Hausdorff spectrum of harmonic measure

For every non-elementary hyperbolic group, we show that for every random walk with finitely supported admissible step distribution, the associated entropy equals the drift times the logarithmic volume growth if and only if the corresponding harmonic measure is comparable with Hausdorfff measure on the boundary. Moreover, we introduce one parameter family of probability measures which interpolates a Patterson-Sullivan measure and the harmonic measure, and establish a formula of Hausdorff spectrum (multifractal spectrum) of the harmonic measure. We also give some finitary versions of dimensional properties of the harmonic measure

Revealing the mechanisms by which magneto-hydrodynamics disrupts solidification microstructures

A key technique for controlling solidification microstructures is magneto-hydrodynamics (MHD), resulting from imposing a magnetic field to solidifying metals and alloys. Applications range from bulk stirring to flow control and turbulence damping via the induced Lorentz force. Over the past two decades the Lorentz force caused by the interaction of thermoelectric currents and the magnetic field, a MHD phenomenon known as Thermoelectric Magnetohydrodynamics (TEMHD), was also shown to drive inter-dendritic flow altering microstructural evolution. In this contribution, high-speed synchrotron X-ray tomography and computational simulation are coupled to reveal the evolution, dynamics and mechanisms of solidification within a magnetic field, resolving the complex interplay and competing flow effects arising from Lorentz forces of different origins. The study enabled us to reveal the mechanisms disrupting the traditional columnar dendritic solidification microstructure, ranging from an Archimedes screw-like structure, to one with a highly refined dendritic primary array. We also demonstrate that alloy composition can be tailored to increase or decrease the influence of MHD depending on the Seebeck coefficient and relative density of the primary phase and interdendritic liquid. This work paves the way towards novel computational and experimental methods of exploiting and optimising the application of MHD in solidification processes, together with the calculated design of novel alloys that utilise these forces

Ultra-fast quantification of polycrystalline texture via single shot synchrotron X-ray or neutron diffraction

Tracking texture evolution during in situ loading is critical to understand and simulate the dynamic behaviour of microstructure in polycrystalline materials, yet conventional texture quantification methods are sometimes restricted due to various factors, such as acquisition time, sample environment and complex setup. To address this, a novel approach to extract texture information from single shot Time-Of-Flight neutron diffraction pattern has been developed. Another texture analysis approach based on single shot synchrotron X-ray diffraction has also been demonstrated. The effectiveness of two methods is assessed for polycrystalline Nickel-based superalloy polycrystalline samples possessing different textures. Both methods feature a moderate acquisition time of ~10 min and 30 s respectively, as well as a simplified setup which allows adding complex sample environments and the use of additional equipment. Comparison with the referential EBSD texture suggests that both approaches achieve a satisfactory match, though some details of the complex contour profiles in inverse pole figures may be missing. Besides that, a novel metric has been proposed to quantify the matching quality of pole figures. By employing the EPSC modelling approach, it is shown that the texture deviation due to the technique chosen for its evaluation exerts a subtle influence on th macro- and mesoscale simulation results, highlighting the significance of this approach for underpinning robust computational modelling

TbO⁺ in a calcium apatite matrix featuring a triple trigger-type relaxation of magnetization

Tb for Ca substituted hydroxyapatite ceramic samples with composition Ca10-xTbx(PO4)(6)(OH1-x/2-)(2), where x = 0.1, 0.5, were synthesized by solid-state reaction at 1300 degrees C in air, and their crystal structure, vibrational spectra, luminescence, and magnetic properties were studied. Implanting Tb3+ into the calcium apatite crystal lattice results in formation of an effective TbO+ ion which displays a short terbium-oxygen bond of 2.15 angstrom and a stretching vibration at 534 cm(-1). The Tb3+ electronic structure has been revealed by analyzing the luminescence spectra and dc/ac magnetization data. Accordingly, the ground state represents a pseudo doublet with M-J = +/- 6 and the first exited level is by 112 cm(-1) higher in energy. The ion exhibits field induced magnetic bistability with the magnetization reversing over the first exited state. Three paths of magnetization relaxation with field-temperature controlled switching between the paths have been identified

Angewandte Chemie

Abstract Meeting the challenges of Moore's Law, predicting ambitious miniaturization rates of integrated circuits, requires to go beyond the traditional top?down approaches, and to employ synthetic chemistry methods, to use bottom?up techniques. During the recent decades, it has been shown that open?shell coordination compounds may exhibit intramolecular spontaneous magnetization, thus offering promising prospects for storage and processing of digital information. Against this background we regarded it rewarding to implement similar magnetic centers into a ceramic material, which would provide better long?term mechanical and chemical durability. Here we present new robust inorganic compounds containing separate DyO+ ions in an apatite matrix, which behave like single?molecule magnets. The materials exhibit a blocking temperature of 11?K and an energy barrier for spin reversal of a thousand inverse centimeters which is among the highest values ever achieved

"Isolated" DyO⁺ Embedded in a Ceramic Apatite Matrix Featuring Single-Molecule Magnet Behavior with a High Energy Barrier for Magnetization Relaxation

Meeting the challenges of Moore's Law, predicting ambitious miniaturization rates of integrated circuits, requires to go beyond the traditional top-down approaches, and to employ synthetic chemistry methods, to use bottom-up techniques. During the recent decades, it has been shown that open-shell coordination compounds may exhibit intramolecular spontaneous magnetization, thus offering promising prospects for storage and processing of digital information. Against this background we regarded it rewarding to implement similar magnetic centers into a ceramic material, which would provide better long-term mechanical and chemical durability. Here we present new robust inorganic compounds containing separate DyO+ ions in an apatite matrix, which behave like single-molecule magnets. The materials exhibit a blocking temperature of 11K and an energy barrier for spin reversal of a thousand inverse centimeters which is among the highest values ever achieved

Slow Spin Relaxation in Dioxocobaltate(II) Anions Embedded in the Lattice of Calcium Hydroxyapatite

Pure-phase cobalt-doped calcium hydroxyapatite ceramic samples with composition Ca₁₀(PO₄)₆[(CoO₂)_<i>x</i>(OH)_{1–2<i>x</i>}]₂, where <i>x</i> = 0–0.2, were synthesized by high-temperature solid-state reaction, and their crystal structures, vibrational spectra, and magnetic properties were studied. Co atoms are found to enter into the apatite trigonal channel formally substituting H atoms and forming bent dioxocobaltate­(II) anions. The anion exhibits single-molecule-magnet (SMM) behavior: slow relaxation of magnetization below 8 K under a nonzero magnetic field with an energy barrier of 63 cm^–1. The barrier value does not depend on the concentration of Co ions, virtually coincides with the zero-field-splitting energy as determined from direct-current magnetization, and is very close to the value obtained earlier for cobalt-doped strontium hydroxyapatite. Moreover, the vibration frequencies of the dioxocobaltate­(II) anion are found to be the same in calcium and strontium apatite matrixes. The very weak dependence of the SMM parameters on the matrix nature in combination with good chemical and thermal stabilities of the compounds provides wide opportunities to exploit the intrinsic properties of such a SMM-like anion