Crystallographic study of the phase transition in (Me4P)2ZnBr4

The compound (Me₄P)₂ZnBr₄, a member of the β-K₂SO₄ structure class, undergoes a phase transition at 84°C from the room temperature space group P12₁/c1 to the parent Pmcn structure. The room temperature structure corresponds to a ferrodistortive transition of B_1g symmetry at the zone center. At room temperature, the compound has lattice constants a=9.501(1), b=16.055(2), c=13.127(2) Å and β=90.43(1)°. For the high temperature phase, the orthorhombic cell has dimensions a=9.466(2), b=16.351(3) and c=13.284(2) Å. The structures consist of two crystallographically independent Me₄P⁺ cations and the ZnBr₄²⁻ anions. In the room temperature phase, all three ionic species show substantial displacement from the mirror plane perpendicular to the a-axis that exists in the high temperature phase, as well as rotations out of that plane. The thermal parameters of the cations are indicative of substantial librational motion. Measurements of lattice parameters have been made at 2-5°C intervals over the temperature range 40-140°C. The changes in the lattice constants appear continuous at T_c (within experimental limits) indicating that the phase transition is likely second-order. The a lattice constant shows an anomalous shortening as T_c is approached. Thermal expansion coefficients are calculated from this data. An application of Landau theory is used to derive the temperature dependencies of spontaneous shear strain and corresponding elastic stiffness constants associated with the primary order parameter.     

The diffraction mechanism of electron-positron pair photoproduction

We examine a mechanism of electron-positron pair photoproduction near a giant resonance. The mechanism is based on the possibility of photons being absorbed by nuclei. Our calculations set the cross section of this process at roughly 10⁻³⁰ cm². We also discuss the feasibility of observing the effect. Zh. éksp. Teor. Fiz. 112, 1959–1965 (December 1997)     

Self-similar potentials and theq-oscillator algebra at roots of unity

Properties of the simplest class of self-similar potentials are analyzed. Wave functions of the corresponding Schrödinger equation provide bases of representations of theq-deformed Heisenberg-Weyl algebra. When the parameterq is a root of unity, the functional form of the potentials can be found explicitly. The generalq ³ = 1 and the particularq ⁴ = 1 potentials are given by the equi-anharmonic and (pseudo) lemniscatic Weierstrass functions, respectively.     

Convergence Properties of a Conditional ε-Subgradient Method Applied to Linear Programs

We propose a new conditional ε-subgradient method intended for solving general convex programs, Convergence properties of the method are investigated. It is proved that for a linear program with a compact set of solutions, the method generates a sequence of feasible approximations whose objective function values converge to the optimal value at a rate that is at least linear.     

Intermediate-spin state of a 3d ion in the octahedral environment and generalization of the Tanabe-Sugano diagrams

Electronic spectra of 3d(n) transition ions in an octahedral ligand surrounding have been studied using the modified crystal field approach (MCFA), which includes a relativistic spin-orbital interaction. A new variable parameter, the effective nuclear charge Z(eff) of a metal ion that allows accounting implicitly the covalence degree of a metal-ligand bond, has been introduced. Energy diagrams similar to the Tanabe-Sugano ones have been calculated. To study the spin state evolution of the metal ion in an arbitrary distorted octahedral complex, a spin state diagram approach has been proposed. The intermediate-spin (IS) state problem for 3d(4), 3d(5), and 3d(6) metal ions has been considered and conditions for the IS state realization have been formulated. The regions of the mixed high-, intermediate-, and low-spin states have been found. The possibility of coexistence of the different spin states of 3d ions in the octahedral complexes has been considered using crystallography data for the YBaCo(2)O(5.5) layered cobaltite.     

Near-field diffraction in a two-dimensional V-groove and its role in SERS

Optical field distribution in micro-nano geometries of miniaturized optical devices is often significantly different from that in identical but macroscopic geometries. Plasmon effects and near-field diffraction can enhance the local field intensity, leading to enhanced cross section for light absorption and scattering, which can be utilized in substrate-enhanced spectroscopies for the detection of trace amounts of adsorbed chemicals. A specific problem is an ingenious but only empirically described way to enhance signal intensity in Raman spectroscopy by the use of a substrate patterned with gold coated micron size pyramidal pits. While Raman enhancement on nanostructured substrates is generally attributed to surface plasmons, here the micron size, and thus the sub-wavelength to near-wavelength dimensions suggest that resonant enhancement emanating from optical near-field diffraction might also play a role. To answer this question, light diffraction in a projection of the pyramidal pit: a V-groove, was modelled with a modified Neerhoff-Mur formalism suitable to calculate electromagnetic field distribution in sub-wavelength structures. Under the boundary conditions a perfect conductor screen was assumed, which excludes plasmon effects. The calculations show that interference in the cavity causes a modest resonant increase in local intensity and that near-field diffraction strongly influences the field distribution, which is explained with the electrodynamic edge effect. The magnitude of the resonant electric field on its own cannot account for the experimentally observed Raman enhancement. However, a resonant enhancement of a similar magnitude is expected for the emitted Stokes frequencies. In this case the geometry implements the conditions for the classical electromagnetic Raman enhancement, ~E(4), in a good agreement with experimental results.