Intrinsic stress and local rigidity in tetrahedral amorphous carbon

Atomic level quantities are valuable tools in probing the local structural characteristics of amorphous materials. In this paper, we utilize the concept of atomic level stresses to study the problem of intrinsic stress in tetrahedral amorphous carbon. The stresses are extracted from the local energetics, based on the empirical potential approach, while the finite temperature statistics of the system are described by Monte Carlo simulations. We show that contrary to the nonequilibrium as-grown structures that are left intrinsically stressed by the deposition process, equilibrated/annealed films that relax the external constraints and pressure possess zero total intrinsic stress without reduction of the desired high fraction of ${\mathrm{sp}}^3$ sites. We also address in this paper the issue of local rigidity by introducing the concept of local bulk modulus, as a measure of the rigidity contributed by each atomic site. We find that the ${\mathrm{sp}}^2$ sites are not floppy elements in the amorphous network but that they contribute rigidity, although significantly less than the ${\mathrm{sp}}^3$ sites.