Next, we investigate the diffusion of H in diamond. First we
qualitatively follow, for 50 psec, the trajectories that the H atom,
initially placed at the T
site, assumes at different
temperatures, using MD calculations and visualization techniques
[129,57] to trace the path of the H atom. Only the
point is
used to sample the Brillouin zone in these calculations. The equations
of motion are solved by a velocity-Verlet algorithm, with a time step
of 10^{-15} sec, and the temperature is controlled by a Gaussian
thermostat. We find that up to a temperature of
400 K, the H
atom vibrates around the initial T
site. By
600 K, it
already finds its way to the nearest ET site, and jumps between the
three equivalent ET sites of the same triangle (sites 1,2 and 3 in
figure (11.3), for example). Around 1200 K, the H atom begins
to jump back and forth between the six ET sites around the same C-C
bond. The trajectory of an H atom is depicted in figure
(11.6) for 30 ps at 1200 K. Finally, at a temperature of
1700 K, it jumps to the nearest ET site of the neighboring bond
(site 7 or 8 in figure (11.3), for example). At this stage,
real diffusion sets in. It has to be noted that the temperatures
mentioned above are not precise, but rather provide a hierarchy of the
energetic barriers involved in the H motion in diamond. The present
results can be compared with the experimental temperature of 450 K at which the Mu-to-Mu
transition occurs in diamond
[82].

When a second H atom is added to the sample at an adjacent non-occupied ET site (as in our C-H-H-C complex mentioned above; see figure (11.5)), the two H atoms are found to jump between the ET sites of their respective equilateral triangle, even at 1700 K, and are unable to jump to another ET site of an adjacent bond, for a simulation time of 50 psec. The presence of the second neighboring H atom should therefore reduce the possibility of diffusion.

In order to quantify the migration process of H in diamond, we
evaluate the potential barrier that separates two adjacent ET sites on
neighboring bonds (sites labeled 6 and 7 in figure (11.3), for
example), as it is the relevant barrier for actual diffusion. We
notice that the jump of H from one carbon-carbon bond (A-B in figure
(11.3)) to the adjacent one (associated with site 7) involves
the rebonding of bond A-B and the breaking of the adjacent one. This
change of bonding is due to a *coordinated motion* of both the H
(from site 6 to 7) and the carbon (labeled B) atoms (see figure
(11.7)). Therefore the diffusion of H involves also the
passage of the C atom over a barrier. Exactly such a coupled-barrier
diffusion process has been found by Ramamoorthy *et. al.*
[130] for diffusion of oxygen in silicon.

We therefore calculate the energy of the sample as a function of the
positions of *both atoms* (H and adjacent C), in an adiabatic
migration process. We move the H atom step by step from the initial
relaxed site (number 6) to the final one (number 7), along the
direction 6-7. Concurrently, the carbon atom (labeled B) is displaced
step by step along the direction defined by its initial and final
relaxed positioned. At each step, we relax the sample such that the H
and the C atom are constrained to remain on the plane perpendicular to
their respective directions of displacement. Four atoms are fixed on
the faces of the supercell to prevent center of mass motion. This
procedure yields the shape of the barrier for the coupled-barrier
diffusion, shown in figure (11.8). As can be seen from the
figure, the barrier is symmetric, with a maximum of 0.9 eV at the
center of the paths. It is found that during the coordinated motion,
the distance between H and its adjacent C atom remains
1.08
Å.