Diamond and graphite properties

The electronic configuration of carbon is 1s²2s²2p², i.e. with four valence electrons spread in the s and p orbitals. In order to create covalent bonds in diamond, the s orbital mixes with the three p orbitals to form sp³ hybridization. The four valence electrons are thus equally distributed among the sp³orbitals, while each orbital points to one of the four corners of a tetrahedron. The tetrahedral structure, together with the highly directed charge density, give strength and stability to the bonds. Consequently, all the bonds in diamond are of the same length (1.54 $\AA$), with the same bond angle (109.47^o).

Natural diamond can be divided into four types, according to the percentage and kind of impurities they contain, mainly nitrogen and boron. Type IIa diamond is the purest natural diamond and contains very few nitrogen atoms, of the order of 10¹⁸ cm^-3, while the atomic density of diamond is 1.77 $\times 10^{23}$ cm^-3. It has a high electronic mobility of 1800 cm²/V sec at room temperature, compared to 1500 cm²/V sec in silicon. The donor level associated with nitrogen lies relatively deep, at $\sim$ 1.7 eV, while the band gap in diamond is 5.47 eV. Diamond is an insulator at room temperature, with a resistivity larger than 10 $^{12} \ \Omega$ cm.

Type IIb natural diamond contains boron, with a density of 10¹⁷cm^-3. It has a p-type conductivity, with an activation energy of 0.37 eV. The hole mobility measured at room temperature is $\sim$ 1500 cm²/V sec, compared to 450 cm²/V sec in silicon.

In Type Ib natural diamond the concentration of nitrogen is $\sim 5 \times 10 ^{18}$ cm^-3, with a resistivity similar to that of type IIa diamond at room temperature, but much lower at high temperature. A very low electronic mobility was measured at room temperature, of the order of 100 cm²/V sec.

Finally, type Ia natural diamond has the highest concentration of nitrogen, namely $\sim 10^{20}$ cm^-3. However the nitrogen atoms can appear not only as substitutional impurities but also as aggregates in the form of platelets or adjacent pairs. In that case, in addition to the 1.7 eV energy level, another level at $\sim$ 4 eV below the conduction band exits.

In the graphite crystal, the s orbital mixes with two p orbitals only, and each of the new three sp² orbitals points to one of the three vertices of a triangle which lies in the x-y plane (for instance). Three electrons occupy these orbitals and one electron stays in the p_z orbital which is directed perpendicular to the x-y plane. Hence, the carbon atoms are bonded by three $\sigma$bonds (the charge density lies between two atoms) and one $\pi$ bond (the charge density is concentrated above and under the x-y plane, perpendicular to the atomic bond). Since there is no preference as to which atom the p_z-electron should bond to, the bond formed ($\pi$bond) with all three neighbors is weaker than the $\sigma$ bonds, this electron is more free to move and contributes to conduction. Furthermore, the $\pi$ bond stabilizes the structure and ``locks'' it in the plane. The whole crystal is made of sheets held together by weak Van der Waals forces, separated by a distance of 3.40 Å. This gives softness to the structure [1,2].

The stable bonding configuration of carbon at NTP is graphite, as shown in figure 2.1, 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 stablest phase of graphite at normal conditions is very 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 compared to that of diamond, the electronic, mechanical and optical properties of these two phases of carbon are very different. In table 2.1 few 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 on the right.

  

Figure: P, T phase diagram of carbon reproduced from ref. [3]

 

Table 2.1: Properties of diamond and graphite.

Property	Graphite	Diamond
Lattice constant (RT) [$\AA$]	2.462 6.708	3.567
Bond length (RT) [$\AA$]	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 [cm2/V-sec]	20 $\times 10^3$ 100	1800
Hole mobility [cm2/V-sec]	15 $\times 10^3$ 90	1500
Melting point K	4200	4500
Band gape [eV]	-0.04	5.47