Another notable solid-solid equilibrium is the graphite-to-diamond transition in the element carbon. Graphite is fairly common in the earth's crust but the rarity of diamond is the origin of its value. Under normal terrestrial conditions (300 K, 1 atm) the two forms of carbon are not in equilibrium and so, thermodynamically speaking, only one form should exist. The stable form is the one with the lowest Gibbs free energy. At 300 K, the enthalpy difference between diamond and graphite is Ahd-g = 1900 J/mole, with diamond less stable than graphite in this regard. Being a highly ordered structure, diamond has a molar entropy lower than that of graphite, and Asd-g = -3.3 J/mole-K (see Fig. 3.6). This difference also favors the stability of graphite. The combination of the enthalpy and entropy effects produces a free-energy difference of:
Agd-g = gdiamond - ggraphite = Ahd-g -TAsd-g = 1900 - 300(-3.3) = 2880 J/mole
Since the phase with the lowest free energy (graphite) is stable, diamond is a metastable phase. It exists only because the kinetics of transformation to graphite is extremely slow at ambient temperature. How then does diamond form?
The phase diagram of carbon is shown in Fig. 5.5. At low pressure, graphite is stable at all temperatures up to the melting point. In order to transform graphite into diamond at constant temperature, the pressure must be very high. This is how, deep under the earth, diamond was created.
There is a considerable industrial market for synthetic diamonds, and the pressure required for the transformation can be read from the phase diagram of Fig. 5.5, or it can be calculated by applying the fundamental differential dg = vdp at constant temperature to both phases and taking the difference:
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