Thermodynamic optimization of the PbO–FeO–Fe2O3–SiO2 system

Liquidus phase equilibrium data of the present authors for the PbO–FeO–Fe₂O₃ system at various oxygen potentials, PbO–“Fe₂O₃”–SiO₂ system in air, and PbO–“FeO”–SiO₂ in equilibrium with metallic Pb, combined with phase equilibrium and thermodynamic data from the literature, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases in the PbO–FeO–Fe₂O₃–SiO₂ system. The modified quasichemical model is used for the liquid slag phase. For the liquid phase, the PbO–FeO, PbO–Fe₂O₃, PbO–FeO–Fe₂O₃, PbO–FeO–SiO₂ and PbO–Fe₂O₃–SiO₂ parameters are optimized in the present study. From these model parameters, the optimized ternary phase diagram is back calculated. Present set of parameters describe previous and new experimental data well, and can be used for predictions of the PbO–FeO–Fe₂O₃–SiO₂ phase equilibria over wide ranges of oxygen partial pressured, compositions and temperatures, as well as multicomponent systems.     

Modelling and calculation of the phase diagrams of the LiF–NaF–RbF–LaF3 system

Four ternary phase diagrams of the quaternary system LiF–NaF–RbF–LaF₃ were calculated from the data of LiF–NaF, LiF–RbF, LiF–LaF₃, NaF–RbF, NaF–LaF₃ and RbF–LaF₃ binary phase diagrams using the Kohler symmetric and Kohler–Toop asymmetric approximation. Excess Gibbs parameters of all six mentioned binaries were optimized using the experimental results taken from the literature. For the LiF–RbF system our own data were used. In all cases very good agreement between the experimental data and our optimized values was achieved. Excess Gibbs functions for the liquid phases were obtained using the modified quasi-chemical method based on quadruplet interactions and the excess Gibbs function for the solid solution was calculated by a sublattice model. The quaternary eutectic was determined and a set of pseudo-ternary systems with fixed ratio of LaF₃ was calculated in order to find the optimal composition for a molten salt fuel.     

Thermodynamic optimization of the ZnO–FeO–Fe2O3–SiO2 system

Liquidus phase equilibria experimental data of the present authors for the ZnO–“Fe₂O₃”–SiO₂ system in air, ZnO–“FeO”–SiO₂ in equilibrium with metallic Fe, and ZnO–“FeO”–SiO₂–minor Cu₂O at p(O₂) ~10⁻⁷ … 10⁻⁸ atm (obtained as a part the research on the multicomponent PbO–ZnO–FeO–Fe₂O₃–Cu₂O–CaO–SiO₂ system), combined with phase equilibrium and thermodynamic data from the literature, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases in the ZnO–FeO–Fe₂O₃–SiO₂ system for the whole range of compositions, p(O₂) between ~10⁻¹³ to 1 atm, and temperature range corresponding to liquid slag existence (1150–1700 °C). The modified quasichemical model is used for the liquid slag phase. From these optimized model parameters, the ternary phase diagrams are back calculated. The model based on the present set of parameters is in a good agreement with previous and new experimental data, and can be used for predictions of the ZnO–FeO–Fe₂O₃–SiO₂ phase equilibria over wide ranges of p(O₂), compositions and temperatures, as well as multicomponent systems.     

Data analysis using a geometrical representation of predicate calculus

This paper proposes an approach to database analysis and design, utilizing predicate calculus in the “infospace,” i.e. in the space of the attributes. The difference B₁ − B₂ of two Boolean predicates in the canonical form, B₁ and B₂, is discussed, and a geometrical representation is given in an n-dimensional space. A tabular method is derived to help in query decomposition. The approach is the basis of the “infospatial derivative” (defined by the second author in [47,45,48]), and underlies the “projection-solid infospatial approach” to the decomposition of noncanonical-query retrieval into steps enjoying the consecutive-retrieval property [46,44]. Extension to expert database systems is investigated at the end, through a comparison with other trends: the universal relation, the relation-valued relational approach, and frame algebra.     

Thermodynamic optimization of the binary PbO-“Cu2O”, “Cu2O”-SiO2 and ternary PbO-“Cu2O”-SiO2 systems

Liquidus phase equilibrium data obtained in the recent study by the authors for the binary PbO–“Cu₂O”, “Cu₂O”–SiO₂ and the ternary PbO–“Cu₂O”–SiO₂ systems in equilibrium with metallic Cu or Pb–Cu alloy (as a part of research program on the characterization of the multicomponent PbO–ZnO–FeO–Fe₂O₃–“Cu₂O”–CaO–SiO₂ system), combined with phase equilibrium and thermodynamic data from the literature, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases. The modified quasichemical model is used for the liquid slag phase. From these model parameters, the optimized ternary phase diagram is back calculated. Liquidus surface with cristobalite, tridymite and quartz (SiO₂), two immiscible liquids, cuprite (Cu₂O), lead silicates (PbSiO₃, Pb₂SiO₄, Pb₁₁Si₃O₁₇, Pb₅SiO₇), massicot (PbO) and copper plumbite Cu₂PbO₂ primary phase fields has been constructed. Available experimental data are described within uncertainties. Oxygen partial pressures and distribution of lead between slag and metal have been calculated.     

A thermodynamic analysis of the ti-h system

A partial phase diagram of the Ti-H system has been calculated by combining available thermodynamical and equilibrium solubility data of the system. This was accomplished by applying a two sublattice model to the interstitial solution phases having different lattice ratios. Excluding the position of the eutectoid point and the αsolvus the agreement between the calculated and experimental results is satisfactory. In particular, the assessment of the phase diagram produced optimized parameter values for the titanium-hydrogen and hydrogen-hydrogen interactions as well as an estimate for the lattice stability of the fcc titanium, which together with the sublattice model used are expected to be useful also in the study of multicomponent titanium-hydrogen systems.     

Thermodynamic description of the constitutive binaries of the NaCl-KCl-UCl3-PuCl3 system

Thermodynamic assessment of the constitutive binaries of the NaCl-KCl-UCl₃-PuCl₃ system was carried out by CALPHAD (CALculation of PHase Diagrams) approach. The liquid phase was described by the substitutional solution model, and the intermediate compounds were treated as stoichiometric phases. The thermodynamic parameters of the binary systems were obtained based on experimental phase equilibria data available in the literature and theoretical prediction data by first-principles calculations and empirical equations. A set of self-consistent thermodynamic parameters for each of the binary system was finally obtained. Some representative liquidus surface projections, isothermal sections and pseudo-binary phase diagram for the sub-ternary and quaternary systems were calculated by model extrapolation. The influence of KCl on the thermodynamic behavior of NaCl-UCl₃-PuCl₃ matrix salt was analyzed. The extrapolated results indicated that KCl can be used as a candidate additive component of NaCl-UCl₃-PuCl₃ matrix salt from the point of view of thermodynamics. This study provided a comprehensive understanding for the thermodynamic behavior of a candidate molten salt fast reactor nuclear fuel and a fundament for the design of nuclear fuel.     

Critical thermodynamic evaluation and optimization of the MnO–SiO2–“ TiO2 ”–“ Ti2O3 ” system

A complete review, critical evaluation, and thermodynamic optimization of phase equilibrium and thermodynamic properties of the MnO–SiO₂–“ TiO₂”–“ Ti₂O₃” systems at 1 bar pressure are presented. The molten oxide phase was described by the Modified Quasichemical Model. The Gibbs energies of the manganosite, spinel, pyrophanite and pseudobrookite and rutile solid solutions were taken from the previous study. A set of optimized model parameters for the molten oxide phase was obtained which reproduces all available reliable thermodynamic and phase equilibrium data within experimental error limits from 25 ^°C to above the liquidus temperatures over the entire range of compositions and oxygen partial pressure in the range of pO₂ from 10⁻²⁰ bar to 10⁻⁷ bar. Complex phase relationships in these systems have been elucidated, and discrepancies among the data have been resolved. The database of model parameters can be used along with software for Gibbs energy minimization in order to calculate any phase diagram section or thermodynamic properties.     

A crystallographically consistent optimization of the Zn–Fe system

Crystallographically based sublattice models have been constructed for all intermediate phases in the Zn–Fe system. The parameters of the models describing the Gibbs energies of these phases, as well as LIQUID, BCC, FCC and HCP substitutional solutions, were found by means of the CALPHAD technique. In comparison with the most recent model, the number of coefficients in the expressions for the excess Gibbs energies is significantly reduced. That decrease, however, is accompanied by a greater number of parameters needed in the expressions attributed to the Gibbs energies of end members. An advantage claimed for the present work lies in the models’ improved ability to predict which particular sublattice(s) will be capable of accommodating additional components. This property is of importance for the future extension to the Zn–Fe–Al system, and to other multicomponent systems of relevance to galvanizing and galvannealing practices.     

Modelling the density of Al2O3–CaO–MgO–SiO2 system using the CALPHAD approach

The density of Al₂O₃–CaO–MgO–SiO₂ system is calculated using a model for molar volume. The model is similar to the one used for enthalpy of a multicomponent solution in the CALPHAD approach. The expression for molar volume consists of two terms: one representing the volume contribution from pure components and the other the volume of mixing. The molar volume of mixing takes into account of the binary and the ternary interactions. A total of 565 experimental density data for the constituent unary, binary and ternary systems were collected from the literature. These were used as input to simultaneously optimise the model parameters describing the molar volume, after ensuring that the data belong to a fully molten state. During the optimisation 48 data points that showed significant deviation from the average trend were excluded. The optimised model parameters for the unary, binary and ternary subsystems were used to calculate the density of the quaternary system. The calculated results were compared with experimental data. Finally, it is shown that the volume of mixing of binary systems correlates well with the corresponding enthalpy of mixing.     

Experimental determination and thermodynamic optimization of the CuCl–ZnCl2, ZnCl2–FeCl3, CuCl–FeCl3, CuCl–CuCl2, FeCl2–FeCl3, FeCl2–CuCl2 and CuCl–PbCl2 phase equilibria

In copper flash smelting, flue dust causes corrosion problems in the heat recovery boiler of the gas train due to formation of dust accretions on the boiler walls. Within these, presence of heavy metal chlorides results in formation of molten salt deposits causing rapid corrosion. CuCl–ZnCl₂, FeCl₃–ZnCl₂ and CuCl–FeCl₃ systems were studied experimentally by equilibration-quenching, scanning electron microscopy and energy-dispersive X-ray spectroscopy in order to evaluate melting behaviour of these chlorides, typically present in the corrosive dust deposits. In addition, CuCl–PbCl₂, CuCl–CuCl₂, FeCl₂–FeCl₃ and CuCl₂–FeCl₂ phase diagrams were optimized incorporating and evaluating all available phase diagram and thermodynamic data on the systems. The modified quasi-chemical model was used to describe the thermodynamic properties of molten phases and compound energy formalism was used to model the terminal solid solutions. The calculated phase diagrams are presented and compared with experimental observations as well as with all available phase diagram data from existing literature.     

A critical thermodynamic assessment of the Mg–Ni, Ni–Y binary and Mg–Ni–Y ternary systems

A thorough review and critical evaluation of phase equilibria and thermodynamic data for the phases in the Mg–Ni–Y ternary system have been carried out over the entire composition range from room temperature to above the liquidus. This system is being modeled for the first time using the modified quasichemical model which considers the presence of short range ordering in the liquid. The Gibbs energies of the different phases have been modeled, and optimized model parameters that reproduce all the experimental data simultaneously within experimental error limits have been obtained. For the liquid phases, the modified quasichemical model is applied. A sublattice model within the compound-energy formalism is used to take proper account of the structures of the binary intermediate solid solutions. The Mg–Ni and Ni–Y binary systems have been re-optimized based on the experimental phase equilibrium and thermodynamic data available in the literature. The optimized thermodynamic parameters for the Mg–Y system are taken from the previous thermodynamic assessment of the Mg–Cu–Y system by the same authors. The constructed database has been used to calculate liquidus projection, isothermal and vertical sections which are compared with the available experimental information on this system. The current calculations are in a good agreement with the experimental data reported in the literature.     

On the abilities and limitations of the linear,exponential and combined models to describe the temperature dependence of the excess Gibbs energy of solutions

In this paper the performance of the linear, exponential and combined models to describe the temperature dependence of the excess Gibbs energy of solutions in the framework of the Redlich–Kister model is discussed. The models are not compared to existing Calphad optimized databases, rather they are tested against the 209 binary solid and liquid metallic alloys, for which reliable experimental data exist on the heat of mixing and Gibbs energy of mixing in the handbook of Predel. It was found that the linear model often leads to high-T artifact (artificial inverted miscibility gaps) and the excess Gibbs energy approaches infinity at high temperatures, which seems unreasonable. It was also found that although both the exponential and combined models can in principle lead to low-T artifact (liquid re-stabilization), in real systems it probably does not take place, at least for the “normal” systems (a system is “normal”, if the heat of mixing, excess entropy of mixing and excess Gibbs energy of mixing have the same sign at the temperature of measurement; 86% of all systems are found “normal”). The problem with the exponential model is that it is unable to describe the “exceptional” systems (14% of all systems). It is shown that the combined model is able to describe also these “exceptional” systems, as well. An algorithm is worked out to ensure that the combined model does not run into any high-T or low-T artifact, even when it is used to describe the “exceptional” systems. It is concluded that the T-dependence of the interaction energies for all solution phases described by the Redlich–Kister polynomials should be described by the combined model. In this way an improved databank on excess Gibbs energies of solution phases can be gradually built, not leading to any artifact.     

An extension of the inverse method to probabilistic timed automata

Probabilistic timed automata can be used to model systems in which probabilistic and timing behaviour coexist. Verification of probabilistic timed automata models is generally performed with regard to a single reference valuation π ₀ of the timing parameters. Given such a parameter valuation, we present a method for obtaining automatically a constraint K ₀ on timing parameters for which the reachability probabilities (1) remain invariant and (2) are equal to the reachability probabilities for the reference valuation. The method relies on parametric analysis of a non-probabilistic version of the probabilistic timed automata model using the “inverse method”. The method presents the following advantages. First, since K ₀ corresponds to a dense domain around π ₀ on which the system behaves uniformly, it gives us a measure of robustness of the system. Second, it allows us to obtain a valuation satisfying K ₀ which is as small as possible while preserving reachability probabilities, thus making the probabilistic analysis of the system easier and faster in practice. We provide examples of the application of our technique to models of randomized protocols, and introduce an extension of the method allowing the generation of a “probabilistic cartography” of a system.     

A consideration on motion‐image‐quality improvement of LCDs and video systems

Abstract— The motion image quality of video systems with hold‐type displays, such as LCDs or OLEDs, were studied with regard to dynamic spatial frequency response and data from subjective evaluations on motion blur. The system parameters of motion image quality, or frame rate (F) and temporal aperture (A^t), were investigated and their required values were derived. A smaller temporal aperture and/or higher frame rate can improve the dynamic response and motion image quality, but the parameters required in order to maintain a good dynamic response for high motion image velocity seems very difficult to implement, such as a frame rate of 900 Hz. Therefore, the performance goal of video systems is set on “limit of acceptance” for motion image quality, as a compromise. An equation or the relational expression between motion image velocity and required parameter values is derived based on dynamic response and data from subjective evaluations found in published studies. Possible examples of parameter sets are obtained from the equation. Those are (F = 300 Hz, A_t = 5/6), (F = 240 Hz, A_t = 2/3), (F = 120 Hz, A_t = 1/3), and (F > 360 Hz, A_t = 1).     

Coupled experimental study and thermodynamic modeling of the MnO-Mn2O3-Ti2O3-TiO2 system

A coupled experimental study and thermodynamic modeling of the MnO-Mn₂O₃-Ti₂O₃-TiO₂ system at 1 bar total pressure is presented. Classical equilibration and quenching experiments followed by the phase analysis using electron probe microanalysis (EPMA) and X-ray diffraction (XRD) were employed to obtain equilibrium compositions of the liquid and solid solutions in air. The molten oxide phase was described by using the Modified Quasichemical Model which considers short-range ordering, and the Gibbs energies of the solid solutions (pseudobrookite, ilmenite and spinel) were described using the Compound Energy Formalism based on their crystal structures. A set of optimized model parameters of all phases was obtained, which reproduces all available and reliable thermodynamic data and phase diagrams within experimental error limits from 298 K (25 °C) to above the liquidus temperatures over the entire range of composition under oxygen partial pressures from metallic saturation to 1 bar. The complex phase relationships in the system have been elucidated and discrepancies among the experimental data have been resolved. The database of the model parameters can be accessed by FactSage software with the Gibbs energy minimization to calculate any phase diagrams and thermodynamic properties of the MnO-Mn₂O₃-Ti₂O₃-TiO₂ system.     

Thermodynamics and Phase Diagram of the Salt Lake Brine System at 25°C I. Li+, K+, Mg2+/Cl−, SiO42−, -H2O System

Most salt lakes on Qinghai-Xizang Plateau belong to “Salt Lake Brine System” Li⁺,Na⁺,K⁺,Mg²⁺/Cl⁻,SO₄²⁻,borate—H₂O. The system has high concentrations of lithium and boron and is different from the classical sea-water system. The investigation of the system is of theoretical and practical importance.The Pitzer ion interaction model for aqueous electrolytes has been used to describe the thermodynamics and phase equilibria of the salt brine system. Experimental studies of phase diagrams and thermodynamics for its many subsystems (ternary, quaternary and quinary) were performed. All the necessary parameters for the modeling the system were fitted by using a least-square analysis program thermodynamic and solubility data determined by us and those in literature. Finally, a prediction of solubilities for various systems was made. Calculated and experimental phase equilibrium for the system Li⁺, K⁺, Mg²⁺/Cl⁻,SO₄²⁻ — H₂O are presented for comparison in this paper.