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liquid. (Surface tension makes the pressure inside a bubble exceed the pressure of its Section 7.4
surroundings; see Sec. 7.8.) Liquid helium II has a very high thermal conductivity, Solid–Solid Phase Transitions
which prevents local hot spots from developing. When helium II is vaporized at its
boiling point, it does not bubble.

Some physicists have speculated that the universe might currently exist in a metastable
high-energy false-vacuum state that is separated by an energy barrier from the lower-
energy true vacuum state. If this is so, there is a slight probability for the universe to spon-
taneously undergo a phase transition to the true vacuum state. The transition would start at
a particular location and would propagate throughout the universe at nearly the speed of
light. In the true vacuum state, the laws of physics would differ from those in the false-
vacuum state (P. Davies, The Last Three Minutes, BasicBooks, 1994, chap. 10). “Vacuum
decay is the ultimate ecological catastrophe . . . after vacuum decay . . . life as we know it
[is] impossible [S. Coleman and F. DeLuccia, Phys. Rev. D, 21, 3305 (1980)]. It has even
been suggested that just as a tiny crystal of ice dropped into supercooled water nucleates
the formation of ice, a high concentration of energy produced in a collision experiment by
particle physicists might nucleate a phase transition to the true vacuum state, thereby de-
stroying the universe as we know it. Since the energies produced by particle physicists are
less than the highest energies that occur naturally in cosmic rays, such a catastrophic
laboratory accident is extremely unlikely [P. Hut and M. Rees, Nature, 302, 508 (1983);
M. Rees, Our Final Hour, Basic Books, 2003, chap. 9.]

The phase diagram of water is actually far more complex than the one shown in
Fig. 7.1. At high pressures, the familiar form of ice is not stable and other forms exist
(Fig. 7.9b). Note the existence of several triple points at high pressure and the high
freezing point of water at high P.
Ordinary ice is ice Ih (where the h is for hexagonal and describes the crystal struc-
ture). Not shown in Fig. 7.9b are the metastable forms ice Ic (cubic) (obtained by con-
densation of water vapor below 80°C) and ices IV and XII [C. Lobban et al., Nature,
391, 268 (1998)], which exist in the same region as ice V. Also not shown are the low-
temperature forms ice IX and ice XI, and the very-high-pressure form ice X, all of
whose phase boundaries are not well established. The low-temperature forms ice XIII
and XIV were reported in 2006 [C. G. Salzmann et al., Science, 311, 1758 (2006)].
In addition to the crystalline forms ices I to XIV, at least two amorphous forms of
ice exist. Structures of the various forms of ice are discussed in Franks, vol. 1,
pp. 116–129; V. F. Petrenko and R. W. Whitworth, Physics of Ice, Oxford University
Press, 1999, chap. 11; www.lsbu.ac.uk/water/phase.html.

The plot of Kurt Vonnegut’s novel Cat’s Cradle (Dell, 1963), written when only ices I to
VIII were known, involves the discovery of ice IX, a form supposed to exist at 1 atm with
a melting point of 114°F, relative to which liquid water is unstable. Ice IX brings about the
destruction of life on earth. (Kurt Vonnegut’s brother Bernard helped develop the method
of seeding supercooled clouds with AgI crystals to induce ice formation and increase the
probability of snow or rain.)
The properties of matter at high pressures are of obvious interest to geologists.
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4
Some pressures in the earth are 10 bar at the deepest part of the ocean, 10 bar at the
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boundary between the crust and mantle, 1.4 10 bar at the boundary between the
6
mantle and core, and 3.6 10 bar at the center of the earth. The pressure at the cen-
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ter of the sun is 10 bar.
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Matter has been studied in the laboratory at pressures exceeding 10 bar. Such
pressures are produced in a diamond-anvil cell, in which the sample is mechanically
compressed between the polished faces of two diamonds. Because diamonds are
transparent, the optical properties of the compressed sample can be studied. The
diamond-anvil cell is small enough to be held in one’s hand and the diamond faces that