ICAMS / Interdisciplinary Centre for Advanced Materials Simulation


The challenge of covering thermodynamic properties not only at high temperature but also at low temperature: a progress report

Date: 24.05.2011
Place: XL CALPHAD, Computer Coupling of Phase Diagrams and Thermochemistry, Rio de Janeiro, Brazil

Mauro Palumbo
Suzana Fries
Tilmann Hickel
Andrea Dal Corso, SISSA-ISAS, Trieste, Italy
Michael Jacobs, TU Clausthal, Clausthal-Zellerfeld, Germany
Ursula Kattner, Department of Metallurgy Division, National Institute of Standards and Technology, Gaithersburg, USA
Bo Sundman, Department of Materials Science and Engineering, KTH Royal Institute of Technology, Stockholm, Sweden

As it was pointed out recently [1], a revision of the lattice stabilities presently used in the CALPHAD community [2] is necessary to achieve a description of thermodynamic properties not only in the temperature regime above room temperature, but also in the temperature regime from room temperature down to zero Kelvin. That requires consideration of physically realistic models in Calphad methodology [3]. Our efforts in this direction are underway as part of the Sapiens project, presented in last CALPHAD XXXIX meeting held in Korea. In the present paper we report progress on this subject.

To test our formalism we have selected the pure elements Cr and Ni as they are part of the selected elements of the Sapiens project. We started our analysis by collecting experimental data from the literature and results calculated by first principles methods. The reliability of these data was critically evaluated using several test criteria, such as experimental conditions, uncertainties in these data, and measuring methods. Additional, first principles calculations were carried out to determine lattice parameters, energies, bulk moduli and the vibrational contribution to the free energy in the harmonic and quasi-harmonic approach. One of the results, which we will discuss, is the partitioning of physical effects in the heat capacity. We have tested a combined approach using first principles and fitting methods. We show results of this approach by comparing our calculations with experimental data. Both the Debye and Einstein model plus additional contributions for electronic excitations, quasi and anharmonic vibrations and effects of lattice vacancies were tested by adapting optimization programs from Lukas [4]. We show a numerical scheme to calculate the Debye integral, which we implemented in this program.

[1] B.J. Lee, A summary of the CALPHAD XXXIX conference, CALPHAD (2011), doi:10:1016/j.calphad.2010.11.005
[2] A. T. Dinsdale, CALPHAD, 15, 4 (1991) p. 317
[3] M. H. G. Jacobs, R. Schmid-Fetzer, Phys. Chem. Minerals 37, 10 (2010) p.721
[3] H.L. Lukas, Reference Manual (1995)
ThyssenKrupp AG, Salzgitter Mannesmann Forschung GmbH, Robert Bosch GmbH, Bayer Materials Science AG, Bayer Technology Services GmbH, Benteler Stahl/Rohr AG, the state of North Rhine-Westphalia and the European Commission in the framework of the European Regional Development Fund (ERDF).

Supporting information:

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