Thermodynamic assessments of the (Zr,Hf) carbides and borides revisited and informed by the calculation of defect formation energies in ZrC

Some transition metal carbides and borides are ultra-high temperature ceramic compounds that have application in the nuclear and aerospace industries. The existing thermodynamic assessments of the systems containing the hafnium and zirconium carbides and borides were examined, along with all available experimental and theoretical data. One of the challenges of thermodynamic modelling is in accurately describing the point defects in ordered compounds. In the transition metal carbides and borides, vacancies and substitutional defects are common and play a significant role in determining the material behaviour. Hafnium and zirconium are very difficult to separate, and as such there is always some level of contamination in these compounds. Despite this, there is very limited quantitative information available about the effect that this contamination has on the properties of the material. Using first principles calculations of substitutional point defects in UHTC compounds, the CALPHAD modelling in existing thermodynamic assessments of the ternary boron-hafnium-zirconium and carbon-hafnium-zirconium systems was considered and areas for improvement were identified using the first principles insights. Hafnium and zirconium carbide have a wide range of stoichiometry facilitated by carbon vacancies. Developments to first principles techniques have allowed calculations of properties such as the vacancy formation energy that should be considered in thermodynamic assessment, but are currently not explicitly considered in the modelling. Using the carbon-zirconium system as an example, a method was developed by which the vacancy formation energy and vacancy-vacancy interaction energies can be considered directly in an existing CALPHAD optimisation without losing any of the information already encoded within it. This was applied to a thermodynamic assessment in the literature and to a new assessment of the carbon-zirconium system that was performed incorporating new experimental insights.