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Implementation of a new model for pressure dependence of condensed phases in Thermo-Calc
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.ORCID iD: 0000-0001-5031-919X
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
2005 (English)In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 29, no 1, 49-55 p.Article in journal (Refereed) Published
Abstract [en]

The high pressure modelling of condensed phases has mainly been a topic for geophysics, but there is an interest in modelling moderate pressure dependence also for materials science and engineering. The Murnaghan equation of state has been implemented in the Thermo-Calc software to represent the pressure-dependent part of the Gibbs energy. Recently it has been shown by Jacobs and Oonk that an equation of state derived from an empirical relationship between volume and isothermal bulk modulus can be applied to represent experimental data in volume-pressure-temperature space with equal or better accuracy then the Murnaghan equation of state. In this paper we extend this equation of state and show that a simpler expression for the Gibbs energy can be derived than that given by Jacobs and Oonk. The resulting expression for the Gibbs energy has been implemented in the Thermo-Calc software.

Place, publisher, year, edition, pages
2005. Vol. 29, no 1, 49-55 p.
Keyword [en]
Equation of state, Modelling, Pressure, Thermo-Calc, Thermodynamic
National Category
Materials Engineering
Identifiers
URN: urn:nbn:se:kth:diva-5246DOI: 10.1016/j.calphad.2005.04.001ISI: 000231153300007Scopus ID: 2-s2.0-21844476821OAI: oai:DiVA.org:kth-5246DiVA: diva2:8130
Note
QC 20100917. Uppdaterad från In press till Published (20100917)Available from: 2005-06-01 Created: 2005-06-01 Last updated: 2017-12-04Bibliographically approved
In thesis
1. Theoretical modeling of molar volume and thermal expansion
Open this publication in new window or tab >>Theoretical modeling of molar volume and thermal expansion
2005 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Combination of the Calphad method and theoretical calculations provides new possibilities for the study of materials science. This work is a part of the efforts within the CCT project (Centre of Computational Thermodynamics) to combine these methods to facilitate modeling and to extend the thermodynamic databases with critically assessed volume data. In this work, the theoretical calculations refer to first-principles and Debye-Grüneisen calculations. The first-principles (i.e. ab initio) electronic structure calculations, based on the Density- Functional Theory (DFT), are capable of predicting various physical properties at 0 K, such as formation energy, volume and bulk modulus. The ab initio simulation software, VASP, was used to calculate the binding curves (i.e. equation of state at 0 K) of metallic elements, cubic carbides and nitrides. From the binding curves, the equilibrium volumes at 0 K were calculated for several metastable structures as well as stable structures. The vibrational contribution to the free energy was calculated using the Debye-Grüneisen model combined with first-principles calculations. Two different approximations for the Grüneisen parameter, γ, were used in the Debye-Grüneisen model, i.e. Slater’s and Dugdale-MacDonald’s expressions. The thermal electronic contribution was evaluated from the calculated electronic density of states. The calculated thermal expansivities for metallic elements, cubic carbides and nitrides were compared with Calphad assessments. It was found that the experimental data are within the limits of the calculations using the two approximations for γ. By fitting experimental heat capacity and thermal expansivity around Debye temperatures, we obtained optimal Poisson’s ratio values and used them to evaluate Young’s and Shear moduli. In order to reach a reasonable agreement with the experiments, it is necessary to use the logarithmic averaged mass of the constitutional atoms. The agreements between the calculations and experiments are generally better for bulk modulus and Young’s modulus than that for shear modulus. A new model describing thermodynamic properties at high pressures was implemented in Thermo-Calc. The model is based on an empirical relation between volume and isothermal bulk modulus. Pure Fe and solid MgO were assessed using this model. Solution phases will be considered in a future work to check the model for compositional dependence.

Keyword
Materials science, first-principles calculations, ab initio, Calphad, Debye-Grüneisen model, thermodynamic properties, elastic modulus, volume, thermal expansivity, pressure, Thermo-Calc, VASP, element, carbide, nitride, Materialvetenskap
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-252 (URN)91-7178-086-0 (ISBN)
Public defence
2005-06-07, Salongen, KTHB, Osquars backe 31, Stockholm, 10:00
Opponent
Supervisors
Available from: 2005-06-01 Created: 2005-06-01 Last updated: 2012-03-22

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Selleby, Malin

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