Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Coordination chemistry of a new P,Te-centred ligand: synthesis, NMR spectra and X-ray structures of M(TePPri2NPPri2)2 (M = Zn, Cd, Hg)

The lithiation of the monotelluride TePPri2NP(H)Pri2 (2) with BunLi at -78 degrees C results in the formation of the reagent [LiTePPri2NPPri2] (5), which was characterized by 31P NMR spectroscopy but not isolated due to disproportionation upon solvent removal. Salt metathesis reactions of 5, generated in situ, with group 12 metal chlorides produce the complexes M(TePPri2NPPri2)2 (6, M = Zn; 7, M = Cd; 8, M = Hg), which were characterized by single crystal X-ray diffraction, multinuclear NMR spectroscopy and thermal analyses. The X-ray structures reveal distorted tetrahedral structures with two P,Te-chelating anionic ligands [TePPri2NPPri2](-). The 31P NMR spectra exhibit second order behaviour that arises from an AA'XX' spin system; the spectra were simulated to determine the 31P, 31P spin-spin coupling constants.     

The single molecular precursor approach to metal telluride thin films: imino-bis(diisopropylphosphine tellurides) as examples

Interest in metal telluride thin films as components in electronic devices has grown recently. This tutorial review describes the use of single-source precursors for the preparation of metal telluride materials by aerosol-assisted chemical vapour deposition (AACVD) and acquaints the reader with the basic techniques of materials characterization. The challenges in the design and synthesis of suitable precursors are discussed, focusing on metal complexes of the recently-developed imino-bis(diisopropylphosphine telluride) ligand. The generation of thin films and nanoplates of CdTe, Sb(2)Te(3) and In(2)Te(3) from these precursors are used as illustrative examples.     

Experimental and Theoretical Investigations of Structural Isomers of Dichalcogenoimidodiphosphinate Dimers: Dichalcogenides or Spirocyclic Contact Ion Pairs?

A synthetic protocol for the tert-butyl-substituted dichalcogenoimidodiphosphinates [Na(tmeda){(EPtBu(2))(2)N}] (3 a, E=S; 3 b, E=Se; 3 c, E=Te) has been developed. The one-electron oxidation of the sodium complexes [Na(tmeda){(EPR(2))(2)N}] with iodine produces a series of neutral dimers (EPR(2)NPR(2)E--)(2) (4 b, E=Se, R=iPr; 4 c, E=Te, R=iPr; 5 a, E=S, R=tBu; 5 b, E=Se, R=tBu; 5 c, E=Te, R=tBu). Attempts to prepare 4 a (E=S, R=iPr) in a similar manner produced a mixture including HN(SPiPr(2)). Compounds 4 b, 4 c and 5 a-c were characterised by multinuclear NMR spectra and by X-ray crystallography, which revealed two alternative structures for these dimeric molecules. The derivatives 4 b, 4 c, 5 a and 5 b exhibit acyclic structures with a central chalcogen-chalcogen linkage that is elongated by approximately 2 % (E=S), 6 % (E=Se) and 8 % (E=Te) compared to typical single-bond values. By contrast, 5 c adopts an unique spirocyclic contact ion-pair structure in which a [(TePtBu(2))(2)N](-) ion is Te,Te' chelated to an incipient [(TePtBu(2))(2)N](+) cyclic ion. DFT calculations of the relative energies of the two structural isomers indicate a trend towards increasing stability for the contact ion pair relative to the corresponding dichalcogenide on going from S to Se to Te for both the isopropyl and tert-butyl series. The two-electron oxidation of [Na(tmeda){(EPtBu(2))(2)N}] (E=S, Se, Te) with iodine produced the salts [(EPtBu(2))(2)N](+)X(-) (7 a, E=S, X=I(3); 7 b, E=Se, X=I; 7 c, E=Te, X=I), which were characterised by X-ray crystallography. Compound 7 a exists as a monomeric, ion-separated complex with [d(S--S)=2.084(2) A]; 7 b and 7 c are dimeric [d(Se--Se)=2.502(1) A; d(Te--Te)=2.884(1) A].