Angular Dependence of Lateral and Levitation Forces in Asymmetric Small Magnet/Superconducting Systems

The dipole-dipole interaction model is used to calculate the angular dependence of lateral and levitation forces on a small permanent magnet and a cylindrical superconductor in the Meissner state lying laterally off the symmetric axis of the cylinder. Under the assumption that the lateral displacement of the magnet is small compared with the physical dimensions of the system, we obtain analytical expressions for the lateral and levitation forces as functions of geometrical parameters of the superconductor as well as the height, the lateral displacement and the orientation of magnetic moment of the magnet. The effect of thickness and radius of the superconductor on the levitation force is similar to that for a symmetric magnet/superconducting cylinder system, but within the range of lateral displacement. The splitting in the levitation force increases with the increasing angle of orientation of the magnetic moment of the magnet. For a given lateral displacement of the magnet, the lateral force vanishes when the magnetic moment is perpendicular to the surface of the superconductor and has a maximum value when the moment is parallel to the surface. For a given orientation of the magnetic moment, the lateral force has a linear relationship with the lateral displacement. The stability of the magnet above the superconducting cylinder is discussed in detail.     

Ligand Exchange Processes on Solvated Zinc Cations – DFT Analysis of Hydrogen Cyanide Exchange on [Zn(HCN)6]2+

The mechanisms for hydrogen cyanide exchange on [Zn(HCN)₆]²⁺ were studied using density functional theory (B3LYP/6‐311+G**), and showed that the limiting dissociative (D) pathway is more favorable than the associative interchange (I_a) mechanism. The activation barrier for the dissociative mechanism (7 kcal · mol^–1) is clearly lower than for the interchange mechanism (15.9 kcal · mol^–1).     

Vibrations in Magnet/Superconductor Levitation Systems

The problem of a small magnet levitating above a very thin superconducting disc in the Meissner state is analysed. The dipole-dipole interaction model is employed to derive analytical expressions for the interaction energy, levitation force, magnetic stiffness and frequency of small vibrations about the equilibrium position in two different configurations, i.e. with the magnetic moment parallel and perpendicular to the superconductor. The results show that the frequency of small vibrations decreases with the increasing levitation height for a particular radius of the superconducting disc, which is in good agreement with the experimental results. However, the frequency increases monotonically up to saturation by increasing the radius of the disc for a particular height of the magnet. In addition, the frequency of vibrations is higher when the system is in the vertical configuration than that when the system is in the horizontal configuration.     

Ligand‐Exchange Processes on Solvated Zinc Cations: Water Exchange on [Zn(H2O)4(L)]2+⋅2 H2O (L=Heterocyclic Ligand)

The water‐exchange mechanisms of [Zn(H₂O)₄(L)]²⁺?2 H₂O (L=imidazole, pyrazole, 1,2,4‐triazole, pyridine, 4‐cyanopyridine, 4‐aminopyridine, 2‐azaphosphole, 2‐azafuran, 2‐azathiophene, and 2‐azaselenophene) have been investigated by DFT calculations (RB3LYP/6‐311+G**). The results support limiting associative reaction pathways that involve the formation of six‐coordinate intermediates [Zn(H₂O)₅(L)]²⁺?H₂O. The basicity of the coordinated heterocyclic ligands shows a good correlation with the activation barriers, structural parameters, and stability of the transition and intermediate states.     

Pressure and temperature effects on metal-to-metal charge transfer in cyano-bridged CoIII-FeII complexes

The effects of pressure and temperature on the energy (Eop) of the metal-to-metal charge transfer (MMCT, FeII-->CoIII) transition of the cyano-bridged complexes trans-[L14CoNCFe(CN)5]- and cis-[L14CoNCFe(CN)5]- (where L14=6-methyl-1,4,8,11-tetraazacyclotetradecan-6-amine) were examined. The changes in the redox potentials of the cobalt and iron metal centres with pressure and temperature were also examined and the results interpreted with Marcus-Hush theory. The observed redox reaction volumes can mainly be accounted for in terms of localised electrostriction effects. The shifts in Eop due to both pressure and temperature were found to be less than the shifts in the energy difference (DeltaE degrees]) between the CoIII-FeII and CoII-FeIII redox isomers. The pressure and temperature dependence of the reorganisational energy, as well as contributions arising from the different spin states of CoII, are discussed in order to account for this trend. To study the effect of pressure on CoIII electronic absorption bands, a new cyano-bridged complex, trans-[L14CoNCCo(CN)5], was prepared and characterised spectroscopically and structurally. X-Ray crystallography revealed this complex to be isostructural with trans-[L14CoNCFe(CN)5].5H2O.     

Mechanistic elucidation of the substitution behavior of alkyl cobaloximes in water and methanol as solvents

The ligand substitution behavior of trans-[Co(Hdmg)2(R)S] (R = CH3, PhCH2; Hdmg = dimethylglyoximate; S = H2O and/or MeOH) was studied for imidazole, pyrazole, 1,2,4-triazole, N-acetylimidazole, 5-chloro-1-methylimidazole, NO2-, Ph3P, Ph3As, and Ph3Sb as entering ligands. In all cases, except for Ph3As and Ph3Sb, the observed kinetics shows a linear dependence on the entering nucleophile concentration with no evidence for a back reaction. In the case of Ph3As and Ph3Sb as entering nucleophiles, kinetic evidence for a reverse solvolysis reaction is at hand. Activation parameters (DeltaH++, DeltaS++, and DeltaV++) were determined from the temperature and pressure dependence of all studied reactions and support the operation of a dissociatively activated substitution mechanism. The rate and activation parameters show that there is an increase in the dissociative character from a dissociative interchange to a limiting dissociative mechanism that depends on the nature of R and the entering nucleophile. The crystal structure of trans-[Co(en)2(Me)H2O]2+ was determined by X-ray analysis. The Co-O and Co-C bond lengths were found to be 2.153(6) and 1.995(10) angstroms, respectively. The kinetic and structural data are discussed in reference to a series of earlier studied systems for which data are reported in the literature.     

The basis number of the composition of theta graphs with stars and wheels

he basis number, b(G), of a graph G is defined to be the least integer k such that G has a k-fold basis for its cycle space. In this paper we investigate the basis number of the composition of theta graphs with stars and wheels. This revised version was published online in June 2006 with corrections to the Cover Date.     

Phase coherence of conduction electrons below the Kondo temperature

We have measured the phase decoherence rate tau_{varphi};{-1} of conduction electrons in disordered Ag wires implanted with 2 and 10 ppm Fe impurities, by means of the weak-localization magnetoresistance. The Kondo temperature of Fe in Ag, T_{K} approximately 4 K, is in the ideal temperature range to study the progressive screening of the Fe spins as the temperature T falls below T_{K}. The contribution to tau_{varphi};{-1} from the Fe impurities is clearly visible over the temperature range 40 mK-10 K. Below T_{K}, tau_{varphi};{-1} falls rapidly until T/T_{K} approximately 0.1, in agreement with recent theoretical calculations. At lower T tau_{varphi};{-1} deviates from theory with a flatter T-dependence. Understanding this anomalous dephasing for T/T_{K}<0.1 may require theoretical models with larger spin and number of channels.     

A new method for measuring tracks density in CR-39 detectors by compensating for overlapping tracks

CR-39 nuclear track detectors have been used as an efficient radon monitoring system. Exposing these detectors to radon would result in tracks where ever particles hit the surface of the detector. Natural radioactivity of alpha particles (radon concentration) is measured based on the count of these tracks on CR-39 detector. Counting these tracks by eye is not an easy task especially when the density of the tracks is high. Automated tracks counting systems are attractive solution for this problem. However, as the density of tracks increases the accuracy of these methods deteriorates. This is due to the fact that overlapped tracks are counted as one track during the segmentation process resulting in an underestimation of the real count of the tracks. This work proposes a new image processing based automated approach for tracks counting. This new automated approach solves the problem of counting overlapping tracks by approximating their number and then adjusting the final count of tracks by compensating for those uncounted tracks. The experimental results show that the proposed approach reduces the counting percentage error from 5.64% to 2.54% by solving the counting problem of the overlapped tracks.     

Investigations on the Enantiomerization Mechanism of an ­Organophosphorus Cages – DFT Study

The enantiomerization pathways of the organophosphorus cages Bz₃XPO₄ (X = N, P, As, CH, SiH, and GeH) were studied by quantum chemical calculations (RB3LYP/LANL2DZp), where Bz₃PPO₄ is octadecahydro‐2,8‐(epoxy 1 , 2 benzeno)dibenzo[d,g] 1 , 3 , 2 , 6 dioxadiphosphocine‐2‐oxide. The twist angles of the organophosphorus cage decrease in the order Bz₃GeHPO₄ > Bz₃AsPO₄ > Bz₃SiHPO₄ > Bz₃PPO₄ > Bz₃CHPO₄ > Bz₃NPO₄. The steric factors affect mainly the activation energy and the structural data of the organophosphorus cages.