Preparation, IR spectroscopy, and time-of-flight mass spectrometry of halogenated and methylated Si(111)

The preparation of chlorine-, bromine-, and iodine-terminated silicon surfaces (Si(111):Cl, Br, and I) using atomically flat Si(111)-(1×1):H is described. The halogenated surfaces were obtained by photochemically induced radical substitution reactions with the corresponding dihalogen in a Schlenk tube by conventional inert gas chemistry. The nucleophilic substitution of the Si-Cl functionality with the Grignard reagent (CH₃MgCl) resulted in the unreconstructed methylated Si(111)-(1×1):CH₃ surface. The halogenated and methylated silicon surfaces were characterized by Fourier transform infrared (FTIR) spectroscopy and laser-induced desorption of monolayers (LIDOM). Calibration of the desorption temperature via analysis of time-of-flight (TOF) distributions as a function of laser fluence allowed the determination of the originally emitted neutral fragments by TOF mass spectrometry using electron-impact ionization. The halogens were desorbed atomically and as SiX _n (X = Cl, Br) clusters. The methyl groups mainly desorbed as methyl and ethyl fragments and a small amount of ⁺SiCH₃.     

Dielectric properties of thin-film ZrO<Subscript>2</Subscript> up to 50 GHz for RF MEMS switches

The dielectric properties of zirconium dioxide (ZrO₂) ceramic thin films were characterized up to 50 GHz using coplanar waveguides (CPWs) and metal–insulator–metal (MIM) capacitors with top circular electrodes. The ZrO₂ films were deposited using a chemical solution onto high-resistivity Si wafers and metal layers. The real part of the dielectric constant of approximately 22 and 26 was extracted at 50 GHz for CPW and MIM structures, respectively, and the loss tangent was approximately 0.09 at 50 GHz. C–V and I–V measurements were carried out to determine low-frequency and DC dielectric properties. The measurement results indicate that ZrO₂ is a promising material to be used as a dielectric layer for radio-frequency (RF) microelectromechanical systems (MEMS) capacitive switches.     

Strichartz estimates for Schrödinger equations on irrational tori in two and three dimensions

In this paper, we prove new multilinear Strichartz estimates, which are obtained by using techniques of Bourgain. These estimates lead to new critical well-posedness results for the nonlinear Schrödinger equation on irrational tori in two and three dimensions with small initial data. In three dimensions, this includes the energy critical case. This extends recent work of Guo–Oh–Wang.     

Towards peptide-substituted titanocene anticancer drugs

An alkyne-substituted fulvene was transformed via hydridolithiation followed by transmetallation with titanium tetrachloride into bis-[p-(prop-2-ynyloxy)-benzyl-cyclopentadienyl] titanium(IV) dichloride. Single crystals of this titanocene derivative could be obtained and the structure determined by X-ray diffraction. It showed that this compound crystallises in the space group C2/c with four molecules in the monoclinic cell. The alkyne-substituted titanocene dichloride derivative was then subject to a copper-catalysed azide-alkyne cycloaddition with its azide-functionalised methylester-protected phenylalanine reaction partner in order to form a linking triazole. This reaction was performed under anhydrous conditions employing a dichloromethane/acetonitrile solvent mixture with copper(I) iodide and 2,6-lutidine as the catalyst system. Under these conditions the adduct between the protein mimic and the titanocene was formed without hydrolysing the titanium dichloride moiety.     

Non-Algebraic Quadrature Domains

It is well known that, in the plane, the boundary of any quadrature domain (in the classical sense) coincides with the zero set of a polynomial. We show, by explicitly constructing some four-dimensional examples, that this is not always the case. This confirms, in dimension 4, a conjecture of the second author. Our method is based on the Schwarz potential and involves elliptic integrals of the third kind.