Chemistry Reference
In-Depth Information
0
(a)
-50
-100
50
100
150
200
250
300
350
0.5
(b)
0.4
0.3
0.2
0.1
0
50
100
150
200
250
300
350
T
(K)
Figure 19.
(a) Average energy plotted as a function of temperature from Metropolis Monte
Carlo simulations for large simulation cell of ice VII/VIII. Data is presented for series of Metropolis
Monte Carlo runs ascending(
) and descending (
) in temperature. The vertical line is located at the
calculated transition temperature near 228 K. (b) Entropy plotted as a function of temperature. The
horizontal line is the Pauling entropy for a fully disordered ice lattice subject to the ice rules.
cell. Metropolis Monte Carlo simulations were performed on a simulation cell
measuring eight primitive cells on each side containing 1024 water molecules. The
Monte Carlo simulations yield a prediction of a first-order phase transition near
228 K with significant hysteresis, as shown in Fig. 19a. The transition temperature
is calculated as the point of equal free energy(
A
0) between the two phases as
determined by thermodynamic integration of the low-temperature proton-ordered
phase from 0 K and the high-temperature proton-disordered phase from infinite
temperature. Since we neglect the effect of what is known to be a small change in
the lattice constant with temperature, we do not include a pressure-volume term
in the free energy. Entropy as a function of temperature is plotted in Fig. 19b. With
decreasing temperature, 7% of the ideal entropy for a fully disorder ice phase is
lost before the transition. The calculated entropy at the transition, 228 K, is 91%
of the ideal configurational entropy associated with H-bond disordering compared
with experimentally reported values of 83% for H
2
O and 91% for D
2
O [130].
Umemoto et al. [62] recently calculated the ice VII/VIII phase boundary as
a function of increasing density or pressure. To our knowledge, this is the first
calculation of this sort with variable cell size. They obtained the isomer ener-
gies
E
i
from electronic DFT, and
A
vib
in the harmonic approximation for the 52
symmetry-distinct isomers of a 16-water unit cell. They estimated the VII/VIII
=
