Experimental and ab initio infrared study of χ-, κ‐ and α-aluminas formed from gibbsite

χ-, κ- and α-alumina phases formed by dehydration of micro-grained gibbsite between 773 and 1573 K are studied using infrared spectroscopy (IR). The structural transitions evidenced by X-ray diffraction (XRD) were interpreted by comparing IR measurements with ab initio simulations (except for the χ form whose complexity does not allow a reliable simulation). For each phase, IR spectrum presents specific bands corresponding to transverse optical (TO) modes of Al-O stretching and bending under 900 cm⁻¹. The very complex χ phase, obtained at 773 K, provides a distinctive XRD pattern in contrast with the IR absorbance appearing as a broad structure extending between 200 and 900 cm⁻¹ resembling the equivalent spectra for γ-alumina phase. κ-alumina is forming at 1173 K and its rich IR spectrum is in good qualitative agreement with ab initio simulations. This complexity reflects the large number of atoms in the κ-alumina unit cell and the wide range of internuclear distances as well as the various coordinances of both Al and O atoms. Ab initio simulations suggest that this form of transition alumina demonstrates a strong departure from the simple pattern observed for other transition alumina. At 1573 K, the stable α-Αl₂Ο₃ develops. Its IR spectra extends in a narrower energy range as compared to transition alumina and presents characteristics features similar to model α-Αl₂Ο₃⋅ Ab initio calculations show again a very good general agreement with the observed IR spectra for this phase. In addition, for both κ- and α-Αl₂Ο₃, extra modes, measured at high energy (above 790 cm⁻¹ for κ and above 650 cm⁻¹ for α), can originate from either remnant χ-alumina or from surface modes.     

Homotopy of ends and boundaries of CAT(0) groups

For n ≥ 0, we exhibit CAT(0) groups that are n-connected at infinity, and have boundary which is (n − 1)-connected, but this boundary has non-trivial nth-homotopy group. In particular, we construct 1-ended CAT(0) groups that are simply connected at infinity, but have a boundary with non-trivial fundamental group. Our base examples are 1-ended CAT(0) groups that have non-path connected boundaries. In particular, we show all parabolic semidirect products of the free group of rank 2 and have a non-path connected boundary.     

Centers of Convex Subsets of Buildings

We prove that two-dimensional convex subsets of spherical buildings are either buildings or have a center.     

Two New Multi-component BKP Hierarchies

We firstly propose two kinds of new multi-component BKP （mcBKP） hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources whose Lax representations are presented. The two mcBKP hierarchies both admit reductions to the k-constrained BKP hierarchy and to integrable （1＋1）-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of hi-directional SK equations with self-consistent     

Stable Exponents in Discrete Groups

It is known that in a word hyperbolic group the stable exponent of every nontorsion element is an integer. We prove that this is also true in finitely generated nilpotent groups. On the other hand, we show that for any rational number 1 there exists a torsionfree CAT(0) group containing an element whose stable exponent is equal to .     

X-ray metrology for advanced silicon processes

X-ray reflectivity (XRR), X-ray fluorescence (XRF) and small angle X-ray scattering (SAXS) techniques are used to the monitoring of Cu/porous low κ processes, which are developed for the next generation (≤65 nm) integrated circuits. Sensitivity of XRR and XRF is sufficient to detect drifts of the copper barrier layer, copper seed layer and Cu CMP (chemical-mechanical polishing) processes. Their metrology key parameters comply with production requirements. SAXS allows determining the pore structure of low κ films: average pore size and pore size distribution.