On Gibbs Energy for the Metastable bcc_A2 Phase with a Thermal Vacancy in Metals and Alloys

An approach was proposed to obtain a reasonable thermodynamic description of a thermal vacancy in the metastable disordered body centered cubic (bcc_A2) phase, which had been consistently ignored in previous thermodynamic assessments. The present approach was first applied to obtain the thermodynamic descriptions for pure metastable bcc Ni and Zn, and then in the binary Ni-Zn system. The thermodynamic descriptions for both the metastable disordered bcc_A2 phase and the stable ordered bcc_B2  phases in the Ni-Zn binary system were updated based on the corresponding experimental equilibria. With these updated thermodynamic descriptions, several drawbacks, including the multiple solutions for thermal vacancy concentrations and the artificial phase boundaries in previous assessments, can be avoided. Moreover, the calculated phase boundaries and invariant reactions related to the  phase agree well with the experimental data.

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Thermodynamic assessment of the Co-Mg binary system

Journal of Mining and Metallurgy Section B Metallurgy ◽

10.2298/jmmb210606051y ◽

2021 ◽

pp. 51-51

Author(s):

L.-F. Yang ◽

X-D Si ◽

H.-D. Zhang ◽

F.-G. Gao ◽

Y.-P. Zeng ◽

...

Keyword(s):

Experimental Data ◽

Phase Diagram ◽

Binary System ◽

Literature Review ◽

Thermodynamic Assessment ◽

Thermodynamic Description ◽

Thermodynamic Optimization ◽

Experimental Phase ◽

Experimental Phase Diagram ◽

Self Consistent

No thermodynamic description was performed for the Co-Mg binary system according to literature review. Consequently, this binary system has been investigated by means of CALPHAD (CALculation of PHAse Diagrams) approach in the present work. The experimental phase diagram and thermodynamic data available in the literature were critically assessed. Based on the reliable literature data, a new set of self-consistent thermodynamic parameters for the Co-Mg system is obtained. The calculated results agree well with the experimental data from the literature, indicating the reasonability of the present thermodynamic optimization.

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Thermodynamic modeling of the Fe−Zn system using exponential temperature dependence for the excess Gibbs energy

Journal of Mining and Metallurgy Section B Metallurgy ◽

10.2298/jmmb1101001t ◽

2011 ◽

Vol 47 (1) ◽

pp. 1-10 ◽

Cited By ~ 7

Author(s):

Y. Tang ◽

X. Yuan ◽

Y. Du ◽

W. Xiong

Keyword(s):

Experimental Data ◽

Liquid Phase ◽

Binary System ◽

Thermodynamic Properties ◽

Gibbs Energy ◽

Excess Gibbs Energy ◽

Miscibility Gap ◽

Exponential Equation ◽

Self Consistent ◽

Exponential Temperature Dependence

The Fe-Zn binary system was re?modeled using exponential equation Li=hi?exp(-T/?i) (i=0,1,2?) to describe the excess Gibbs energy of the solution phases and intermetallic compounds with large homogeneities. A self-consistent set of thermodynamic parameters is obtained and the calculated phase diagrams and thermodynamic properties using the exponential equation agree well with the experimental data. Compared with previous assessments using the linear equation to describe the interaction parameters, the artificial miscibility gap at high temperatures was removed. In addition, the calculated thermodynamic properties of the liquid phase were more reasonable than those resulting from all the previous calculations. The present calculations yield noticeable improvements to the previous calculations.

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Thermodynamic Evaluation of the Fe-Pr Binary System

Materials Science Forum ◽

10.4028/www.scientific.net/msf.654-656.2442 ◽

2010 ◽

Vol 654-656 ◽

pp. 2442-2445 ◽

Cited By ~ 2

Author(s):

Guo Jun Zhou ◽

De Chang Zeng

Keyword(s):

Experimental Data ◽

Phase Diagram ◽

Binary System ◽

Intermediate Phase ◽

Eutectic Reaction ◽

Thermodynamic Description ◽

Liquid Solution ◽

Solution Phase ◽

Mixing Enthalpy ◽

Thermodynamic Evaluation

The Fe–Pr binary system was thermodynamic evaluation by means of the CALPHAD method based on phase diagram experimental data from the literature and a few values of the mixing enthalpy in the liquid phase obtained by the Miedema theory technique. Each of the selected data values is given a certain weight, which is chosen and adjusted based on the thermodynamic data and diagram phase data. A consistent thermodynamic description of the Fe–Pr binary system is presented: only one intermediate compound, Fe17Pr2, is stable in the system and forms peritectically at 1371K. An eutectic reaction L↔Pr+ Fe17Pr2 occurs at 939K and the eutectic liquid contains 82 at% Pr, five solid solution phases (Fe-rich αFe, γFe and δFe, Pr-rich αPr and βPr) and the liquid solution phase were considered in the evaluation. The intermediate phase was treated as stoichiometric compound, the solid solutions as ideal and the liquid solution phase by the Redlich–Kister formalism. The calculated phase diagram and thermodynamic properties are in good agreement with available experimental data.

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A Thermodynamic Description of the Al-Ir System

Materials Science Forum ◽

10.4028/www.scientific.net/msf.539-543.2389 ◽

2007 ◽

Vol 539-543 ◽

pp. 2389-2394 ◽

Cited By ~ 5

Author(s):

Taichi Abe ◽

Machiko Ode ◽

Hideyuki Murakami ◽

Chang Seok Oh ◽

Cenk Kocer ◽

...

Keyword(s):

Experimental Data ◽

Binary System ◽

Thermodynamic Assessment ◽

Thermodynamic Description ◽

Calculated Data ◽

Intermetallic Phases ◽

Sublattice Model ◽

Calphad Technique ◽

Formation Enthalpies ◽

B2 Phase

The thermodynamic assessment of the Al-Ir binary system, one of the key sub-systems of the Ir-based alloys, was performed using the CALPHAD technique. The AlIr(B2) phase was described using the two sublattice model with the formula (Al,Ir)0.5(Ir,Va)0.5, while other intermetallic phases were treated as stoichiometric compounds. The calculated data of the phases in the Al-Ir system can be used to accurately reproduce experimental data, such as phase equilibria, invariant reactions, and formation enthalpies of the intermetallic phases.

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Thermodynamic Description of the ACl-ThCl4 (A = Li, Na, K) Systems

Thermo ◽

10.3390/thermo1020009 ◽

2021 ◽

Vol 1 (2) ◽

pp. 122-133

Author(s):

Jaén A. Ocádiz Flores ◽

Bas A. S. Rooijakkers ◽

Rudy J. M. Konings ◽

Anna Louise Smith

Keyword(s):

Experimental Data ◽

Phase Diagram ◽

Gibbs Energy ◽

Binary Systems ◽

Thermodynamic Description ◽

Structural Models ◽

Nuclear Industry ◽

Thermodynamic Investigation ◽

Liquid Solutions ◽

Near Future

The ACl-ThCl4 (A = Li, Na, K) systems could be of relevance to the nuclear industry in the near future. A thermodynamic investigation of the three binary systems is presented herein. The excess Gibbs energy of the liquid solutions is described using the quasi-chemical formalism in the quadruplet approximation. The phase diagram optimisations are based on the experimental data available in the literature. The thermodynamic stability of the liquid solutions increases in the order Li < Na < K, in agreement with idealised interactions and structural models.

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Multiple Solutions When Fitting Excess Gibbs Energy Models and Implications for Process Simulation

Chemie Ingenieur Technik ◽

10.1002/cite.202000162 ◽

2020 ◽

Author(s):

Dan Vasiliu ◽

Quirin Göttl ◽

Sönke Bröcker ◽

Jakob Burger

Keyword(s):

Gibbs Energy ◽

Process Simulation ◽

Excess Gibbs Energy ◽

Multiple Solutions ◽

Energy Models

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Thermodynamic description of the Al–Mg–Si system using a new formulation for the temperature dependence of the excess Gibbs energy

Thermochimica Acta ◽

10.1016/j.tca.2011.10.017 ◽

2012 ◽

Vol 527 ◽

pp. 131-142 ◽

Cited By ~ 46

Author(s):

Ying Tang ◽

Yong Du ◽

Lijun Zhang ◽

Xiaoming Yuan ◽

George Kaptay

Keyword(s):

Gibbs Energy ◽

Temperature Dependence ◽

Excess Gibbs Energy ◽

Thermodynamic Description ◽

New Formulation

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A thermodynamic description of metastable c-TiAlZrN coatings with triple spinodally decomposed domains

Journal of Mining and Metallurgy Section B Metallurgy ◽

10.2298/jmmb161017001z ◽

2017 ◽

Vol 53 (2) ◽

pp. 85-93 ◽

Cited By ~ 2

Author(s):

J. Zhou ◽

L. Zhang ◽

L. Chen ◽

Y. Du ◽

Z.K. Liu

Keyword(s):

Experimental Data ◽

Phase Equilibria ◽

First Principles ◽

Thermodynamic Description ◽

Quantitative Description ◽

Experimental Phase Equilibria ◽

Free Energies ◽

Calphad Technique ◽

Important Input ◽

Good Agreement

A critical thermodynamic assessment of the metastable c-TiAlZrN coatings, which are reported to spinodally decompose into triple domains, i.e., c-TiN, c-AlN, and c-ZrN, was performed via the CALculation of PHAse Diagram (CALPHAD) technique based on the limited experimental data as well as the first-principles computed free energies. The metastable c-TiAlZrN coatings were modeled as a pseudo-ternary phase consisting of c-TiN, c-AlN and c-ZrN species, and described using the substitutional solution model. The thermodynamic descriptions for the three boundary binaries were directly taken from either the CALPHAD assessment or the first-principles results available in the literature except for a re-adjustment of the pseudo-binary c-AlN/c-ZrN system based on the experimental phase equilibria in the pseudo-ternary system. The good agreement between the calculated phase equilibria and the experimental data over the wide temperature range was obtained, validating the reliability of the presently obtained thermodynamic descriptions for the c-TiAlZrN system. Based on the present thermodynamic description, different phase diagrams and thermodynamic properties can be easily predicted. It is anticipated that the present thermodynamic description of the metastable c-TiAlZrN coatings can serve as the important input for the later quantitative description of the microstructure evolution during service life.

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