Picometre-Precision Analysis of Scanning Transmission Electron Microscopy Images of Platinum Nanocatalysts
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ARTICLE Received 13 Dec 2013 | Accepted 19 May 2014 | Published 11 Jun 2014 DOI: 10.1038/ncomms5155 Picometre-precision analysis of scanning transmission electron microscopy images of platinum nanocatalysts Andrew B. Yankovich1, Benjamin Berkels2,3, W. Dahmen2,4, P. Binev2, S.I. Sanchez5, S.A. Bradley5,AoLi1, Izabela Szlufarska1 & Paul M. Voyles1 Measuring picometre-scale shifts in the positions of individual atoms in materials provides new insight into the structure of surfaces, defects and interfaces that influence a broad variety of materials’ behaviour. Here we demonstrate sub-picometre precision measurements of atom positions in aberration-corrected Z-contrast scanning transmission electron micro- scopy images based on the non-rigid registration and averaging of an image series. Non-rigid registration achieves five to seven times better precision than previous methods. Non-rigidly registered images of a silica-supported platinum nanocatalyst show pm-scale contraction of atoms at a (111)/(111) corner towards the particle centre and expansion of a flat (111) facet. Sub-picometre precision and standardless atom counting with o1 atom uncertainty in the same scanning transmission electron microscopy image provide new insight into the three- dimensional atomic structure of catalyst nanoparticle surfaces, which contain the active sites controlling catalytic reactions. 1 Department of Materials Science and Engineering, University of Wisconsin—Madison, Madison, Wisconsin 53706, USA. 2 Interdisciplinary Mathematics Institute, University of South Carolina, Columbia, South Carolina 29208, USA. 3 Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen, Schinkelstrasse 2, Aachen 52062, Germany. 4 Institut fu¨r Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, Aachen 52056, Germany. 5 UOP LLC a Honeywell Company, Des Plaines, Illinois 60017, USA. Correspondence and requests for materials should be addressed to P.M.V. (email: [email protected]). NATURE COMMUNICATIONS | 5:4155 | DOI: 10.1038/ncomms5155 | www.nature.com/naturecommunications 1 & 2014 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5155 anometre-scale, heterogeneous objects often depend on Jacobian of f and 1 is the identity matrix. To avoid being trapped their surfaces for important properties and function; by local minima in E[fNR] for nearly periodic STEM images, we Nhowever, solving such structures is difficult enough use a coarse-to-fine multilevel approach. It initially registers to have earned the name ‘the nanostructure problem’1. down-sampled variants of the images, and then uses the resulting Nanocatalysts, such as platinum (Pt) nanoparticles (NPs), are a fNR as an initial guess at the next finer sampling levels, iterating prototypical example of the nanostructure problem2, since their up to the original sampling. At each level, we solve the morphology and especially the detailed atomic structure of their minimization problem by relating it to a time-dependent partial surfaces is crucial to their catalytic activity3–6. differential equation and using a regularized gradient descent18 Transmission electron microscopy (TEM) and scanning TEM with explicit time discretization and step size control19. (STEM) have been used nearly since their inception for NP To register the entire sequence of images T0, y, TN,wefirstfind characterization but have been limited by the available resolution the NR deformations fj þ 1,j between all pairs Tj and Tj þ 1,andthen 7–10 and precision . Aberration correction has made sub-Angstrom register the entire series to T0 using fj þ 1,j3fj,0 as the initial guess spatial resolution routine in TEM and STEM. Once atoms can be for fj þ 1,0. Then, we repeat the registration using the average of the resolved, the question becomes how precisely can their positions registered frames T as the reference frame and iterate to find the be measured. (Resolution is the smallest distance between two final set of deformations. The NR registration technique makes objects in an image at which the objects appear distinct. Precision some assumptions about the imaging process (discussed in the is the statistical spread of repeated distance measurements Supplementary Methods) but no assumptions about the object. In in an image.) Precision smaller than the resolution is routinely principle, any technique subject to pixel distortions can benefit from achievable11–14: the best reported precision for TEM and NR registration, including cryo-TEM and atomic force, scanning STEM images is 1–3 picometre (pm) (refs 11,12) and 4–5 pm tunnelling or scanning electron microscopy. The NR registration (refs 13,14), respectively. Precision is fundamentally limited by software is available by request to the authors. the signal-to-noise ratio (SNR)15; however, in STEM serial acquisition of pixels translates instabilities in the sample and probe positions into displacements of the imaged atoms, limiting Sub-pm precision on single crystal materials. Figure 1c–g precision well above the SNR limit. Averaging many frames can demonstrates that NR registration of aberration-corrected STEM reduce instabilities and increase SNR11,13; however before images achieves sub-pm precision. Experimental details are in the averaging, the frames must be registered to one another to Methods section and in Supplementary Note 1. Figure 1c shows account for, for example, drift of the sample between frames. the first image of a 512-high-angle annular dark-field (HAADF) Here we develop a non-rigid (NR) registration scheme that STEM image series of silicon (Si) [110]. The image series was enables us to achieve extremely high SNR images. We averaged after NR registration to create the final HAADF image demonstrate sub-picometre (pm) precision measurements of in Fig. 1d, which therefore shows the average sample structure atom positions in aberration-corrected Z-contrast STEM images, over the image series acquisition time. Owing to the long more than five times better than previous methods13,14, based on acquisition time of the averaged image, fast processes such as NR registration and averaging of an image series. NR registered thermal displacements and atom displacements from electron images of a Pt nanocatalyst show pm-scale contraction of atoms beam momentum transfer are not captured. The entire series is at a (111)/(111) corner towards the particle centre and expansion shown raw in Supplementary Movie 1 and registered in of a (111) facet. Combined with standardless atom counting16 to Supplementary Movie 2. Typical NR pixel deformations for one determine three-dimensional (3D) structure, sub-pm precision image in the series are shown in Supplementary Fig. 1 and dis- STEM can give new insight into the active sites controlling cussed in Supplementary Note 1. Distortions from circular catalytic reactions, and the displacements from defects, interfaces symmetry in the Si atomic columns in Fig. 1d are likely due to or various ferroic phenomena. residual lower-order aberrations in the electron probe. Each Si dumbbell was fit to the sum of two, two-dimensional (2D) Results Gaussian functions to find the series-averaged atomic column Non-rigid registration. Registering two images, R and T, requires positions. Figure 1e shows a typical featureless fit residual. finding a deformation f of the image domain such that the Figure 1f,g shows histograms of the 98 and 58 measured x and y composition T3f agrees with R. Figure 1a shows the conventional Si column separations, respectively, defined in Fig. 1d. Following approach, in which f is a rigid translation11,13,14. A rigid f works Bals et al.11, we define the precision s of the image as the for the unchanging pixel grid in Fig. 1a, but it can lead to a loss of standard deviation (s.d.) of these separations; therefore, resolution and precision if there are distortions from serial sx ¼ 0.86 pm and sy ¼ 0.72 pm. Another measure of image acquisition, as shown in Fig. 1b. Our NR registration scheme uses precision is the uncertainty in the atom column’s fit position20, a pixelwise, non-parametric deformation fNR, which can account which yields sx ¼ 0.36 pm and sy ¼ 0.60 pm, again sub-pm. A for all sources of image distortion including probe instabilities similar experiment showing sub-pm precision for gallium nitride and sample drift. (GaN) is shown in Supplementary Fig. 2 and Supplementary Estimating fNR is an underconstrained problem. Our solution Movies 3 and 4, and discussed in Supplementary Note 2. is summarized here and described in greater detail in the Supplementary Fig. 3 and Supplementary Note 3 show that rigid Supplementary Methods and elsewhere17. We employ a registration of the same Si HAADF image series results in variational approach to minimize the sum of the negative precisions of sx ¼ 5.3 pm and sy ¼ 4.0 pm, five to seven times normalized cross correlation, ENCC,ofT3fNR and R, and the larger than NR registration. NR registration is further validated Dirichlet energy of the displacement, as a regularizer on fNR. using simulated STEM distortions, including preservation of Thus, we seek to minimize inhomogeneous strain fields with pm precision, as shown in Z Supplementary Fig. 4 and Supplementary Movie 5, and discussed l 2 in Supplementary Note 4. Supplementary Figs 5 and 6 and E½fNR¼ENCC½fNRþ kkDfNRðxÞÀ1 dx; ð1Þ 2 Supplementary Note 5 show how NR registration enables the O tracking of image precision, resolution, sample damage and focus where l is a non-negative, constant