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by decay of
Crystallization of amorphous ice triggered by radiogenic heating is another heating mechanism. When amorphous ice crystallizes, latent heat is released, because a crystalline state is more stable than an amorphous state. However, there is an energy barrier called an activation energy for the transition of amorphous ice to crystalline ice. The situation is illustrated in Fig. 7.
For the transition of amorphous ice to crystalline ice I (cubic ice),
we take the latent heat
(Ghormley, 1968), and the activation energy
per H
O molecule (Schmitt et al., 1989). In terms of temperature,
K and E/k=5370,K, where
is mass of an H
O molecule.
The rate of the transition from amorphous to crystalline ice at temperature T may be expressed by
where A is a constant and is given by
s for a transition from amorphous ice to crystalline (cubic) ice (Schmitt
et al., 1989). The value of
of
is on the order of the lattice vibration frequency. It should be noted
from eq. (10)
that the rate of crystallization rapidly increases with increasing temperature,
since
in the relevant temperatures. Theoretical derivation of eq. (10)
is given by Kouchi et al. (1994).