title: Picometre-precision analysis of scanning transmission electron microscopy images of platinum nanocatalysts.
abstract: 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 microscopy 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 <1 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.
authors.affiliation: Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.
authors.forename: Andrew B
authors.initials: AB
authors.lastname: Yankovich
authors.affiliation: 1] Interdisciplinary Mathematics Institute, University of South Carolina, Columbia, South Carolina 29208, USA [2] Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen, Schinkelstrasse 2, Aachen 52062, Germany.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Berkels
authors.affiliation: 1] Interdisciplinary Mathematics Institute, University of South Carolina, Columbia, South Carolina 29208, USA [2] Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, Aachen 52056, Germany.
authors.forename: W
authors.initials: W
authors.lastname: Dahmen
authors.affiliation: Interdisciplinary Mathematics Institute, University of South Carolina, Columbia, South Carolina 29208, USA.
authors.forename: P
authors.initials: P
authors.lastname: Binev
authors.affiliation: UOP LLC a Honeywell Company, Des Plaines, Illinois 60017, USA.
authors.forename: S I
authors.initials: SI
authors.lastname: Sanchez
authors.affiliation: UOP LLC a Honeywell Company, Des Plaines, Illinois 60017, USA.
authors.forename: S A
authors.initials: SA
authors.lastname: Bradley
authors.affiliation: Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.
authors.forename: Ao
authors.initials: A
authors.lastname: Li
authors.affiliation: Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.
authors.forename: Izabela
authors.initials: I
authors.lastname: Szlufarska
authors.affiliation: Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.
authors.forename: Paul M
authors.initials: PM
authors.lastname: Voyles