Metal organic polyhedra (MOPs) such as coordination cages and clusters are increasingly utilized across many fields, but their geometrically selective assembly during synthesis is nontrivial. When ligand along these polyhedral edges arranged in an unsymmetrical mode or the bridging itself nonsymmetric, a vast combinatorial space of potential isomers exists complicating formation isolation. Here...

111 sitzr measurements of the Ni and Co K-edge XAFS spectra of Li1.~Ni02 and Lil.,CoOz as a function of x were successfully carried out for the first time using an electrocl~emical ceii. It is observed that a local Jahn-Teller distortion of the Ni06 octahedron in LiN102 was reduced with deintercalation of Li which caused oxidatiou of the Jahn-Teller d7 ~ i ~ * ion to do Ni4+i011. A substitution...

The crystal structure of four synthetic samples of melanterite, (Fe,Cu)SO4 •7H2O, and six natural samples of melanterite and one of zinc-melanterite from the Richmond mine, Iron Mountain, California, has been refined in space group P21/c. The structure refinements show that substitution of Cu for Fe at the M2 site distorts the octahedron in a square-planar fashion. This behavior is attributed t...

We study a recurrence defined on a three dimensional lattice and prove that its values are Laurent polynomials in the initial conditions with all coefficients equal to one. This recurrence was studied by Propp and by Fomin and Zelivinsky. Fomin and Zelivinsky were able to prove Laurentness and conjectured that the coefficients were 1. Our proof establishes a bijection between the terms of the L...

We define the hive ring, which has a basis indexed by dominant weights for GLn(C), and structure constants given by counting hives [KT1] (or equivalently honeycombs, or Berenstein-Zelevinsky patterns [BZ1]). We use the octahedron rule from [RR, FZ, P, S] to prove bijectively that this “ring” is indeed associative. This, and the Pieri rule, give a self-contained proof that the hive ring is isomo...