Due to its widespread use in nuclear and high temperature applications, the quaternary system B-C-Hf-Zr has recently been reviewed with respect to experimental data , within the framework of the CALPHAD thermodynamic model .
This system contains the important ultra-high temperature ceramic compounds HfB2(hexagonal crystal structure, melting temperature, Tm~3525K), HfC (cubic, Tm~4200K), ZrB2 (hexagonal, Tm~3525K), and ZrC (cubic, Tm~3700K), which each deserve special attention, especially in the cases where experimental investigations are currently very limited.
We present ab initio calculations of the thermal properties of HfB2, HfC, ZrB2, and ZrC calculated within the quasi-harmonic approximation, and for the case of ZrC and HfC using a fully-anharmonic first principles approach. These are compared with the current CALPHAD assessment for each binary system and with existing experimental data. Any inconsistencies are highlighted and discussed, particularly in volume and thermal expansion, which have not been considered in previous assessments.
The figure shows specific heat capacity calculated within the quasi-harmonic approximation (DFT-LDA) plotted against experimental and calculated values for ZrC. In general, good agreement is found. The effect of electronic and anharmonic contributions will be explored in this work. The importance of the inclusion of finite temperature first principles calculations in future CALPHAD assessments is discussed, with particular regard to volumetric data.
 T. Davey et al., TMS Annual Meeting and Exhibition (2015).
 H.L. Lukas et al., Computational Thermodynamics: The Calphad Method, Cambridge University Press, 2007.