Convergent beam electron diffraction study of Pb2CoWO6 at 100 K

A study by convergent beam electron diffraction has been performed in order to clarify the symmetry of the phase III of Pb₂CoWO₆. Microdiffractions with higher-order Laue zone on monodomain areas have confirmed the cell proposed in our preceding study. In addition, an ‘axial’ glide plane (c) has been found normal to the b axis. In the conditions of observation, the convergent beam electron diffraction patterns lead to an apparent point group mmm. No breakdown of a mirror symmetry could be found. The discrepancy between this result and the existence of a spontaneous polarisation is discussed.     

Rapid identification of trimethyl and triethyl amines using sulphonic acidic ionic liquids: A time-of-flight secondary ion mass spectrometry study of fragmentation reactions

The time-of-flight secondary ion mass spectrometry (TOF-SIMS) has emerged as a powerful tool for the unswerving detection of biomolecules, in particular, proteins and peptides. To date, there is very little information available on the direct determination of trimethyl/triethyl amines using TOF-SIMS. One major hurdle in this regard is an ultrahigh vacuum system, usually needed in TOF-SIMS, which hampers its usability to trimethyl/triethyl amines owing to their high evaporation rate. We designed an efficient and sensitive protocol for rapid identification and sensitive determination of tertiaryalkyl amines using TOF-SIMS. The amines were derivatized by reaction with 1,4-butane sultone and sulphuric acid sequentially to afford the corresponding sulphonic acidic ionic liquids (ILs). The TOF-SIMS analysis of these task-specific ILs (TSILs) was carried out in both positive and negative polarity. The positive ion mass spectra of TSILs showed sharp fragmented peaks for tertiaryalkyl amines at typical level and up to 10 ppm. The possible mechanism for different fragmentation pathways in positive polarity was discussed.     

On the long‐range relativistic effects in the 15N NMR chemical shifts of halogenated azines

Long‐range β‐ and γ‐relativistic effects of halogens in ¹⁵N NMR chemical shifts of 20 halogenated azines (pyridines, pyrimidines, pyrazines, and 1,3,5‐triazines) are shown to be unessential for fluoro‐, chloro‐, and bromo‐derivatives (1–2 ppm in average). However, for iodocontaining compounds, β‐ and γ‐relativistic effects are important contributors to the accuracy of the ¹⁵N calculation. Taking into account long‐range relativistic effects slightly improves the agreement of calculation with experiment. Thus, mean average errors (MAE) of ¹⁵N NMR chemical shifts of the title compounds calculated at the non‐relativistic and full 4‐component relativistic levels in gas phase are accordingly 7.8 and 5.5 ppm for the range of about 150 ppm. Taking into account solvent effects within the polarizable continuum model scheme marginally improves agreement of computational results with experiment decreasing MAEs from 7.8 to 7.4 ppm and from 5.5 to 5.3 ppm at the non‐relativistic and relativistic levels, respectively. The best result (MAE: 5.3 ppm) is achieved at the 4‐component relativistic level using Keal and Tozer's KT3 functional used in combination with Dyall's relativistic basis set dyall.av3z with taking into account solvent effects within the polarizable continuum solvation model. The long‐range relativistic effects play a major role (of up to dozen of parts per million) in ¹⁵N NMR chemical shifts of halogenated nitrogen‐containing heterocycles, which is especially crucial for iodine derivatives. This effect should apparently be taken into account for practical purposes.     

Influence of methyl‐modified silyl groups on the properties of polymers and Si/B/N/C ceramics derived from N‐silylated borazine derivatives

Thermal silazane cleavage of dichloroboryldisilylamines (SiCl_mMe_3?m)N(SiMe₃)(BCl₂) (1: m = 1; 2: m = 2) at 196 °C leads to the borazine derivates [(SiCl_mMe_3?m)NB(Cl_nMe_1?n)]₃ (3: m = 1, n = 0.185; 4: m = 2, n = 0.111) characterized by NMR and IR spectroscopy and mass spectrometry. Single‐crystal X‐ray diffraction structure analyses reveal (BN)₃ units with unusual twisted boat conformations in both compounds. Additionally, more detailed studies are done to clear up the function of the by‐products (SiCl_mMe_3?m)N(SiClMe₂)(BClMe) formed during the cyclization step leading to asymmetrically boron substituted borazine derivatives. The single‐source precursors 3 and 4 were cross‐linked with methylamine producing polymers 3P and 4P, which were transformed into black amorphous materials with ceramic yields of 20.8 % and 50.3 %, respectively. Ceramic 4C (Si_1.00B_0.98 N_2.55 C_1.37O_0.05) was further investigated by ¹¹B and ²⁹Si magic angle spinning (MAS) NMR spectroscopy. A combined study of high‐temperature TG analyses and X‐ray powder diffraction analyses confirms the thermal stability of 4C up to 1670 °C. Copyright © 2012 John Wiley & Sons, Ltd.     

On the rate of change of the sharp constant in the Sobolev–Poincaré inequality

The rate of change of the sharp constant in the Sobolev–Poincaré or Friedrichs inequality is estimated for a Euclidean domain that moves outward. The key ingredients are a Hadamard variation formula and an inequality that reverses the usual Hölder inequality.