Chemical diffusion of fluorine in jadeite melt at high pressure

The chemical diffusion of fluorine in jadeite melt has been investigated from 10 to 15 kbars and 1200 to 1400°C using diffusion couples of Jadeite melt and fluorine-bearing jadeite melt (6.3 wt.% F). The diffusion profile data indicate that the diffusion process is concentration-independent, binary, F-O interdiffusion. The F-O interdiffusion coefficient ranges from 1.3 × 10−7 to 7.1 × 10−7 cm2/sec and is much larger than those obtained by Kushiro (1983) for Si-Ge and Al-Ga interdimision in jadeitic melts. The Arrhenius activation energy of diffusion is in the range of 36 to 39 kcal/mole as compared with 19 kcal/mole for fluorine tracer diffusion in a lime-aluminosilicate melt. The diffusivity and activation energy of F-O interdiffusion vary slightly with pressure, but the pressure dependence of F-O, Al-Ga and Si-Ge interdiffusion may be related to the relative volumes of the interdiffusing species for each pair. The magnitude of chemical diffusivity of fluorine is comparable to that of the chemical diffusivity of water in obsidian melts. The diffusivities of various cations are significantly increased by the addition of fluorine or water to a silicate melt. This fact, combined with the high diffusivity of fluorine, suggests that the F− ion is the principal diffusing species in dry aluminosilicate melts and that dissolved fluorine will accelerate chemical equilibration in dry igneous melts

Operator monotones, the reduction criterion and the relative entropy

We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we prove a new lower bound on the relative entropy of entanglement and other properties of entanglement measures.Comment: Final version accepted for publication, added references in reference [1] and [13

The effect of fluorine on viscosities in the system Na2O-Al2O3-SiO2: implications for phonolites, trachytes and rhyolites

The effect of fluorine on melt viscosities of five compositions in the system Na2O-Al2O3- SiO2h as been investigateda t one atmospherea nd 1000-1600'Cb y concentric-cylinder viscometry. The compositions chosen were albite, jadeite and nepheline on the join NaAlOlSiO2 and two others of the join at 75 mole percent SiO2, one peralkaline and one peraluminous. All melt viscosities were independent of shear rate over two orders of magnitude, indicating Newtonian behavior. All viscosity-temperature relationships were Arrhenian within error. Fluorine reduces the viscosities and activation energies of all melts investigated. The viscosity-reducing power of fluorine increases with the SiO2 content of melts on the join NaAlO2-SiO2 and is a maximum at Na/Al (molar) = I for melts containing 75 mole percent SiO2. Fluorine and water have similar effects on aluminosilicate melt viscosities, probably due to depolymerization of these melts by replacement of Si-O-(Si, Al) bridges with Si-OH and Si-F bonds, respectively. Evidence from slag systems shows that fluorine also reduces the viscosity of depolymerized silicate melts. The viscous flow of phonolites, trachytes and rhyolites will be strongly afected by fluorine. It appears that fluorine contents of igneous rocks may be combined with water in calculation schemes for determining the viscosity of natural melts

Observations of cosmic ray electrons between 2.7 and 21.5 MeV

Intensity of 2.7 to 21.5 MeV electrons in interplanetary space from Explorer 34 measurement

Optimal dense coding with mixed state entanglement

I investigate dense coding with a general mixed state on the Hilbert space $C^{d}\otimes C^{d}$ shared between a sender and receiver. The following result is proved. When the sender prepares the signal states by mutually orthogonal unitary transformations with equal {\it a priori} probabilities, the capacity of dense coding is maximized. It is also proved that the optimal capacity of dense coding $\chi ^{*}$ satisfies $E_{R}(\rho)\leq \chi ^{*}\leq E_{R}(\rho )+\log_{2}d$, where $E_{R}(\rho)$ is the relative entropy of entanglement of the shared entangled state.Comment: Revised. To appear in J. Phys. A: Math. Gen. (Special Issue: Quantum Information and Computation). LaTeX2e (iopart.cls), 8 pages, no figure