A New Pressure Induced Phase in Silica
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Department of Chemical Engineering and Materials Science, Minnesota Supercomputer
Institute, University of Minnesota, Minneapolis, MN 55455, USA **Institut de Physique Appliqu~e, Ecole Polytechnique F~d~rale de Lausanne, PHB-Ecublens, 1015 Lausanne, Switzerland ABSTRACT We predict a new pressure induced phase for silica via first principles variable-cell-shape molecular dynamics. The structure results from annealing a-quartz at pressures near a phonon instability. The mechanism which produces this new phase is similar to that proposed for structural transitions in silicate melts. The diffraction pattern of the new phase compares favorably with that of the unidentified intermediate crystal phase found in silica near the pressure induced amorphization transformation.
INTRODUCTION Pressure induced amorphization is a poorly understood phenomenon which occurs in a wide variety of solids [1]. One of the more interesting pressure induced amorphization transformations occurs in a-quartz. In contrast to systems in which the crystal phase transforms directly into an amorphous phase, quartz transforms concurrently to a new crystalline phase [2,3]. The structure of the new phase is unknown. Since diamond anvil experiments have suggested that the the amorphous phase develops out this new crystalline phase, there is great interest in clarifying the nature of this new phase and the role it might play in the amorphization process.
SOFT MODES IN Os-QUARTZ It is has been proposed that a "major" phonon softening plays an important role in the amorphization process [4-8]. The corresponding phonon instability is predicted to occur at the K point of the Brillouin zone. These predictions are based on lattice dynamics calculations using interatomic potentials. The softening occurs along the entire lowest acoustic branch. In Figure 1, we illustrate the pressure dependence of the lowest acoustic branches at ambient pressure and at the pressure at which the zone edge becomes soft ('• 19 GPa).
243 Mat. Res. Soc. Syrup. Proc. Voh. 499 © 1998 Materials Research Society
[nn
30
'7
V
S20 1I0
.10
P=19 GPa
30
1o
.10
K Figure 1. Phonon dispersion curves for the r - K direction in quartz. A soft mode appears in this direction under pressure.
Ab initio pseudopotential calculations of the Born stability criteria yield consistent results, i.e., a shear instability at similar pressures [7,8]. Under initial hydrostatic pressure, the elastic constants, cij, are related to the energy variation, AE, to second order in the strains, cij:
AE Vo
AV P--Vo
1 2 .cij ii
where (p,Vo) are the initial pressure and volume, respectively. For the quartz symmetry, it is possible to reduce the number of independent elastic constants to six: c11 , c12 , c 13 , c 14, c33, c44. If we demand the elastic energy be positive, this imposes the following constraints:
B1= c11 - cI121 > 0 B2 = (c11 + c12)c33 - 2c1 3 > 0 B 3 = (Cl
- c 1 2)c
44
- 2c1 4 > 0
for the quartz crystal to be mechanically stable. The first criterion, B1 , insures that the squared veloci
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