No abstract

Some ABX 3 perovskites exhibit different local environments (DLE) for the same B atoms in the lattice, an effect referred to as disproportionation, distinguishing such compounds from common perovskites that have single local environments (SLE). The basic phenomenology associated with such disproportionation involves the absence of B-atom charge ordering, the creation of different B-X bond length ('bond alternation') for different local environments, the appearance of metal (in SLE) to insulator (in DLE) transition, and the formation of ligand holes. We point out that this phenomenology is common to a broad range of chemical bonding patterns in ABX 3 compounds, either with s-p electron B-metal cations (BaBiO 3 , CsTlF 3 ), or noble metal cation (CsAuCl 3 ), as well as d-electron cations (SmNiO 3 , CaFeO 3 ). We show that underlying much of this phenomenology is the 'self-regulating response', whereby in strongly bonded metal-ligand systems with high lying ligand orbitals, the system protects itself from creating highly charged cations by transferring ligand electrons to the metal, thus preserving a nearly constant metal charge in different local environments, while creating B-ligand bond alternation and ligand-like conduction band ('ligand hole' states). We are asking what are the minimal theory ingredients needed to explain the main features of this SLE-to-DLE phenomenology, such as its energetic driving force, bond length changes, possible modifications in charge density and density of state changes. Using as a guide the lowering of the total energy in DLE relative to SLE, we show that § Current address:

Self-assembly of colloidal particles due to elastic interactions in nematic liquid crystals promises tunable composite materials and can be guided by exploiting surface functionalization, geometric shape and topology, though these means of controlling self-assembly remain limited. Here, we realize low-symmetry achiral and chiral elastic colloids in the nematic liquid crystals using colloidal polygonal concave and convex prisms. We show that the controlled pinning of disclinations at the prisms edges alters the symmetry of director distortions around the prisms and their orientation with respect to the far-field director. The controlled localization of the disclinations at the prism's edges significantly influences anisotropy of the diffusion properties of prisms dispersed in liquid crystals and allows one to modify their self-assembly. We show that elastic interactions between polygonal prisms can be switched between repulsive and attractive just by controlled re-pinning the disclinations at different edges using laser tweezers. Our findings demonstrate that elastic interactions between colloidal particles dispersed in nematic liquid crystals are sensitive to the topologically equivalent but geometrically rich controlled configurations of the particle-induced defects.