Magnetic order in RCr\mathsf{_{2}}Si\mathsf{_{2}} intermetallics

The magnetic structure and ordering temperatures of three intermetallic compounds which crystallize in the tetragonal ThCr₂Si₂ structure, TbCr₂Si₂, HoCr₂Si₂ and ErCr₂Si₂, have been determined by neutron diffraction, differential scanning calorimetry and magnetization measurements. The Cr-sublattice orders anti-ferromagnetically with Néel temperatures of 758 K for TbCr₂Si₂, 718 K for HoCr₂Si₂ and 692 K for ErCr₂Si₂. Chromium atoms located at 4d crystallographic sites are aligned anti-parallel along the c-axis, with G_ZCr magnetic modes. In contrast with metallic bcc Cr, the refined room temperature value of the ordered Cr moment is anomalously large for all three compounds. No long range magnetic order of the R sublattice in TbCr₂Si₂ and HoCr₂Si₂ is observed, whilst the Er sublattice in ErCr₂Si₂ orders independently of the Cr sublattice below 2.4 K with moments ferromagnetically aligned in the basal plane.Received: 4 November 2003, Published online: 30 January 2004PACS: 75.25. + z Spin arrangements in magnetically ordered materials (including neutron and spin-polarized electron studies, synchrotron-source X-ray scattering, etc.) - 75.30.Cr Saturation moments and magnetic susceptibilities - 75.50.Ee Antiferromagnetics     

3,4‐[2,2‐Bis(methoxyethoxymethoxymethyl)propylenedithio]‐3′,4′‐(ethylenedithio)tetrathiafulvalene: a spiro‐substituted BEDT–TTF analogue

The crystal structure of the title compound [systematic name: 2‐(1,3‐dithiolo[4,5‐b][1,4]dithiin‐2‐ylidene)‐6,6‐bis(methoxyethoxymethoxymethyl)‐1,3‐dithiolo[4,5‐b][1,4]dithiepine], C₂₁H₃₀O₆S₈, a spiro‐substituted BEDT–TTF analogue [BEDT–TTF is bis(ethylenedithio)tetrathiafulvalene], has a strongly bent heterocyclic framework. The seven‐membered ring adopts a pseudo‐chair conformation with notably widened ring bond angles, especially at the methylene C atoms [119.49 (11) and 117.60 (11)°]. The axial side chain adopts an extended conformation, but the equatorial side chain curls back on itself and the O atom nearest the ring system is involved in three short contacts to H atoms (2.45–2.53 Å). The molecules pack in centrosymmetrically related pairs, which are isolated from each other by columns of the polyether side chains. This study emphasizes the ease of distortion of the neutral bis(propylenedithio)tetrathiafulvalene ring structure, and how the need to accommodate side chains can easily override the tendency of these donor systems to form stacks in the crystalline state.     

Monofunctionalised resorcinarenes

A convenient methodology for introducing single functional groups to the lower rim of resorcinarenes is described. The methodology allows for very convenient differential protection or derivatisation of the upper and lower rims, and a wide range of functional groups (alcohol, carboxylic acid, thiol, amine, carbamate, alkyl halide) can be incorporated as a single unit at the lower rim, opening up the way to further modification at this point and generally widening the scope for further utilising resorcinarenes. Furthermore, our approach has enabled us to link two resorcinarenes together to form novel resorcinarene dimers.     

A Law of Large Numbers for the Zeroes of Heine–Stieltjes Polynomials

We determine the limiting density of the zeroes of Heine–Stieltjes polynomials (or of any set of points satisfying the conclusion of Heine–Stieltjes Theorem) in the thermodynamic limit and use this to prove a strong law of large numbers for the zeroes.     

The comparison of detailed chemical kinetic mechanisms: Application to the combustion of methane

Detailed chemical kinetic mechanisms of complex chemical phenomena may be composed of hundreds of species and thousands of individual elementary reactions. It can be an extremely laborious and error‐prone procedure to compare two of these mechanisms, particularly if they come from different sources. We have created software tools which help to highlight the differences between mechanisms written in a Chemkin format and demonstrate their applicability to five literature mechanisms describing the high temperature oxidation of methane. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36:467–471, 2004     

Asymptotic Regimes of Magnetic Bianchi Cosmologies

We consider the asymptotic dynamics of the Einstein-Maxwell field equations for the class of non-tilted Bianchi cosmologies with a barotropic perfect fluid and a pure homogeneous source-free magnetic field, with emphasis on models of Bianchi type VII₀, which have not been previously studied. Using the orthonormal frame formalism and Hubble-normalized variables, we show that, as is the case for the previously studied class A magnetic Bianchi models, the magnetic Bianchi VII₀ cosmologies also exhibit an oscillatory approach to the initial singularity. However, in contrast to the other magnetic Bianchi models, we rigorously establish that typical magnetic Bianchi VII₀ cosmologies exhibit the phenomena of asymptotic self-similarity breaking and Weyl curvature dominance in the late-time regime.     

Multiplicity distributions inb →s gluon decays

The final states for the processb→sy have been extensively discussed in the literature. Similarly-detailed analyses for the caseb→s gluon have not been performed. Generally this process is searched for in 2-body decays such as B⁰→K⁺ π ^?. We present simple arguments to suggest that most of the time the quark-level process will give rise to final states with rather high multiplicities. Comments are made about the applicability of these results tob→d gluon and hadronicb→u decays.     

Surface tension and density measurements for indium and uranium using a sessile-drop apparatus with glow discharge cleaning

The sessile-drop method is used to measure the surface tension and density of liquid indium and uranium under high vacuum. Measurements are made over the temperature range 156–500°C for In and at the melting point for U. Surface oxides are efficiently removed with a glow discharge system. Drop profiles are captured by photograph and processed using nonlinear regression to yield the surface tension and density. In this regression procedure, normal distances from calculated profiles to data points are minimized. For indium, the density and surface tension measurements yield _mp = 7.05 × 10³kg/m³, d/dT = −0.776 kg/m³·°C, and γ_mp = 0.568 N/m, dγ/dT = −9.45 × 10⁻⁵ N/m·°C. The results for uranium at the melting point are _mp = 17.47 × 10³ kg/m³ and γ_mp = 1.653 N/m.     

Chaotic resonance: A simulation

Stochastic resonance is a statistical phenomenon that has been observed in periodically modulated, noise-driven, bistable systems. The characteristic signatures of the effect include an increase in the signal-to-noise of the output as noise is added to the system, and exponentially decreasing peaks in the probability density as a function of residence times in one state. Presented are the results of a numerical simulation where these same signatures were observed by adding achaotic driving term instead of a white noise term. Although the probability distributions of the noise and chaos inputs were significantly different, the stochastic and chaotic resonances were equal within the experimental error.     

Degenerate Solutions of General Relativity from Topological Field Theory

Working in the Palatini formalism, we describe a procedure for constructing degenerate solutions of general relativity on 4-manifold M from certain solutions of 2-dimensional $BF$ theory on any framed surface Σ embedded in M. In these solutions the cotetrad field e (and thus the metric) vanishes outside a neighborhood of Σ, while inside this neighborhood the connection A and the field satisfy the equations of 4-dimensional BF theory. Our construction works in any signature and with any value of the cosmological constant. If for some 3-manifold S, at fixed time our solutions typically describe “flux tubes of area”: the 3-metric vanishes outside a collection of thickened links embedded in S, while inside these thickened links it is nondegenerate only in the two transverse directions. We comment on the quantization of the theory of solutions of this form and its relation to the loop representation of quantum gravity. Received: 21 April 1997 / Accepted: 22 August 1997