Fig. 17. Pressure-induced vanishing of atomic migration barrier.
(a) Measured quartz growth rate into amorphous SiO2
vs. pressure at 1200 °C. Sharp peak at 3 GPa might be due to
unusual kinetics or unusual thermodynamics. The latter occurs because the
amorphous phase is more compressible than quartz and therefore the amorphous
phase is more stable than quartz below 0 and above 16 GPa. However, the
thermodynamics alone cannot account for the data as shown in the inset.
Our explanation for this unprecedented sharp peak in the growth rate is
described in (b)-(d). (b) Standard Gibbs free energy vs. configuration
for 3 states: A: quartz + amorphous SiO2 + interface
with no defect; B: same system with defect (non-bridging oxygen (shown
in red in (d)), after O-Si bond has been broken at O-Si-OH site) in high-volume
state; C: same system with defect in low-volume state. The "reaction coordinate"
is a path through configuration space along which the reaction proceeds;
it is proportional to the number of atoms in the crystal. (c) Pressure
dependence: by the thermodynamic relation (¶G/¶P)T
= V, the slopes of curves A, B, and C are the volumes, VA,
VB, and VC,
of the system in these respective configurations. (d) Possible migration
mechanism, alternating between low-coordination state B (non-bridging O)
and high-coordination state C (overcoordinated Si). Si is at each vertex;
solid circles represent Si-O bonds normal to the page. The migration barrier
is | GC - GB | which vanishes at PC,
as shown in (c). Overall activation barrier in (c) is the greater of {GC,
GB} minus GA , which is smallest at PC.
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