159 research outputs found

    Raman elastic geobarometry for anisotropic mineral inclusions

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    Elastic geobarometry for host-inclusion systems can provide new constraints to assess the pressure and temperature conditions attained during metamorphism. Current experimental approaches and theory are developed only for crystals immersed in a hydrostatic stress field, whereas inclusions experience deviatoric stress. We have developed a method to determine the strains in quartz inclusions from Raman spectroscopy using the concept of the phonon-mode Grüneisen tensor. We used ab initio Hartree-Fock/Density Functional Theory to calculate the wavenumbers of the Raman-active modes as a function of different strain conditions. Least-squares fits of the phonon-wavenumber shifts against strains have been used to obtain the components of the mode Grüneisen tensor of quartz (γm1 and γm3) that can be used to calculate the strains in inclusions directly from the measured Raman shifts. The concept is demonstrated with the example of a natural quartz inclusion in eclogitic garnet from Mir kimberlite and has been validated against direct X-ray diffraction measurement of the strains in the same inclusion

    Raman elastic geobarometry for anisotropic mineral inclusions

    Get PDF
    Elastic geobarometry for host-inclusion systems can provide new constraints to assess the pressure and temperature conditions attained during metamorphism. Current experimental approaches and theory are developed only for crystals immersed in a hydrostatic stress field, whereas inclusions experience deviatoric stress. We have developed a method to determine the strains in quartz inclusions from Raman spectroscopy using the concept of the phonon-mode Gr\ufcneisen tensor. We used ab initio Hartree-Fock/Density Functional Theory to calculate the wavenumbers of the Raman-active modes as a function of different strain conditions. Least-squares fits of the phonon-wavenumber shifts against strains have been used to obtain the components of the mode Gr\ufcneisen tensor of quartz (\u2060\u3b3m1 and \u3b3m3\u2060) that can be used to calculate the strains in inclusions directly from the measured Raman shifts. The concept is demonstrated with the example of a natural quartz inclusion in eclogitic garnet from Mir kimberlite and has been validated against direct X-ray diffraction measurement of the strains in the same inclusio

    On regularity and the word problem for free idempotent generated semigroups

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    The category of all idempotent generated semigroups with a prescribed structure E of their idempotents E (called the biordered set) has an initial object called the free idempotent generated semigroup over E, defined by a presentation over alphabet E, and denoted by IG(E). Recently, much effort has been put into investigating the structure of semigroups of the form IG(E), especially regarding their maximal subgroups. In this paper we take these investigations in a new direction by considering the word problem for IG(E). We prove two principal results, one positive and one negative. We show that, for a finite biordered set E, it is decidable whether a given word w ∈ E∗represents a regular element; if in addition one assumes that all maximal subgroups of IG(E) have decidable word problems, then the word problem in IG(E) restricted to regular words is decidable. On the other hand, we exhibit a biorder E arising from a finite idempotent semigroup S, such that the word problem for IG(E) is undecidable, even though all the maximal subgroups have decidable word problems. This is achieved by relating the word problem of IG(E) to the subgroup membership problem in finitely presented groups

    Numerical simulation of atmospheric-pressure 200 kHz / 13.56 MHz dual-frequency dielectric barrier discharges

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    A one-dimensional drift-diffusion model is used to study atmospheric-pressure dual frequency (DF) dielectric barrier discharges in argon using the plasma modelling platform PLASIMO. The simulation exhibits an excellent agreement with the experimental results and gives insight into the DF plasma dynamics e.g. the electric field, the sheath edge profiles, the ionization/excitation rate and the electron energy distribution function (EEDF) profiles. The results indicate that due to the RF oscillation, the electric field, the sheath edge and thus the ionization/excitation are temporally modulated. As a result, the plasma conductivity is enhanced as the plasma density is higher. The discharge development is slowed down with a lower current amplitude and a longer duration. The time-averaged sheath is getting thinner with a more pronounced ionization rate and a longer contacting time near the substrate, which could help to improve the efficiency of plasma-assisted surface processing. In addition, the DF excitation exhibits a capability of modifying the EEDF profiles and controlling the plasma chemical kinetics, which can be applied to the other relevant fields e.g. gas phase chemical conversion.</p
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