AN INTRODUCTION TO THE CALPHAD METHOD AND THE COMPOUND ENERGY FORMALISM (CEF)

Most models currently used for complex phases in the calculation of phase diagrams (Calphad) method are based on the compound energy formalism. The way this formalism is presently used, however, is prone to poor extrapolation behavior in higher-order systems, especially when treating phases with complex crystal structures. In this paper, a partition of the Gibbs energy into effective bond energies, without changing its confgurational entropy expression, is proposed, thereby remarkably improving the extrapolation behavior. The proposed model allows the use of as many sublattices as there are occupied Wyckoff sites and has great potential for reducing the number of necessary parameters, thus allowing shorter computational time. Examples for face centered cubic (fcc) ordering and the σ phase are given.

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Researching nitrogen solubility in nitrogen-containing austenitic steels at melting and recrystallization by CALPHAD method

Voprosy Materialovedeniya ◽

10.22349/1994-6716-2018-96-4-53-66 ◽

2019 ◽

pp. 53-66 ◽

Cited By ~ 1

Author(s):

L. A. Smirnov ◽

I. I. Gorbachev ◽

V. V. Popov ◽

A. Yu. Pasynkov ◽

A. S. Oryshchenko ◽

...

Keyword(s):

Global Minimum ◽

Nitrogen Solubility ◽

Thermodynamic Description ◽

Solidus Temperature ◽

Liquidus Line ◽

Calphad Method ◽

Austenitic Steels ◽

Nitrogen Transfer ◽

Fixed Nitrogen ◽

System Phase

The CALPHAD method has been employed to compose thermodynamic description of the Fe–Cr–Mn–Ni–Si–C–N system. Using an algorithm based on finding a global minimum of Gibbs energy, the calculations of system phase composition were performed in the temperature range from 1750°C to hardening and in the range of compositions corresponding to 04Kh20N6G11M2AFB steel. Calculations showed that at temperatures above liquidus line, Cr and Mn increase nitrogen solubility in the melt, while Ni and Si reduce it. With an increase in the content of Cr, Mn, Ni, and Si in steel in the studied composition range, both liquidus and solidus temperature decrease. The degree of influence on these temperatures of Cr, Mn, Ni and Si within the steel grade is different and ranges from ~3 to ~14°C. Calculations taking into account the possibility of nitrogen transfer between steel and the atmosphere of air showed that the amount of fixed nitrogen in the alloy under study varies, depending on the composition of the steel and temperature, from ~0.3 to ~0.6 wt%. As the temperature decreases from liquidus to solidus, the amount of fixed nitrogen increases, with the exception of those steel compositions when ferrite and not austenite is released from the liquid phase.

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Phase Diagram of Binary Alloy Nanoparticles under High Pressure

Materials ◽

10.3390/ma14112929 ◽

2021 ◽

Vol 14 (11) ◽

pp. 2929

Author(s):

Han Gyeol Kim ◽

Joonho Lee ◽

Guy Makov

Keyword(s):

Phase Diagram ◽

Phase Diagrams ◽

Interaction Parameter ◽

Excess Volume ◽

Eutectic Temperature ◽

Calphad Method ◽

Alloy Nanoparticles ◽

Thermodynamic Conditions ◽

Nanoparticle System ◽

Pressure Phase

CALPHAD (CALculation of PHAse Diagram) is a useful tool to construct phase diagrams of various materials under different thermodynamic conditions. Researchers have extended the use of the CALPHAD method to nanophase diagrams and pressure phase diagrams. In this study, the phase diagram of an arbitrary A–B nanoparticle system under pressure was investigated. The effects of the interaction parameter and excess volume were investigated with increasing pressure. The eutectic temperature was found to decrease in most cases, except when the interaction parameter in the liquid was zero and that in the solid was positive, while the excess volume parameter of the liquid was positive. Under these conditions, the eutectic temperature increased with increasing pressure.

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Emulation of short-range ordering within the Compound Energy Formalism: Application to the calcite-magnesite solid solution

Calphad ◽

10.1016/j.calphad.2018.11.012 ◽

2019 ◽

Vol 64 ◽

pp. 115-125 ◽

Cited By ~ 1

Author(s):

Xin Liu ◽

Victor L. Vinograd ◽

Sergii Nichenko ◽

Dmitrii A. Kulik ◽

Xiancai Lu ◽

...

Keyword(s):

Solid Solution ◽

Short Range ◽

Compound Energy Formalism ◽

Short Range Ordering

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Parameters in the compound energy formalism for ionic systems

Calphad ◽

10.1016/j.calphad.2008.05.006 ◽

2009 ◽

Vol 33 (1) ◽

pp. 227-232 ◽

Cited By ~ 24

Author(s):

M. Hillert ◽

L. Kjellqvist ◽

H. Mao ◽

M. Selleby ◽

B. Sundman

Keyword(s):

Compound Energy Formalism ◽

Ionic Systems

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Thermodynamic Calculation of Phase Equilibria in the Mn-RE (RE=Nd, Gd, Dy) Binary Systems

Materials Science Forum ◽

10.4028/www.scientific.net/msf.898.1036 ◽

2017 ◽

Vol 898 ◽

pp. 1036-1041

Author(s):

M.H. Rong ◽

S.D. Lin ◽

Jiang Wang ◽

H.Y. Zhou ◽

G.H. Rao

Keyword(s):

Magnetic Properties ◽

Thermodynamic Properties ◽

Phase Equilibria ◽

Thermodynamic Calculation ◽

Binary Systems ◽

Ternary Systems ◽

Experimental Information ◽

Calphad Method ◽

Self Consistent ◽

Ternary Intermetallic Compounds

Ternary intermetallic compounds with rare earth elements and transition metals in the RE-Mn-X (X=Si, Ge, Sn etc.) ternary systems show interesting magnetic properties. As key sub-binary systems of the RE-Mn-X (X=Si, Ge, Sn etc.) ternary systems, the information of phase equilibria and thermodynamic properties of the Mn-RE (RE=Nd, Gd, Dy) binary systems are indispensable to explore the RE-Mn-X (X=Si, Ge, Sn etc.) alloys with better magnetic properties. In this work, the experimental data of phase equilibria and thermodynamic properties of the Mn-RE (RE=Nd, Gd, Dy) binary systems in the published literature were reviewed. Based on the available experimental information, thermodynamic calculation of phase equilibria of the Mn-RE (RE=Nd, Gd, Dy) binary systems was performed using the CALPHAD method. As a result, further experimental investigation and thermodynamic optimization would be still necessary in order to develop the self-consistent and compatible thermodynamic database of the RE-Mn-based alloy systems.

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The Bragg-Williams-Gorsky (BWG) ordering treatment in the compound energy formalism (CEF)

Berichte der Bunsengesellschaft für physikalische Chemie ◽

10.1002/bbpc.19981020907 ◽

1998 ◽

Vol 102 (9) ◽

pp. 1102-1110 ◽

Cited By ~ 8

Author(s):

Suzana G. Fries ◽

Hans Leo Lukas ◽

Ibrahim Ansara ◽

Bo Sundman

Keyword(s):

Compound Energy Formalism

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Experimental Study of Phase Composition of B-Fe-Mn-V Alloys and Thermodynamic Calculations of Phase Equilibria in the B-Mn-V and B-Fe-Mn-V Systems

Advances in Materials Science and Engineering ◽

10.1155/2018/3950980 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10

Author(s):

Viera Homolová ◽

Ján Kepič ◽

Adéla Zemanová ◽

Ondřej Zobač

Keyword(s):

Electron Microscopy ◽

Experimental Study ◽

Quaternary System ◽

Experimental Methods ◽

Calphad Method ◽

Thermodynamic Calculations ◽

Interstitial Element ◽

X Ray ◽

Scanning Electron ◽

Good Agreement

Phase compositions of B-Fe-Mn-V alloys were studied by several experimental methods (DTA measurement, X-ray diffractions, and scanning electron microscopy). Besides the experimental study of the quaternary system, thermodynamic modelling of the ternary B-Mn-V system by the Calphad method and thermodynamic calculations for the quaternary B-Fe-Mn-V system were performed. Calculations for the quaternary system are based on the ternary subsystems (B-Mn-V, B-Fe-V, B-Fe-Mn, and Fe-Mn-V). Boron is modelled as an interstitial element in all solid solutions of vanadium, manganese, and iron. Very good agreement between experimental results and thermodynamic calculations was achieved. The created thermodynamic database is suitable for thermodynamic calculations of phase diagrams for all the ternary subsystems and also for the B-Fe-Mn-V quaternary system.

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The development of phase-based property data using the CALPHAD method and infrastructure needs

Integrating Materials and Manufacturing Innovation ◽

10.1186/2193-9772-3-12 ◽

2014 ◽

Vol 3 (1) ◽

pp. 158-180 ◽

Cited By ~ 19

Author(s):

Carelyn E Campbell ◽

Ursula R Kattner ◽

Zi-Kui Liu

Keyword(s):

Calphad Method ◽

Property Data

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Calphad description of the Ge-Mn system

MRS Proceedings ◽

10.1557/opl.2014.444 ◽

2014 ◽

Vol 1642 ◽

Author(s):

Alexandre Berche ◽

Jean-Claude Tédenac ◽

Philippe Jund ◽

Stéphane Gorsse

Keyword(s):

Phase Diagram ◽

Liquid Phase ◽

Thermodynamic Properties ◽

Gibbs Energy ◽

Critical Review ◽

Thermodynamic Description ◽

Calphad Method ◽

Review Of The Literature ◽

Solid Phases

ABSTRACTThe germanium-manganese system has been experimentally studied but no Calphad description is available yet. After a critical review of the literature concerning the phase diagram and the thermodynamic properties, a thermodynamic description of the Gibbs energy of the phases is performed using the Calphad method. The liquid phase is described with an associated model and the variation to the stoichiometry of the solid phases is taken into account.

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