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

Abstract

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: Nb 3Si is only stable at temperatures above 2043 K, whereas Mo 3Si is always stable; Nb 5Si 3 and MoSi 2 undergo phase changes at elevated temperatures, in contrast to Mo 5Si 3 and NbSi 2. 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 Nb 5Si 3 and MoSi 2 βphases cause their stabilities over the α phases at elevated temperature.