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Theoretical modeling of molar volume and thermal expansion
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
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.

Place, publisher, year, edition, pages
2005.
Keyword [en]
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
Keyword [sv]
Materialvetenskap
National Category
Materials Engineering
Identifiers
URN: urn:nbn:se:kth:diva-252ISBN: 91-7178-086-0 OAI: oai:DiVA.org:kth-252DiVA: diva2:8131
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
List of papers
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)In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 53, no 8, 2259-2272 p.Article in journal (Refereed) Published
Abstract [en]

The molar volumes and thermal expansions of transition cubic metals were studied by means of the Calphad approach and the Debye-Gruneisen model. Experimental data were collected and assessed using Calphad procedures, and consistent results were obtained which give the best description of all experimental data. In order to put the prediction of the thermodynamic properties of metastable phases on a sound physical basis, the Debye-Gruneisen model was chosen to account for the vibrational contribution and calculate the coefficients of linear thermal expansion (CLEs) of stable cubic metals. Two approximations for Gruneisen parameter gamma, i.e. Slater ' s and Dugdale and MacDonald ' s expressions were adopted. A modified calculation scheme, first proposed by Wang et al., was derived in a straightforward way and used to evaluate the Debye temperature from ab initio electronic total-energy calculations at T = 0 K. The thermal electronic contribution to CLE was also evaluated from the electronic density of states. The calculated total CLEs were compared with those from the Calphad assessments. A satisfactory agreement is reached.

Keyword
molar volume, thermal expansion, ab initio calculations, Debye-Gruneisen model, calphad
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-5243 (URN)10.1016/j.actamat.2005.01.049 (DOI)000228818600007 ()2-s2.0-16344390584 (Scopus ID)
Note
QC 20101004Available from: 2005-06-01 Created: 2005-06-01 Last updated: 2017-12-04Bibliographically approved
2. Assessments of molar volume and thermal expansion for selected bcc, fcc and hcp metallic elements
Open this publication in new window or tab >>Assessments of molar volume and thermal expansion for selected bcc, fcc and hcp metallic elements
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.

Keyword
molar volume, thermal expansion, metallic element, CALPHAD
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-5244 (URN)10.1016/j.calphad.2005.05.001 (DOI)000231153300009 ()2-s2.0-21844473052 (Scopus ID)
Note
QC 20100831 Uppdaterad från In press till Published (20108831)Available from: 2005-06-01 Created: 2005-06-01 Last updated: 2017-12-04Bibliographically approved
3. Calculations of thermophysical properties of cubic carbides and nitrides using Debye-Grüneisen model
Open this publication in new window or tab >>Calculations of thermophysical properties of cubic carbides and nitrides using Debye-Grüneisen model
2007 (English)In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 55, no 4, 1215-1226 p.Article in journal (Refereed) Published
Abstract [en]

The thermal expansivities and heat capacities of NIX (M = Ti, Zr, Hf, V, Nb, Ta; X = C, N) carbides and nitrides with NaCl structure were calculated using the Debye-Gruneisen model combined with ab initio calculations. Two different approximations for the Gruneisen parameter gamma were used in the Debye-Gruneisen model, i.e. the expressions proposed by Slater and by Dugdale and MacDonald. The thermal electronic contribution was evaluated from ab initio calculations of the electronic density of states. The calculated results were compared with CALPHAD assessments and experimental data. It was found that the calculations using the Dugdale-MacDonald gamma can account for most of the experimental data. By fitting experimental heat capacity and thermal expansivity data below the Debye temperatures, an estimation of Poisson's ratio was obtained and Young's and shear moduli were evaluated. In order to reach a reasonable agreement with experimental data, it was necessary to use the logarithmic averaged mass of the constituent atoms. The agreements between the calculated and the experimental values for the bulk and Young's moduli are generally better than the agreement for shear modulus.

Keyword
heat capacity, thermal expansivity, ab initio calculations, debye-gruneisen model, elastic modulus
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-5245 (URN)10.1016/j.actamat.2006.05.054 (DOI)000244548100009 ()2-s2.0-33846575177 (Scopus ID)
Note
Uppdaterad från submitted till published: 20101020. QC 20101020Available from: 2005-06-01 Created: 2005-06-01 Last updated: 2017-12-04Bibliographically approved
4. Implementation of a new model for pressure dependence of condensed phases in Thermo-Calc
Open this publication in new window or tab >>Implementation of a new model for pressure dependence of condensed phases in Thermo-Calc
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.

Keyword
Equation of state, Modelling, Pressure, Thermo-Calc, Thermodynamic
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-5246 (URN)10.1016/j.calphad.2005.04.001 (DOI)000231153300007 ()2-s2.0-21844476821 (Scopus ID)
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

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