Topological defects can affect the physical properties of graphene in unexpected ways.Harnessing their influence may lead to enhanced control of both material strength and electrical properties. Here we present a new class of topological defects in graphene composed of a rotating sequence of dislocations that close on themselves, forming grain boundary loops that either conserve the number of atoms in the hexagonal lattice or accommodate vacancy/interstitial reconstruction, while leaving no unsatisfied bonds. One grain boundary loop is observed as a "flower" pattern in scanning tunneling microscopy (STM) studies of epitaxial graphene grown on SiC(0001). We show that the flower defect has the lowest energy per dislocation core of any known topological defect in graphene, providing a natural explanation for its growth via the coalescence of mobile dislocations. §

The full phonon dispersion relations of lead titanate and lead zirconate in the cubic perovskite structure are computed using first-principles variational density-functional perturbation theory, with ab initio pseudopotentials and a plane-wave basis set. Comparison with the results previously obtained for barium titanate shows that the change of a single constituent (Ba to Pb, Ti to Zr) has profound effects on the character and dispersion of unstable modes, with significant implications for the nature of the phase transitions and the dielectric and piezoelectric responses of the compounds. Examination of the interatomic force constants in real space, obtained by a transformation which correctly treats the long-range dipolar contribution, shows that most are strikingly similar, while it is the differences in a few key interactions which produce the observed changes in the phonon dispersions. These trends suggest the possibility of the transferability of force constants to predict the lattice dynamics of perovskite solid solutions.

a b s t r a c tDensity functional theory DFT + U calculations are used to investigate a-MnO 2 , a structure containing a framework of corner and edge sharing MnO 6 octahedra with tunnels in between. Placing K + ions into the tunnels stabilizes a-MnO 2 with respect to the rutile-structure b-MnO 2 phase, in agreement with experiment. The computed magnetic structure has antiferromagnetic (ferromagnetic) Mn-Mn interactions between corner-sharing (edge-sharing) octahedra. Pure a-MnO 2 is found to be a semiconductor with an indirect band gap of 1.3 eV. Water and related hydrides (OH À ; H 3 O + ) can also be accommodated in the tunnels; the equilibrium K-O distance increases with increasing oxygen hydride charge.Published by Elsevier B.V.

Quasicrystals are metal alloys whose noncrystallographic symmetry and lack of structural periodicity challenge methods of experimental structure determination. Here we employ quantum-based total-energy calculations to predict the structure of a decagonal quasicrystal from first principles considerations.We employ Monte Carlo simulations, taking as input the knowledge that a decagonal phase occurs in Al-Ni-Co near a given composition, and using a few features of the experimental Patterson function. The resulting structure obeys a nearly deterministic decoration of tiles on a hierarchy of length scales related by powers of τ , the golden mean.