The phase diagram of carbon

The stable bonding configuration of carbon at NTP is graphite, as shown in Figure [2.3], with an energy difference between the graphite and the diamond of $\approx$ 0.02 eV per atom. Due to the high energetic barrier between the two phases of carbon, the transition from diamond to the most stable phase of graphite at normal conditions is extremely slow. This transition can also occurs more rapidly, when diamond is exposed to ion bombardment or high temperature for example. Due to the high anisotropy in the graphite structure as compared to that of diamond, the electronic, mechanical and optical properties of these two phases of carbon are very different. In Table [2.1] some properties of diamond and graphite crystals are presented. In the column related to graphite, the in-plane properties appears on the left and the transverse one between planes on the right.

Table 2.1: Properties of diamond and graphite.

Property	Graphite	Diamond
Lattice constant (RT) [Å]	2.462 6.708	3.567
Bond length (RT) [Å]	1.421	1.545
Atomic density [cm$^{-3}$]	1.14 $\times 10^{23}$	1.77 $\times 10^{23}$
Thermal conductivity [W/cm-K]	30 0.06	25
Debye temperature [K]	2500 950	1860
Electron mobility [cm$^2$/V-sec]	20$\times 10^3$ 100	1800
Hole mobility [cm$^2$/V-sec]	15$\times 10^3$ 90	1500
Melting point K	4200	4500
Band gap [eV]	-0.04	5.47

Bridging between these two allotropes of carbon lie a whole variety of carbon materials which include, among others, amorphous $sp^2$ bonded carbon (such as thermally evaporated carbon), micropolycrystalline $sp^2$ bonded graphite (such as glassy carbon), nanodiamond films, and amorphous $sp^3$ bonded carbon (sometimes referred to as amorphous diamond), which is structurally analogous to amorphous Si and is formed during low energy carbon ions deposition. Nanodiamond films, for example, can been grown by different deposition techniques such as dc assisted plasma chemical vapor deposition (CVD) from a methane-hydrogen mixture and others [12,13,14]. The criteria of quality of the nanodiamond films include low-contents of nondiamond phases, nano-sizes crystallites, uniform nanocrystallinity throughout thick films and random grain orientation.

Figure 2.3: P, T phase diagram of carbon reproduced from ref. [17]

Another polymorphic form of carbon was discovered in 1985. It exists in discrete molecular form, and consists of a hollow spherical cluster of carbon atoms. Each molecule is composed of groups of carbon atoms that are bonded to one another form both hexagons and pentagons geometrical configuration. The material composed of C$_{60}$ is known as buckminsterfullerene, named in honor of R. Buckminster Fuller, who invented the geodesic dome. In the solid state, the C$_{60}$ units form a crystalline structure and pack together in a face-centered cubic array. Molecular shapes other than the ball clusters recently have been discovered: these include nanoscale tubular and polyhedral structures. It is anticipated that, with further developments, the fullerenes will become technologically important materials [7].