Page 243 - Physical Chemistry

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Chapter 7 compress the sample are less than 1 mm in diameter. To detect a phase transition and
One-Component Phase Equilibrium find the structure of the new phase formed in a diamond-anvil cell, one commonly
and Surfaces
uses x-ray diffraction (Sec. 23.9). The pressure can be found from the pressure-
induced shift in spectral lines of a tiny chip of ruby that is included in the sample cell.
Pressures of 5 megabars have been obtained with a diamond-anvil cell [A. L. Ruoff
et al., Rev. Sci. Instrum., 63, 4342 (1992)]. Theoretical calculations indicate that, at
sufficiently high pressures, every solid is converted to a metallic form. This has been
verified for I , CsI, Xe, S, and oxygen.
2
Metallic solid hydrogen has been called “the holy grail of high-pressure physics.”
Theoretical estimates of the required pressure vary widely. Solid hydrogen has been
compressed to 3.4 megabars without being metallized [C. Narayana et al., Nature,
393, 46 (1998)]. It has been speculated that once metallic solid hydrogen is formed,
it might remain in the metastable metallic form when the pressure is released and
might be usable as a lightweight structural material to make such things as automo-
biles. Solid metallic hydrogen might be a superconductor at low temperatures.
Although metallic solid hydrogen has not been achieved, metallic liquid hydrogen
has been formed very briefly at 1.4 Mbar and 2600 K by shock-wave compression
[W. J. Nellis et al., Phys. Rev. B, 59, 3434 (1999)]. The planet Jupiter is 90% hydro-
gen and at the very high pressures and temperatures of its interior, much of this hy-
drogen likely exists in a metallic liquid state, giving rise to the magnetic field of
Jupiter (www.llnl.gov/str/Nellis.html).

EXAMPLE 7.7 Phase stability

At 25°C and 1 bar, the densities of diamond and graphite are r 3.52 g/cm 3
di
3
and r 2.25 g/cm . Use Appendix data to find the minimum pressure needed
gr
to convert graphite to diamond at 25°C. State any approximations made.
As noted in Sec. 7.2, the stable phase is the one with the lowest G .
m
Appendix G°values show that for the transformation diamond → graphite at
f
25°C and 1 bar,
¢G° 2.90 kJ>mol G m,gr 11 bar2 G m,di 11 bar2
Thus at room T and P, graphite is the stable phase and diamond is metastable.
How does changing the pressure affect G and affect the relative stability of
m
the two forms? From dG S dT V dP, we have ( G / P) V
m m m m T m
M/r, where M is the molar mass. The smaller density of graphite makes V of
m
graphite greater than V of diamond, so G of graphite increases faster than G
m m m
of diamond as P is increased, and eventually diamond becomes the more-stable
phase. At the pressure P at which the graphite-to-diamond phase transition
2
occurs, we have G (P ) G (P ).
m,gr 2 m,di 2
Integrating dG V dP (T const.) at constant T and neglecting the change
m
m
of V m with pressure, we have
G 1P 2 G 1P 2 V 1P P 2
2
m
2
1
1
m
m
Substitution of this equation into G m,gr 1P 2 G m,di 1P 2 and use of V M>r gives
2
2
m
G m,gr 1P 2 V m,gr 1P P 2 G m,di 1P 2 V m,di 1P P 2
1
1
2
1
1
2
G m,gr 1P 2 G m,di 1P 2 2900 J>mol
1
1
P P
1
2
3
1
V m,di V m,gr 112.01 g>mol213.52 1 2.25 21cm >g2
P P 1506 J>cm 3
2
1