(8.14) |

where

(8.15) |

the time constant of this coupling,

leading to a new equation

where only global coupling appears. Then, to conserve only the global coupling and minimize local disturbance, from eq. (8.17) it can be seen that velocity rescaling should be made each time-step by a factor

where . The current kinetic temperature

Thus, this method is very convenient since no new solutions of the
motion equations are needed, the rate of the energy dissipation can be
easily controlled by the time constant of the coupling
and
the final sample temperature is initially determined by *T*'. But
velocity rescaling would affect the speed and the position of the
atoms, and therefore the structure of the crystal. Thus no realistic
results can be obtained from such calculations. A way to impose global
coupling to an external bath with fixed temperature and to avoid, at
the same time, perturbation of the atomic motion, is to apply velocity
rescaling to only few atoms of the sample that do not lie in the
damaged region. These atoms are chosen from the three outermost
layers, including the periodic boundaries, keeping the crystal density
constant. Thus, the rescaling velocity will maintain the bulk atoms,
in a global way, at a kinetic temperature defined by eq. (9.6).

For the simulation of defect formation in the diamond crystal by energetic atoms, at 0 K, the atoms in the boundaries are kept fixed in their ``pure'' diamond lattice sites, and the three outermost layers are coupled to a bath held at a temperature of 0 K, in the way explained above. Thus, energy reflection from the boundaries is minimized and the structure of the disrupted region is determined only by the motion of the displaced atoms.

Since the model is deterministic, the initial configuration and the speed of the atoms play a crucial role in the simulation and will determine the nature of the motion. In the present research, the initial configuration for the post implantation annealing is the disrupted sample obtained from the 0 K ion impact. For the ``hot'' implantation simulation, the initial configuration is that of the perfect diamond crystal. The initial velocities are chosen randomly and suit the annealing temperature according to eq. (9.6).