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Constant Volume (constant + volume)
Selected AbstractsEquilibrium and growth shapes of crystals: how do they differ and why should we care?CRYSTAL RESEARCH AND TECHNOLOGY, Issue 4-5 2005Robert F. SekerkaArticle first published online: 15 MAR 200 Abstract Since the death of Prof. Dr. Jan Czochralski nearly 50 years ago, crystals grown by the Czochralski method have increased remarkably in size and perfection, resulting today in the industrial production of silicon crystals about 30 cm in diameter and two meters in length. The Czochralski method is of great technological and economic importance for semiconductors and optical crystals. Over this same time period, there have been equally dramatic improvements in our theoretical understanding of crystal growth morphology. Today we can compute complex crystal growth shapes from robust models that reproduce most of the features and phenomena observed experimentally. We should care about this because it is likely to result in the development of powerful and economical design tools to enable future progress. Crystal growth morphology results from an interplay of crystallographic anisotropy and growth kinetics by means of interfacial processes and long-range transport. The equilibrium shape of a crystal results from minimizing its anisotropic surface free energy under the constraint of constant volume; it is given by the classical Wulff construction but can also be represented by an analytical formula based on the ,-vector formalism of Hoffman and Cahn. We now have analytic criteria for missing orientations (sharp corners or edges) on the equilibrium shape, both in two (classical) and three (new) dimensions. Crystals that grow under the control of interfacial kinetic processes tend asymptotically toward a "kinetic Wulff shape", the analogue of the Wulff shape, except it is based on the anisotropic interfacial kinetic coefficient. If it were not for long range transport, crystals would presumably nucleate with their equilibrium shape and then evolve toward their "kinetic Wulff shape". Allowing for long range transport leads to morphological instabilities on the scale of the geometric mean of a transport length (typically a diffusivity divided by the growth speed) and a capillary length (of the order of atomic dimensions). Resulting crystal growth shapes can be cellular or dendritic, but can also exhibit corners and facets related to the underlying crystallographic anisotropy. Within the last decade, powerful phase field models, based on a diffuse interface, have been used to treat simultaneously all of the above phenomena. Computed morphologies can exhibit cells, dendrites and facets, and the geometry of isotherms and isoconcentrates can also be determined. Results of such computations are illustrated in both two and three dimensions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Compositional constraints on the equation of state and thermal properties of the lower mantleGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2001Frank D. Stacey SUMMARY By extrapolating the lower mantle equation of state (EoS) to P=0, T=290 K, we determine the EoS parameters that are compatible with a mixture of (Mg, Fe)SiO3 perovskite (with a small admixture of Al2O3), (Mg, Fe)O magnesiowüstite and CaSiO3 perovskite in arbitrary proportions and with arbitrary Fe/(Fe+Mg) ratio. The parameters fitted are density, ,, adiabatic incompressibility, KS, and its pressure derivative, K,S,(,KS/,P)S. The first stage is adiabatic extrapolation to P=0, T=T0, that is, to the foot of the lower mantle adiabat, at which K,0(T0) is allowed to have any value between 3.8 and 4.6, and 1500 K,T0,2000 K. It is important to use an equation for which the lower mantle fitting does not prescribe K,0(T0) and this rules out the third-order Birch theory, which gives a seriously wrong value. The further extrapolation to 290 K at P=0 uses thermodynamic relationships with maximum generality, allowing all of the following thermoelastic parameters to be arbitrary functions of temperature: K;,; Grüneisen parameter, ,;q=(, ln ,/, ln V)T, where V is volume; volume coefficient of thermal expansion, ,; adiabatic Anderson,Grüneisen parameter, ,S=(1/,) (, ln KS/,T)P; and the mixed P, T derivative (,K,S/,T)P. The heat capacity at constant volume, CV, is assumed to follow the Debye function, so , is controlled by that. The temperature dependences of the dimensionless parameters ,, q and ,S at P=0 are slight. We find , to be precisely independent of T at constant V. The parameter dK,0/dT increases strongly with T, as well as with the assumed value of K,0(T0), where K,0 is K,S at P=0. The fitting disallows significant parameter ranges. In particular, we find solutions only if K,0(T0),4.2 and the 290 K value of K,0 for Mg perovskite is less than 3.8. Conclusions about composition are less secure, partly because of doubt about individual mineral properties. The volume of magnesiowüstite is found to be between 10 and 25 per cent for respective T0 values of 2000 and 1500 K, but the Ca-perovskite volume is no more than 6 per cent and has little influence on the other conclusions. The resulting overall Fe/(Fe+Mg) ratio is 0.12 to 0.15. Although this ratio is higher than expected for a pyrolite composition, the ratio depends critically on the assumed mineral densities; some adjustment of the mineral mix may need to be considered. [source] Deformation, mass transfer and mineral reactions in an eclogite facies shear zone in a polymetamorphic metapelite (Monte Rosa nappe, western Alps)JOURNAL OF METAMORPHIC GEOLOGY, Issue 2 2004L. M. Keller Abstract This study analyses the mineralogical and chemical transformations associated with an Alpine shear zone in polymetamorphic metapelites from the Monte Rosa nappe in the upper Val Loranco (N-Italy). In the shear zone, the pre-Alpine assemblage plagioclase + biotite + kyanite is replaced by the assemblage garnet + phengite + paragonite at eclogite facies conditions of about 650 °C at 12.5 kbar. Outside the shear zone, only minute progress of the same metamorphic reaction was attained during the Alpine metamorphic overprint and the pre-Alpine mineral assemblage is largely preserved. Textures of incomplete reaction, such as garnet rims at former grain contacts between pre-existing plagioclase and biotite, are preserved in the country rocks of the shear zone. Reaction textures and phase relations indicate that the Alpine metamorphic overprint occurred under largely anhydrous conditions in low strain domains. In contrast, the mineralogical changes and phase equilibrium diagrams indicate water saturation within the Alpine shear zones. Shear zone formation occurred at approximately constant volume but was associated with substantial gains in silica and losses in aluminium and potassium. Changes in mineral modes associated with chemical alteration and progressive deformation indicate that plagioclase, biotite and kyanite were not only consumed in the course of the garnet-and phengite-producing reactions, but were also dissolved ,congruently' during shear zone formation. A large fraction of the silica liberated by plagioclase, biotite and kyanite dissolution was immediately re-precipitated to form quartz, but the dissolved aluminium- and potassium-bearing species appear to have been stable in solution and were removed via the pore fluid. The reaction causes the localization of deformation by producing fine-grained white mica, which forms a mechanically weak aggregate. [source] Experimental and theoretical study of the influence of pressure on SCWOAICHE JOURNAL, Issue 11 2006M. D. Bermejo Abstract It is well known that pressure is an important parameter in the SCWO process, because it produces changes in the phase behavior and thermodynamics properties of the system. The influence of pressure on the oxidation efficiency of feeds containing isopropyl alcohol as fuel and acetic acid as waste was studied in an autothermal adiabatic transpiring wall reactor at pilot-plant scale, at pressures from 13 to 25 Mpa, and temperatures from 600 to 750°C. It was found that reaction temperature decreased between 40 and 100°C, when pressure was lowered, and, subsequently TOC removal decreased. At higher-temperatures, the decreasing of TOC removal due to pressure difference was reduced. The process was simulated at different pressures using a mathematical model previously developed for the reactor. The Anderko-Pitzer EoS, especially developed for aqueous systems at high-temperatures and pressures, was used to have accurate values of the heat capacities of the reaction mixture. It was found that having into account only the effect of pressure in the thermodynamical properties and in the concentration of the reagents, the experimental results could not be explained. Thus, the influence of the pressure in the reaction rate equation had to be considered. Results were qualitatively reproduced considering the reaction rate constant variable with pressure, using a constant volume of activation of ,1400 cm3/mol. © 2006 American Institute of Chemical Engineers AIChE J, 2006 [source] Optimization of cure kinetics parameter estimation for structural reaction injection molding/resin transfer moldingPOLYMER COMPOSITES, Issue 6 2001Robert J. Duh A numerical method is proposed for polymer kinetic parameter estimation of either Structural Reaction Injection Molding (SRIM) or Resin Transfer Molding (RTM). The method simulates either radial flow or axial flow of reactive resins through a fiber preform inside a mold cavity. This method considers a non-isothermal environment with different inlet boundary conditions. Based on the molding conditions, this method can find the best values of chemical kinetic parameters by comparing the simulated temperature history and the experimental temperature history. Since the kinetic parameters are estimated with the real molding conditions, the simulations using these parameter values can have better agreement with molding data than those parameters which are obtained from idealized conditions such as Differential Scanning Calorimeter (DSC). The optimization approach was verified by estimating kinetics parameters for RTM data available in the literature. Temperatures predicted by the optimized kinetics parameters are compared with experimental data for two different molding conditions: injection of a thermally activated resin into a radial mold under constant pressure flow, and injection of a mix activated resin into a radial mold under constant volume. In both cases, the optimized kinetics parameters fit the temperature data well. [source] Chromogenic polymer gels for reversible transparency and color control with temperature at a constant volumePOLYMERS FOR ADVANCED TECHNOLOGIES, Issue 7 2002A. Seeboth Abstract The preparation and characterization of novel chromogenic materials has developed extremely rapid in the last years. Among them, thermotropic and thermochromic polymer gel networks have met with growing interest, because of their advanced properties. These novel polymer gels exhibit pronounced changes in transparency and/or color intensity in a practically relevant temperature range. For many future technical applications it is an essential condition, that the volume of the used gel materials is independent of temperature. A current overview of this field is given. Copyright © 2002 John Wiley & Sons, Ltd. [source] | |||||||||||||