Fig. 2: 3D atomic displacements and strain maps of the Pd@Pt nanoparticle.

a Atomic layers (sliced along the [001] direction) of the core-shell nanoparticle. Note that only one layer per every two atomic layers is plotted. Red and blue dots represent the positions of the Pd and Pt atoms assigned to the fcc lattice, respectively, and black dots represent the positions of atoms not assigned to the fcc lattice (Methods). b–c 3D atomic displacement maps, along the radial direction (\({d}_{r}\)) (b), and along the azimuthal direction (\({d}_{\phi }\)) (c) in the spherical coordinate system. d–e 3D strain maps in spherical coordinates, representing radial (\({\varepsilon }_{{rr}}\)) (d) and azimuthal (\({\varepsilon }_{\phi \phi }\)) (e) strains, respectively (Methods). The atomic displacement and strain maps presented in b–e were calculated from the corresponding layer presented in a. f A map showing the 3D radial strain, atomic positions (only half of the atomic positions are plotted for better visualization), and radial displacement vectors of an atomic layer at the middle of the particle. g Similar plot with f, for azimuthal strain and displacements. Note that the radial displacements (\({d}_{r}\)) point outward in the region where the azimuthal displacements (\({d}_{\phi }\)) converge in (the region pointed by red arrows), and the opposite behavior can be observed in the region where radial displacements point inward, where the azimuthal displacements diverge (the region pointed by blue arrows).