Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

Multi-zone TAP-reactors theory and application - IV. Ideal and non-ideal boundary conditions

We study the influence of non-ideal boundary and initial conditions (BIC) of a temporal analysis of products (TAP) reactor model on the data (observed exit flux) analysis. The general theory of multi-response state-defining experiments for a multi-zone TAP reactor is extended and applied to model several alternative boundary and initial conditions proposed in the literature. The method used is based on the Laplace transform and the transfer matrix formalism for multi-response experiments. Two non-idealities are studied: (1) the inlet pulse not being narrow enough (gas pulse not entering the reactor in Dirac delta function shape) and (2) the outlet non-ideality due to imperfect vacuum. The effect of these non-idealities is analyzed to the first and second order of approximation. The corresponding corrections were obtained and discussed in detail. It was found that they are negligible. Therefore, the model with ideal boundary conditions is proven to be completely adequate to the description and interpretation of transport-reaction data obtained with TAP-2 reactors.

Boron in copper: A perfect misfit in the bulk and cohesion enhancer at a grain boundary

Using first principles electronic structure methods, we calculate the effects of boron impurities in bulk copper and at surfaces and grain boundaries. We find that boron segregation to the Sigma5(310)[001] grain boundary should strengthen the boundary up to 1.5 ML coverage (15.24 at./nm2). The maximal effect is observed at 0.5 ML and corresponds to boron atoms filling exclusively grain boundary interstices. In copper bulk, B causes significant distortion both in interstitial and regular lattice sites, for which boron atoms are either too big or too small. The distortion is compensated to a large extent when the interstitial and substitutional boron combine together to form a strongly bound dumbbell. Our prediction is that bound boron impurities should appear in a sizable proportion if not dominate in most experimental conditions. A large discrepancy between calculated heats of solution and experimental terminal solubility of B in Cu is found, indicating either a significant failure of the density functional approach or, more likely, strongly overestimated solubility limits in the existing B-Cu phase diagram.

Plasma boundary sheath in the afterglow of a pulsed inductively coupled RF plasma

The sheath dynamics in the afterglow of a pulsed inductively coupled plasma, operated in hydrogen, is investigated. It is found that the sheath potential does not fully collapse in the early post-discharge. Time resolved measurements of the positive ion flux in a hydrogen plasma, using a mass resolved ion energy analyser, reveal that a constant 2 eV mean ion energy persists for several hundred micro-seconds in the afterglow. The presence of a finite sheath potential is explained by super-elastic collisions between vibrationally excited hydrogen molecules and electrons in the afterglow, leading to an electron temperature of about 0.5 eV. Plasma density decay times measured using both the mass resolved energy analyser and a Langmuir probe are in good agreement. Vibrational temperatures measured using optical emission spectroscopy support the theory of electron heating through super-elastic collisions with vibrationally excited hydrogen molecules. Measurements are also supported by numerical simulations and modelling results.