Crystalline A-DNA: The X-Ray Analysis of the Fragment d(G-G-T-A-T-A-C-C)

An A-DNA type double helical conformation was observed in the single crystal X-ray structure of the octamer d(G-G-T-A-T-A-C-C), 1, and its 5-bromouracil-containing analogue, 2. The structure of the isomorphous crystals (space group P61) was solved by a search technique based on packing criteria and R-factor calculations, with use of only low order data. At the present stage of refinement the R factors are 31 % for 1 and 28 % for 2 at a resolution of 2.25 A (0.225 nm). The molecules interact through their minor grooves by hydrogen bonding and base to sugar van der Waals contacts. The stable A conformation observed in the crystal may have some structural relevance to promoter regions where the T-A-T-A sequence is frequently found.

Bismuth tungsten-oxide bronzes - a study of intergrowth phases and related aspects

Reaction of bismuth metal with WO$_3$ in the absence of oxygen yields interesting bronze-like phases. From analytical electron microscopy and X-ray photoelectron spectroscopy, the product phases are found to have the general composition Bi$_x$ WO$_3$ with bismuth in the 3+ state. Structural investigations made with high resolution electron micrscopy and cognate techniques reveal that when x < 0.02, a perovskite bronze is formed. When x $\geqslant$ 0.02, however, intergrowth tungsten bronzes (i.t.b.) containing varying widths of the WO$_3$ slab are formed, the lattice periodicity being in the range 2.3-5.1 nm in a direction perpendicular to the WO$_3$ slabs. Image-matching studies indicate that the bismuth atoms are in the tunnels of the hexagonal tungsten bronze (h.t.b.) strips and the h.t.b. strips always remain one-tunnel wide. Annealed samples show a satellite structure around the superlattice spots in the electron diffraction patterns, possibly owing to ordering of the bismuth atoms in the tunnels. The i.t.b. phases show recurrent intergrowths extending up to 100 nm in several crystals. The periodicity varies considerably within the same crystal wherever there is disordered intergrowth, but unit cell dimensions can be assigned from X-ray and electron diffraction patterns. The maximum value of x in the i.t.b. phases is ca. 0.07 and there is no evidence for the i.t.b. phase progressively giving way to the h.t.b. phase with increase in x. Hexagonal tungsten bronzes that contain bismuth with x up to 0.02 can be formed by starting from hexagonal WO$_3$, but the h.t.b. phase seems to be metastable. Optical, magnetic and electron transport properties of the i.t.b. phases have been measured and it appears that the electrons become itinerant when x > 0.05.

Studies of Solids and Surfaces by Auger Electron Spectroscopy

Although the applications of Auger electron spectroscopy in surface analysis have by far outweighed its use as a tool to investigate electron states of solids and surfaces, there are a variety of situations where Auger spectroscopy provides unique information. Apart from the chemical shifts, Auger intensities are useful in determining the number of d-electron states in transition metal systems. Auger spectroscopy is a good probe to investigate the surface oxidation of metals. In addition to the intra-atomic Auger transitions, inter-atomic transitions observed in oxides and other systems reveal the nature of electron states of surfaces. Charge-transfer and hybridization effects in alloys are also usefully studied by Auger spectroscopy. Auger electron spectroscopy has not been a popular technique to investigate adsorption of molecules on surfaces, but the technique is useful to obtain fingerprints of surface species.

Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

Structure and Bonding in N-Methylacetamide Complexes of Alkali and Alkaline Earth Metals

A detailed crystallographic investigation of N-methylacetamide complexes of Li, Na, K, Mg and Ca has been made in view of its importance in the coordination chemistry and biochemistry of alkali and alkaline earth metals. The metal ions bind to the amide oxygen causing an increase in the carbonyl distance and a proportionate decrease in the central C-N bond distance. The decrease in the central C-N distance is accompanied by an increase in the distance of the adjacent C-C bond and a decrease in the adjacent C-N bond distance. The metal ion generally deviates from the direction of the lone pair of the carbonyl oxygen and also from the plane of the peptide, the out-of-plane deviation varying with the ionic potential of the cation. The metal-oxygen distance in alkali and alkaline earth metal complexes of a given coordination number also varies with the ionic potential of the cation, as does the strength of binding of the cations to the amide. The amide molecules are essentially planar in these complexes, as expected from the increased bond order of the central C-N bond. The NH bonds of the amide are generally hydrogen bonded to anions. The structures of the amide complexes are compared with those of other oxygen donor complexes of alkali and alkaline earth metals. The structural study described here also provides a basis for the interpretation of results from spectroscopic and theoretical investigations of the interaction of alkali and alkaline earth metal cations with amides.

The Electronic Structure of Graphite from Compton Profile Measurements

Compton profile data are used to investigate the ground state wavefunction of graphite. The results of two new $\gamma$-ray measurements are reported and compared with the results of earlier $\gamma$-ray and electron scattering measurements. A tight-binding calculation has been carried out and the results of earlier calculations based on a molecular model and a pseudo-potential wavefunction are considered. The analysis, in terms of the reciprocal form factor, shows that none of the calculations gives an adequate description of the data in the basal plane although the pseudo-potential calculation describes the anisotropy in the plane reasonably well. In the basal plane the zero-crossing theorem appears to be violated and this problem must be resolved before more accurate models can be derived. In the c-axis direction the molecular model and the tight binding calculation give better agreement with the experimental data than does the pseudopotential calculation.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

General classical theory of spinning particles in a meson field

An exact classical theory of the motion of a point dipole in a meson field is given which takes into account the effects of the reaction of the emitted meson field. The meson field is characterized by a constant $\chi =\mu /\hslash $ of the dimensions of a reciprocal length, $\mu $ being the meson mass, and as $\chi \rightarrow $ 0 the theory of this paper goes over continuously into the theory of the preceding paper for the motion of a spinning particle in a Maxwell field. The mass of the particle and the spin angular momentum are arbitrary mechanical constants. The field contributes a small finite addition to the mass, and a negative moment of inertia about an axis perpendicular to the spin axis. A cross-section (formula (88 a)) is given for the scattering of transversely polarized neutral mesons by the rotation of the spin of the neutron or proton which should be valid up to energies of 10$^{9}$ eV. For low energies E it agrees completely with the old quantum cross-section, having a dependence on energy proportional to p$^{4}$/E$^{2}$ (p being the meson momentum). At higher energies it deviates completely from the quantum cross-section, which it supersedes by taking into account the effects of radiation reaction on the rotation of the spin. The cross-section is a maximum at E $\sim $ 3$\cdot $5$\mu $, its value at this point being 3 $\times $ 10$^{-26}$ cm.$^{2}$, after which it decreases rapidly, becoming proportional to E$^{-2}$ at high energies. Thus the quantum theory of the interaction of neutrons with mesons goes wrong for E $\gtrsim $ 3$\mu $. The scattering of longitudinally polarized mesons is due to the translational but not the rotational motion of the dipole and is at least twenty thousand times smaller. With the assumption previously made by the present author that the heavy partilesc may exist in states of any integral charge, and in particular that protons of charge 2e and - e may occur in nature, the above results can be applied to charged mesons. Thus transversely polarised mesons should undergo a very big scattering and consequent absorption at energies near 3$\cdot $5$\mu $. Hence the energy spectrum of transversely polarized mesons should fall off rapidly for energies below about 3$\mu $. Scattering plays a relatively unimportant part in the absorption of longitudinally polarized mesons, and they are therefore much more penetrating. The theory does not lead to Heisenberg explosions and multiple processes.