Zernike apodized photon sieves for high-resolution phase-contrast x-ray microscopy

We present a type of diffractive lens, Zernike apodized photon sieves (ZAPS), used as the objective for high spatial resolution and high phase-contrast imaging of weakly absorbing materials in x rays. The structure of ZAPS is based on the combination of two concepts: apodized photon sieves and Zernike phase contrast. The ZAPS is a single optic that integrates the appropriate ±π/2 rad phase shift through selective zone placement shifts in an apodized photon sieve. Analysis of the focusing properties of the apodized photon sieve in terms of point-spread function show that the sidelobes have been significantly suppressed at the expense of slightly widening the width of the main lobe. In combination with synchrotron light sources, ZAPS offers new opportunities for high-resolution phase-contrast x-ray microscopy in the physical and life sciences.     

Quadratic grating apodized photon sieves for simultaneous multiplane microscopy

We present a new type of imaging device, named quadratic grating apodized photon sieve (QGPS), used as the objective for simultaneous multiplane imaging in X-rays. The proposed QGPS is structured based on the combination of two concepts: photon sieves and quadratic gratings. Its design principles are also expounded in detail. Analysis of imaging properties of QGPS in terms of point-spread function shows that QGPS can image multiple layers within an object field onto a single image plane. Simulated and experimental results in visible light both demonstrate the feasibility of QGPS for simultaneous multiplane imaging, which is extremely promising to detect dynamic specimens by X-ray microscopy in the physical and life sciences.     

spin-lattice relaxation in cobalt-containing aluminophosphate molecular sieves

Phosphorus spin-lattice relaxation was studied in aluminophosphate molecular sieves containing various concentrations of either framework or non-framework cobalt. The behaviour of nuclear magnetisation in the presence of these paramagnetic centres was described successfully in the limit of no spin-diffusion. The diffusionless regime was strongly indicated with non-exponential magnetisation recovery and was therefore easy to recognise. According to the model, spin-lattice relaxation rates depend on the square of cobalt concentration. Measured relaxation rates agreed well with calculations if effective cobalt concentration was considered rather than the average one. The latter was obtained by bulk elemental analysis, while the former was extracted from cobalt concentration depth-profiles measured with Auger electron spectroscopy. These measurements indicated that in impregnated samples containing non-framework cobalt there could be much more cobalt near the crystal surface than within the crystal. Because high cobalt concentration can lead to an invisible phosphorus, only nuclei deep within the crystal contribute to the NMR signal. In such a case, the effective concentration is simply the concentration of cobalt far from the crystal surface. In our case, two impregnated samples with different bulk cobalt concentrations exhibited equal relaxation rates. Previously, such a case was misinterpreted as a case, in which nuclear spin-lattice relaxation was independent of cobalt concentration. AES measurements, however, revealed, that although average concentrations of the two samples were different by a factor of two, their effective concentrations were equal and thus in complete agreement with observed relaxation rates.     

Double rotation27Al NMR in molecular sieves

Although high-resolution NMR spectra can be obtained in solids, the use of²⁷Al NMR to investigate the structure of aluminosilicate and aluminophosphate molecular sieves has been severely limited because anisotropic second-order quadrupolar interactions, responsible for spectral broadening, cannot be eliminated by conventional magic angle spinning (MAS) or multiple pulse techniques. Here we give the principles of the double rotation (DOR) NMR technique which can remove not only the first-order broadenings but also the second-order broadenings in the NMR spectra of quadrupolar nuclei in solids. High-resolution²⁷Al NMR using DOR is capable of resolving discrete framework aluminum sites in aluminophosphate molecular sieves, permitting quantitative investigation of site-specific adsorbate-host interactions, and of discriminating different aluminum species in zeolites.     

Dynamics of water in molecular sieves by dielectric spectroscopy

We present recent dielectric data on the dynamics of water confined in molecular sieves with pore sizes 5 and 10 A. The dielectric measurements in the frequency and temperature ranges 10(-2)-10(6) Hz and 120-300 K show three relaxation processes for both samples. In the case of the 10 A pore the slowest process shows an Arrhenius temperature dependence at low temperatures (<220 K), while at high temperatures the relaxation appears to follow a more Vogel-Fulcher-Tammann (VFT) like behaviour. The relaxation time for this process is 100 s at about 170 K. The second slowest process is at low temperatures very similar to the main process of (bulk-like) water in a fully hydrated clay, but also this process seems to exhibit some kind of dynamical transition, in this case at T approximately 185 K. All the three processes in the 5 A pore exhibit Arrhenius temperature dependence, and two of them are considerably slower than the main relaxation in the hydrated clay. Thus, dynamics of bulk-like water is only observed in the 10 A molecular sieves, and most of the water molecules in both 5 and 10 A pores have considerably slower dielectric relaxation than has been observed for water confined in clay, most likely due to strong interactions with the considerably more hydrophilic inner surfaces of molecular sieves.     

Silver atoms and clusters in molecular sieves and clays

Electron spin resonance (ESR) and electron spin echo modulation (ESEM) studies on small paramagnetic silver clusters generated radiolytically in molecular sieves and clays are reviewed. Special attention is paid to the role of framework structure with respect to cluster nuclearity and stability. In general, geometrical size constraints play a crucial role and molecular sieves with cage-like structures with small openings between the cages such as A and rho zeolites stabilize cationic silver clusters more efficiently than channel-like zeolite structures. In addition, other factors like total cation capacity, type of cocation and/or molecular adsorbate in the cages can affect the silver agglomeration process to a great extent. The mechanism of silver agglomeration in irradiated molecular sieves and clays based on the ESR results is described as well as the reactivity of tetrameric and hexameric silver clusters with various molecular adsorbates.     

Application of percolation theory to ion-exchanged molecular sieves A

The unit cell of dehydrated zeolite A is cubic and its {100} faces constitute “windows” of a large cavity located at the center. In sodium-form zeolite A, Na⁺ partially blocks the window, through which oxygen but not nitrogen molecules can pass. By ion-exchanging two Na⁺s with one Ca²⁺, an unblocked or “open window” can be introduced. By preparing well defined (Na, Ca)-A zeolites having various compositions, the nitrogen percolation process was quantitatively studied. A curve for the number of percolatable cells vs the open-window concentration was deduced, and compared with Hammersley's theoretical curve. The theoretical curve has a sharp cut-oft at a concentration of one open-window per unit cell. The observed curve was steeper in this transition region than the theoretical one, but has a tail in the region corresponding to lower concentrations of open windows. The first tendency is ascribed to an ordered alignment of open-windows in their spatial distribution. The second is attributed to incompleteness of the blocking action of Na⁺. Substituted Ca²⁺ and vacant cation sites change the Madelung potential at the Na⁺ site, so that the curvature of the potential valley for Na⁺ may become gentle. As a result, Na⁺ can easily be displaced and make way for a visiting nitrogen molecule.     

Magnetic properties of iron loaded MCM-48 molecular sieves

Mesoporous molecular sieves of MCM-48 type were loaded with iron by the wet impregnation method, using Fe(III) nitrate or Fe(II) sulfate aqueous solutions as Fe sources, to obtain a magnetic porous composite. The iron loaded materials were characterized by XRD, N₂ adsorption and DRUV-vis and compared with the Si-MCM-48 host. Their magnetic properties were studied by measuring the hysteresis loops up to 1.5 T at different temperatures (5-300 K) and by magnetization vs. temperature curves following the conventional zero field cooling (ZFC) and field cooling (FC) protocols. Materials with high structure regularity and surface area are obtained, which exhibit a mixed paramagnetic and superparamagnetic behavior, arising in isolated iron ions inserted in the host framework, and in small iron oxide clusters or nanoparticles forming inside the pores, respectively. Larger hematite particles (8-13 nm) grown on the external surface provide a quite small ferromagnetic contribution to the hysteresis loop.     

Optical potential for composite particles

Optical potentials for the elastic scattering of deuterons, ³He and tritons are calculated in terms of the optical potentials of neutrons and protons forming the projectile. The angular distributions for the elastic scattering of these particles from various targets are calculated and compared with experimental results.     

Torus quantization for spinning particles

We derive semiclassical quantization conditions for particles with spin. These generalize the Einstein-Brillouin-Keller quantization in such a way that, in addition to the Maslov correction, there appears another term which is a remnant of a non-Abelian geometric or Berry phase. This correction is interpreted in terms of a rotation angle for a classical spin vector.     

Canonical transformations for relativistic particles

A class of relatively simple canonical transformations of the Dirac equation, which contains as a particular case the Foldy-Wouthuysen transformation, is determined. An exact form for the hamiltonian of a Dirac-Pauli electron is obtained.     

Geometric model for fundamental particles

An attempt is made to show that fundamental particles are manifestations of the geometry of space-time. This is done by demonstrating the existence of a purely geometrical model, which we have calledspherical rotation, that satisfies Dirac's equation. The model is developed and illustrated both mathematically and mechanically. It indicates that the mass of a particle is entirely due to the spinning of the space-time continuum. Using the model, we can show the distinction between spin-up and spin-down states and also between particle and antiparticle states. It satisfies Einstein's criteria for a model that has both wave and particle properties, and it does so without introducing a singularity into the continuum     

Cooper's evidence for faster-than-light particles

Cooper has claimed to have found evidence for faster-than-light particles by reanalyzing the data of Chamberlain et al. in their paper reporting the discovery of the antiproton. A careful reanalysis of this same data gives no evidence to support Cooper's claim.     

Signatures for new colored particles

The contributions of new light colored particles to total hadronic decay widths of heavy quarkonia are studied with the purpose of delineating the possibilities for their experimental detection. It is shown that in spite of their large contributions to individual processes the experimental accuracies needed for their unambiguous observation are on the 10% level.     

Memory function for dressed particles

This paper is concerned with the calculation of the memory function and derivation of a kinetic equation for one-body phase space correlation functions. The theory uses a one-body additive projection operator and a division of the Liouville operator with an unperturbed part that describes dressed particles. Binary collisions are neglected, for the theory aims at describing the screening and backflow effects of a type contained in the plasma kinetic theory of Balescu and Lenard. We obtain an explicit kinetic equation which is an improvement of these theories for the plasma case, and involves the exact equilibrium pair and triplet distributions. The equation also describes systems with strong short-range forces and shows how the screening effects occur in this case as well. The unifying function is the direct correlation function. The theory is meant to provide understanding for a more complete theory of fluids where a proper account is given of close collisions.Work supported by National Science Foundation, Grant No. GH 35691.     

Local supersymmetry for spinning particles

First and second order forms of the covariant action for a spinning particle are exhibited. The action consistently incorporates the necessary constraints and is invariant under both local supersymmetry and general time parameter transformations, and provides a simple one-dimensional model for the interaction between matter and supergravity. A formulation invariant under general co-ordinate transformations in superspace is also given and shown to be equivalent to the locally supersymmetric one.     

Improved S-approximation for dielectric particles

The range of the applicability of the soft particles approximation (S-approximation) has been extended by means of the procedure which may be considered as a specific form of the analytic continuation. The initial element is represented by the standard version of the approximation while the branch of the continuation should be chosen in correspondence with the short wavelength asymptotic of the optical characteristic under consideration. As for the extinction efficiency of dielectric spherical particles, the improved version of the S-approximation fairly well describes the behaviour of Mie curves for particles with the refractive indices up to 2.0 or more and may be useful in order to get in the analytical form the “smoothed” Mie curves when the ripple-type fluctuations were averaged. The leading role of the van de Hulst approximation both for the electric and magnetic components of the extinction efficiency has been shown.     

Time reversal for unstable particles

The time reversal operator (T) for unstable particles is defined such that the fact of decay of the particle is not mistaken for a dynamical violation of T in the decay. This definition is not valid where the medium in which the decay takes place may have its own intrinsic T violation. Based on this limitation, some effort is made to restrict the conclusions drawn from apparent T violation in K meson decay.     

Direct search for relic particles

One of the most important issues in fundamental physics is identifying the major component of the dark matter of the universe. Thus there has been a rapid expansion in techniques to pursue this goal, with about 27 experiments in various stages to look for dark matter particles by detecting the cold dark matter particle directly. While axion experiments, now producing useful limits, seek a unique signature, experiments to find WIMPs seek nuclear recoils via semiconductors, scintillators, a variety of cryogenic techniques, superheated droplets, and some visual means. Some of these experiments will be utilized here to illustrate features relevant to the search and give some idea of the progress and prospects of this vital task.