A twinning study

For some materials the constitutive function may be multi-valued. One such material is a twinned crystal, which consists of two regions related by a symmetry transformation. In this paper, multi-valued functions based on twinning, trilling, etc., are examined. Group theory is used to obtain some new results on the invariance groups of multi-valued constitutive functions. With these results and ideas of material symmetry used in classical elasticity, estimates for the invariance groups are provided. In addition, a theorem is proved which gives a necessary and sufficient condition relating the invariance group of any branch to the number of branches of the constitutive function. Finally, an example is worked out which uses the theory of stress-free joints. In this example, various ways of bonding two regions together so that the resulting crystals forms a twin are shown.     

Photoinduced C-N bond cleavage in 2-azido-1,3-diphenyl-propan-1-one derivatives: photorelease of hydrazoic acid

Photolysis of 3-azido-1,3-diphenyl-propan-1-one (1a) in toluene yields 1,3-diphenyl-propen-1-one (2), whereas irradiation of 3-azido-2,2-dimethyl-1,3-diphenyl-propan-1-one (1b) results in the formation of mainly 2,2-dimethyl-1,3-diphenyl-propan-1-one. Laser flash photolysis (308 nm) of 1a,b in acetonitrile reveals a transient absorption (lambda max = approximately 310 nm) due to the formation of radicals 4a and 4b, respectively, which have lifetimes of approximately 14 micros at ambient temperature. TD-DFT calculations (B3LYP/6-31+G(d)) reveal that the first and second excited states of the triplet ketone (T1K (n,pi*) and T2K (pi,pi*)) in azide 1a are almost degenerate, at approximately 74 and 76 kcal/mol above the ground state (S0), respectively. Similarly, azide 1b has T1K and T2K 75 and 82 kcal/mol above S0, respectively. The calculated transition state for cleaving the C-N bond is located 71 and 74 kcal/mol above S0 in azides 1a and 1b, respectively. The calculated bond dissociation energies for breaking the C-N bond are 55 and 58 kcal/mol for azides 1a and 1b, respectively, making C-N bond breakage accessible from T1K in azides 1 at ambient temperature. In comparison, the irradiation of azides 1 in argon matrices at 14 K lead to the formation of the corresponding triplet alkyl nitrenes (1-n), via intramolecular energy transfer from T2K. The characterization of 1-n was supported by isotope labeling, IR spectroscopy, and molecular modeling.     

Base-stabilized amidodiarsenes: synthesis, structure, and theoretical studies

The guanidinato- or amidinato-bridged diarsenes [As2{mu-(ArN)2CR}2] (Ar = C6H3Pri2-2,6; R = N(C6H11)2, NPri2, or But) have been prepared by reduction of the corresponding As(III) precursors, [Cl2As{kappa2-N,N'-(ArN)2CR}]. Theoretical studies suggest that the As-As bonds of the dimers have significant double-bond character, the sigma and pi components of which are derived mainly from As p orbital overlaps.     

Homo- and heteroleptic complexes of four-membered group 13 metal(I) N-heterocyclic carbene analogues with group 10 metal(0) fragments

A series of complexes between recently developed four-membered group 13 metal(I) heterocycles and group 10 metal(0) fragments have been prepared and structurally characterized. One prepared complex, [Pt{Ga[N(Ar)]2CNCy2}3] (Ar = C6H3Pri2-2,6; Cy = cyclohexyl), possesses the shortest Pt-Ga bonds yet reported, the covalent components of which are suggested by theoretical studies to have significant pi character.     

A Metastable p-Type Semiconductor as a Defect-Tolerant Photoelectrode

A p-type Cu₃Ta₇O₁₉ semiconductor was synthesized using a CuCl flux-based approach and investigated for its crystalline structure and photoelectrochemical properties. The semiconductor was found to be metastable, i.e., thermodynamically unstable, and to slowly oxidize at its surfaces upon heating in air, yielding CuO as nano-sized islands. However, the bulk crystalline structure was maintained, with up to 50% Cu(I)-vacancies and a concomitant oxidation of the Cu(I) to Cu(II) cations within the structure. Thermogravimetric and magnetic susceptibility measurements showed the formation of increasing amounts of Cu(II) cations, according to the following reaction: Cu₃Ta₇O₁₉ + x/2 O₂ → Cu_(3−x)Ta₇O₁₉ + x CuO (surface) (x = 0 to ~0.8). With minor amounts of surface oxidation, the cathodic photocurrents of the polycrystalline films increase significantly, from <0.1 mA cm⁻² up to >0.5 mA cm⁻², under visible-light irradiation (pH = 6.3; irradiant powder density of ~500 mW cm⁻²) at an applied bias of −0.6 V vs. SCE. Electronic structure calculations revealed that its defect tolerance arises from the antibonding nature of its valence band edge, with the formation of defect states in resonance with the valence band, rather than as mid-gap states that function as recombination centers. Thus, the metastable Cu(I)-containing semiconductor was demonstrated to possess a high defect tolerance, which facilitates its high cathodic photocurrents.     

Multifractal analysis of foreign exchange data

In this paper we perform multifractal analyses of five daily Foreign Exchange (FX) rates. These techniques are currently used in turbulence to characterize scaling and intermittency. We show the multifractal nature of FX returns, and estimate the three parameters in the universal multifactal framework, which characterize all small and medium intensity fluctuations, at all scales. For large fluctuations, we address the question of hyperbolic (fat) tails of the distributions which are characterized by a fourth parameter, the tail index. We studied both the prices fluctuations and the returns, finding no systematic difference in the scaling exponents in the two cases. We discuss and compare our results with several recent studies, and show how the additive models are not compatible with data: Brownian, fractional Brownian, Lévy, Truncated Lévy and fractional Lévy models. We analyse in this framework the ARCH(1), GARCH(1,1) and HARCH (7) models, and show that their structure functions scaling exponents are undistinguishable from that of Brownian motion, which means that these models do not adequately describe the scaling properties of the statistics of the data. Our results indicate that there might exist a multiplicative ‘flux of financial information’, which conditions small‐scale statistics to large‐scale values, as an analogy with the energy flux in turbulence. Copyright © 1999 John Wiley & Sons, Ltd.     

Melt Motion Due to Peltier Marking during Bridgman Crystal Growth with an Axial Magnetic Field

This paper treats a liquid-metal flow inside an electrically insulating cylinder with electrically conducting solids above and below the liquid region. There is a uniform axial magnetic field, and there is an electric current through the liquid and both solids. Since the lower liquid-solid interface is concave into the solid and since the liquid is a better electrical conductor than the adjacent solid, the electric current is locally concentrated near the centerline. The return to a uniform current distribution involves a radial electric current which interacts with the axial magnetic field to drive an azimuthal flow. The axial variation of the centrifugal force due to the azimuthal velocity drives a meridional circulation with radial and axial velocities. This problem models the effects of Peltier marking during the vertical Bridgman growth of semiconductor crystals with an externally applied magnetic field, where the meridional circulation due to the Peltier current may produce important mixing in the molten semiconductor. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of molecular weight on the capillary absorption of polymer droplets

We study capillary absorption of small polymer droplets into nonwettable capillaries using coarse-grained molecular dynamics simulations and a simple analytical model. Studies of droplets of simple fluids have revealed that the capillary process depends on the ratio of tube-to-droplet radii [Willmott Faraday Discuss., 2010, 146, 233; Marmur J. Colloid Interface Sci. 1988, 122, 209]. Here we consider the absorption of droplets of polymers and study the effect of polymer chain length on the capillary absorption process. Our simulations reveal that for droplets of the same size (radius), the critical tube radius, below which there is no absorption, increases with the length of the polymer chains that constitute the droplets. We propose a model to explain this effect, which incorporates an entropic penalty for polymer confinement and find that this model agrees quantitatively with the simulations. We also find that the absorption dynamics is sensitive to the polymer chain length. In some cases during the capillary uptake transient partial absorption states, where the droplet is partially in and partially out of the tube, were observed. Such dynamics cannot be explained by a generalized Lucas-Washburn approach.