MOLTEN SALT PHASE DIAGRAMS CALCULATION USING ARTIFICIAL NEURAL NETWORK OR PATTERN RECOGNITION-BOND PARAMETERS PART 3.ESTIMATION OF LIQUIDUS TEMPERATURE AND EXPERT SYSTEM

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Calculations of phase diagrams in associated solution model

The development of an ideal associated solution model concerned with complexes of various compositions, sizes, and shapes is described. Such models were used earlier to calculate thermodynamic characteristics and the position of the liquidus line for binary eutectic systems as well as those having a stable compound in the solid phase. In all the cases, the model parameters were not adjusted but were estimated from melting temperatures of the components. The latest studies deal with the influence of arbitrary stoichiometry associates on the equilibrium thermodynamic properties of liquid alloys. The application of the model to eutectic systems and systems having an unlimited miscibility in solid and liquid states close to the liquidus has been considered. It was shown that if the difference in melting temperatures of the components was small, different types of fusibility diagrams were possible: eutectic diagrams, cigar-shaped diagrams, or diagrams with upper or lower azeotropic points. Peritectic transformations could take place if the difference in melting temperatures of the components were large.     

DETERMINATION OF PrCl_3-NaCl-LiCl PHASE DIAGRAM

PrCl_3-NaCl-LiCl phase diagram has been constructed from the phase diagrams of itssub-binary systems and of six quasi-binary systems measured by DTA technique.It is foundthat this ternary system is composed of five liquidus surfaces,seven second crystallizationlines,two peritectic points and one eutectie point.The temperatures and compositions ofinvariant points are as follows:P_1(416℃,30.3 mol% NaCl,44.2 mol% LiCl,25.5 mol%PrCl_3);P_2(409℃,25.0 mol% NaCl,50.0 mol% LiCl,25.0 mol% PrCl_3);E(404℃,20.0mol% NaCl,55.4 mol% LiCl,24.6 mol% PrCl_3).     

Phase diagram features associated with multicritical points in alloy systems

Many features in the vicinity of critical points in phase diagrams can be illustrated using a Landau-type free energy expansion as a power series in one or more order parameters and composition. This simple approach can be used with any solution model. It also predicts limits to metastability and is useful for understanding mechanisms of phase change. The theory is applied to all the critical points that can occur in binary systems according to a Landau theory: critical consolute points, order-disorder transitions, tricritical points, critical end points, as well as systems in which two transitions such as chemical and magnetic ordering occur.     

High Entropy Alloys,Miscibility Gaps and the Rose Geometry

Recent review articles on high entropy alloys (HEAs) provide little information about miscibility gaps in multicomponent systems, especially about how to respond with alloying should they be found. Also, there is a lack of information about how miscibility gaps might appear on calculated or measured multicomponent phase diagrams. In this work concepts concerning miscibility gaps that form in binary and ternary systems are reviewed. Then the work is extended to alloys with more components including HEAs. The previous work predicts that there are significant differences between binary systems and those with three or more components. For example, miscibility gaps do not form in binary systems that have a negative heat of mixing, but they do form in ternary systems. Also, ternary systems with a positive heat of mixing can have their stability temperature lowered by adding ternary components that add positive heats of mixing. The morphology and topology of multicomponent/multiphase miscibility gaps differ from typical phase diagrams, as well. For example, one type of miscibility gap is said to have the rose geometry, because of its floral design. Normally only 2-phase miscibility gaps can form in binary and ternary systems. However using the Graph Method it is suggested that 3-phase miscibility gaps might form in HEA systems, even while trying to avoid them. A conclusion of this investigation is that with additional computational and experimental work it may be possible to expand the boundaries of where HEAs can be found.     

Nonequilibrium Lever Principle and New Type of Dynamic Phase Diagrams for Si2Mn-Type Steel

A new type of dynamic phase diagrams for spring steels of the Si2Mn type is presented and a formula is suggested for describing the lever principle as applied to such diagrams. The structure and chemical composition of the studied steels are analyzed.     

从三元混合气氛腐蚀相图到四元热腐蚀相图

三元混合气氛腐蚀相图和四元热腐蚀相图的计算具有相通性。三元体系中,将一凝聚相视为由单质金属和气相中两个组元反应生成,而在四元体系内把凝聚相设为由单质金属、Na-O-S体系中一凝聚相和气相中的两个组元反应而成。通过其反应自由能的变化来衡量判断相图中凝聚相西两组合的平衡线和叁叁组合的三相点。     

Development of databases and generation of stability diagrams pertaining to the modelling of processes during hot corrosion of heat exchanger components

The purpose of the project “Optimisation of In‐Service Performance of Boiler Steels by Modelling High Temperature Corrosion” (G5RD‐CT‐2001‐00593, acronym OptiCorr) was to establish a set of focused procedures, both in terms of applications of thermochemical standard software and in terms of dedicated new developments, which enable a user to investigate the behaviour of boiler components based on the application of rigorous thermodynamics. Thermodynamic databases which cover the materials involved had to be compiled and assessed in order to be able to apply the appropriate software. Particular new results coming from the databases work will be highlighted. The results of phase equilibrium calculations are shown in appropriate diagrams and compared with published experimental data. The thermochemical standard software FactSage permits the investigation of stoichiometric reactions, complex equilibria and phase diagrams. These calculational capabilities have been applied for the purposes of investigation of (1) the composition of complex combustion gases, (2) metal‐gas interactions and (3) metal‐gas‐molten salt interactions, since these have been established to be the key points for the understanding of the corrosion of heat exchanger components. Selected results from these calculations will be demonstrated and discussed. Application specific software has been developed using the approach of local chemical equilibrium calculated by the programmer's library ChemApp and the add‐in ChemSheet for Microsoft EXCEL™. Two key processes have been treated: The internal corrosion of the metallic material by diffusion of gases and metals and local phase formation as well as the corrosion of heat exchanger material under a molten salt layer which is in contact with an outer gas phase. The general principles of the code development will be outlined while the details of the programs are given in separate presentations in this volume.     

Computation of Eutectic Concentrations and Temperature in Two-Component and Multicomponent Systems

The initial data for computation of eutectic temperature in two-component and multicomponent systems are the form of the binary phase diagrams and the melting temperatures of the components of the eutectic. The eutectic components can be pure elements, chemical compounds, or solid solutions with ultimate solubility. In salt systems these are oxides, salts, or their complexes. Statistical analysis of some phase diagrams of binary, ternary, and other multicomponent systems makes it possible to formalize the interrelation between the eutectic temperature and the melting temperature of eutectic components. The dependences obtained have been used for developing methods of direct and successive computation of eutectic temperature and concentration in two-component and multicomponent systems. In order to reduce the error the elements and their compounds have been classified according to the electron structure and physicochemical properties in accordance with the Periodic System. The methods developed have been used for determining the temperature and concentration conditions of a boronizing process ensuring a liquid crystal state of treated surfaces at saturation temperatures with the aim of formation of pseudoeutectic structures of boronized layers on nickel alloys and high-speed steels.     

Computer generation of binary and ternary phase diagrams via a convex hull method

A rapid computational technique for determining equilibrium phase diagrams of multicomponent systems by constructing the convex hull of the free energy surface is introduced. Rather than calculating tangent lines or planes, this method guarantees a convex representation of the equilibrium free energy surface on a discrete set of points in composition space. Although the accuracy of these phase diagrams is limited by the spacing of points, there are no restrictions on the number or types of free energy functions that may be considered; functions with singular or unknown derivatives may even be used. This method is then applied to generate several model binary and ternary phase diagrams. This paper was presented at the International Phase Diagram Prediction Symposium sponsored by the ASM/MSD Thermodynamics and Phase Equilibria Committee at Materials Week, October21–23,1991, in Cincinnati, Ohio. The symposium was organized by John Morral, University of Connecticut, and Philip Nash, Illinois Institute of Technology.     

由三元相图计算活度

采用熔化自由能法、标准生成自由能法和化学平衡法推导出利用8种类型的三元相图计算活度的公式,覆盖了三元相图的点、线、面全部范围。公式本身没有引进假设和近似。这8种类型的三元相图涵盖了有液相面各种类型的三元相图。本研究的计算方法和计算公式可以应用于各种复杂的三元相图,该方法也可以推广到三元等温截面相图和三元以上的多元相图。     

The construction of isothermal quaternary phase diagrams of the Na-M-O-S type for hot corrosion applications

This paper presents a computer program for the calculation of the isothermal phase diagrams of quaternary systems involving sodium, a pure metal, oxygen and sulfur, which are useful for examining the experimental results concerning the hot corrosion of metallic materials. The procedures adopted to calculate the location of the points where four condensed phases are simultaneously present (quadruple points) and to draw the regions of stability of each phase containing the metal are presented by means of examples concerning a practical system. The nature of these quaternary phase diagrams is examined with reference to the various types of quadruple points and to their interconnections with lines of equilibrium involving the participation of three different phases. Examples of phase diagrams of some quaternary systems calculated by means of the present program are given.     

Relationship between the types of binary alloy phase diagrams of VIII and IB group elements and the Mendeleev numbers

The relationship between the types of binary alloy phase diagrams of Vlll and IB group elements and the Men deleev numbers was discussed for the first time using the Vlll and IB group elements as solvent metals (A) and the other elements as solute metals (B), basesd on their alloy phase diagram types. The Mendeleev numbers of the solvent metals and the solute metals were expressed as Ma and MB, respectively. A two-dimension map of MdMB was drawn. It is indicated that there is an oblique line in the map, which divides the binary alloy phase diagram types of solvent metals into two symmetry parts, the phase diagram types of the other elements with solvent metals located at the above or down of the line respectively, while on the line, AM= 0. The phase diagrams between the solvent metals basically are simple systems, mainly belong to the types of continues solid solution and the peritectic (about 40% for each type). The solvent metals can be divided into three groups: Co, Ir, Rh, Ni, Pt, and Pd as the first group; Ag, Au, and Cu as the second group;and Fe, Os, and Ru as the third group. The characteristics of the phase diagrams formed between the elements in each group were discussed. About 80% phase diagrams belong to complex systems and less than 20% belong to the simple systems. The regular variation of the chemical scale, the metallic radii of the atoms, the number of valence electrons, and the first ionization energy with the Mendeleev numbers and the crystal structure were introduced as well.     

Gibbs’ phase rule applied to phase diagrams and transformations

The phase rule is derived using only potentials as variables. It is then modified in order to apply to phase diagrams obtained by sectioning and by introducing molar quantities as variables. When modified for constant composition, the phase rule takes its original form but now applies only when the predicted variance is 2 or less. When the composition is kept constant, one must consider compositional constraints, but this is not necessary when potential variables are considered. The character of a phase transformation can be studied by considering the character of the corresponding one-di-mensional phase diagram.     

Computational thermodynamic model for the Mg−Al−Y system

The ternary Mg−Al−Y system was thermodynamically modeled based on the optimization of the binary subsystems Mg−Al, Mg−Y, and Al−Y using the CALPHAD approach. Mg−Al data was taken from the COST507 database, whereas the other two binary systems were reoptimized in this work. The liquid phase was described by a Redlich-Kister polynomial model, and the intermediate solid solutions were described by a sublattice model. Ternary interaction parameters were introduced to enable the best representation of the experimental data while considering the occurrence of the ternary compound Al₄MgY. The constructed database is used to calculate and predict thermodynamic properties, binary phase diagrams of Al−Y and Mg−Y, and liquidus projections of the ternary Mg−Al−Y. The calculated phase diagrams and the thermodynamic properties are in good agreement with the corresponding experimental data from the literature. Sixteen ternary four-phase-equilibria invariant points were predicted in the Mg−Al−Y system: seven ternary eutectic points, eight ternary quasi peritectic points, and one ternary peritectic point. Further, fifteen three-phase-equilibria in variant points were determined: eight saddle points and seven binary eutectic points.     

An Approximate Analysis of the External Oxidation of Ternary Alloys Forming Insoluble Oxides. I: High Oxidant Pressures

The general properties of the isothermal thermodynamic phase diagrams for ternary A–B–C alloys exposed to a single oxidant at high temperatures are examined, assuming, for simplicity, the formation of insoluble p-type oxides, an ideal behavior of the alloy, and a common value of the self-diffusion coefficient for the alloy components, independent of the alloy composition, but disregarding the possibility of internal oxidation. Simplified two-dimensional phase diagrams are produced by projecting the lines and points of equilibrium of the complete three-dimensional diagrams on the base triangle, which gives the composition of the system in terms of the metal components only. Similar kinetics diagrams concerning the nature and the growth kinetics of the scales formed on ternary alloys as functions of the bulk substrate composition are also calculated for oxidant pressures above the stability of the oxides of all the alloy components and some of their general features are examined. The kinetics diagrams for ternary alloys exposed to a single oxidant contain seven regions, three of which correspond to the areas of stability of each single oxide, three to the possible mixtures of two oxides, and one to a mixture of all three oxides.     

Thermodynamics of constrained and unconstrained equilibrium systems and their phase rules

The two types of phase equilibria, the normal unconstrained one and the constrained one, and their thermodynamics are discussed. The concepts of potential and phase rule, which have recently been discussed in the literature, are reconsidered, and their formal definitions are analyzed in some detail. It is realized that in the unconstrained equilibrium system, the properly defined chemical potentials of all components must be constant across the phase interface in both the hydrostatically and nonhydrostatically stressed systems. It is demonstrated that in a constrained equilibrium system, e.g. with a coherent equilibrium or paraequilibrium, the discussion of the phase rule is rather meaningless even though it is possible to find a relationship between the number of independent potentials and phases. On the other hand, a constrained equilibrium system may be treated as a normal equilibrium by describing its equilibrium features with a different definition of the system.     

Gibbs Energy of Formation of Ca3Ti8Al12O37 and Phase Relations and Chemical Potentials in the System Al2O3-TiO2-CaO

The quaternary oxide in the system Al₂O₃-CaO-TiO₂ is found to have the composition Ca₃Ti₈Al₁₂O₃₇ rather than CaTi₃Al₈O₁₉ as reported in the literature. The standard Gibbs energy of formation of Ca₃Ti₈Al₁₂O₃₇ from component binary oxides is measured in the temperature range from 900 to 1250?K using a solid-state electrochemical cell incorporating single crystal CaF₂ as the solid electrolyte. The results can be represented by the equation: $$ \Updelta G_{\text{f(ox)}}^{\text{o}} ( \pm 70)/{\text{J}}\,{\text{mol}}^{ - 1} = - 248474 - 15.706(T/{\text{K}}). $$ Combining this information with thermodynamic data on calcium aluminates and titanates available in the literature, subsolidus phase relations in the pseudo-ternary system Al₂O₃-CaO-TiO₂ are computed and presented as isothermal sections. The evolution of phase relations with temperature is highlighted. Chemical potential diagrams are computed at 1200?K, showing the stability domains of the various phases in the chemical potential-composition space. In each chemical potential diagram, chemical potential of one component is plotted against the cationic fraction of the other two components. The diagrams are valid at relatively high oxygen potentials where Ti is present in its four-valent state in all the oxide phases.     

Modern thermodynamics in CVD of hard materials

The diamond growth together with the graphite etching under low pressure had often been regarded as a “thermodynamic paradox” maybe “violating the second law of thermodynamics”, since the success of the activated chemical vapor deposited (CVD) diamond processes in 1970. After quantitative verification of reaction coupling, a series of nonequilibrium phase diagrams for the activated diamond processes have been quantitatively calculated. These nonequilibrium phase diagrams agree excellently with experiments. However, there is no room for the nonequilibrium phase diagram in both classical equilibrium thermodynamics and traditional nonequilibrium thermodynamics. Therefore, the systematization of modern thermodynamics has been drastically changed and a new field for nonequilibrium phase diagrams emerges. Nonequilibrium phase diagrams for activated CVD cubic boron nitride processes have also been calculated in this paper.