Synthesis and structures of niobium(V) complexes stabilized by linear-linked aryloxide trimers

The preparation and characterization of a series of niobium(V) complexes that incorporate the linear-linked aryloxide trimers 2,6-bis(4,6-dimethylsalicyl)-4-tert-butylphenol [H3(Me-L)] and 2,6-bis(4-methyl-6-tert-butylsalicyl)-4-tert-butylphenol [H3(tBu-L)] are described. The chloride complex [Nb(Me-L)Cl2]2 (1) was prepared in high yield by reaction of NbCl5 with H3(Me-L) in toluene. In contrast, the analogous reaction with H3(tBu-L) gave a mixture of [Nb(tBu-L)Cl2]2 (2) and [Nb(de-tBu-L)Cl2]2 (3a). During the formation of 3a, one of tert-butyl groups at the ortho position in the tBu-L ligand was lost. When the NbCl5/H3(tBu-L) reaction was carried out in acetonitrile, Nb[H(tBu-L)]Cl3(NCMe) (4) was obtained. Heating a solution of 4 in toluene generated 2 and 3a. The isolated complex 4 underwent ligand redistribution in acetonitrile to produce Nb[H(tBu-L)]2Cl(NCMe) (5). Treatment of NbCl5 with Li3(tBu-L) in toluene afforded 2. The chloride ligands in 1 and 2 smoothly reacted with 4 equiv of MeMgI and LiStBu, resulting in [Nb(R-L)Me2]2 [R = Me (6), tBu (7)] and Nb(Me-L)(StBu)2 (8), respectively. A number of the above complexes have been characterized by X-ray crystallography. In the structures of 1, 2, and 6, the R-L ligand is bound to the metal center with a U-coordination mode, while an alternative S-conformation is adopted for 3a and 8. Complexes 4 and 5 contain a bidentate H(tBu-L) diphenoxide-monophenol ligand.     

Mössbauer Spectroscopic Study on Vertical Distribution of Iron Species in Sediments from Qinghai Lake,China

In this study, ⁵⁷Fe Mössbauer spectroscopy has been applied to sediments collected from Qinghai Lake in Qinghai Province, China, to investigate the vertical distribution of iron species. Their Mössbauer spectra consisted of four doublets ascribable to one paramagnetic high-spin Fe³⁺, two paramagnetic high-spin Fe²⁺ with different quadrupole splittings, and one diamagnetic low-spin Fe²⁺ that corresponds to pyrite (FeS₂). The distribution of pyrite suggested climatic changes during the past nine thousand years. It was demonstrated that the iron speciation in the salt lake sediments by Mössbauer spectroscopy can be used to reconstruct the past environment.

     

Brownian motion of nonlinear oscillators: The projection operator method and its application to a double-well-potential oscillator

A projection operator method is presented, which provides the most efficient way for calculating the stationary behavior of nonlinear Brownian motion. A continued-fraction expansion of the Fourier-Laplace transform of the displacement correlation function or the spectral density is used. This method utilizes a successive optimization procedure on the nonlinear terms and includes the method of statistical linearization as the lowest order approximation. A systematic way to calculate the continued fraction numerically up to sufficient order for convergence is developed, which enables us to obtain the spectral density of a system previously uncomputable.Numerical computations of the spectral density of a nonlinear oscillator with a double-well potential are presented and compared with the results obtained by statistical linearization.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

Heat capacities of copper(II) formate tetrahydrate and tetradeuterate: A comparative study of phase transitions in layer hydrate crystals

The heat capacities of copper(II) formate tetrahydrate and tetradeuterate have been measured from 12 to 300 K with an adiabatic calorimeter. They have sigmoidal temperature dependence except near the antiferroelectric-paraelectric transition temperatures, 235.78 ± 0.05 K and 245.64 ± 0.05 K, respectively. The corresponding enthalpy changes are 836.0 ± 1.0 J mol^?1 and 936.9 ± 0.5 J mor^?1. The entropy changes are 3.546 ± 0.005 JK^?1mol^?1 and 3.814 ± 0.002 JK^?1 mol^?1. The heat capacities are larger in the high temperature phase than in the low temperature phase, the difference amounting to 5.74 JK^?1 mol^?1 and 7.15 JK^?1 mol^?1 for the hydrate and the deuterate, respectively. The heat capacity anomaly is compared with those in tin(II) chloride dihydrate and potassium hexacyanoferrate trihydrate and discussed in relation to the structure of the hydrogen bond networks in these substances. The discussion is extended to include possible properties of the hydrogen bond frameworks in ices I_h and II.     

Superstring thermodynamics and its application to cosmology

The thermodynamics of superstring theories (SST-I, SST-II and heterotic string theory) and its application to the cosmology are studied. The free energy of superstring gas is calculated in the one-loop approximation and the stability of the extra torus dimensions is discussed. Assuming that the Einstein equation dictates the evolution of the universe, we show that matter dominated universe filled with massive particles would never be realized at the beginning of the universe, contrary to the naive expectation in the superstring cosmology.     

Phase transition in ammonium hexafluorovanadate (III)

Heat capacity of ammonium hexafluorovanadate (NH₄)₃ [VF₆] has been measured with a miniaturized adiabatic calorimeter from 20 to 300 K. A phase transition was found at 280.44 ± 0.05 K with the associated entropy change Δ_trs S = 24.9 ± 0.5 JK^?1 mol^?1. The entropy transition is accounted for by the orientational order-disorder changes of hexafluorovanadate ion and ammonium ion occupying respective octahedral sites, as in the cases of (NH₄)₃AlF₆ and (NH₄)₃FeF₆ crystals. Changes in infrared spectra relative to v₃ vibrational mode of [VF₆]^3? ion can be explained by an orientational disorder of the anions in the high-temperature phase (HTP). The dependence of cubic root of the unit-cell volume of a family of ammonium cryolites on their transition temperatures is discussed in relation to the nature of interactions which induce the phase transition.     

Development of a “Built-in” Scanning Near Field Microscope Head for an Atomic Force Microscope System and Stress Mapping of an Al2O3/ZrO2 Eutectic Composite

We constructed a scanning near-field optical microscope (SNOM) on a commercially available atomic force microscopy (AFM) apparatus (SPM-9500J2; Shimadzu Corp.) to measure the stress distribution in ceramic composite materials. Features of our SNOM system are: (1) a compact SNOM head substituted for the original AFM head; (2) a wide scanning range (125 × 125 μm²) inherited from the original scanner; (3) use of conventional shear-force regulation; (4) an optical system for the illumination-collection (I-C) mode; (5) excitation by a 488 nm line of an Ar-ion laser, and (6) light detection by photon counting or a polychromator equipped with an electronically cooled charge coupled device (CCD). This SNOM system was used to measure the surface structure and stress distribution of an Al₂O₃/ZrO₂ eutectic composite. We simultaneously measured topographic images and fluorescence spectra of an Al₂O₃/ZrO₂ eutectic composite. We estimated its peak intensity, peak position, and peak width from the fluorescence spectrum during scanning, which respectively correspond to the abundance of Al₂O₃, stress in the grain, and the anisotropy of that stress. Mapping images showed that the stress and its anisotropy were weaker in the center of the Al₂O₃ grain than its boundary between Al₂O₃ and ZrO₂. That observation suggests that Al₂O₃ underwent intense anisotropic stress induced by volume expansion in the phase transition of ZrO₂ from the cubic phase to the monoclinic phase during preparation.     

Design of a widely tunable laser with a chirped ladder filter

We theoretically investigated a digitally tunable laser with a chirped ladder filter and a ring resonator to obtain a wide wavelength tuning range covering the whole C- or L- band. The clear relation between the tuning range and laser structure, especially the ladder filter, is described analytically. The introduction of a chirped structure into a ladder filter is effective in achieving both wide tunability and a stable lasing mode. A numerical simulation based on multimode rate equations shows that a tuning range of over 40 nm and a mode suppression ratio over 40 dB can be achieved by introducing a chirped ladder filter.     

Mode-mode coupling theory of itinerant electron antiferromagnetism in superconducting state

It has been considered since the first discovery of a high-T(c) cuprate that an antiferromagnetic (AF) state and a superconducting (SC) state are separated in it. However, it is very intriguing that the coexistence of the AF and SC states has recently been observed in HgBa(2)Ca(4)Cu(5)O(12+) (Hg-1245). Moreover, it is very novel that this coexistence of these two states appears if the SC-transition temperature T(c) is higher than the AF-transition temperature T(N). The mode-mode coupling theory can provide a clear elucidation of this novel phenomenon. A key point of this theory is that the AF susceptibility consists of the random-phase-approximation (RPA) term and the mode-mode coupling one. The RPA term works to make a positive contribution to the emergence of the antiferromagnetic critical point (AF-CP). In contrast, the mode-mode coupling term works to make a negative contribution to the emergence of the AF-CP. However, the growth of the SC-gap function in the d(x(2)-y(2))-wave SC state works to suppress the negative contribution of the mode-mode coupling term to the emergence of the AF-CP. Moreover, the effect of SC fluctuations near the SC-transition temperature T(c) suppresses the mode-mode coupling term of the AF susceptibility that works to hinder the AF ordering. For these two reasons, there is a possibility that the d(x(2)-y(2))-wave SC state is likely to promote the emergence of the AF-CP. Namely, the appearance of the above-mentioned novel coexistence of the AF and SC states observed in Hg-1245 can be explained qualitatively on the basis of this idea.     

An energy-conserving Galerkin scheme for a class of nonlinear dispersive equations

A Galerkin scheme is presented for a class of conservative nonlinear dispersive equations, such as the Camassa–Holm equation and the regularized long wave equation. The scheme has two advantageous features: first, it is conservative in that it keeps the discrete analogue of the continuous energy conservation property in the original equations; second, it can be formulated only with cheap H¹$H^1$-elements even if the original equations include third derivative u_xxx$u_{\mathit{xxx}}$. Numerical experiments confirm the stability and effectiveness of the proposed scheme.