Structural stability and lattice dynamics of SiO2 cristobalite

Among the phases of SiO2 are alpha and beta cristobalites, which have a long and somewhat controversial history of proposed structural assignments and phase-transition mechanisms. Recently, Zhang and Scott found new indications that the higher-temperature beta phase has space group 1 (4) over bar 2d and, by assuming a group-subgroup relationship between phases, they argued that the lower-temperature a phase should have lower symmetry than that of the widely accepted P4(1)2(1)2 space group. With this motivation, we use first-principles calculations to investigate the energy, structure, and local stability of P4(1)2(1)2 and 1 (4) over bar 2d structures. We also compute the frequencies of the zone-center phonon modes in both structures, as well as certain zone-boundary modes in the 1 (4) over bar 2d structure, and compare with experiment. We then argue that the various P4(1)2(1)2 and 1 (4) over bar 2d enantiomorphs can be grouped into three clusters, each of which is identified with a three-dimensional manifold of structures of P2(1)2(1)2(1) symmetry in which the P4(1)2(1)2 and 1 (4) over bar 2d appear as higher-symmetry special cases. We find that there are relatively high energy barriers between manifolds, but low barriers within a manifold. Exploring the energy landscape within one of these manifolds, we find a minimal-energy path connecting P4(1)2(1)2 and 1 (4) over bar 2d structures with a surprisingly low barrier of similar to 5 meV per formula unit. Possible implications for the phase-transition mechanism are discussed.