Influence of vibrational entropy on structural stability of Nb–Si and Mo–Si systems at elevated temperatures

The heats of formation of stable and metastable phases of the Nb–Si and Mo–Si systems were studied using density functional theory (DFT). The high-temperature behavior of the competing phases was studied by performing additional phonon calculations. Our theoretical results rationalize the major differences observed in the behavior of the Nb–Si and Mo–Si systems: Nb3Si is only stable at temperatures above 2043 K, whereas Mo3Si is always stable; Nb5Si3 and MoSi2 undergo phase changes at elevated temperatures, in contrast to Mo5Si3 and NbSi2. These differences are qualitatively explained by including the vibrational entropy to the free energies within the harmonic approximation. In particular, the softer shear moduli of the Nb5Si3 and MoSi2 βphases cause their stabilities over the α phases at elevated temperature.