Korn inequality for a thin rod with rounded ends

We consider an elastic rod with rounded ends and diameter proportional to a small parameter h > 0. The roundness of the ends is described by an exponent m ∈ (0,1). We derive for the rod an asymptotically sharp Korn inequality with a special weighted anisotropic norm. Weight factors with m‐dependent powers of h appear both in the anisotropic norm and the Korn inequality itself, and we discover three critical values m = 1 ∕ 4, m = 1 ∕ 2 and m = 3 ∕ 4 at which these exponents are crucially changed. Copyright © 2014 John Wiley & Sons, Ltd.     

Rational Development of Guanidinate and Amidinate Based Cerium and Ytterbium Complexes as Atomic Layer Deposition Precursors: Synthesis,Modeling, and Application

Owing to the limited availability of suitable precursors for vapor phase deposition of rare-earth containing thin-film materials, new or improved precursors are sought after. In this study, we explored new precursors for atomic layer deposition (ALD) of cerium (Ce) and ytterbium (Yb) containing thin films. A series of homoleptic tris-guanidinate and tris-amidinate complexes of cerium (Ce) and ytterbium (Yb) were synthesized and thoroughly characterized. The C-substituents on the N-C-N backbone (Me, NMe₂, NEt₂, where Me=methyl, Et=ethyl) and the N-substituents from symmetrical iso-propyl (iPr) to asymmetrical tertiary-butyl (tBu) and Et were systematically varied to study the influence of the substituents on the physicochemical properties of the resulting compounds. Single crystal structures of [Ce(dpdmg)₃] 1 and [Yb(dpdmg)₃] 6 (dpdmg=N,N'-diisopropyl-2-dimethylamido-guanidinate) highlight a monomeric nature in the solid-state with a distorted trigonal prismatic geometry. The thermogravimetric analysis shows that the complexes are volatile and emphasize that increasing asymmetry in the complexes lowers their melting points while reducing their thermal stability. Density functional theory (DFT) was used to study the reactivity of amidinates and guanidinates of Ce and Yb complexes towards oxygen (O₂) and water (H₂O). Signified by the DFT calculations, the guanidinates show an increased reactivity toward water compared to the amidinate complexes. Furthermore, the Ce complexes are more reactive compared to the Yb complexes, indicating even a reactivity towards oxygen potentially exploitable for ALD purposes. As a representative precursor, the highly reactive [Ce(dpdmg)₃] 1 was used for proof-of-principle ALD depositions of CeO₂ thin films using water as co-reactant. The self-limited ALD growth process could be confirmed at 160 °C with polycrystalline cubic CeO₂ films formed on Si(100) substrates. This study confirms that moving towards nitrogen-coordinated rare-earth complexes bearing the guanidinate and amidinate ligands can indeed be very appealing in terms of new precursors for ALD of rare earth based materials.     

The effect of side-chain length of cellulose fatty acid esters on their thermal,barrier and mechanical properties

Currently, long-chain cellulose esters are not produced commercially because of high price, and since their preparation typically requires a large quantity of chemicals. To reduce the chemical consumption, cellulose reactivity needs to be increased without losing its quality. One way to increase the reactivity of cellulose is to decrease its molar mass in a controlled manner. In this study, we have synthesized cellulose esters with different side-chain length (C6–C18) in a homogeneous system using ozone molar mass-controlled cellulose. The target was to keep the degree of substitution as low as possible while still ensuring the suitability of cellulose esters for solvent casting. Thermal, barrier and mechanical properties were studied depending on cellulose fatty acid ester side-chain length. All our molar mass-controlled cellulose esters form optically transparent, flexible and heat-sealable films with good water barrier properties and are processable without the addition of an external plasticizer. Furthermore, the films have mechanical properties comparable to some generally used plastics. These good properties suggest that our molar mass-controlled cellulose esters could be potential candidates for various applications such as films and composites.     

Preparative and Mössbauer studies of Bi2Sr2Ca n-1Cu n O y compounds withn=2 or 3

The influence of sintering temperatures and nominal starting compositions on the phase contents of polycrystalline Bi₂Sr₂Ca _n-1Cu _n O_4+2n samples are reported. After every sintering the samples were characterized with X-ray diffraction and magnetic AC susceptibility measurements. For Mössbauer studies, in each case also a corresponding specimen containing⁵⁷Fe was synthetized. The identification of various superconducting Bi₂Sr₂Ca _n-1Cu _n O_4+2n phases on the basis of Mössbauer spectra consisting usually of three quadrupole doublets is discussed.     

Synthesis and redox behaviour of the chalcogenocarbonyl dianions [(E)C(PPh(2)S)(2)](2-): formation and structures of chalcogen-chalcogen bonded dimers and a novel selone

The lithium salts of the chalcogenocarbonyl dianions [(E)C(PPh₂S)₂]^2? (E=S ( 4 b ), Se ( 4 c )) were produced through the reactions between Li₂[C(PPh₂S)₂] and elemental chalcogens in the presence of tetramethylethylenediamine (TMEDA). The solid‐state structure of {[Li(TMEDA)]₂[(Se)C(PPh₂S)₂]}—[{Li(TMEDA)}₂ 4 c ]—was shown to be bicyclic with the Li⁺ cations bis‐S,Se‐chelated by the dianionic ligand. One‐electron oxidation of the dianions 4 b and 4 c with iodine afforded the diamagnetic complexes {[Li(TMEDA)]₂[(SPh₂P)₂CEEC(PPh₂S)₂]} ([Li(TMEDA)]₂ 7 b (E=S), [Li(TMEDA)]₂ 7 c (E=Se)), which are formally dimers of the radical anions [(E)C(PPh₂S)₂]^{? .} (E=S ( 5 b ), Se ( 5 c )) with elongated central E? E bonds. Two‐electron oxidation of the selenium‐containing dianion 4 c with I₂ yielded the LiI adduct of a neutral selone {[Li(TMEDA)][I(Se)C(PPh₂S)₂]}—[{LiI(TMEDA)} 6 c ]—whereas the analogous reaction with 4 b resulted in the formation of 7 b followed by protonation to give {[Li(TMEDA)][(SPh₂P)₂CSS(H)C(PPh₂S)₂]}—[Li(TMEDA)] 8 b . Attempts to identify the transient radicals 5 b and 5 c by EPR spectroscopy in conjunction with DFT calculations of the electronic structures of these paramagnetic species and their dimers are also described. The crystal structures of [{Li(TMEDA)}₂ 4 c ], [{LiI(TMEDA)} 6 c ] ? C₇H₈, [Li(TMEDA)]₂ 7 b? (CH₂Cl₂)_0.33, [Li(THF)₂]₂ 7 b , [Li(TMEDA)]₂ 7 c , [Li(TMEDA)] 8 b? (CH₂Cl₂)₂ and [Li([12]crown‐4)₂] 8 b were determined and salient structural features are discussed.     

Degree of order and redox balance in B-site ordered double-perovskite oxides, Sr2MMoO6−δ (M=Mg, Mn, Fe, Co, Ni, Zn)

We have investigated a series of double-perovskite oxides Sr₂MMoO_6−δ (M=Mg, Mn, Fe, Co, Ni, Zn) for redox stability, oxygen content and crystal structure. Phases with M=Co, Ni and Zn were found to be oxygen-stoichiometric and stable under oxidizing conditions, whereas those with M=Mn and Fe were oxygen-deficient and stable under reducing conditions. The M=Mg phase is stable both under reducing and oxidizing conditions, showing variable oxygen contents within 0.00≤δ≤0.04 depending on the annealing conditions. Structural data indicate somewhat depressed values for the degree of M/Mo cation order and also evidence of electron transfer from M^II to Mo^VI for M=Mn, Fe and Co.     

Cobalt complexes of a selenium diimide and a tellurium diimide dimer

[CoCl₂{N,N′-Te₂(N^tBu)₄}] (1) was obtained in good yields by the reaction of equimolar amounts of (^tBu)NTe(μ-N^tBu)₂TeN(^tBu) and CoCl₂ in toluene under an argon atmosphere. The crystal structure of 1·CH₂Cl₂ showed that the dimeric tellurium diimide ligand is N,N′-chelated to cobalt. The related reaction of Se(N^tBu)₂ and CoCl₂ affords a green product tentatively identified as a 1:1 adduct [CoCl₂{N,N′-Se(N^tBu)₂}] (CHN analysis). However, recrystallization from thf produces the ion-separated complex [Co₂(μ-Cl)₃{N,N′-Se(N^tBu)₂}₂(thf)₂][CoCl₃{NH₂(^tBu)}]·1½thf (2·1½thf), in which the monomeric selenium diimide ligand is N,N′-chelated to cobalt in the cation. A pathway for the formation of 2 from [CoCl₂{N,N′-Se(N^tBu)₂}] in thf is proposed.     

Techniques of differential scanning calorimetry for quantification of low contents of amorphous phases

Differential scanning calorimetry (DSC) is one of the most frequently used techniques for analyzing small concentrations of amorphous phases in a crystalline matrix. In recent years novel enhanced DSC approaches have been intensively looked for to improve parameters such as sensitivity, accuracy, and detection limit of the technique. Low levels of amorphous phases can be quantitatively determined in DSC by measuring the heat capacity change associated with the glass transition. In this short review the potentials provided by the HyperDSC and StepScan DSC techniques are discussed. Examples illustrate the advantages and disadvantages of the techniques and compare their abilities to detect small glass transitions and determine low contents of amorphous phases in samples which are mostly crystalline.     

Avoiding eddy-current problems in ultra-low-field MRI with self-shielded polarizing coils

In ultra-low-field magnetic resonance imaging (ULF MRI), superconductive sensors are used to detect MRI signals typically in fields on the order of 10-100 μT. Despite the highly sensitive detectors, it is necessary to prepolarize the sample in a stronger magnetic field on the order of 10-100 mT, which has to be switched off rapidly in a few milliseconds before signal acquisition. In addition, external magnetic interference is commonly reduced by situating the ULF-MRI system inside a magnetically shielded room (MSR). With typical dipolar polarizing coil designs, the stray field induces strong eddy currents in the conductive layers of the MSR. These eddy currents cause significant secondary magnetic fields that may distort the spin dynamics of the sample, exceed the dynamic range of the sensors, and prevent simultaneous magnetoencephalography and MRI acquisitions. In this paper, we describe a method to design self-shielded polarizing coils for ULF MRI. The experimental results show that with a simple self-shielded polarizing coil, the magnetic fields caused by the eddy currents are largely reduced. With the presented shielding technique, ULF-MRI devices can utilize stronger and spatially broader polarizing fields than achievable with unshielded polarizing coils.