The elasticity and hardness of a-C and a-C:H are related to their mean network coordinations. It is shown that ${\mathit{sp}}^2$ sites contribute no rigidity if they form graphitic clusters, as suggested by experiment and electronic structure calculations, despite their having coordinations above the critical value 2.4. Hence both ${\mathit{sp}}^2$ sites and polymeric =${\mathrm{CH}}_2$ groups can severely lower the hardness of amorphous carbons.

• Received 11 February 1991

DOI:https://doi.org/10.1103/PhysRevLett.68.220