The three dimensional (3D) structural characterization of nanoparticles is crucial in materials science since many properties heavily depend on size, surface to volume ratio and morphology.  In addition, the ability to investigate the crystal structure is just as essential because the presence of defects and surface relaxation will directly affect plasmonic or catalytic properties. A well-known example of strained nanoparticles are the so-called “nanodecahedra” or “pentagonal bipyramids”. Such particles consist of five segments bound by {111} twin boundaries, yielding a crystallographic forbidden morphology. Therefore, measuring strain fields in nanodecahedra by transmission electron microscopy (TEM) has been the topic of several studies. However, it is important to note that such studies are based on 2D projections, hereby neglecting the 3D nature of the lattice strain. [1,2] Here, we will quantify the lattice strain in 3D based on high resolution electron tomography reconstructions. [3]

Therefore, a continuous tilt series of 2D projection images was acquired using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) and a dedicated alignment procedure was applied. These projection images are then used as an input for a model based tomography reconstruction algorithm. A major disadvantage of conventional reconstruction techniques is that a continuous volume is reconstructed hampering the extraction of atom coordinates without the use of dedicated post-processing methods. [4] We could overcome this limitation by assuming that the 3D atomic potential can be modelled by 3D Gaussian functions. This hypothesis significantly simplifies the reconstruction problem to a sparse inverse problem, yielding the coordinates of the individual atoms as a direct outcome of the reconstruction.

Visualizations of the final 3D reconstruction, obtained for a Au nanodecahedron containing more than 90,000 atoms, are presented in Figure 1.a-c along different viewing directions. Since the coordinates of the atoms are a direct outcome of the reconstruction, it becomes straightforward to calculate the 3D displacement map. We computed derivatives of the displacement map in such a manner that 3D volumes were obtained corresponding to ε_xx and ε_zz. Slices through the resulting ε_xx and ε_zz volumes are presented in Figure 1.d and Figure 1.f. Furthermore, the variation of the lattice parameters was investigated along x and z based on the same slices (Figure 1.e and Figure 1.g). Both along the x and z direction a systematic outward expansion of the lattice can be observed. The expansion along z is limited to a few of the outer atomic layers and shows an asymmetry (Figure 1.f-g) that is likely related to the fact that the decahedron is deposited on a carbon support.

[1] C.L. Johnson, et al., Nat. Mater. 7 (2007) 120-124

[2] M.J. Walsh, et al., Nano Letters 12 (2012) 2027-2031

[3] B. Goris, et al., Nano Letters 15 (2015) 6996-7001

[4] R. Xu, et al., Nat. Mater. 14 (2015) 1099–1103

[5] The authors gratefully acknowledge funding from the Research Foundation Flanders (project numbers G.0369.15, G.0374.13  and a post-doctoral grant to B.G. and A.D.B.). S.B. and D.Z. acknowledge the European Research Council, ERC grant N°335078 – Colouratom. The research leading to these results has received funding from the European Union Seventh Framework Programme under Grant Agreements 312483 (ESTEEM2).  

Figures:

(a-c) 3D visualizations of the reconstruction showing the atomic lattice of a Au nanodecahedron. (d,f) Two components of the strain field showing a surface relaxation in two directions. (e,g) This surface relaxation is confirmed by measuring the lattice parameter on slices through the reconstructions.

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