The Concept of the Estimation of Phase Diagrams (An Optimised Set of Simplified Equations to Estimate Equilibrium Liquidus and Solidus Temperatures, Partition Ratios, and Liquidus Slopes for Quick Access to Equilibrium Data in Solidification Software) Part I: Binary Equilibrium Phase Diagrams

This paper presents equations derived from thermodynamic equations for calculating the liquidus and solidus temperatures, the liquidus slope, and the partition ratio for solidification simulations. The constants of these equations can be easily determined from measurement data obtained by digitalisa...

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Main Authors: Gergely Kőrösy, András Roósz, Tamás Mende
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Metals
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Online Access:https://www.mdpi.com/2075-4701/14/11/1266
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author Gergely Kőrösy
András Roósz
Tamás Mende
author_facet Gergely Kőrösy
András Roósz
Tamás Mende
author_sort Gergely Kőrösy
collection DOAJ
description This paper presents equations derived from thermodynamic equations for calculating the liquidus and solidus temperatures, the liquidus slope, and the partition ratio for solidification simulations. The constants of these equations can be easily determined from measurement data obtained by digitalisation from known diagrams or can be calculated using a CALPHAD-based software. ESTPHAD has a hierarchical system; the developed functions of the binary systems are used in the calculation of the functions of the ternary systems, the functions of the ternary systems in the calculation of the function of quaternary systems, and so on. The developed method is demonstrated by processing the liquidus and solidus of Si–Ge isomorphous and Al–Mg and Al–Si eutectic equilibrium phase diagrams. The use of this method for calculating the functions of ternary systems will be shown in Part II. The advantages of this method are that the equations are simple, can be determined very quickly, and can be built into the simulation software very easily. The most significant advantage is that the calculation time is shorter by some order of magnitude than that of a CALPHAD-type calculation.
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spelling doaj-art-a3e9be63d64442149b56e60a73251f492024-11-26T18:13:31ZengMDPI AGMetals2075-47012024-11-011411126610.3390/met14111266The Concept of the Estimation of Phase Diagrams (An Optimised Set of Simplified Equations to Estimate Equilibrium Liquidus and Solidus Temperatures, Partition Ratios, and Liquidus Slopes for Quick Access to Equilibrium Data in Solidification Software) Part I: Binary Equilibrium Phase DiagramsGergely Kőrösy0András Roósz1Tamás Mende2Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, Faculty of Materials and Chemical Engineering, Egyetemváros, University of Miskolc, 3515 Miskolc, HungaryInstitute of Physical Metallurgy, Metal Forming, and Nanotechnology, Faculty of Materials and Chemical Engineering, Egyetemváros, University of Miskolc, 3515 Miskolc, HungaryInstitute of Physical Metallurgy, Metal Forming, and Nanotechnology, Faculty of Materials and Chemical Engineering, Egyetemváros, University of Miskolc, 3515 Miskolc, HungaryThis paper presents equations derived from thermodynamic equations for calculating the liquidus and solidus temperatures, the liquidus slope, and the partition ratio for solidification simulations. The constants of these equations can be easily determined from measurement data obtained by digitalisation from known diagrams or can be calculated using a CALPHAD-based software. ESTPHAD has a hierarchical system; the developed functions of the binary systems are used in the calculation of the functions of the ternary systems, the functions of the ternary systems in the calculation of the function of quaternary systems, and so on. The developed method is demonstrated by processing the liquidus and solidus of Si–Ge isomorphous and Al–Mg and Al–Si eutectic equilibrium phase diagrams. The use of this method for calculating the functions of ternary systems will be shown in Part II. The advantages of this method are that the equations are simple, can be determined very quickly, and can be built into the simulation software very easily. The most significant advantage is that the calculation time is shorter by some order of magnitude than that of a CALPHAD-type calculation.https://www.mdpi.com/2075-4701/14/11/1266thermodynamic-based functionsliquidussoliduspartition ratioCALPHAD
spellingShingle Gergely Kőrösy
András Roósz
Tamás Mende
The Concept of the Estimation of Phase Diagrams (An Optimised Set of Simplified Equations to Estimate Equilibrium Liquidus and Solidus Temperatures, Partition Ratios, and Liquidus Slopes for Quick Access to Equilibrium Data in Solidification Software) Part I: Binary Equilibrium Phase Diagrams
Metals
thermodynamic-based functions
liquidus
solidus
partition ratio
CALPHAD
title The Concept of the Estimation of Phase Diagrams (An Optimised Set of Simplified Equations to Estimate Equilibrium Liquidus and Solidus Temperatures, Partition Ratios, and Liquidus Slopes for Quick Access to Equilibrium Data in Solidification Software) Part I: Binary Equilibrium Phase Diagrams
title_full The Concept of the Estimation of Phase Diagrams (An Optimised Set of Simplified Equations to Estimate Equilibrium Liquidus and Solidus Temperatures, Partition Ratios, and Liquidus Slopes for Quick Access to Equilibrium Data in Solidification Software) Part I: Binary Equilibrium Phase Diagrams
title_fullStr The Concept of the Estimation of Phase Diagrams (An Optimised Set of Simplified Equations to Estimate Equilibrium Liquidus and Solidus Temperatures, Partition Ratios, and Liquidus Slopes for Quick Access to Equilibrium Data in Solidification Software) Part I: Binary Equilibrium Phase Diagrams
title_full_unstemmed The Concept of the Estimation of Phase Diagrams (An Optimised Set of Simplified Equations to Estimate Equilibrium Liquidus and Solidus Temperatures, Partition Ratios, and Liquidus Slopes for Quick Access to Equilibrium Data in Solidification Software) Part I: Binary Equilibrium Phase Diagrams
title_short The Concept of the Estimation of Phase Diagrams (An Optimised Set of Simplified Equations to Estimate Equilibrium Liquidus and Solidus Temperatures, Partition Ratios, and Liquidus Slopes for Quick Access to Equilibrium Data in Solidification Software) Part I: Binary Equilibrium Phase Diagrams
title_sort concept of the estimation of phase diagrams an optimised set of simplified equations to estimate equilibrium liquidus and solidus temperatures partition ratios and liquidus slopes for quick access to equilibrium data in solidification software part i binary equilibrium phase diagrams
topic thermodynamic-based functions
liquidus
solidus
partition ratio
CALPHAD
url https://www.mdpi.com/2075-4701/14/11/1266
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