Phase Diagram for Carbon
From: F.P. Bundy, The P,T Phase and Reaction diagram for elemental Carbon, 1979; J.
Geophys. Res. 85 (B12) (1980) 6930.
The phase diagram of water/ice
and a new metastable phase of ice
The ice phase diagram is extremely rich, comprising 11 confirmed crystalline
phases, in which the water molecules link through hydrogen bonds to form
tetrahedral frameworks. The structures and stabilities of many of these phases
have been established definitively by means of neutron powder-diffraction in
collaboration with Prof. Werner Kuhs, University of Göttingen, Germany. This
work is of importance to a large interdisciplinary group of researchers interested
in the hydrogen bond, while the versatility of the water molecule in forming so
many different structures is relevant to its biological importance.
15 years ago, little was known about the structures of ice under pressure, most
information in the literature being obtained from samples 'recovered' to ambient pressure
at liquid nitrogen temperatures. In the early 1980s, the high-pressure facilities at ILL,
together with the Rietveld powder refinement technique, had developed to a stage where
the structures of most of these phases could be studied under their conditions of stability.
So began our collaboration which has, through neutron work both at ILL and ISIS, not
only sorted out a good part of the phase diagram (Fig. 1), but has also led to new,
unexpected results of wide significance.
The earliest work using clamped high-pressure cells found that ice VIII was
antiferroelectrically ordered with non-bonded oxygen-oxygen contacts shorter than the
bonded distances. Although this might seem a strange result, it confirmed beautifully
other ideas which stressed the importance of non-bonded repulsions in determining
hydrogen bonded structures in general. In addition to the expected hydrogen disorder, ice
VII was shown to have oxygen disorder. Again, this was initially unexpected, though it
has been found more generally since, e.g. in the disordered medium pressure phase ice VI.
The lower pressure part of the phase diagram was probed using the He-gas cell. This
raised many experimental difficulties: ice V was almost impossible to form and ice III
was very difficult. The problem was resolved when it was discovered that the helium gas
was stabilising a previously unknown He-hydrate with a water molecule topology
identical to that of ice II - another unexpected result and new structure.
The work on ice III and IX revealed that, in contrast to earlier assumptions, both ices are
partially (dis)ordered. Very recently, full sets of data on ices III and V under various
conditions of temperature and pressure have been obtained, thus ending a long-standing
uncertainty about H-ordering in these phases. Ice III and ice V both show partial ordering
in the 20 to 30% range even close to the melting point.
having a number of triple points and one or possibly two critical points. Figure 1:
The phase
diagram of
water/ice.
Inset: The
medium
pressure
range
showing
the melting
curves of
metastable
ices IV and
XII.
All the solid phases of ice involve
Figure 2: The H-bond framework of
tetragonal ice XII viewed down the caxis. The spacegroup is I42d, lattice
constants are a = 8.304 Å and c = 4.024
Å.
However, the phase diagram is still not fully
understood. On several occasions during the last
15 years, powder lines have been seen that could
not be identified with any known ice or clathrate
phase. As we have pinned down with increasing
precision the preparation conditions for these
phases, we have begun to back them into a
corner. The first success has been ice XII, a
totally new structure that we have found within
the stability region of ice V and which was
prepared by crystallisation from the liquid
phase. The topology of ice XII is unlike any of
the known ice phases, and contains a mixture of
5 and 7 membered rings. The inset in Fig. 1
shows the tentative stability region and Fig. 2
the structure clearly exhibiting the 5 membered
rings organised to form channels along the
unique axis.
Figure 3: The H-bond framework of
rhombohedral ice IV showing the autoclathrate arrangement with H-bonds
passing through the centre of 6
membered rings.
Another metastable phase of ice, ice IV (Fig. 3),
discovered in the 1930s by Bridgman, was
obtained in situ in our experiments for the first
time by following a slightly different preparation
recipe. The density of ice V (1.402 g.cm-3 for
D2O) is smaller than the densities of ice IV and
XII (1.436 and 1.437 g.cm-3 resp.), which are
quite similar to each other. Both ice IV and XII
are fully hydrogen disordered, while ice V is
partially ordered as mentioned above. On the
other hand, differences occur in the degree of
hydrogen-bond bending: compared to ice V and
XII the structure of ice IV shows distinctly
smaller bending, yet exhibits interpenetration of
the H-bond framework, a phenomenon
sometimes referred to as auto-clathration.
Clearly there are two ways of increasing the
density in water structures: additional hydrogen
bond bending as in ice V and XII or hydrogen
bond interpenetration as in ice IV and also in the
next highest pressure phase, ice VI. At present,
ice XII is the densest known phase of the water
substance without interpenetration. Yet in all
these structures the non-bonded repulsive
constraints are active and confirmed by our
neutron results.
Two lines of further research are now developing from these findings. First, the enhanced
richness of the ice phase-diagram in the medium pressure range is an excellent
demonstration of the versatility of the water molecule that enables the building of a
variety of hydrogen-bonded structures sometimes in very close competition for
occupying the same region of p-T space. The seemingly delicate balance of enthalpic and
entropic contributions to the total energy will thus allow us to test very critically the
viability of water potential functions used widely in computer calculations in chemical
and biomolecular systems. Secondly, the fact that we have formed metastable phases
directly from the liquid makes the water system now an excellent candidate for studies of
metastability, including both thermodynamic and kinetic aspects of phase formation.
This work has also demonstrated that neutron diffraction is by far the best method to
explore the phase diagram of ice as it allows the detection of topological phase changes
and any sudden or continuous changes in H-ordering. At the same time, information on
expansivities and compressibilities is obtained which gives us further quantitative
information on the details of the chemically
Phase diagram for water.
sulfur