A mesoporous non-precious metal boride system: synthesis of mesoporous cobalt boride by strictly controlled chemical reduction

Generating high surface area mesoporous transition metal boride is interesting because the incorporation of boron atoms generates lattice distortions that lead to the formation of amorphous metal boride with unique properties in catalysis. Here we report the first synthesis of mesoporous cobalt boron amorphous alloy colloidal particles using a soft template-directed assembly approach. Dual reducing agents are used to precisely control the chemical reduction process of mesoporous cobalt boron nanospheres. The Earth-abundance of cobalt boride combined with the high surface area and mesoporous nanoarchitecture enables solar-energy efficient photothermal conversion of CO₂ into CO compared to non-porous cobalt boron alloys and commercial cobalt catalysts.

Generating high surface area mesoporous transition metal boride is challenging but interesting because incorporation of boron atoms can generate lattice distortion to form amorphous metal boride which has unique properties in catalysis.     

Determination of oxygen content in YBa2Cu3O6.5+x

A method for determining the oxygen content of the high-temperature superconductor YBa₂Cu₃O_6.5+x is described. The superconductor is dissolved in 4.4 M hydrobromic acid, forming bromine. The mixture is then diluted with hydrochloric acid to obtain a solution of bromine and Cu(II) in 0.44 M hydrobromic acid and 1.1 M hydrochloric acid. As(III) is added in slight excess of that required to react with the bromine and the unreacted As(III) is determined by titration with potassium bromate. Oxygen does not interfere. The results of this method are in agreement with those of other iodimetric procedures. The dissolution of the superconductor in 4.4 M hydrobromic acid is much faster than in hydrochloric acid, the medium used in one iodimetric technique. YBa₂Cu₃O_6.5+x sintered fibers and powder samples weighing from ca. 0.5 to 200 mg were analyzed for oxygen content.     

Some graphs with small second eigenvalue

For any prime,p, we construct a Cayley graph on the group,G, of affine linear transformations ofℤ/pℤ of degree 2(p−1) and second eigenvalue with the following special property: the adjacency matrix of the graph is supported on the “blocks” associated to the trivial representation and the irreducible representation of sizep−1. SinceG is of orderp(p−1), the correspondingt-uniform Cayley hypergraph has essentially optimal second eigenvalue for this degree and size of the graph (see [2] for definitions). En route we give, for any integerk>1, a simple Cayley graph onp ^k nodes of degreep of second eigenvalue . The author wishes to acknowledge the National Science Foundation for supporting this research in part under Grant CCR-8858788, and the Office of Naval Research under Grant N00014-87-K-0467.     

Triazene proton affinities: A comparison between density functional,Hartree–Fock,and post-Hartree–Fock methods

The consistency of three density functional computational implementations (DMol, DGauss, and deMon) are compared with high-level Hartree–Fock and Møller–Plesset (MP) calculations for triazene (HN?NNH₂) and formyl triazene (HN?NNHCOH). Proton affinities on all electronegative sites are investigated as well as the geometries of the neutral and protonated species. Density functional calculations employing the nonlocal gradient corrections show agreement with MP calculations for both proton affinities and geometries of neutral and protonated triazenes. Local spin density approximation DMol calculations using numerical basis sets must employ an extended basis to agree with other density functional codes using analytic Gaussian basis sets. The lowest energy conformation of triazene was found to be nonplanar; however, the degree of nonplanarity, as well as some bond lengths, is dependent on the basis set, electron correlation treatment, and methods used for the calculation. © 1994 by John Wiley & Sons, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain in the United States of America.

     

Existence and positivity of solutions of a fourth-order nonlinear PDE describing interface fluctuations

We study the partial differential equation which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case × R S¹. We establish existence, uniqueness, and regularity of solutions, locally in time, for positive initial data in H¹(S¹), and prove the existence of several families of Lyapunov functions for the evolution. From the latter we establish a sharp connection between existence globally in time and positivity preservation: if [0], T*) is a maximal half open interval of existence for a positive solution of the equation, with T* < ∞, then lim_tT* w(t,·) exists in C¹(S¹) but vanishes at some point. We show further that if T* > (1 + √3)/16π² √3 then T* = ∞ and lim_t∞ w(t,.) exists and is constant. We discuss also some explicit solutions and propose a generalization to higher dimensions. © 1994 John Wiley & Sons, Inc.     

Energy-level statistics of model quantum systems: Universality and scaling in a lattice-point problem

We investigate the statistics of the numberN(R, S) of lattice pointsnZ ², in an annular domain (R, w)=(R+w)A\RA, whereR, w>0. HereA is a fixed convex set with smooth boundary andw is chosen so that the area of (R, w) isS. The statistics comes fromR being taken as random (with a smooth density) in some interval [c ₁ T,c ₂,T],c ₂>c ₁>0. We find that in the limitT the variance and distribution of N=N(R; S)–S depend strongly on howS grows withT. There is a saturation regimeS/T, asT, in which the fluctuations in N coming from the two boundaries of are independent. Then there is a scaling regime,S/Tz, 0<z<, in which the distribution depends onz in an almost periodic way going to a Gaussian asz0. The variance in this limit approachesz for genericA, but can be larger for degenerate cases. The former behavior is what one would expect from the Poisson limit of a distribution for annuli of finite area.