ABSTRACT
Carbon with its unique physical and mechanical properties, as well as its structural analogue boron nitride, is of great interest for research. Suffice it to say that carbon is the most refractory and, in the crystal lattice of diamond, the hardest substance in nature. All major modifications of boron nitride have crystallographic counterparts among the polymorphs of carbon. Table 2.1 shows the basic physical properties of crystalline modifications of carbon and boron nitride. The isotype nature of the polymorphs of carbon and boron nitride is due to their isoelectronic structure. For an isolated carbon atom the filling scheme of the electron shells is 1s22s22p2, for boron – 1s22s22p, nitrogen – 1s22s22p3. This structure of nitrogen and boron atoms provides the possibility of bonds in the crystal lattice by hybridization of the s-and p-orbitals. With sp2-hybridization, carbon and boron nitride show the formation of three valence bonds located in one plane (0001) and forming an angle of 120°. Trigonal bonds between the atoms form a hexagonal grid – a flat layer, which is the basic structural unit of all types of graphite and graphite-like boron nitride (Fig. 2.1a, b). In sp3-hybridization, carbon and boron nitride show the formation of four bonds per atom, oriented towards the vertices of a regular tetrahedron. The tetrahedral distribution of sp3-hybridized bonds in carbon is shown by diamond and lonsdaleite, in boron nitride – sphalerite and wurtzite. The crystallographic structure of the lattice of graphite and graphite-like BN, in which the distance between the planar layers is 2.5 times greater than the shortest interatomic distances within the layers, makes them typical representatives of the layered structures and explains some features of the physical and mechanical properties. Between the layers there is a weak van der Waals interaction, and for graphite-like BNG also the electrostatic interaction between the atoms of nitrogen and boron. The energy of van der Waals interaction for graphite is U1 = –4.99 kJ/mol for BNG = U1 + U2 = –7.92 + (–0.13) = –8.05 kJ/mol, where U2 is the energy of the electrostatic interaction [2.1]. Within the layer there are much stronger covalent bonds. Thus, the binding energy of carbon within the layers (U3 = –347 kJ/mol [2.2]) is almost 70
Table 2.1. Some physical properties of carbon and boron nitride
Property Carbon Boron nitride The lattice parameters (T = 300K)
Graphite a, Å 2.4611 2.5040 c, Å 6.7076 6.6612
Diamond (sphalerite) a, Å 3.5670 3.615
Lonsdaleite (wurtzite) a, Å 2.52 2.55 c, Å 4.12 4.23
density ρ, g/cm3 (T = 300K) Graphite 2.265 2.29
Diamond (sphalerite) 3.515 3.51 Lonsdaleite (wurtzite) 3.51 3.49
Elastic moduli of diamond (sphalerite)
С11, GPa 1070 783 С12, GPa 125 107 С44, GPa 576 418
The hardness of diamond (sphalerite)
H μ , GPa 100 67
Melting point Tm, K p = 0.1 МPа 4320±50 3243
The Debye temperature θ, K 2230 1720 The coordinates of the triple point (graphite – diamond (sphalerite) –
liquid): p, GPа 11.0 9.5
T, K 3973 3450
times greater than U1. For the graphite-like BNG ratio U
U U 3
82 +
= [2.3]. This leads to the fact that the shear resistance of the layers relative to each other is very small, and the layers can easily slip. It should also be noted that the mobility of defects formed during deformation in carbon and boron nitride at T = 300 K is very small, because this temperature is well below the Debye temperature for C (θ = 2230 K) and BNG (θ = 1720 K). For this
reason, graphite and graphite-like boron nitride are convenient objects for studying the process of accumulation of defects in shear and obtaining in this way the disordered (amorphous) state.
