Theory

Carbon has several different allotropes - materials made entirely out of carbon, that differ in their spatial structure, rendering different properties as well. Two such allotropes are the Diamond and the Graphite.

The diamond's lattice is a variation on the FCC, having two inter-penetrating displaced FCC sub lattices. Each carbon is covalently bonded with 4 other neighbours in the SP3 hybridization.

The carbon has a lattice consisting of stacked honeycombs planes. Bonds between coplanar atoms are covalent, and each atom has 3 neighbours. Bonding of different layers is done by weak Van Der Waals bonds, making it easy to separate different layers.

Since SP3 bonds have higher energies compared to SP2 bonds, diamond is less stable than graphite, though in standard conditions conversions from diamonds to graphites are negligible. This means, however, that transferring energy to a diamond might break the SP3 bonds, and with sufficient damage the crystal might, under annealing, reform as a graphite. This result is well known and previously observed in laboratories and can be achieved by ion implantation, which creates a spherical damaged area, as can be seen on the image to the left.

As previously mentioned, each carbon atom in a diamond has 4 neighbours, in an SP3 hybridization. This means all sites are occupied, and electrons are bound to the respective atoms, making the diamond a great insulator. In contrary, carbon atoms in graphite have 3 neighbours, in an SP2 hybridization, allowing one free electron per atom to travel between different sites. This makes graphite a conductor. It is a known fact that diamonds have a threshold in which their resistance drops, given a large enough concentration of implanted ions. We can then deduce that if we use ion implantation to create overlapping graphitic spheres in the diamond, electrons would be able to percolate across the spheres turning the diamond to a conductor. Indeed, observations reveal a threshold of ion concentration, after which the diamond model loses its insulator attributes.

My project aims to simulate and investigate the behaviour of a single damaged area in different scenarios - damages done by ion implantation, damages done by laser heating and the behaviour of damaged areas with different spheres radii. In the future, it should include a simulation of several regions, investigating the percolation explanation to the diamond loosing its insulator attributes.

Simulations are done in MD, using LAMMPS. This site would also, I hope, serve as a reference to other students starting to work with LAMMPS.

Previous results and simulations of graphitization can be found in the works of Dr. David Saada and Dr. Anastasia Sorkin.
For Dr. Sorkin's thesis on Computational Study of Structures of Diamonds and Amorphous Carbon Under Extreme Heating and Cooling, press here.
For Dr. Saada's dissertation on Comparison Between Tersoff Potential and Ab Initio Results for Surface Graphitization of Diamond, press here.

Origin of figures:
Damage By Carbon Ion Implantation, Insulation Threshold In Diamond - R. Kalish, Ion implantation in diamond; damage, annealing and doping, Proceedings of the National School of Physics "Enrico Fermi", Course CXXXV, The Physics of Diamonds(1997), pp. 373-409.
Diamond Lattice - Synthetic CVD Diamond. http://www.e6cvd.com/cvd/page.jsp?pageid=361 .
Graphite Lattice - Dr. Basko, Theory of optical properties of graphene and graphite, http://lpmmc.grenoble.cnrs.fr/spip.php?article407&lang=fr .

To continue to results, press here.