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Assessments of molar volume and thermal expansion for selected bcc, fcc and hcp metallic elements
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.ORCID iD: 0000-0001-5031-919X
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
2005 (English)In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 29, no 1, 68-89 p.Article in journal (Refereed) Published
Abstract [en]

 The molar volume and thermal expansion of selected metallic elements with the bcc, fcc and hcp structures were studied by means of the Calphad approach. Experimental data were critically assessed, and model parameters were obtained yielding reasonable descriptions of all experimental data on molar volume and thermal expansion. The descriptions are valid between room temperature and the melting points at atmospheric pressure.

Place, publisher, year, edition, pages
2005. Vol. 29, no 1, 68-89 p.
Keyword [en]
molar volume, thermal expansion, metallic element, CALPHAD
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-5244DOI: 10.1016/j.calphad.2005.05.001ISI: 000231153300009ScopusID: 2-s2.0-21844473052OAI: diva2:8128
QC 20100831 Uppdaterad från In press till Published (20108831)Available from: 2005-06-01 Created: 2005-06-01 Last updated: 2010-08-31Bibliographically 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.

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
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
Available from: 2005-06-01 Created: 2005-06-01 Last updated: 2012-03-22

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