Using DFT data to inform the CALPHAD assessment of the carbon-zirconium phase diagram

Theresa Davey1, A. I. Duff1, S.G. Fries2, M.W. Finnis1,3

1. Department of Materials, Imperial College London, UK
2. ICAMS, Ruhr-Universität Bochum, Germany
3. Thomas Young Centre, Department of Physics, Imperial College London, UK
4. NUST “MISiS”, Russia

International Workshop on Theory and Modelling of Materials in Extreme Environments, Oxford, UK

Contributed poster presentation

One of the challenges of thermodynamic modelling has been in accurately representing the vacancies in ordered compounds, which are often stable over a wide range in stoichiometry. Individual defect energies of formation are difficult to measure experimentally, and such data is not included explicitly in phase diagram assessments.

In recent years, it has become possible to use Density Functional Theory (DFT) to calculate the formation energy of vacancies, or other point defects, with accuracy comparable to experiment [1]. In many systems, no reliable experimental data is available. We show here how such DFT data can be used to inform the assessment of a phase diagram, with reference to the carbon-zirconium system. This system has one intermediate phase, ZrCx (rocksalt structure), which is stable over a wide range of carbon content, depending on temperature. The vacancy formation energy of a compound is expressed in terms of the Gibbs energy parameters in a thermodynamic description [2]. Using DFT calculations of the vacancy formation energy we place a constraint on the excess parameters in an assessment of the phase diagram, the consequences of which we discuss.

[1] Nazarov, R.; Hickel, T.; Neugebauer, J., Vacancy formation energies in fcc metals: Influence of exchange-correlation functionals and correction schemes. Physical Review B 2012, 85 (14), 144118-1-7.
[2] Rogal, J.; Divinski, S. V.; Finnis, M. W.; Glensk, A.; Neugebauer, J.; Perepezko, J. H.; Schuwalow, S.; Sluiter, M. H. F.; Sundman, B., Perspectives on point defect thermodynamics. Physica Status Solidi B 2014, 251, 97-129.