Using DFT calculations of the vacancy formation energy to inform the assessment of the C-Zr 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-Universit├Ąt Bochum, Germany
3. Thomas Young Centre, Department of Physics, Imperial College London, UK

TOFA 2016, Santos, Brazil

Contributed oral presentation

One of the challenges of thermodynamic modelling has been in accurately representing the vacancies in ordered compounds, which can have a wide range of stability. 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. Using DFT calculations of the vacancy formation energy [2] we place a constraint on the excess parameters in an assessment of the phase diagram, the consequences of which we discuss. It is shown that it is possible to conduct a phase diagram assessment with a reduced number of degrees of freedom by including such data.

[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] Duff, A.I. et al. to be published