First-principles lattice dynamics calculations of the phase boundary between beta-Si3N4 and gamma-Si3N4 at elevated temperatures and pressures.
The phase boundary between beta-Si(3)N(4) and gamma-Si(3)N(4) is investigated at high pressure and high temperature using first-principles lattice dynamics calculations within the quasi-harmonic approximation. We find a positive slope of the phase boundary, hence, at higher temperatures it requires higher pressures to synthesize the high-pressure polymorph of silicon nitride. It turns out that the thermal expansion of the spinel-type gamma-phase is larger than that of the phenacite-type beta-phase. On the other side, pressure affects more the volume of beta-Si(3)N(4) than of gamma-Si(3)N(4), reflected in the higher bulk modulus of gamma-Si(3)N(4) up to about 40 GPa. The origin of the different temperature behavior of these phases, consequently, is rooted in a larger volume dependence of the zero point energy in gamma-Si(3)N(4) in comparison to beta-Si(3)N(4).
Institut für Anorganische Chemie Rheinisch-Westfälische Technische Hochschule Aachen Landoltweg 1, 52056 Aachen, Germany.
Atsushi
A
Togo
Peter
P
Kroll