The influence of heat treatment on the phase relations in mineral growth systems

ABSTRACT Corundum is one of the most famous gems materials. Different heat treatment methods for enhancement purposes are commonly applied and accepted in the gem market. With this reason, the identification of the natural, unheated corundum is intensively investigated. In this study, aluminium hydroxide minerals and zircon are focused to observe the crystallization and phase change of these minerals during heat treatment procedures. Aluminium hydroxide minerals can be transformed to alumina with the corundum structure by heating. The reaction history of aluminium hydroxide minerals containing corundum was investigated comparing it with diaspore, boehmite, gibbsite and bayerite by TG and DTA methods. These hydroxide minerals were entirely transformed to corundum after heating at 600°C. Zircon inclusions in corundums from Ilakaka, Madagascar, were investigated for the influence of different heat-treatment temperatures on the recovery of their crystalline structure and on possible reactions within and with the host crystals. The host corundum was heated at 500, 800, 1000, 1200, 1400, 1600 and 1800°C. The crystallinity, the trapped pressure, and the decomposition of the zircon inclusions within the host corundum have been investigated by Raman spectroscopy. Radiation-damaged zircon inclusions may be used as an indicator for unheated Ilakaka corundum crystals. They are fully recrystallized after heating at 1000°C influencing the lowering of the 3 Raman band shift, the decreasing of FWHM of the 3 Raman band and the decreasing of the trapped pressure between the inclusion and the host corundum. Under microscopic observation, surface alterations of the inclusions can be firstly seen from transparent into frosted-like appearance at 1400°C. Then, between 1600°C and 1800 °C, the inclusion becomes partly or even completely molten. The decomposition of the zircon inclusion to m-ZrO2 and SiO2-glass phases begins at the rim of the inclusion after heating from 1200°C to 1600°C which can be detected by the surface change, the increase of the 3 Raman band position and the trapped pressure. At 1800°C, the zircon inclusions entirely melt transforming to solid phases during cooling like m-ZrO2 and SiO2-glass accompanied by an increase of pressure between the transformed inclusion and its host.

Structure property relations in complex copolymer systems

A thorough investigation was made of the structure-property relation of well-defined statistical, gradient and block copolymers of various compositions. Among the copolymers studied were those which were synthesized using isobornyl acrylate (IBA) and n-butyl acrylate (nBA) monomer units. The copolymers exhibited several unique properties that make them suitable materials for a range of applications. The thermomechanical properties of these new materials were compared to acrylate homopolymers. By the proper choice of the IBA/nBA monomer ratio, it was possible to tune the glass transition temperature of the statistical P(IBA-co-nBA) copolymers. The measured Tg’s of the copolymers with different IBA/nBA monomer ratios followed a trend that fitted well with the Fox equation prediction. While statistical copolymers showed a single glass transition (Tg between -50 and 90 ºC depending on composition), DSC block copolymers showed two Tg’s and the gradient copolymer showed a single, but very broad, glass transition. PMBL-PBA-PMBL triblock copolymers of different composition ratios were also studied and revealed a microphase separated morphology of mostly cylindrical PMBL domains hexagonally arranged in the PBA matrix. DMA studies confirmed the phase separated morphology of the copolymers. Tensile studies showed the linear PMBL-PBA-PMBL triblock copolymers having a relatively low elongation at break that was increased by replacing the PMBL hard blocks with the less brittle random PMBL-r-PMMA blocks. The 10- and 20-arm PBA-PMBL copolymers which were studied revealed even more unique properties. SAXS results showed a mixture of cylindrical PMBL domains hexagonally arranged in the PBA matrix, as well as lamellar. Despite PMBL’s brittleness, the triblock and multi-arm PBA-PMBL copolymers could become suitable materials for high temperature applications due to PMBL’s high glass transition temperature and high thermal stability. The structure-property relation of multi-arm star PBA-PMMA block copolymers was also investigated. Small-angle X-ray scattering revealed a phase separated morphology of cylindrical PMMA domains hexagonally arranged in the PBA matrix. DMA studies found that these materials possess typical elastomeric behavior in a broad range of service temperatures up to at least 250°C. The ultimate tensile strength and the elastic modulus of the 10- and 20-arm star PBA-PMMA block copolymers are significantly higher than those of their 3-arm or linear ABA type counterparts with similar composition, indicating a strong effect of the number of arms on the tensile properties. Siloxane-based copolymers were also studied and one of the main objectives here was to examine the possibility to synthesize trifluoropropyl-containing siloxane copolymers of gradient distribution of trifluoropropyl groups along the chain. DMA results of the PDMS-PMTFPS siloxane copolymers synthesized via simultaneous copolymerization showed that due to the large difference in reactivity rates of 2,4,6-tris(3,3,3-trifluoropropyl)-2,4,6-trimethylcyclotrisiloxane (F) and hexamethylcyclotrisiloxane (D), a copolymer of almost block structure containing only a narrow intermediate fragment with gradient distribution of the component units was obtained. A more dispersed distribution of the trifluoropropyl groups was obtained by the semi-batch copolymerization process, as the DMA results revealed more ‘‘pure gradient type’’ features for the siloxane copolymers which were synthesized by adding F at a controlled rate to the polymerization of the less reactive D. As with trifluoropropyl-containing siloxane copolymers, vinyl-containing polysiloxanes may be converted to a variety of useful polysiloxane materials by chemical modification. But much like the trifluoropropyl-containing siloxane copolymers, as a result of so much difference in the reactivities between the component units 2,4,6-trivinyl-2,4,6-trimethylcyclotrisiloxane (V) and hexamethylcyclotrisiloxane (D), thermal and mechanical properties of the PDMS-PMVS copolymers obtained by simultaneous copolymerization was similar to those of block copolymers. Only the copolymers obtained by semi-batch method showed properties typical for gradient copolymers.

BCJ-relations in quantum field theory

BCJ-relations have a series of important consequences in Quantum FieldrnTheory and in Gravity. In QFT, one can use BCJ-relations to reduce thernnumber of independent colour-ordered partial amplitudes and to relate nonplanarrnand planar diagrams in loop calculations. In addition, one can usernBCJ-numerators to construct gravity scattering amplitudes through a squaringrn procedure. For these reasons, it is important to nd a prescription tornobtain BCJ-numerators without requiring a diagram by diagram approach.rnIn this thesis, after introducing some basic concepts needed for the discussion,rnI will examine the existing diagrammatic prescriptions to obtainrnBCJ-numerators. Subsequently, I will present an algorithm to construct anrneective Yang-Mills Lagrangian which automatically produces kinematic numeratorsrnsatisfying BCJ-relations. A discussion on the kinematic algebrarnfound through scattering equations will then be presented as a way to xrnnon-uniqueness problems in the algorithm.