${\it Ab\ initio}$ thermodynamic properties of certain compounds in Nd-Fe-B system

In this work, we report the results of \emph{ab initio} calculations of thermochemical properties of several compounds in the Fe-Nd, B-Nd and B-Fe-Nd systems. We have performed DFT+U calculations to compute the enthalpy of formation of the compounds NdB$_6$, NdB$_4$, Nd$_2$B$_5$, Nd$_2$Fe$_{17}$ and Nd$_5$Fe$_2$B$_6$. It was found that the values obtained with an effective Hubbard $U$ correction have better agreement with the experimental data. We have also computed the vibrational contribution to the heat capacity ($C_p$) of the compounds as a function of temperature was computed using the quasharmonic approximation. For most of the compounds these properties have not been experimentally determined until now. Hence, the computed \emph{ab initio} thermodynamic properties will serve as useful input for the Gibbs energy model parameter assessment using the CALPHAD method.