Theoretical Aspects of Structure, Electronic, Optical and Elastic Properties of Ca(1-X)Cxse Mixed Alloys in Binary and Ternary Phases for Consideration
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Download This Paper Open PDF in Browser Add Paper to My Library Share: Permalink Using these links will ensure access to this page indefinitely Copy URL Copy DOITwo algorithms for evaluating liquid−liquid equilibria (LLE) for binary and ternary polymer solutions are presented. The binary algorithm provides the temperature versus concentration cloud-point curve at fixed pressure, whereas the ternary algorithm provides component 1 versus component 2 concentration coexistence curves at fixed pressure and temperature. The algorithms automatically trace the entire liquid−liquid coexistence curves in steps by adjusting the step size, generating initial estimates, and subsequently solving the phase-equilibrium problem by a second-order method. The algorithms are used for investigating the correlative and predictive capabilities of the thermodynamic model PC-SAFT. The investigation shows that the model correlates well experimental LLE data for binary as well as ternary systems but further predicts the behavior of the ternary systems with reasonably good accuracy, even by using interaction parameters obtained from binary vapor−liquid equlibrium data.
Component (thermodynamics)
Ternary numeral system
Liquid liquid
TRACE (psycholinguistics)
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Abstract Ternary vapor compositions have been successfully calculated from total‐pressure measurements for four systems by means of a modified direct method, which involves the previously proposed concept of hypothetical binary mixtures, and permits the numerical integration using a simple P‐x relationship. The results of the systems tested further indicate that the ternary y values predicted from only binary P‐x data are not significantly different from the y values obtained when binary together with ternary P‐x values were used in the calculation, provided that the initial fit of binary P‐x data is successful.
Ternary numeral system
Binary data
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Utilizing a general equation in which pitch in a mixture of liquid crystals is a quadratic function of the number densities of component molecules of given molecular twisting powers, we treat two special cases: binary cholesteric mixtures and a ternary mixture of two cholesteric and one nematic compounds. Experimental data are shown to be adequately described by the equation over the entire concentration range.
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An attempt was made on applying the Wilson equation to predict the thermodynamic properties of ternary liquid alloys. The activity of each component in ternary liquid alloys was found to be conveniently calculated from the equation with the related binary bimolecular interaction parameters. The calculated values are in fair agreement with experimental data, and are verified to be reliable by the criterion of classical thermodynamics.
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Abstract Computer programs in use in our laboratory for the calculation of binary and ternary copolymerization behavior are reviewed. In the case of binary copolymerization an analytical equation is available, allowing rapid and precise calculations of various parameters of interest. In the case of ternary and higher component systems numerical methods of integration are required. The application of the Runge‐Kutta method to ternary copolymerization systems is outlined. Examples and some of the difficulties encountered with both systems are presented.
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This paper provides the first rigorous derivation of a binary-ternary Boltzmann equation describing the kinetic properties of a dense hard-spheres gas, where particles undergo either binary or ternary instantaneous interactions, while preserving momentum and energy. An important challenge we overcome in deriving this equation is related to providing a mathematical framework that allows us to detect both binary and ternary interactions. Furthermore, this paper introduces new algebraic and geometric techniques in order to eventually decouple binary and ternary interactions and understand the way they could succeed one another in time.
Hard spheres
Momentum (technical analysis)
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This paper provides the first rigorous derivation of a binary-ternary Boltzmann equation describing the kinetic properties of a dense hard-spheres gas, where particles undergo either binary or ternary instantaneous interactions, while preserving momentum and energy. An important challenge we overcome in deriving this equation is related to providing a mathematical framework that allows us to detect both binary and ternary interactions. Furthermore, this paper introduces new algebraic and geometric techniques in order to eventually decouple binary and ternary interactions and understand the way they could succeed one another in time.
Hard spheres
Momentum (technical analysis)
Lattice Boltzmann methods
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Component (thermodynamics)
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Nanocrystalline material
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