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Once the specific form of the potential is established, the forces
between the atoms can be compute from the gradient of the
potential. We are then lead to solve the differential equations :



(8.1) 







(8.2) 
in order to obtain the position r_{i} and the velocity v_{i} of each
atom of mass m as a function of the time t. i is the atom in
consideration and
the coordinates x, y and z. As
explained before, in the case of the tight binding model, a force
emerging from the electronic part of the total energy should also be
calculated. However, like in the classical models, in the quantum or
semiclassical approaches, the atoms are considered as classical, so
that also in these cases, the Newton equations have to be solved.
The first step of the calculation consists of determining the
neighbors of each atom within the limit of the force range. Then, for
each atom the force applied by its neighbors is computed and added all
together to get the total force on the atom. From the forces
evaluation, the Newton's equations (8.1) and (8.2) are
solved for coordinates x, y and z and velocities v_{x}, v_{y}and v_{z}. For this purpose, two different algorithm were used in the
present research and compared regarding the total energy obtained and
the average atomic positions during the processes of bombardment and
annealing.
Next: The leapfrog algorithm
Up: The numerical techniques
Previous: The numerical techniques
David Saada
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