Singularity-free cosmology: A simple model

The nonminimal coupling of a self-interacting complex scalar field with gravity is studied. For a Robertson-Walker open universe the stable solutions of the scalar-field equations are time dependent. As a result of this, a novel spontaneous symmetry breaking occurs which leads to a varying effective gravitational coupling coefficient. It is found that the coupling coefficient changes sign below a critical ‘‘radius’’ of the Universe implying the appearance of repulsive gravity. The occurrence of the repulsive interaction at an early epoch facilitates singularity avoidance. The model also provides a solution to the horizon problem.

An electron microscopic study of quasicrystals in a quaternary alloy : Mg32(Al, Zn, Cu)49

The discovery of a solid exhibiting m 3 5 point group symmetry by Shechtman et. al. (l) in a rapidly solidified Al-14at%Mn alloy has activated intensive studies of a new class of solids, termed as quasicrystals (2). While the original discovery reported the existence of quasicrystals in AI-Mn. AI-Fe and AI-Cr alloys, subsequent work has revealed their existence in Mg-Zn-Al(3,4), Mg-A]-Cu(5), AI-Mn-Si(6) and Ti-Ni-V(7) alloys (Table l).

Strategies for collecting screen-less oscillation data

Screen-less oscillation photography is the method of choice for recording three-dimensional X-ray diffraction data for crystals of biological macromolecules. The geometry of an oscillation camera is extremely simple. However, the manner in which the reciprocal lattice is recorded in any experiment is fairly complex. This depends on the Laue symmetry of the reciprocal lattice, the lattice type, the orientation of the crystal on the camera and to a lesser extent on the unit-cell dimensions. Exploring the relative efficiency of collecting X-ray diffraction data for different crystal orientations prior to data collection might reduce the number of films required to record most of the unique data and the consequent amount of time required for processing these films. Here algorithms are presented suitable for this purpose and results are reported for the 11 Laue groups, different lattice types and crystal orientations often employed in data collection.

A new method for generation of quasi-periodic structures withn fold axes: Application to five and seven folds

A new geometrical method for generating aperiodic lattices forn-fold non-crystallographic axes is described. The method is based on the self-similarity principle. It makes use of the principles of gnomons to divide the basic triangle of a regular polygon of 2n sides to appropriate isosceles triangles and to generate a minimum set of rhombi required to fill that polygon. The method is applicable to anyn-fold noncrystallographic axis. It is first shown how these regular polygons can be obtained and how these can be used to generate aperiodic structures. In particular, the application of this method to the cases of five-fold and seven-fold axes is discussed. The present method indicates that the recursion rule used by others earlier is a restricted one and that several aperiodic lattices with five fold symmetry could be generated. It is also shown how a limited array of approximately square cells with large dimensions could be detected in a quasi lattice and these are compared with the unit cell dimensions of MnAl6 suggested by Pauling. In addition, the recursion rule for sub-dividing the three basic rhombi of seven-fold structure was obtained and the aperiodic lattice thus generated is also shown.

Electron spin resonance studies of d5 ions (Fe3+ and Mn2+) in lead oxide-lead halide glasses

Electron spin resonance (ESR) of d5 ions (Fe3+ and Mn2+) has been investigated in PbO---PbF2 and PbO---PbCl2 glasses in wide ranges of composition. ESR spectra of d5 ions in these glasses exhibit significant differences which we have attributed to at least three important causes: (i) The ionic potentials of Fe3+ and Mn2+ are different. Hence Fe3+ ions tend to acquire their own environment while Mn2+ ions take up substitutional (Pb2+ ion) positions. (ii) The sizes and nephelauxetic behaviours of O2- and F- ions are similar. Thus even when there is a mixed anionic coordination, the environment of Mn2+ ions is highly symmetrical in oxyfluoride glasses. The Mn2+ spectra in oxychloride glasses are considerably different. (iii) Increase in halide ion concentration increases the ionicity of lead-ligand bonding and favours a more symmetrical environment around dopant ions in halide-rich glasses. The features in ESR spectra have been interpreted in the light of known behaviour of d5 ions in glasses and also in the context of known structural features of PbO---PbX2 glasses. Dopant ions appear to cluster at high concentrations although isolated low-symmetry sites are still observed. Effects of crystallization and annealing upon ESR spectra have also been investigated.

High Resoulution Electron Microscopy of Chloritoid Minerals From Different Geological Melieu

Structural defects of three chloritoid minerals from distinet geologic melieu have been investigated by high resolution electron microscopy. X-ray powder and electron diffraction patterns indicate that the chloritoid from one geological source (A) is2M 1+2M2 monoclinic variant while those from another geological source (B) are 2M 2 monoclinic variants. In a typical one-dimensional lattice image of a crystal from sourceA, the 2M 2 matrix is broken by insertion of triclinic inter-growths. Another crystal with the 2M 2 matrix showed single, triple, quadruple and quintuple layers displaying an unusually high degree of disorder. Lattice images of 2M 2 monoclinic variants from sourceB yielded more homogeneous micrographs. The important finding from the present studies is that the chloritoid from sourceA is a severely disordered low-temperature intermediate phase in the conversion of the triclinic chloritoid to the high-temperature ordered monoclinic variants of sourceB. Severely disordered chloritoids, marking the beginning of low grade metamorphism, are generated as intermediates between the state of complete disordered arrangement towards the end of low grade metamorphism within the narrow stability range of 400°–500°C.

Non-Abelian monopoles break color. I. Classical mechanics

Monopoles which are sources of non-Abelian magnetic flux are predicted by many models of grand unification. It has been argued elsewhere that a generic transformation of the "unbroken" symmetry group H cannot be globally implemented on such monopoles for reasons of topology. In this paper, we show that similar topological obstructions are encountered in the mechanics of a test particle in the field of these monopoles and that the transformations of H cannot all be globally implemented as canonical transformations. For the SU(5) model, if H is SU(3)C×U(1)em, a consequence is that color multiplets are not globally defined, while if H is SU(3)C×SU(2)WS×U(1)Y, the same is the case for both color and electroweak multiplets. There are, however, several subgroups KT, KT′,… of H which can be globally implemented, with the transformation laws of the observables differing from group to group in a novel way. For H=SU(3)C×U(1)em, a choice for KT is SU(2)C×U(1)em, while for H=SU(3)C×SU(2)WS×U(1)Y, a choice is SU(2)C×U(1)×U(1)×U(1). The paper also develops the differential geometry of monopoles in a form convenient for computations.

Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.

Porphyrins with multiple crown ether voids: novel systems for cation complexation studies

Porphyrins appended with crown ether, benzo-15-crown-5, at the methine positions have been synthesized and characterized. The fully and partially substituted porphyrins and their metallo (Co, Cu, and Zn) derivatives describe one or more ether cavities in the periphery that are capable of recognizing spherical cations. The ability of these macrocycles to complex cations (Na+, K+, Mg2+, Ca2+, Ba2', and NH4+) is investigated by use of visible, 'H NMR, ESR, and emission spectral studies. The tetrasubstituted crown porphyrin (TCP) exhibits very high selectivity for K+. The cations (K', Ba2+, and NH4+) that require two crown ether cavities for complexation promote dimerization of the porphyrins. The ESR study of the cation-induced porphyrin dimers reveals axial symmetry with the porphyrin planes separated by -4.2 A. This distance increases from the fully substituted to partially substituted porphyrins. The cations (K', Ba2+, and NH4') quench efficiently the fluorescence of the free base porphyrins and their metallo derivatives. The quenching process is attributed to the steric geometry of the dimers.

Laser Raman spectroscopic study of ferroelastic LiCsSO4

Lithium caesium sulphate has been reported to undergo a phase transition from the room temperature orthorhombic phase with space groupP cmn to a final phase with space groupP 22/n. Though a sharp anomaly in its physical properties has been found at 202.0;K, it was found that there was a need for careful investigations in the vicinity of 240 and 210.0;K. Since the changes in the crystal structure involve primarily a rotation of the SO4 tetrahedron about thec-axis and as this may be reflected both in the intensity and polarisation of the internal as well as external phonon modes, the laser Raman spectra of oriented single crystals of LiCsSO4 at different temperatures were investigated. For correlation and definite identification of the spectral features, its infrared absorption spectrum was also studied. An analysis of the intensities and polarizations of the internal modes of the sulphate ions reveals the change in symmetry of the crystal. The integrated intensity and peak height of thev 1 line, plotted against temperature show anomalous peaks in the region of the phase transition. Differential scanning calorimetric study gives the enthalpy change ΔH across the phase transition to be 0.213 kJ/mol.

Zeeman effect of nuclear quadrupole resonance in 1-chloro-2,4-dinitrobenzene

The Zeeman effect of NQR was studied in 1-chloro-2,4-dinitrobenzene. A low value of the asymmetry parameter (0.10) was obtained. Four physically inequivalent field gradients were located and their orientations in the crystallographic abc system were determined using symmetry considerations. From these data the orientations of the molecules in the unit cell were determined. The results agree well with the two-dimensional x-ray structural data. The bond characters of the C[Single Bond]Cl bond were calculated, and the values compare well with those generally obtained for C[Single Bond]Cl bonds in chlorine derivatives of benzene. ©1973 The American Institute of Physics.

Structure of pentacyclo[7.4.2.02,6.06,15.011,14]pentadec-4-ene-7,13-dione, a novel pentacyclic C15 quinane system

C 15H 1602 (a synthetic precursor to dodecahedrane), monoclinic, P21/n, a = 12.171 (5), b = 6.976(5), c = 13.868 (3) A, B = 102.56 (3) ° , Z = 4, D m = 1.30, D c = 1.318 g cm -3, F(000) = 488, g(Mo K¢t) = 0.92 cm- 1. Intensity data were collected on a Nonius CAD-4 diffractometer and the structure was solved by direct methods. Full-matrix least-squares refinement gave R = 0.077 (R w = 0.076) for 1337 observed reflections. All the five-membered rings are cis fused and have envelope (C s symmetry) conformations.

Nonequilibrium charge transport in an interacting open system: Two-particle resonance and current asymmetry

We use the Lippman-Schwinger scattering theory to study nonequilibrium electron transport through an interacting open quantum dot. The two-particle current is evaluated exactly while we use perturbation theory to calculate the current when the leads are Fermi liquids at different chemical potentials. We find an interesting two-particle resonance induced by the interaction and obtain criteria to observe it when a small bias is applied across the dot. Finally, for a system without spatial inversion symmetry, we find that the two-particle current is quite different depending on whether the electrons are incident from the left or the right lead.

Isotope shifts and hyperfine structure in the 555.8-nm S-1(0) -> P-3(1) line of Yb

We apply our technique of using a Rb-stabilized ring-cavity resonator to measure the frequencies of various spectral components in the 555.8-nm 1S0-->3P1 line of Yb. We determine the isotope shifts with 60 kHz precision, which is an order-of-magnitude improvement over the best previous measurement on this line. There are two overlapping transitions, 171Yb(1/2-->3/2) and 173Yb(5/2-->3/2), which we resolve by applying a magnetic field. We thus obtain the hyperfine constants in the 3P1 state of the odd isotopes with a significantly improved precision. Knowledge of isotope shifts and hyperfine structure should prove useful for high-precision calculations in Yb necessary to interpret ongoing experiments testing parity and time-reversal symmetry violation in the laws of physics.

ESR study of copper diethyldithiophosphate

ESR investigations are reported in single crystals of copper diethyldithiophosphate, magnetically diluted with the corresponding diamagnetic nickel complex. The spectrum at normal gain shows hyperfine components from 63Cu, 65Cu, and 31P nuclei. At much higher gain, hyperfine interaction from 33S nuclei in the ligand is detected. The spin Hamiltonian parameters relating to copper show tetragonal symmetry. The measured parameters are g = 2.085, g =2.025, A63Cu = 149.6 × 10−4 cm−1, A65Cu = 160.8 × 10−4 cm−1, BCu = 32.5 × 10−4 cm−1 and QCu 5.5 × 10−4cm−1. The 31P interaction is isotropic with a coupling constant AP = 9.6 × 10−4 cm−1. Angular variation of the 33S lines shows two different hyperfine tensors indicating the presence of two chemically inequivalent Cu S bonds. The experimentally determined hyperfine constants are A =34.9×10−4 cm−1, B =26.1×10−4 cm−1, A =60.4×10−4 cm−1, B =55.5×10−4 cm−1. The hyperfine parameters show that the hybridization of the ligand orbitals is very sensitive to the symmetry around the ligand. The g values and Cu hyperfine parameters are not much affected by the distortions occurring in the ligand. The energies of the d-d transitions are determined by optical absorption measurements on Cu diethyldithiophosphate in solution. Using the spin Hamiltonian parameters together with optical absorption results, the MO parameters for the complex are calculated. It is found that in addition to the bond, the bonds are also strongly covalent. ©1973 The American Institute of Physics