Compressibility of hexagonal selenium to 45 kbar

Compression data to 45 kbar have been obtained for hexagonal selenium by static methods in a piston-cylinder apparatus. Cylindrical samples (1 cm dia. and 1·2 cm length) of polycrystalline hexagonal selenium, with a bulk density close to the X-ray density, were prepared by pressing the samples at 7 kbar and 170°C. The compression data are described by a third degree polynomial,

$?\left(\frac{\Delta V}{V_O}\right)=?64·14\times {10}^{?4}P+109·9\times {10}^{?6}{P}^2?96·77\times {10}^{?8}{P}^3$

,where P is pressure in kbar. The zero pressure bulk modulus and the pressure derivative of the bulk modulus are 156 ± 10 kbar and 4·33 respectively.     

Persistent luminescence and synchrotron radiation study of the Ca2MgSi2O7:Eu2+,R3+ materials

The tetragonal ${\mathrm{Ca}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+},{\mathrm{R}}^{3+}$ persistent luminescence materials were prepared by a solid state reaction. The UV excited and persistent luminescence was observed in the green region centred at 535 nm. Both luminescence phenomena are due to the same ${\mathrm{Eu}}^{2+}$ ion occupying the single ${\mathrm{Ca}}^{2+}$ site in the host lattice. The ${\mathrm{R}}^{3+}$ codoping usually reduced the persistent luminescence of ${\mathrm{Ca}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$, which differs from the ${\mathrm{M}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$ $(\mathrm{M}=\mathrm{Sr},\mathrm{Ba})$ and ${\mathrm{MAl}}_2{\mathrm{O}}_4$:${\mathrm{Eu}}^{2+}$ $(\mathrm{M}=\mathrm{Ca},\mathrm{Sr})$ materials. Only the ${\mathrm{Tb}}^{3+}$ ion enhanced slightly the persistent luminescence. With the aid of synchrotron radiation, the band gap energy of ${\mathrm{Ca}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$ was found to be about 7 eV that is very similar to those of the ${\mathrm{M}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$ $(\mathrm{M}=\mathrm{Sr},\mathrm{Ba})$ materials. Thermoluminescence results suggested that the ${\mathrm{R}}^{3+}$ ions might act as electron traps, but only the TL peaks created by ${\mathrm{Tm}}^{3+}$ and ${\mathrm{Sm}}^{3+}$ can be found in the temperature range accessible. Lattice defects (e.g. oxygen vacancies) are also important, since the same main thermoluminescence peak was observed at about $100{}^{\circ }\mathrm{C}$ with and without ${\mathrm{R}}^{3+}$ codoping.     

Pressure dependence of negative thermal expansion in Zr2(WO4)(PO4)2

Negative thermal expansion materials can experience significant stresses when they are used in composites. Under ambient conditions Zr₂(WO₄)(PO₄)₂ displays anisotropic negative thermal expansion (NTE) (${\alpha }_v=?14.0\left(10\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_a=?7.9\left(5\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_b=2.5\left(5\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_c=?8.7\left(2\right)\times 10^{?6}{K}^{?1}$ at 0 GPa). The effect of hydrostatic pressure on its thermal expansion characteristics was investigated by neutron diffraction between 300 and 60 K at pressures up to 0.3 GPa. No phase transitions were observed in the pressure and temperature range examined. The material was found to have a bulk modulus, B₀, of 61.3(8) GPa at ambient temperature, and unlike some other NTE materials, pressure had no detectable effect on thermal expansion (${\alpha }_v=?14.2\left(8\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_a=?7.9\left(3\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_b=2.9\left(5\right)\times 10^{?6}{K}^{?1}$, ${\alpha }_c=?9.2\left(2\right)\times 10^{?6}{K}^{?1}$ at 0.3 GPa).     

Bulk and shear mechanical loss of titania-doped tantala

We report on the mechanical loss from bulk and shear stresses in thin film, ion beam deposited, titania-doped tantala. The numerical values of these mechanical losses are necessary to fully calculate the Brownian thermal noise in precision optical cavities, including interferometric gravitational wave detectors like LIGO. We found the values from measuring the normal mode mechanical quality factors, Q's, in the frequency range of about 2000-10,000 Hz, of silica disks coated with titania-doped tantala coupled with calculating the elastic energy in shear and bulk stresses in the coating using a finite element model. We fit the results to both a frequency independent and frequency dependent model and find ${?}_{\mathrm{shear}}=(8.3\pm 1.1)\times {10}^{?4}$, ${?}_{\mathrm{bulk}}=(6.6\pm 3.8)\times {10}^{?4}$ with a frequency independent model and ${?}_{\mathrm{shear}}\left(f\right)=(5.0\pm 0.7)\times {10}^{?4}+(5.4\pm 1.1)\times {10}^{?8}f$, ${?}_{\mathrm{bulk}}\left(f\right)=(11\pm 2.8)\times {10}^{?4}?(8.7\pm 4.7)\times {10}^{?8}f$ with a frequency dependent (linear) model. The ratio of these values suggest that modest improvement in the coating thermal noise may be possible in future gravitational wave detector optics made with titania-doped tantala as the high index coating material by optimizing the coating design to take advantage of the two different mechanical loss angles.     

Pseudo anti-commuting and Ricci soliton real hypersurfaces in complex two-plane Grassmannians

In this paper, first we introduce a new notion of pseudo anti-commuting for real hypersurfaces in complex two-plane Grassmannians $G_2\left({\mathbb{C}}^{m+2}\right)$ and prove a complete classification theorem, which gives a shrinking Ricci soliton with potential Reeb flow on Hopf real hypersurfaces and a tube over a totally real totally geodesic $\mathbb{Q}{P}^n$, $m=2n$ in $G_2\left({\mathbb{C}}^{m+2}\right)$.     

Leibniz algebroids,generalized Bismut connections and Einstein–Hilbert actions

Connection, torsion and curvature are introduced for general (local) Leibniz algebroids. Generalized Bismut connection on $TM\oplus {\Lambda }^p{T}^{1}M$ is an example leading to a scalar curvature of the form $R+H^2$ for a closed $(p+2)$-form $H$.     

SUSY structures,representations and Peter–Weyl theorem for S1|1

The real compact supergroup $S^{1|1}$ is analysed from different perspectives and its representation theory is studied. We prove it is the only (up to isomorphism) supergroup, which is a real form of ${\left({\mathbb{C}}^{1|1}\right)}^{\times }$ with reduced Lie group $S^1$, and a link with SUSY structures on ${\mathbb{C}}^{1|1}$ is established. We describe a large family of complex semisimple representations of $S^{1|1}$ and we show that any $S^{1|1}$-representation whose weights are all nonzero is a direct sum of members of our family. We also compute the matrix elements of the members of this family and we give a proof of the Peter–Weyl theorem for $S^{1|1}$.     

Monopoles on the Bryant–Salamon G2-manifolds

$G_2$-monopoles are solutions to gauge theoretical equations on noncompact $7$-manifolds of $G_2$ holonomy. We shall study this equation on the $3$ Bryant–Salamon manifolds. We construct examples of $G_2$-monopoles on two of these manifolds, namely the total space of the bundle of anti-self-dual two forms over the ${\mathbb{S}}^4$ and ${\mathbb{C}\mathbb{P}}^2$. These are the first nontrivial examples of $G_2$-monopoles.Associated with each monopole there is a parameter $m\in {\mathbb{R}}^{+}$, known as the mass of the monopole. We prove that under a symmetry assumption, for each given $m\in {\mathbb{R}}^{+}$ there is a unique monopole with mass $m$. We also find explicit irreducible $G_2$-instantons on ${\Lambda }_{-}^2\left({\mathbb{S}}^4\right)$ and on ${\Lambda }_{-}^2\left({\mathbb{C}\mathbb{P}}^2\right)$.The third Bryant–Salamon $G_2$-metric lives on the spinor bundle over the $3$-sphere. In this case we produce a vanishing theorem for monopoles.     

Thermoelectric and topological properties of half-Heusler compounds ZrIrX(As,Sb, Bi)

The strain dependent electronic structures, thermoelectric and topological properties of the half-Heusler compounds ZrIrX(X=As, Sb, Bi) are investigated by the first-principle calculations. At the equilibrium lattice constants, all the three compounds are trivial insulators and good thermoelectric materials with the Seebeck coefficient S and the power factor over relaxation time $S^2\sigma /\tau$ as large as 1180 (μV/K) and 4.1 (${10}^{11}W{m}^{?1}{K}^{?2}{s}^{?1}$), respectively. The compressive strain enhances the band gap, while the tensile strain decreases the band gap. At some specific tensile strains, the compounds become Dirac-semimetals, with the s-type band ${\mathrm{\Gamma }}_6$ below p-type band ${\mathrm{\Gamma }}_8$, in the cubic phase. When we compress the a(b)-axis and elongate the c-axis of the compounds, they become the type-I Weyl semimetals. For ZrIrAs, the eight Weyl-Points (WPS) locate at (± K_x, 0, ± K_z), (0, ± K_y, ± K_z), ${\mathrm{K}}_x={\mathrm{K}}_y=0.008{\mathrm{\AA }}^{?1}$, ${\mathrm{K}}_z=0.043{\mathrm{\AA }}^{?1}$.     

Quantum point contact conductance in normal metal/insulator/ metal/dx2−y2+idxy mixed wave superconductor junctions

The tunneling conductance in a normal metal/insulator/metal/$d_{x^2?y^2}+i{d}_{xy}$ mixed wave superconductor (N/I/N/$d_{x^2?y^2}+i{d}_{xy}$) junction is calculated, where the N/I/N region is a quantum wire. It is found in the single-mode case that the magnitude of the tunneling conductance near zero voltage is enhanced due to the Andreev bound state by quasiparticles with perpendicular and horizontal injection, and the zero-bias conductance varies with $L$ ($L$ is the distance from insulating layer to the interface of N/$d_{x^2?y^2}+i{d}_{xy}$ mixed wave superconductor). Splitting of the zero-bias conductance peak appears in the quantum point contact tunneling spectra for an N/I/N/$d_{x^2?y^2}+i{d}_{xy}$ junction, and several subgap peaks can split at the same time. On increasing both $L$ and the magnitude ratio of the two components for the $d_{x^2?y^2}+i{d}_{xy}$ mixed wave, the subgap resonances exhibit an alternately high and low behavior inside the energy gap. These results are different from those in d-wave and p-wave superconductor junctions.