Chemistry Reference
In-Depth Information
20
(a)
10
0
-10
-20
-30
-40
0
50
100
150
200
250
300
T
(K)
(b)
0.4
0.08
0.2
0.04
0
100
120
0
0
50
100
150
200
250
300
T
(K)
Figure 24.
(a) Average energy plotted as a function of temperature from Metropolis Monte Carlo
simulations for a simulation cell of ice III containing 1500 waters. Energies are presented for a series
of Metropolis Monte Carlo runs ascending (
) and descending (
) in temperature. (b) Entropy from
the present work (thick solid line) plotted as a function of temperature where the horizontal line is the
Pauling entropy for a fully disordered ice lattice. With decreasing temperature, 29.7% is lost before the
transition, 67.7% at the transition, and 2.6% as the fully ordered ice IX structure is formed. In addition,
entropy as a function of temperature calculated using the occupational probabilities,
α
and
β
obtained
from our simulations, is plotted using the one parameter expressions of Nagle(
) [145] and Howe and
Whitworth(
) [146].
may be obtained directly from calorimetry, or inferred from diffraction data using
mean-field theories [114, 144-147] that relate the system entropy to hydrogen site
occupations
α
and
β
. Because we have a full statistical mechanical model of ice III
and ice IX, we can calculate the exact entropy and exact site occupations. We can
compare the exact entropy with the entropy that would be predicted on the basis
of mean-field theories. We find that all existing mean-field theories significantly
overestimate the entropy of the disordered ice III phase. When used to interpret
diffraction data [45, 46], they imply a value for the transition entropy that is too
large.
In our simulations, the value of
β
never significantly differed from
α
, so we could
effectively model the system with a one parameter theory for partially disordered
ice systems. Using the average of
α
and
β
as the single occupational probability for
each temperature, predicted entropy is plotted as a function of temperature obtained
from the expressions by Nagle(
) [146] in
Fig. 24. Application of the two parameter expression by MacDowell et al. [147],
) [145] and Howe and Whitworth(
