On the efficiency of $Mg/Nb$ diboride solid solution in enhancing the thermal stability of $MgB_2$ superconductor

A comparative analysis of the thermal stability of $Mg$/$Nb$ diboride solid solution and pure $MgB_2$ was carried out. The specific heat capacity of these materials below the critical temperature of $MgB_2$, which is an essential characteristic for assessing their thermal stability, was evaluated. Based on the $ab$ $initio$ calculations of the phonon density of states for both compounds, it was demonstrated that $MgNbB_4$ is characterized by a higher phonon density of states in the frequency range of $5$–$7.5$ THz compared with $MgB_2$. $MgNbB_4$ was also found to exhibit a higher heat absorbing capacity at low temperatures. The specific heat capacity of $MgNbB_4$ at low temperatures exceeds that of $MgB_2$ by $50 \%$, thus indicating its better thermal stability. The potential of $MgNbB_4$ solid solution for practical application in superconducting wires made of $MgB_2$ was outlined.