Unitary and Antiunitary Operators Mapping Vectors to Parallel or to Orthogonal Ones, with Applications to Symmetry Transformations

Unitary and antiunitary operators which map vectors either to parallel or to orthogonal vectors are characterized. As an application the results are used to show that symmetry transformations induced by real functions are identity transformations.     

Nanostructure of Solid Precipitates Obtained by Expansion of Polystyrene-block-Polybutadiene Solutions in Near Critical Propane: Block Ratio and Micellar Solution Effects

In contrast to incompressible liquid solutions, compressible near-critical solutions of block copolymers allow for controlling rapid structure transformations with pressure alone. For example, when dissolved in near-critical propane, polystyrene-block-polybutadiene can form a random molecular solution at high pressures, a micellar solution at moderate pressures, and a solvent-free precipitate at low pressures. In contrast to the unstructured virgin copolymer, such a propane-treated precipitate rapidly self assembles toward structures characteristic of equilibrated block copolymers, such as lamellae, spheres or cylinders, which depend on the block ratio rather than on the decompression rate or temperature, at least within the rate and temperature ranges investigated in this work. At lower temperatures, however, say below 40 °C, glass transition of the styrene-butadiene diblocks can inhibit independent structure formation while crystallization of their hydrogenated-butadiene analogs can preserve the micellar-solution structure.     

Origin of longitudinal spin excitations in iron-pnictide parent compounds

We investigate longitudinal spin excitations (LSEs) as a probe of microscopic origin ofmagnetic ordering in parent pnictides BaFe₂As₂ and NaFeAs. Currently adopted interpretation ofLSEs as bottom of particle-hole continuum points unambiguously toward itinerant-electronmagnetism, but is difficult to reconcile with available optical measurements. We study thepossibility that the LSEs originate from multi-magnon processes which are notenergetically constrained by optical spectroscopy and do not sharply distinguish betweenlocal-moment and itinerant scenarios. Two mechanisms, capable of enhancing multi-magnoncontinuum to the level indicated by neutron scattering experiments, are proposed. Thefirst emphasizes itinerant electrons and is based on electronic transitions betweenmagnetically split bands, while the other relies on purely spin fluctuations close to amagnetic quantum phase transition. Electronic excitations enhance multi-magnoncontribution to LSEs for small Fermi surface taking part in the SDW instability, but areinsufficient to account for measured intensities. The correct order of LSEs, on the otherhand, can be reproduced by the spin fluctuation mechanism for a reasonable set ofparameters.     

Effect of Li<Superscript>+</Superscript> stabilization on smectite intercalate properties

Smectites are widely used minerals whose structure and properties can be modified and controlled. The aim of this study was to improve the sorption capacity and accessibility of interlayer (interpacket) spaces by reducing the pillar density in Chmielnik smectite. The micropore volume increases by increasing one of their dimensions, which is determined as the distance between pillars. This aim was achieved by lowering the resultant packet charge. Changes in intercalate structure and microporosity were studied using X-ray diffractometry and Ar sorption at–196°C. The Li/Na smectite ratio is crucial for modifying the smectite properties, particularly those associated with mineral microporosity. The behavior of the samples with the same interlayer cation composition exhibited two distinct trends. The first one is a decrease in the specific surface value (volume of micropores) accompanied by an increase in the amount of Li in the ion interlayer composition. The second one is a decline in the specific surface (volume of micropores) when the calcination temperature rises.