Chemistry Reference
In-Depth Information
the dislocation line direction is minimal, just the amount needed to fully describe
the crystal structure. The use of such a configuration allows for the modeling of
a single straight dislocation, but not of complex defects such as dislocation inter-
action or kinks. The thickness of the continuum region (region 3 in the figure)
corresponds to the maximum range of the classical potential, i.e., all of the
atoms in the core (region 1) are given a computationally complete set of neigh-
bors. Periodic boundary conditions are applied along the direction of the dislo-
cation line, and atoms inside the atomistic region are allowed to relax during the
simulation. Because the external shell is kept fixed at all times, we can label this
approach as
fixed boundary
. The downside of such a simple approach is that
incompatibility forces arise at the continuum/atomistic interface and become
negligible only when very large atomistic regions are considered.
To overcome this difficulty, and to allow for the use of a much smaller
core region, Rao et al.
141
took the GFBC method originally developed by
Sinclair et al.
140
for 2D simulations and extended it to the 3D case. For sim-
plicity, let us examine the 2D scenario (the same principle applies to 3D simu-
lations as well). Now, a cylindrical shell of thickness equal to the range of the
classical potential [region 2 in Figure 6(b)] is inserted in between the atomistic
and the continuum domains. Because of its thickness, such a shell contains all
of the atoms in the continuum domain on which atoms in region 1 may exert a
force. The simulation is started by placing all of the atoms in the system
(regions 1, 2, and 3) into positions determined using a linear elastic displace-
ment field. Then, atoms in region 1 are individually relaxed, while atoms in
region 2 and 3 are displaced collectively, according to the Green's function
solution for a line force acting on a perfect lattice.
142,143
Equilibrium is
reached through an iterative procedure, where region 1 is relaxed first, and
then the forces still acting on atoms in region 2 are used to determine a cor-
rective displacement field on all three regions from a superposition of Green's
functions. Details on the relaxation procedure, the Green's function solutions,
and the extention of the methodology to the 3D case can be found in the
original studies. Using such a computational technique, Rao et al.
141
managed
to reduce simulation cell sizes by as much as 90%.
Sinclair et al.
140
used the GFBCmethod to investigate [100] edge
Applications
iron, while Rao et al.
141
applied their expanded version to the
study of straight screw dislocations in Ni, kinks (isolated or as a periodic array)
on a screw dislocation in bcc Fe, screw dislocations in Mo, and 3D cross-slip
core structures of screw dislocations in fcc metals.
141,144,145
dislocations in
a
Finite-Temperature Equilibrium Methods
In the following, we present some finite-temperature static/semistatic
methods that utilize a coupled atomistic/continuum description of the system.
As with the zero-temperature case, they are a better choice than dynamical
