### 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 (L_{i}), usually described as linear functions of temperature (L_{i} = a_{i} -b_{i} T), with semi-empirical parameters a_{i} 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: L_{i} = h _{0i} · exp(-T/τ_{0i}). Parameter h_{0i} (J/mol) is the enthalpy part of L_{i} at T = 0 K, while parameter τ_{0i} (K) is the temperature at which L_{i} would change its sign if it were extrapolated linearly from T = 0 K. Parameter h _{0i} can have any sign, but parameter τ_{0i} must be always positive. The new equation can be extended to describe more complex behavior in certain systems as: L_{i} = h_{0i} τ exp(-T/τ_{0i}) · [1 + Σ_{j=l}^{m} a_{ij} · (T/τ_{0i})], with a_{ij} being adjustable semi-empirical parameters for the given L_{i}.

Original language | English |
---|---|

Pages (from-to) | 115-124 |

Number of pages | 10 |

Journal | Calphad: Computer Coupling of Phase Diagrams and Thermochemistry |

Volume | 28 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2004 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Materials Science(all)

### Cite this

**A new equation for the temperature dependence of the excess Gibbs energy of solution phases.** / Kaptay, G.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A new equation for the temperature dependence of the excess Gibbs energy of solution phases

AU - Kaptay, G.

PY - 2004/6

Y1 - 2004/6

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.

KW - CALPHAD method

KW - Interaction parameter; temperature dependence

KW - Optimization

KW - Redlich-Kister equation

UR - http://www.scopus.com/inward/record.url?scp=6344282605&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=6344282605&partnerID=8YFLogxK

U2 - 10.1016/j.calphad.2004.08.005

DO - 10.1016/j.calphad.2004.08.005

M3 - Article

AN - SCOPUS:6344282605

VL - 28

SP - 115

EP - 124

JO - Calphad: Computer Coupling of Phase Diagrams and Thermochemistry

JF - Calphad: Computer Coupling of Phase Diagrams and Thermochemistry

SN - 0364-5916

IS - 2

ER -