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182 PHASE EQUILIBRIA

It should be clear from the graph in Figure 5.2 that G m is
These arguments rep-
negative (as required for a spontaneous change) only if the final
resent a simple ex-
ample of phase equi- state is solid ice and the initial state is liquid water. This sign of
libria. This branch of G m is all that is needed to explain why liquid water freezes at
thermodynamics tells temperatures below T (melt) .
us about the direction Conversely, if an ice cube is warmed beyond T (melt) to the tem-
◦
of change, but says perature of the mouth at 37 C, now it is the solid water that
nothing about the rate has excess energy; to stabilize it relative to liquid water at 37 C
◦
at which such changes requires a different phase change to occur, this time from ice to
occur.
liquid water. This argument again relies on the relative magnitudes
of the molar Gibbs function, so G m is only negative at this higher
temperature if the final state is liquid and the initial state is solid.

Why was Napoleon’s Russian campaign
such a disaster?

Solid-state phase transitions

A large number of French soldiers froze to death in the winter of 1812 within a
matter of weeks of their emperor Napoleon Bonaparte leading them into Russia. The
loss of manpower was one of the principal reasons why Napoleon withdrew from the
outskirts of Moscow, and hence lost his Russian campaign.
But why was so ruthless a general and so obsessively careful a tactician as Napoleon
foolhardy enough to lead an unprepared army into the frozen wastes of Russia? In
fact, he thought he was prepared, and his troops were originally well clothed with
thick winter coats. The only problem was that, so the story goes, he chose at the last
moment to replace the brass of the soldiers’ buttons with tin, to save money.
Metallic tin has many allotropic forms: rhombic white tin (also called β-tin) is
◦
stable at temperatures above 13 C, whereas the stable form at lower temperatures is
cubic grey tin (also called α-tin). A transition such as tin (white) → tin (grey) is called a
solid-state phase transition.
Figure 5.3 shows the phase diagram of tin, and clearly shows the transition from
tin (white) to tin (grey) . Unfortunately, the tin allotropes have very
different densities ρ,so ρ (tin, grey) = 5.8g cm −3 but ρ (tin, white) =
The transition from −3
white tin to grey was 7.3g cm . The difference in ρ during the transition from white to
first noted in Europe grey tin causes such an unbearable mechanical stress that the metal
during the Middle Ages, often cracks and turns to dust – a phenomenon sometimes called
e.g. as the pipes of ‘tin disease’ or ‘tin pest’.
cathedral organs dis- The air temperature when Napoleon entered Russia was appar-
integrated, but the ently as low as −35 C, so the soldiers’ tin buttons converted from
◦
process was thought white to grey tin and, concurrently, disintegrated into powder. So,
to be the work of if this story is true, then Napoleon’s troops froze to death because
the devil.
they lacked effective coat fastenings. Other common metals, such