Role of bonding and coordination in the atomic structure and energy of diamond and silicon grain boundaries

The high-temperature equilibrated atomic structures and energies of large-unit-cell grain boundaries (GB's) in diamond and silicon are determined by means of Monte-Carlo simulations using Tersoff's potentials for the two materials. Silicon provides a relatively simple basis for understanding GB structural disorder in a purely sp³ bonded material against which the greater bond stiffness in diamond combined with its ability to change hybridization in a defected environment from sp³ to sp² can be elucidated. We find that due to the purely sp³-type bonding in Si, even in highly disordered, high-energy GB's at least 80% of the atoms are fourfold coordinated in a rather dense confined amorphous structure. By contrast, in diamond even relatively small bond distortions exact a considerable price in energy that favors a change to sp²-type local bonding; these competing effects translate into considerably more ordered diamond GB's; however, at the price of as many as 80% of the atoms being only threefold coordinated. Structural disorder in the Si GB's is therefore partially replaced by coordination disorder in the diamond GB's. In spite of these large fractions of three-coordinated GB carbon atoms, however, the three-coordinated atoms are rather poorly connected amongst themselves, thus likely preventing any type of graphite-like electrical conduction through the GB's.