1,792 research outputs found
Complexity in surfaces of densest packings for families of polyhedra
Packings of hard polyhedra have been studied for centuries due to their
mathematical aesthetic and more recently for their applications in fields such
as nanoscience, granular and colloidal matter, and biology. In all these
fields, particle shape is important for structure and properties, especially
upon crowding. Here, we explore packing as a function of shape. By combining
simulations and analytic calculations, we study three 2-parameter families of
hard polyhedra and report an extensive and systematic analysis of the densest
packings of more than 55,000 convex shapes. The three families have the
symmetries of triangle groups (icosahedral, octahedral, tetrahedral) and
interpolate between various symmetric solids (Platonic, Archimedean, Catalan).
We find that optimal (maximum) packing density surfaces that reveal unexpected
richness and complexity, containing as many as 130 different structures within
a single family. Our results demonstrate the utility of thinking of shape not
as a static property of an object in the context of packings, but rather as but
one point in a higher dimensional shape space whose neighbors in that space may
have identical or markedly different packings. Finally, we present and
interpret our packing results in a consistent and generally applicable way by
proposing a method to distinguish regions of packings and classify types of
transitions between them.Comment: 16 pages, 8 figure
Suppression of Octahedral Tilts and Associated Changes of Electronic Properties at Epitaxial Oxide Heterostructure Interfaces
Epitaxial oxide interfaces with broken translational symmetry have emerged as
a central paradigm behind the novel behaviors of oxide superlattices. Here, we
use scanning transmission electron microscopy to demonstrate a direct,
quantitative unit-cell-by-unit-cell mapping of lattice parameters and oxygen
octahedral rotations across the BiFeO3-La0.7Sr0.3MnO3 interface to elucidate
how the change of crystal symmetry is accommodated. Combined with low-loss
electron energy loss spectroscopy imaging, we demonstrate a mesoscopic
antiferrodistortive phase transition and elucidate associated changes in
electronic properties in a thin layer directly adjacent to the interface
- …