+
+in md, a system of n particles is described on the microscopic level
+by numerically integrating newtons equations of motion.
+the particle interaction is given by an analytical interaction potential.
+observables are obtained by taking time or ensemble averages.
+
+in this case roughly 6000 atoms were used to investigate defect structures
+and nearly a quater of a million atoms for the precipitation simulations.
+the equations of motion are integrated by the velocity verlet algorithm
+with a time step of 1 fs.
+the interaction is decribed by a Tersoff-like short-range bond order potential,
+developed by erhart and albe.
+the short range character is achieved by a cutoff function,
+which drops the interaction inbetween the first and second next neighbor atom.
+the potential consists of a repulsive and an attractive part associated with
+the bonding, which is limited by the bond order term, which takes
+into consideration all atoms k influencing the bond of atoms i and j.
+simulations are performed in the isothermal-isobaric ensemble
+realized by the berendsen thermostat and barostat.
+
+furthermore, highly accurate quantum mechanical calculations
+based on dft are used.
+the basic concept of dft is the hohenberg kohn (hk) theorem, which states that
+the ground-state wavefunction is a unique functional of the ground-state
+electron density, which minimizes the energy,
+i.e. it has the variational property.
+in that way, the many body problem can be described by the electron density,
+which depends only on the 3 spatial coordinates.
+now, the kohn sham (ks) approach constitutes a hartree-like formulation
+of the hk minimal principle, which maps the system of interacting particles to
+an auxillary system of non-interacting electrons in an effective potential.
+however formally exact by introducing an energy functional,
+which accounts for the exchange and correlation energy.
+the effective potential yields a ground-state density
+for non-interacting electrons, which is equal to that for interacting electrons
+in the external potential.
+the kohn sham equations need to be solved in a self consistency loop.
+
+the vasp code was used for this purpose.
+it utilizes plane waves to expand the ks wavefunctions.
+an energy cut-off of 300 eV is employed.
+the electron-ion interaction is described by ultrasoft pseudopotentials.
+the generalized gradient approximation is used to solve the ks equations.
+brillouin zone sampling is restricted to the gamma point.
+the supercell consists of 216 atoms, 3 silicon unit cells in each direction,
+of course much less atoms compared to the highly efficient md technique.
+