth, Christian Klinke, Ou Chen, # and Zhongwu Wang,*, Cornell High Energy Synchrotron Source, Cornell University, Ithaca, New York 14850, USA;, State Key Laboratory of Heavy Oil Processing, College of Chemical Engineering, China University of Petroleum, Qingdao , China; #, Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA;, Department of Chemistry and Physics, Fayetteville State University, Fayetteville, North Carolina 28301, USA;, Earth and Environmental Sciences Division,, Materials Physics and Applications Division: Center for Integrated Nanotechnology, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA;, Institute of Physical Chemistry, University of Hamburg, Hamburg, Germany. * zw42@cornell.edu 1. Supporting Experiments and Calculations A: Small and Wide Angle X-ray Scattering of Single Supercrystals: Both small and wide angle X-ray scattering (SAXS/WAXS) images were collected from supercrystals made of Pt 3 Ni octahedra at the B1 station of CHESS, Cornell University [S1]. A single supercrystal was loaded onto a MiTeGen mesh grid, which was subsequently mounted on the home-made two-circle rotating diffractometer. The SL[110] orientation of the supercrystal was aligned parallel to the rotation axis of Φ. Upon X-ray illumination, a series of SAXS and WAXS S1

2 images were collected upon rotation of the supercrystal. An angular rotation step of 1 was used, and the full dataset was collected through rotation of Φ over an angular range of 180. The starting position of Φ = 0 was defined at the SL[100] projection, which displays a typical 4-fold symmetrical SAXS spotty pattern. Two-dimensional (2D) images were either reduced to onedimensional (1D) patterns using the Fit2D package [S2] or directly employed for structural reconstruction and other related analyses. B: Determination and Reconstruction of the Supercrystal Structure: Simulations of SAXS/WAXS images were performed using two program packages: CrystalMaker and SingleCrystal. A series of characteristic SAXS images with typical crystallographic orientations were selected and simulated to determine the supercrystal structure. Upon reconstruction of the structure in a bcc superlattice, the detailed structural features of both nanocrystal (NC) translations and atomic crystallographic orientations are obtained, as shown in Figure 2, Figures S5-S7 and Video S1. To facilitate understanding of Figure 2 presented in the main body of the manuscript, Figures S5-S7 include both the collected and simulated SAXS and WAXS images of the supercrystal projected along three major crystallographic directions of SL[100], SL[111] and SL[110] of the bcc superlattice, respectively. The single supercrystal model was constructed and visualized using a VESTA3.1 package [S3]. Individual octahedron was created based on the atomic fcc structure of Pt 3 Ni with the space group Fm m, in which Pt 3 Ni[110] and Pt 3 Ni[111] are normal to the edges and surface faces of the octahedron, respectively. Using the reconstruction process described in our previous publication [S4], the building blocks of octahedra were packed into the bcc superlattice. They have identical orientations to those in the superlattice cell. In other words, the three crystallographic axes of the bcc superlattice and those of the atomic Pt 3 Ni face-centered-cubic lattice are correspondingly parallel to each other. C: Calculation of the bcc Superlattice Parameters: Single supercrystal SAXS characterizations reveal that the supercrystal made of Pt 3 Ni octahedra has a body-centered-cubic (bcc) superlattice. Based on the observed d (110) spacing of the bcc superlattice, the cell parameter ( ) of the superlattice is calculated as: S2

3 ( ) Based on the defined orientations of octahedra in the bcc superlattice in which the triangular surface faces are perpendicular to the SL(111) direction, the distance between the centers of two nearest octahedra (d oct-oct ) along the SL(111) direction is calculated as: ( ) Therefore, the face-to-face separation (gap) between two nearest octahedra in which l represents the edge length is calculated as: ( ) ( ) Similarly, the distance between two neighboring octahedra (next nearest ones) with a tip-totip arranging configuration is calculated as: ( ) ( ) Therefore, the tip-to-tip separation (gap) between two neighboring octahedra is calculated as: ( ) ( ( ) ) ( ) ( ) Using observed d (110) spacings of the bcc superlattices in various environments, the parameters listed above can be similarly calculated using the same formulae. Table S2 lists the calculated parameters of supercrystals at drying, OA-wetting and direct tip-to-tip contacting conditions. S3

4 Note: In the main body of the manuscript, the superlattice parameter represents an average value, but in the late section, calculated from d (110) = 9.96 nm is used for comparison and consistency. D: Calculation of the Space Filling Factor: The space filling factor (also called packing density) is defined as the ratio of the total volume of hard octahedral cores to the unit cell volume of the superlattice. For ease of comparison, the space filling factor is calculated by the total volume of NCs in one primitive superlattice cell divided by the volume of the primitive superlattice cell. As is well known, an octahedron is geometrically composed of eight equilateral triangular facets. For the octahedron made up of Pt 3 Ni that has an atomic cubic structure (Fm m), the triangular surface faces are terminated by atomic Pt 3 Ni(111) facets. Accordingly, the vertex is perpendicular to the Pt 3 Ni [100] direction, and the edge is perpendicular to the Pt 3 Ni [110] direction. High-resolution transmission electron microscopy (HRTEM) reveals the lattice fringes of Pt 3 Ni octahedra, allowing precise determination of the edge length to be l = 9.26 nm, on average. Based on the geometrical shape, the diameter of one circumscribed sphere (d u ), which touches the octahedron at all vertices, can be calculated as: Therefore, the radius of a circumscribed sphere of the octahedron ( ) is: The diameter of one inscribed sphere (d i ), which is tangent to the triangle surface faces of an octahedron, can be calculated as: Accordingly, the radius of an inscribed sphere (tangent to each of the octahedron's faces) is: The surface area (A oct ) and the volume (V oct ) of one octahedron can be obtained: S4

5 nm 2 The number of octahedra in one bcc unit cell is: Z = 2. The volume V of a regular octahedron with an edge length of l=9.26 nm is: nm 3 Therefore, the packing density (i.e. the space filling factor) can be calculated as: E: Calculation of the Face-to-Face (F-F) Configuration: Figure 3(c) shows the face-to-face (F-F) arranging configuration of octahedra in the bcc superlattice, where The inter-nc distance between the octahedra at a given corner and the center of the bcc superlattice cell, which represents the distance of two nearest octahedra, is The radius of an inscribed sphere is: The face-to-face separation (gap) between two nearest octahedra is The length of one oleic acid (OA) molecule (ligand) is Apparently, the face-to-face separation (gap) is larger than twice the extended length of OA molecule. Therefore, the gap between two OA monolayers (void space) is: F: Calculation of the Vertex-to-Vertex Configuration: Figures 3(d, e) and Figure S9 show the vertex-to-vertex (V-V) arranging configuration of octahedra in the bcc superlattice, where S5

6 The inter-nc distance between two neighboring octahedra seated at the corners of a bcc superlattice unit cell, which stands for the distance between two next nearest octahedra, is The radius of an circumscribed sphere is: The vertex-to-vertex separation (gap) between two neighboring octahedra is G: Calculation of the Surface Ligand Packing Configuration: In the case of NC octahedron studied in this work, OA ligands coated on triangle flat surfaces are either parallel or normal to the triangle faces [i.e. Pt 3 Ni(111)]. Here, we assume that OA ligands are straightly radiated out from the flat faces of the octahedron in a perfectly perpendicular way. Each flat face of the octahedron is fully covered by OA ligands, and such typical molecular decorations modify the original octahedral shape to an irregular morphology as shown in Figure S10. Based on the above consideration, the occupation spaces of OA ligands either located on the flat surfaces [Pt 3 Ni(111) or SL(111)] or projected along the typical superlattice directions [Pt 3 Ni[100] or SL[100]; Pt 3 Ni[110] or SL[110]] are calculated as along Pt 3 Ni[111]: along Pt 3 Ni [110]: along Pt 3 Ni [100]: In comparison with the above estimated OA lengths, the vertex-to-vertex separation of 1.08 nm is apparently smaller than even one OA molecular length of 2 nm, so OA ligands cannot be properly filled in the vertex-oriented SL[100] direction. Taking into consideration the vertex-tovertex arranging configuration of octahedra, the projected length of the two oppositely radiated OA ligands, which stand on the triangular surface faces at vertex sites, is estimated as: 2 [Figure S9 (a)], which is significantly greater than the vertex-to-vertex separation of 1.08 nm. If we examine the inset cartoon drawing of Figure S9, the vertex-to-vertex arranging S6

7 configuration allows only for slight contact of small numbers of OA ligands, but a large portion of OA ligands standing straightly on the triangular flat surfaces (i.e. non-vertex area) are not involved. As a series of stiff carbon-bonded hydrocarbon chains, OA ligands localized in the vertex areas are directly touched only through their tails. Due to a smaller vertex-to-vertex separation of 1.08 nm [Figure S9(b)] compared to the estimated ideal arranging distance of 2.31 nm [Figure S9(a)], OA ligands accommodated inside the vertex-to-vertex separation space are apparently strained, giving rise to the strong elastic repulsive forces. There is another possibility which could cause possible intercalation of OAs along the vertex-to-vertex direction. In this case, the elastic repulsion forces should be slightly weakened. Since an OA-wetting-induced superlattice expansion was observed from SAXS measurements, the first arranging configuration of OA ligands in the vertex-to-vertex direction is favorable. Alternatively, we can also consider the ligand-induced morphological development of octahedra. Upon surface decoration by OA ligands, each octahedron develops into a quasi-round shape in which void areas can be easily seen at its vertices and edges [Figure S10]. The perfect arrangement of the quasi-round building blocks in the bcc superlattice favors the first consideration regarding the OA ligand arranging configuration located in the vertex-to-vertex separation space. S7

8 2. Supporting Tables: Table S1 Calculated parameters of a Pt 3 Ni octahedron including the edge length, diameters of inscribed and circumscribed spheres, surface area and volume. Octahedral edge length (nm) Octahedral surface area (nm 2 ) Octahedral volume (nm 3 ) Diameter of inscribed sphere (nm) Diameter of circumscribed sphere (nm) Table S2 Calculated parameters of three superlattices which are under conditions of drying, OA wetting and direct V-to-V contacting of octahedra. Note: V-V, vertex-to-vertex; F-F, face-to-face; NC, nanocrystal (octahedral nanocrystal). Here the packing density is referred to as the space filling factor. SL(110) d-spacing (nm) Superlattice constant (nm) V-V separation (nm) Inter-NC distance (nm) F-F separation (nm) Volume per site (nm 3 ) Packing density (%) Wetting Drying Direct V-V Contact S8

9 3. Supporting Figures: Figure S1 Low resolution transmission electron microscopy (TEM) image showing the size distribution and octahedral morphology of the as-synthetic Pt 3 Ni nanocrystals. Figure S2 High resolution TEM (HRTEM) image showing different crystallographic orientations of Pt 3 Ni octahedra. S9

10 Figure S3 Statistics of the lengths of octahedral edges (>200 nanoparticles) based on HRTEM images. In order to avoid the statistic errors, we only counted on the octahedra which show clear edges. Figure S4 High resolution TEM images showing the three typical orientations of Pt 3 Ni octahedra, including (a) Pt 3 Ni [110], (b) [100] and (c) [111], with the d-spacing values of the corresponding (111), (200) and (110) crystallographic planes. S10

11 Figure S5 Collected and simulated SAXS and WAXS patterns of one Pt 3 Ni octahedral supercrystal viewed along the SL[100] direction: (a, c) experiments and (b, d) simulations. Inset shows the reconstructed superlattice based on collected SAXS and WAXS patterns. S11

12 Figure S6 Collected and simulated SAXS and WAXS patterns of one Pt 3 Ni octahedral supercrystal viewed along the SL[111] direction: (a, c) Experiments and (b, d) simulations. Inset shows the reconstructed superlattice based on collected SAXS and WAXS patterns. S12

13 Figure S7 Collected and simulated SAXS and WAXS patterns of one Pt 3 Ni octahedral supercrystal viewed along the SL[110] direction: (a, c) Experiments and (b, d) simulations. Inset shows the reconstructed superlattice based on the collected SAXS/WAXS patterns. S13

14 Figure S8 In-situ SAXS and WAXS patterns collected upon heating of one supercrystal grain in OA wetting environment at (a) 25 o C, (b) 110 o C and (c) 140 o C. S14

15 Figure S9 Cartoon demonstration of the proposed model for the surface oleic acid (OA) ligand contacting configuration along the SL[100]-oriented vertex-to-vertex direction: (a) ideal tail touch of OA ligands in which the separation of 2.3 nm was calculated based on the projection of 2.0 nm OA length along SL[100]; (b) true contacting configurations of OA ligands in the bcc superlattice, in which the separation of 1.08 nm was determined from the SAXS measurements. OA ligands marked in dark color illustrate ones with direct contact upon approaching of neighboring octahedra. This also shows that a large portion of OA ligands on triangular surfaces of octahedra are not involved in contacting. Figure S10 Morphological development of a Pt 3 Ni octahedron caused by the surface ligands in the bcc superlattice: (a) one hard Pt 3 Ni octahedral core; (b) one octahedron with a full coverage of OA molecules; and (c) one octahedron with a full coverage of highly strained OA molecules. Insets of (a) and (b) show one standing OA molecule and one formed OA monolayer on the flat triangle surface of octahedron, respectively. S15

16 Figure S11 Comparisons of (a) SAXS and (d) WAXS images collected from one Pt 3 Ni supercrystal and integrated plots (b, c) at ambient conditions and (e, f) after high temperature annealing of the supercrystal in OA-wetting environments along (b, e) Q direction and (c, f) azimuthal direction. The arrows in (a, d) represent the integration directions. S16

17 Figure S12 Detailed analysis of SAXS and WAXS patterns collected from one bcc supercrystal at in situ heating conditions, including (a) SL(110) d-spacing and (b) angular width of the supercrystal and (c) Pt 3 Ni(111) d-spacing and (d) angular width of the internal building blocks of Pt 3 Ni octahedra. Inset arrows guide the heating circle from room conditions to high temperature and then back to room temperature. S17

18 4. Supporting Video: Video S1: Pt3Ni_Octahedra_Rotation_SAXS.avi: Experimental and simulated SAXS patterns of a supercrystal in a series of typical orientations upon its rotation around the SL[110] axis of the bcc superlattice. A color bar in log scale was employed for better view of the SAXS spots with higher Miller indices. 5. Supporting References: [S1] Wang, Z. W.; Chen, O.; Cao, C. Y.; Finkelstein, K.; Smilgies, D. M.; Lu, X.; Bassett, W. A. Rev. Sci. Instrum. 2010, 81, [S2] Hammersley, A.P. ESRF Internal Report, [S3] Momma, K.; Izumi, F. J. Appl. Crystallogr. 2011, 44, [S4] Li, R.; Bian, K.; Hanrath, T.; Bassett, W. A.; Wang, Z. J. Am. Chem. Soc. 2014, 136, S18