Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

Fully fluorinated imidodiphosphinate shells for visible- and NIR-Emitting lanthanides: Hitherto unexpected effects of sensitizer fluorination on lanthanide emission properties

In this paper we demonstrate that the effect of aromatic C-F substitution in ligands does not always abide by conventional wisdom for ligand design to enhance sensitisation for visible lanthanide emission, in contrast with NIR emission for which the same effect coupled with shell formation leads to unprecedented long luminescence lifetimes. We have chosen an imidodiphosphinate ligand, N-{P,P-di-(pentafluorophinoyl)}-P,P-dipentafluoro-phenylphosphinimidic acid (HF(20)tpip), to form ideal fluorinated shells about all visible- and NIR-emitting lanthanides. The shell, formed by three ligands, comprises twelve fully fluorinated aryl sensitiser groups, yet no-high energy X-H vibrations that quench lanthanide emission. The synthesis, full characterisation including X-ray and NMR analysis as well as the photophysical properties of the emissive complexes [Ln(F(20)tpip)(3)], in which Ln=Nd, Sm, Eu, Gd, Tb, Dy, Er, Yb, Y, Gd, are reported. The photophysical results contrast previous studies, in which fluorination of alkyl chains tends to lead to more emissive lanthanide complexes for both visible and NIR emission. Analysis of the fluorescence properties of the HF(20)tpip and [Gd(F(20)tpip)(3)] reveals that there is a low-lying state at around 715 nm that is responsible for partially quenching of the signal of the visible emitting lanthanides and we attribute it to a pi-sigma* state. However, all visible emitting lanthanides have long lifetimes and unexpectedly the [Dy(F(20)tpip)(3)] complex shows a lifetime of 0.3 ms, indicating that the elimination of high-energy vibrations from the ligand framework is particularly favourable for Dy. The NIR emitting lanthanides show strong emission signals in powder and solution with unprecedented lifetimes. The luminescence lifetimes of [Nd(F(20)tpip)(3)], [Er(F(20)tpip)(3)] and [Yb(F(20)tpip)(3)] in deuteurated acetonitrile are 44, 741 and 1111 mu s. The highest value observed for the [Yb(F(20)tpip)(3)] complex is more than half the value of the Yb ion radiative lifetime.

Mandelohydroxamic acid as ligand for copper(II) 15-metallacrown-5 lanthanide(III) and copper(II) 15-metallacrown-5 uranyl complexes

The formation of pentanuclear copper(ii) complexes with the mandelohydroxamic ligand was studied in solution by electrospray ionization mass spectrometry (ESI-MS), absorption spectrophotometry, circular dichroism and H-1 NMR spectroscopy. The presence of lanthanide(iii) or uranyl ions is essential for the self-assembly of the 15-metallacrown-5 compounds. The negative mode ESI-MS spectra of solutions containing copper(II), mandelohydroxamic acid and lanthanide(iii) ions (Ln = La, Ce, Nd, Eu, Gd, Dy, Er, Tm, Lu, Y) or uranyl in the ratio 5:5:1 showed only the peaks that could be unambiguously assigned to the following intact molecular ions: {Ln(NO3)(2)[15-MCuIIN(MHA)-5](2-)}(-) and {Ln(NO3)[15-MCCuIIN(MHA)-5](3-)}(-), where MHA represents doubly deprotonated mandelohydroxamic acid. The NMR spectra of the pentanuclear species revealed only one set of peaks indicating a fivefold symmetry of the complex. The pentanuclear complexes synthesized with the enantiomerically pure R- or S-forms of mandelohydroxamic acid ligand, showed circular dichroism spectra which were mirror images of each other. The pentanuclear complex made from the racemic form of the ligand showed no signals in the CD spectrum. The UV/ Vis titration experiments revealed that the order in which the metal salts are added to the solution of the mandelohydroxamic acid ligand is crucial for the formation of metallacrown complexes. The addition of copper(ii) to the solutions containing mandelohydroxamic acid and neodymium(iii) in a 5:1 ratio lead to the formation of a pentanuclear complex in solution. In contrary, titration of lanthanide(iii) salt to the solution containing copper(ii) and mandelohydroxamic acid did not show any evidence for the formation of pentanuclear species. ((c) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2006)

Influence of strain and polycrystalline ordering on magnetic properties of high moment rare earth metals and alloys

Despite being the most suitable candidates for solenoid pole pieces in state-of-the-art superconductor- based electromagnets, the intrinsic magnetic properties of heavy rare earth metals and their alloys have gained comparatively little attention. With the potential of integration in micro- and nanoscale devices, thin films of Gd, Dy, Tb, DyGd and DyTb were plasma-sputtered and investigated for their in-plane magnetic properties, with an emphasis on magnetisation vs. temperature profiles. Based on crystal structure analysis of the polycrystalline rare earth films, which consist of a low magnetic moment FCC layer at the seed interface topped with a higher moment HCP layer, an experimental protocol is introduced which allows the direct magnetic analysis of the individual layers. In line with the general trend of heavy lanthanides, the saturation magnetisation was found to drop with increasing unit cell size. In-situ annealed rare earth films exceeded the saturation magnetisation of a high-moment Fe65Co35 reference film in the cryogenic temperature regime, proving their potential for pole piece applications; however as-deposited rare earth films were found completely unsuitable. In agreement with theoretical predictions, sufficiently strained crystal phases of Tb and Dy did not exhibit an incommensurate magnetic order, unlike their single-crystal counterparts which have a helical phase. DyGd and DyTb alloys followed the trends of the elemental rare earth metals in terms of crystal structure and magnetic properties. Inter-rare-earth alloys hence present a desirable blend of saturation magnetisation and operating temperature.

Easily Accessible Rare-Earth-Containing Phosphonium Room-Temperature Ionic Liquids: EXAFS, Luminescence and Magnetic Properties

A range of liquid rare-earth chlorometallate complexes with alkyl-phosphonium cations, [P666 14]+, has been synthesised and characterised. EXAFS confirmed the predominant liquid-state speciation of the [LnCl6]3- of the series with Ln = Nd, Eu, Dy. The crystal structure of the shorter-alkyl-chain cation analogue [P4444]+ has been determined and exhibits a very large unit cell. The luminescence properties, with visible light emissions of the liquid Tb, Eu, Pr and Sm and the NIR emissions for the Nd and Er compounds were determined. The effective magnetic moments were measured and fitted for the Nd, Tb, Ho, Dy, Gd and Er samples.