Derivation of complete phase diagrams for ternary systems with immiscibility phenomena and solid–fluid equilibria

2002 ◽  
Vol 74 (10) ◽  
pp. 1871-1884 ◽  
Author(s):  
V. M. Valyashko
Keyword(s):  
Phase Diagrams ◽  
Binary Systems ◽  
Volatile Component ◽  
Fluid Phase ◽  
Ternary Systems ◽  
Systematic Classification ◽  
Binary Fluid ◽  
Binary Phase Diagrams ◽  
Starting Point

Four main types of binary fluid-phase diagrams and available experimental data on binary systems are used as a starting point for derivation of the systematic classification of binary complete phase diagrams by the method of continuous topological transformations. This method and the classification of binary phase diagrams, containing the boundary versions of phase diagrams with ternary nonvariant points, are applied to derive the main types of fluid and complete phase diagrams for ternary systems with one volatile component and immiscibility phenomena in two constituent binary subsystems. The results gained from this analysis of derived fluid and complete phase diagrams of ternary systems are represented.

Calculation of phase diagrams and thermodynamic properties of 14 additive and reciprocal ternary systems containing Li2CO3, Na2CO3, K2CO3, Li2SO4, Na2SO4, K2SO4, LiOH, NaOH, and KOH

1984 ◽  
Vol 62 (3) ◽  
pp. 457-474 ◽  
Author(s):  
A. D. Pelton ◽  
C. W. Bale ◽  
P. L. Lin
Keyword(s):  
Phase Diagram ◽  
Thermodynamic Properties ◽  
Molten Salt ◽  
Phase Diagrams ◽  
Binary Systems ◽  
Ternary Phase ◽  
Ternary Phase Diagram ◽  
Ternary Systems ◽  
Maximum Error ◽  
Critical Assessment

Phase diagrams and thermodynamic properties of five additive molten salt ternary systems and nine reciprocal molten salt ternary systems containing the ions Li+, Na+, [Formula: see text], OH− are calculated from the thermodynamic properties of their binary subsystems which were obtained previously by a critical assessment of the thermodynamic data and the phase diagrams in these binary systems. Thermodynamic properties of ternary liquid phases are estimated from the binary properties by means of the Conformal Ionic Solution Theory. The ternary phase diagrams are then calculated from these thermodynamic properties by means of computer programs designed for the purpose. It is found that a ternary phase diagram can generally be calculated in this way with a maximum error about twice that of the maximum error in the binary phase diagrams upon which the calculations are based. If, in addition, some reliable ternary phase diagram measurements are available, these can be used to obtain small ternary correction terms. In this way, ternary phase diagram measurements can be smoothed and the isotherms drawn in a thermodynamically correct way. The thermodynamic approach permits experimental data to be critically assessed in the light of thermodynamic principles and accepted solution models. A critical assessment of error limits on all the calculated ternary diagrams is made, and suggestions as to which composition regions merit further experimental study are given.

scholarly journals Essential Magnesium Alloys Binary Phase Diagrams and Their Thermochemical Data

2014 ◽  
Vol 2014 ◽  
pp. 1-33 ◽  
Author(s):  
Mohammad Mezbahul-Islam ◽  
Ahmad Omar Mostafa ◽  
Mamoun Medraj
Keyword(s):  
Experimental Data ◽  
Phase Diagrams ◽  
Intermetallic Compounds ◽  
Binary Systems ◽  
Heat Of Formation ◽  
Model Parameters ◽  
Binary Phase Diagrams ◽  
Industrial Material ◽  
Structural Applications ◽  
Potential Weight

Magnesium-based alloys are becoming a major industrial material for structural applications because of their potential weight saving characteristics. All the commercial Mg alloys like AZ, AM, AE, EZ, ZK, and so forth series are multicomponent and hence it is important to understand the phase relations of the alloying elements with Mg. In this work, eleven essential Mg-based binary systems including Mg-Al/Zn/Mn/Ca/Sr/Y/Ni/Ce/Nd/Cu/Sn have been reviewed. Each of these systems has been discussed critically on the aspects of phase diagram and thermodynamic properties. All the available experimental data has been summarized and critically assessed to provide detailed understanding of the systems. The phase diagrams are calculated based on the most up-to-date optimized parameters. The thermodynamic model parameters for all the systems except Mg-Nd have been summarized in tables. The crystallographic information of the intermetallic compounds of different binary systems is provided. Also, the heat of formation of the intermetallic compounds obtained from experimental, first principle calculations and CALPHAD optimizations are provided. In addition, reoptimization of the Mg-Y system has been done in this work since new experimental data showed wider solubility of the intermetallic compounds.

Thermodynamic Study of Ag-Au-Gd, Tb Ternary Systems

2015 ◽  
Vol 814 ◽  
pp. 313-318 ◽  
Author(s):  
Jia Lian Li ◽  
Shu Liang Wang ◽  
Lu Jiang Zhou ◽  
Xiao Hong Wang ◽  
Yuan Hua Lin ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Phase Diagrams ◽  
Binary Systems ◽  
Lattice Models ◽  
Ternary Systems ◽  
Calculated Phase Diagram ◽  
Thermodynamic Database ◽  
Filler Alloy ◽  
Free Energies ◽  
Significant Information

The addition of the rare earth elements into the Ag-based filler alloy, which is typical and important, can control and eliminate the negative effect of impurity elements, and furthermore, it improves the spreading property of the Ag-based filler alloy. Phase diagram provides an important direction for materials design of the Ag-based filler alloy. Thus it is necessary to investigate the phase diagrams and construct the thermodynamic database. On the basis of this background, thermodynamic assessments of the Au-Gd, Tb binary systems were carried out by using the CALPHAD (Calculation of Phase Diagrams) method based on the experimental data including thermodynamic properties and phase equilibrium. The Gibbs free energies of the solution phases were described by sub-regular solution models with the Redlich-Kister equation, while all of the intermetallic compounds were described by sub-lattice models. A consistent set of thermodynamic parameters was derived from describing the Gibbs free energies of each solution phase and intermetallic compound. The calculated phase diagram achieved consistency with the available experiments. Then combined with the assessed relevant binary systems, the Ag-Au-Gd, Tb ternary systems have been predicted. The thermodynamic database of these ternary systems has been developed to present the significant information for the design of Ag-based filler alloys.

Classification of 3-DOF 3-UPU Translational Parallel Mechanisms Based on Constraint Singularity Loci Using Gröbner Cover

2021 ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Parallel Mechanism ◽  
Polynomial Systems ◽  
Coordinate Frame ◽  
Parallel Mechanisms ◽  
Systematic Classification ◽  
Starting Point ◽  
Moving Platform ◽  
Singular Configuration ◽  
The Impact

Abstract A 3-UPU translational parallel mechanism (TPM) is one of typical TPMs. Several types of 3-UPU TPMs have been proposed in the literature. Despite comprehensive studies on 3-UPU TPMs in which the joint axes on the base and the moving platform are coplanar, only a few 3-UPU TPMs with a skewed base and moving platform have been proposed. However, the impact of link parameters on singularity loci of such TPMs has not been systematically investigated. The advances in computing CGS (comprehensive Gröbner system) or Gröbner cover of parametric polynomial systems provide an efficient tool for solving this problem. This paper presents a systematic classification of 3-UPU TPMs, especially those with a skewed base and moving platform, based on constraint singularity loci. First, the constraint singularity equation of a 3-UPU TPM is derived. To simplify this equation, the coordinate frame on the base (or moving platform) is set up such that the centers of three U joints are located on different coordinate axes. Using Gröbner Cover, the 3-UPU TPMs are classified into 20 types based on the constraint singularity loci. Finally, a novel 3-UPU TPM is proposed. Unlike most of existing 3-UPU TPMs which can transit to two or more 3-DOF operation modes at a constraint singular configuration, the proposed 3-UPU TPM can only transit to one general 3-DOF operation mode in a constraint singular configuration. The singularity locus divides the workspace of this 3-UPU TPM into two constraint singularity-free regions. This work provides a solid foundation for the design of 3-UPU TPMs and a starting point for the classification of a general 3-UPU parallel mechanism.

scholarly journals THERMODYNAMIC MODELING OF OXIDE MELTS OF CaO - Al2O3 - SiO2 SYSTEMS

2019 ◽  
Vol 63 (1) ◽  
pp. 45-50
Author(s):  
Svetlana E. Pratskova ◽  
Vladimir A. Burmistrov ◽  
Anna A. Starikova
Keyword(s):  
Phase Diagrams ◽  
Thermodynamic Modeling ◽  
Binary Systems ◽  
Thermodynamic Description ◽  
Ternary Systems ◽  
Oxide Melt ◽  
State Diagrams ◽  
Gibbs Energies ◽  
Metallurgical Slags ◽  
Oxide Melts

Oxide melts of the CaO – Al2O3 – SiO2 system are the basis of metallurgical slags. Therefore, the thermodynamic properties of this system have been repeatedly studied experimentally, and attempts have been made to describe them theoretically. Thermodynamic modeling of the state diagrams of the CaO – Al2O3, CaO – SiO2, Al2O3 – SiO2 binary systems, as well as the CaO – Al2O3 – SiO2 ternary system was performed. In the course of the work, expressions for the thermodynamic description of the activities of the components of the oxide melt of this system are derived. For the calculation, a generalized theory of regular ionic solutions was used. The energy parameters of the theory are determined, depending on the temperature and composition of the solution, using experimental data on the heat and melting point of oxides of calcium, aluminum and silicon. According to the results of the simulation, the coordinates of the points of nonvariant transformations in the phase diagrams of the binary and ternary systems under study are determined. The obtained results on thermodynamic modeling of the coordinates of the liquidus lines of the phase diagrams of the CaO – Al2O3, CaO – SiO2, Al2O3 – SiO2 binary systems were compared with the literature data for the studied systems. The calculated diagrams are in good agreement with the experimental ones, which indicates the applicability of the chosen system for the description of such oxide melts. The modeling technique used in this work allowed to estimate the Gibbs energies of formation of silicates and calcium aluminum silicates to be 3Al2O3∙2SiO2, 3CaO∙SiO2, 2CaO∙SiO2, 3CaO∙2SiO2, CaO∙SiO2, CaO∙Al2O3∙2SiO2, 2CaO∙Al2O3∙SiO2 on the base of obtained aquations for of activities of the components and calculated parameters of the theory. The calculated diagrams will allow to determine the nature of the interaction between the components of the system, the conditions of formation, the composition and properties of the compounds formed, without isolating them from the system.

scholarly journals Systematic of binary phase diagrams, formed by low-melting elements (Bi, Sn, Zn, In) and the metals of IV-th and V-th periods

2005 ◽  
Vol 41 (1) ◽  
pp. 79-93 ◽  
Author(s):  
G. Vassilev
Keyword(s):  
Experimental Data ◽  
Theoretical Prediction ◽  
Phase Diagrams ◽  
Enthalpy Of Formation ◽  
Binary Systems ◽  
Size Factor ◽  
Miedema Model ◽  
Metallic Elements ◽  
Binary Phase ◽  
Binary Phase Diagrams

Systematic discussion of the binary phase diagrams formed by low-melting elements (Bi, Sn, Zn, In) and the metallic elements of IV-th and V-th periods has been done. Some options for theoretical prediction of the type of the phase diagrams relying on general criteria (enthalpy of formation, assessed by the Miedema model, and size factor) have been applied, and compared with experimental data about the respective binary systems. The systematization helps to determine the scope and the limits of such an approach. These predictions have been compared with experimental data about the respective binary systems studied by the author. Forecasts for the general features of some unknown binary systems have been deduced.

Classification of and transformations between types of fluid phase behavior in selected ternary systems

1996 ◽  
Vol 116 (1-2) ◽  
pp. 445-453 ◽  
Author(s):  
K. Gauter ◽  
L.J. Florusse ◽  
C.J. Peters ◽  
J. de Swaan Arons
Keyword(s):  
Phase Behavior ◽  
Fluid Phase ◽  
Ternary Systems

Liquidus Temperature Calculation in Sn-Bi-Cd System by ESTPHAD Method

2014 ◽  
Vol 790-791 ◽  
pp. 265-270
Author(s):  
Eszter Tatárka ◽  
Tamás Mende ◽  
András Roósz
Keyword(s):  
Phase Diagram ◽  
Phase Diagrams ◽  
Iteration Method ◽  
Liquidus Temperature ◽  
Binary Systems ◽  
Ternary Phase ◽  
Ternary Phase Diagram ◽  
Eutectic Point ◽  
Temperature Calculation ◽  
Binary Phase Diagrams

This paper includes the binary and ternary liquidus temperature calculations of Sn-Bi-Cd system. The calculation was performed in cases of the surfaces of Sn, Bi and Cd phases too. First of all the liquidus curves were calculated in the binary systems (Bi phase in Bi-Cd and Bi-Sn systems, Sn phase in Sn-Cd and Sn-Bi systems, Cd phase in Cd-Sn and Cd-Bi systems). By using the calculated coefficients of the binary phase diagrams and the data from the digitalized ternary phase diagram, the liquidus temperature of Sn, Bi and the Cd phases were calculated. Finally the eutectic point of the binary liquidus curves and the eutectic valley of the Sn and the Bi surfaces were calculated by means of an iteration method.

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