Abstract
A relationship proposed for minerals was used to calculate the theoretical hardness for the man-made compounds hBN and cBN; these values were then compared to the theoretical hardness for several carbon allotropes. The crystallochemical features of boron nitride (BN) has resulted in a theoretical Vickers hardness equal to half the value for diamond if it adopts the cubic lattice (cBN) and roughly equal to that of graphite if it adopts the hexagonal lattice (hBN). The very low hardness of hBn and graphite is explained by considering these substances as randomly oriented heterodesmic compounds in which the strong covalent σ bonds acting within their graphene layers are not put at work. In contrast to this, such strong bonds are put at work in the hollow cage structures obtained when the planar graphene layers become curved, as for instance in fullerenes, nanotubes or nanofibers. Indeed, the calculated theoretical hardness for carbon nanotubes and nanofibers obtained by chemical vapour deposition proved to be as high as one-third up to one-half the Vickers hardness for diamond.
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