A new equation for the temperature dependence of the excess Gibbs energy of solution phases

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Abstract

During CALPHAD optimization procedures, the excess Gibbs energy of solution phases is usually described by the Redlich-Kister (RK) polynomial. The RK polynomial includes interaction parameters (Li), usually described as linear functions of temperature (Li = ai -bi T), with semi-empirical parameters ai and b i usually having the same signs. Consequently, the excess Gibbs energy will change its sign at a certain high temperature and will have an infinite value at infinitely high temperature. This is in conflict with thermodynamic constraints and can also lead to artificial phase stabilization in some of the calculated phase diagrams, such as the appearance of an artificial miscibility gap having no maximum critical temperature. Such artifacts can usually be avoided, if the following new semi-empirical equation is used for the interaction energy of solution phases: Li = h 0i · exp(-T/τ0i). Parameter h0i (J/mol) is the enthalpy part of Li at T = 0 K, while parameter τ0i (K) is the temperature at which Li would change its sign if it were extrapolated linearly from T = 0 K. Parameter h 0i can have any sign, but parameter τ0i must be always positive. The new equation can be extended to describe more complex behavior in certain systems as: Li = h0i τ exp(-T/τ0i) · [1 + Σj=lm aij · (T/τ0i)], with aij being adjustable semi-empirical parameters for the given Li.

Original languageEnglish
Pages (from-to)115-124
Number of pages10
JournalCalphad: Computer Coupling of Phase Diagrams and Thermochemistry
Volume28
Issue number2
DOIs
Publication statusPublished - Jun 2004

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Gibbs free energy
Temperature
Polynomials
Phase diagrams
Enthalpy
Stabilization
Solubility
Thermodynamics

Keywords

  • CALPHAD method
  • Interaction parameter; temperature dependence
  • Optimization
  • Redlich-Kister equation

ASJC Scopus subject areas

  • Materials Science(all)

Cite this

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title = "A new equation for the temperature dependence of the excess Gibbs energy of solution phases",
abstract = "During CALPHAD optimization procedures, the excess Gibbs energy of solution phases is usually described by the Redlich-Kister (RK) polynomial. The RK polynomial includes interaction parameters (Li), usually described as linear functions of temperature (Li = ai -bi T), with semi-empirical parameters ai and b i usually having the same signs. Consequently, the excess Gibbs energy will change its sign at a certain high temperature and will have an infinite value at infinitely high temperature. This is in conflict with thermodynamic constraints and can also lead to artificial phase stabilization in some of the calculated phase diagrams, such as the appearance of an artificial miscibility gap having no maximum critical temperature. Such artifacts can usually be avoided, if the following new semi-empirical equation is used for the interaction energy of solution phases: Li = h 0i · exp(-T/τ0i). Parameter h0i (J/mol) is the enthalpy part of Li at T = 0 K, while parameter τ0i (K) is the temperature at which Li would change its sign if it were extrapolated linearly from T = 0 K. Parameter h 0i can have any sign, but parameter τ0i must be always positive. The new equation can be extended to describe more complex behavior in certain systems as: Li = h0i τ exp(-T/τ0i) · [1 + Σj=lm aij · (T/τ0i)], with aij being adjustable semi-empirical parameters for the given Li.",
keywords = "CALPHAD method, Interaction parameter; temperature dependence, Optimization, Redlich-Kister equation",
author = "G. Kaptay",
year = "2004",
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language = "English",
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N2 - During CALPHAD optimization procedures, the excess Gibbs energy of solution phases is usually described by the Redlich-Kister (RK) polynomial. The RK polynomial includes interaction parameters (Li), usually described as linear functions of temperature (Li = ai -bi T), with semi-empirical parameters ai and b i usually having the same signs. Consequently, the excess Gibbs energy will change its sign at a certain high temperature and will have an infinite value at infinitely high temperature. This is in conflict with thermodynamic constraints and can also lead to artificial phase stabilization in some of the calculated phase diagrams, such as the appearance of an artificial miscibility gap having no maximum critical temperature. Such artifacts can usually be avoided, if the following new semi-empirical equation is used for the interaction energy of solution phases: Li = h 0i · exp(-T/τ0i). Parameter h0i (J/mol) is the enthalpy part of Li at T = 0 K, while parameter τ0i (K) is the temperature at which Li would change its sign if it were extrapolated linearly from T = 0 K. Parameter h 0i can have any sign, but parameter τ0i must be always positive. The new equation can be extended to describe more complex behavior in certain systems as: Li = h0i τ exp(-T/τ0i) · [1 + Σj=lm aij · (T/τ0i)], with aij being adjustable semi-empirical parameters for the given Li.

AB - During CALPHAD optimization procedures, the excess Gibbs energy of solution phases is usually described by the Redlich-Kister (RK) polynomial. The RK polynomial includes interaction parameters (Li), usually described as linear functions of temperature (Li = ai -bi T), with semi-empirical parameters ai and b i usually having the same signs. Consequently, the excess Gibbs energy will change its sign at a certain high temperature and will have an infinite value at infinitely high temperature. This is in conflict with thermodynamic constraints and can also lead to artificial phase stabilization in some of the calculated phase diagrams, such as the appearance of an artificial miscibility gap having no maximum critical temperature. Such artifacts can usually be avoided, if the following new semi-empirical equation is used for the interaction energy of solution phases: Li = h 0i · exp(-T/τ0i). Parameter h0i (J/mol) is the enthalpy part of Li at T = 0 K, while parameter τ0i (K) is the temperature at which Li would change its sign if it were extrapolated linearly from T = 0 K. Parameter h 0i can have any sign, but parameter τ0i must be always positive. The new equation can be extended to describe more complex behavior in certain systems as: Li = h0i τ exp(-T/τ0i) · [1 + Σj=lm aij · (T/τ0i)], with aij being adjustable semi-empirical parameters for the given Li.

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