Truncated cube

Abstract: Single-molecule magnets (SMMs) have many potential applications including high-density information storage, in which each bit of information is stored as the magnetization orientation of an individual molecule, and as qubits for quantum computation, in which the required arbitrary superposition of quantum states with opposite projections of spin can be produced by either quantum tunneling of the magnetization, intermolecular exchange, or multifrequency EPR pulses. The fundamental requirements for a molecule to behave as an SMM are a) a relatively large spin ground state (S) and b) a large and negative zero-field splitting (zfs) of that ground state (as measured by the zfs parameterD). The upper limit of the barrier to the reorientation of the magnetization is given by S jD j for integer spins and (S 1/4) jD j for halfinteger spins. To make large molecular clusters, two successful, but somewhat opposing, synthetic strategies have generally been employed. The first is the use of rigid bridging ligands, for example, cyanide, that impose the geometry on the resultant cluster, and the second is the use of flexible ligands, for example, carboxylates, that impose little or no geometry. Both approaches have produced molecules with extremely

Abstract: Thanks to recent developments in additive manufacturing techniques, it is now possible to fabricate porous biomaterials with arbitrarily complex micro-architectures Micro-architectures of such biomaterials determine their physical and biological properties, meaning that one could potentially improve the performance of such biomaterials through rational design of micro-architecture The relationship between the micro-architecture of porous biomaterials and their physical and biological properties has therefore received increasing attention recently In this paper, we studied the mechanical properties of porous biomaterials made from a relatively unexplored unit cell, namely rhombicuboctahedron We derived analytical relationships that relate the micro-architecture of such porous biomaterials, ie the dimensions of the rhombicuboctahedron unit cell, to their elastic modulus, Poisson's ratio, and yield stress Finite element models were also developed to validate the analytical solutions Analytical and numerical results were compared with experimental data from one of our recent studies It was found that analytical solutions and numerical results show a very good agreement particularly for smaller values of apparent density The elastic moduli predicted by analytical and numerical models were in very good agreement with experimental observations too While in excellent agreement with each other, analytical and numerical models somewhat over-predicted the yield stress of the porous structures as compared to experimental data As the ratio of the vertical struts to the inclined struts, α, approaches zero and infinity, the rhombicuboctahedron unit cell respectively approaches the octahedron (or truncated cube) and cube unit cells For those limits, the analytical solutions presented here were found to approach the analytic solutions obtained for the octahedron, truncated cube, and cube unit cells, meaning that the presented solutions are generalizations of the analytical solutions obtained for several other types of porous biomaterials

Abstract: Although a number of computational studies have examined the relative stability of icosahedral and decahedral gold clusters from 1 to 3 nm in size, few studies have focussed on the variety of face-centered cubic (fcc) nanoparticles in this size regime. In most cases small fcc gold particles are assumed to adopt the truncated octahedral shape, but in light of the fact that the shape and structure of gold nanoparticles is known to vary, the relative stability of fcc polyhedra may change with size. Presented here are results of first-principles calculations investigating the preferred shape of gold particles less than 3 nm in size. Our results indicate that the equilibrium shape of fcc gold nanoparticles less than 1 nm is the cuboctahedron, but this shape rapidly becomes energetically unstable with respect to the truncated octahedron, octahedron and truncated cube shapes as the size increases.