  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 I-42d and, by assuming a
group-subgroup relationship between phases, they argued that the
lower-temperature alpha phase should have lower symmetry than that of the
widely-accepted P4_12_12 space group. With this motivation, we use
first-principles calculations to investigate the energy, structure, and local
stability of P4_12_12 and I-42d structures. We also compute the frequencies of
the zone-center phonon modes in both structures, as well as certain
zone-boundary modes in the I-42d structure, and compare with experiment. We
then argue that the various P4_12_12 and I-42d enantiomorphs can be grouped
into three clusters, each of which is identified with a three-dimensional
manifold of structures of P2_12_12_1 symmetry in which the P4_12_12 and I-42d
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_12_12 and I-42d structures with a
surprisingly low barrier of ~5 meV per formula unit. Possible implications for
the phase-transition mechanism are discussed.
