Analysis of the ν1 and ν2 + ν4 bands of 12CH4

Line assignments, positions, strengths, and experimentally determined upper states are reported for the ν₁ and ν₂ + ν₄ infrared bands of ¹²CH₄. The bands have been analyzed using infrared spectra recorded with different optical densities and temperatures at 0.02- and 0.01-cm^?1 resolution using a four-passed grating spectrometer at Florida State University and a Fourier transform spectrometer at Kitt Peak National Observatory. Both ν₁ and ν₂ + ν₄ lines are assigned through J′ = 14. For J′ ≥ 10, the upper state of the vibrationally infrared inactive ν₁ band interacts strongly with ν₂ + ν₄ and is observed in the infrared spectrum with line strengths on the order of 10^?3 cm^?2 atm^?1. The upper-state energies and transition intensities are calculated from the molecular constants and transition moment matrix elements obtained through a simultaneous analysis of ν₁, ν₃, ν₂ + ν₄, 2ν₄, and 2ν₂.     

Magnetic ordering in Fe<Subscript>1.087</Subscript>Te under pressure

The crystal and magnetic structures of Fe_1.087Te have been studied by neutron powder diffraction in the temperature range from 1.7 to 80 K at pressures of  ≈0.4 and ≈1.2 GPa. No symmetry change of the tetragonal paramagnetic ambient pressure phase (space group P4/nmm) was observed for temperatures above 60 K and pressures up to  ≈1.2 GPa. A novel pressure-induced phase of Fe_1.087Te having orthorhombic symmetry (space group Pmmn) and incommensurate antiferromagneticbicollinear order was observed in the temperature range from 50 to 60 K at  ≈1.2 GPa. The known monoclinic ambient pressure phase of Fe_1.087Te (space group P2 ₁/n) with commensurate antiferromagnetic order was found to be stable up to at least  ≈1.2 GPa at low temperature.     

Perturbation of the Laplacian supported by null sets,with applications to polymer measures and quantum fields

We discuss hamiltonians in L²(R^d, dx) of the form H = ?Δ + V, with V a potential supported by a zero measure set C. In particular if C is a path of a brownian motion b such that V(x) = ∫₀¹λ(x, ω)δ(x-b(s, ω)) ds, we show that H exists as a nontrivial, self-adjoint, lower bounded perturbation of ?Δ when d ?5. We must choose λ to be an infinitesimal, negative function for d = 4,5, but for d ? 3 any bounded real-valued function λ will do. The connection with Edward's model of polymers as well as with quantum fields of the ?_d⁴-type is also discussed. The proofs use methods of nonstandard analysis.     

A theoretical model for the interacting upper states of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands in methane

The effective vibration-rotation Hamiltonians complete to fourth order in the Amat-Nielsen scheme for the upper states of the ν₁, ν₃, 2ν₂, ν₂ + ν₄, and 2ν₄ bands in methane are reviewed, and the major vibration-rotation interactions (H₃₀, $\text{H}\text{?}{}_{40}$, $\text{H}\text{?}{}_{21}$, $\text{H}{}_{31}$, $\text{H}\text{?}{}_{22}$) connecting the different vibrational states are discussed. Explicit matrix elements in a basis of harmonic oscillator-symmetric rotor basis functions are given for the purely vibrational terms and for the vibration-rotation interactions. Expressions for spectral intensities of infrared and Raman spectra are presented, and the selection rules and transition moment matrix elements are stated. A computer program is described which, incorporating all these features, can be used for prediction of infrared and Raman spectra and for determination of molecular constants from observed spectra by a least-squares routine. As an example the program is applied to the 2ν₄ isotropic Raman spectrum of ¹²CH₄, leading to a very good agreement between the experimental and calculated spectra.     

The ν2 + ν4 and 2ν2 isotropic Raman bands of 12CH4

The purely isotropic Raman spectrum of the ν₁ band, the ν₂ + ν₄ band (enhanced through interaction with ν₁), and the 2ν₂ band of ¹²CH₄ was obtained with a spectral resolution of 0.30–0.35 cm^?1 from exposures with different orientations of the linearly polarized exciting light. The ν₂ + ν₄ and 2ν₂ bands show partially resolved rotational structure. The spectra are interpreted in terms of a model which takes explicitly into account vibrational and rovibrational interactions with other vibrational states, using molecular constants determined primarily from infrared spectra. The computed contours are in excellent agreement with the experimental ones and the observed and calculated peak wavenumbers agree within one tenth of the spectral resolution limit, except for a small region near the ν₁ band. The good overall agreement represents an independent check on the overall correctness of the previously reported molecular constants. A detailed discussion is given of the contributions to the intensities of individual transitions from the three transition moment matrix elements, which in an isolated-band model are the intensity parameters of the ν₁, 2ν₄, and 2ν₂ isotropic bands, respectively.     

Log-symmetry--a new approach to describing thermochemistry, and other mixing properties, of moderately asymmetric mixtures

A new concept is presented for analysing the excess properties of mixing for asymmetric homogeneous mixtures. In its current form the concept is limited to binary mixtures, but applies to numerous classes of materials, and a wide selection of mixing properties. This paper demonstrates that this Log-symmetry concept is general enough to include (as special cases) several existing mixture models; specifically the Regular Solution Theory, van Laar equation, and the Rogalski-Malanowski expression. The above finding suggests log-symmetry is inherently fundamental, in a way that is (yet) not fully explored. In its most basic implementation (the Mirror Data Method) log-symmetric modelling requires merely one independent parameter. This paper employs high-precision experimental data to validate the concept.     

Some Raman bands of C3O2

The ν₁, ν₅, 2ν₅, and 2ν₆ Raman band accumulations of carbon suboxide, C₃O₂, have been photographed with a resolution of 0.2–0.3 cm^?1. Each band accumulation consists, in addition to the main band, of a large number of “hot” bands due to the extremely low, highly anharmonic ν₇ fundamental vibration. In the 2ν₆ band accumulation a few series of unresolved Q branches have been assigned. In the ν₁ and 2ν₅ band accumulations most Q branches almost coincide, forming a very intense peak, whereas the dominating feature of the ν₅ band accumulation is a minimum, in agreement with the expectation of an extremely weak Q branch for a Π_g fundamental band. Tentative values of ν₁ = 2196.9 ± 0.1 cm^?1 and ν₅ = 580.2 ± 0.5 cm^?1 as well as several energy values in the ν₇ manifold of the 2ν₆⁰ state are obtained. Further, improved exposures of the ν₂ + 2ν₇⁰ band accumulation yield some levels in the ν₇ manifold of the ν₂ state, in addition to those determined previously.