Update fix_eco_force.rst

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vmohles 2020-06-03 12:32:05 +02:00
parent def79f246a
commit 08a6efe6b1
1 changed files with 11 additions and 11 deletions

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@ -30,7 +30,7 @@ The fix applies a synthetic driving force to a grain boundary which can
be used for the investigation of grain boundary motion. The affiliation
of atoms to either of the two grains forming the grain boundary is
determined from an orientation-dependent order parameter as described
in (Ulomek). The potential energy of atoms is either increased by an amount
in :ref:`(Ulomek) <Ulomek>`. The potential energy of atoms is either increased by an amount
of 0.5*u0 or -0.5*u0 according to the orientation of the surrounding
crystal. This creates a potential energy gradient which pushes atoms near
the grain boundary to orient according to the energetically favorable
@ -39,8 +39,8 @@ with one grain boundary and open ends, or two opposite grain boundaries in
a periodic system. In either case, the entire system can experience a
displacement during the simulation which needs to be accounted for in the
evaluation of the grain boundary velocity. While the basic method is
described in (Ulomek), the implementation follows the efficient
implementation from (Schratt & Mohles). The synthetic potential energy added to an
described in :ref:`(Ulomek) <Ulomek>`, the implementation follows the efficient
implementation from :ref:`(Schratt & Mohles) <Schratt>`. The synthetic potential energy added to an
atom j is given by the following formulas
.. math::
@ -68,8 +68,8 @@ u(\chi_{j}) & = & \frac{u_{0}}{2}\left\{\begin{array}{lc}
\label{eq:energy-mid}
\end{eqnarray}
which are fully explained in :ref: `(Ulomek) <Ulomek>`
and `(Schratt & Mohles) <Schratt>`.
which are fully explained in :ref:`(Ulomek) <Ulomek>`
and :ref:`(Schratt & Mohles) <Schratt>`.
The force on each atom is the negative gradient of the synthetic potential energy. It
depends on the surrounding of this atom. An atom far from the grain boundary does not
@ -94,7 +94,7 @@ the 6 oriented crystal basis vectors is specified. Each line of the input file
contains the three components of a primitive lattice vector oriented according to
the grain orientation in the simulation box. The first (last) three lines correspond
to the primitive lattice vectors of the first (second) grain. An example for
a Σ5⟨001⟩ misorientation is given at the end.
a :math:`\Sigma\langle001\rangle` misorientation is given at the end.
If no synthetic energy difference between the grains is created, u0=0, the
force computation is omitted. In this case, the order parameter of the
@ -114,8 +114,8 @@ The total sum of added synthetic potential energy is computed and can be accesse
by various output options. The order parameter as well as the thermally masked
output parameter are stored in per-atom arrays and can also be accessed by various
output commands.
No parameter of this fix
can be used with the start/stop keywords of the run command. This fix is
No parameter of this fix can be used with the start/stop keywords of the run command. This fix is
not invoked during energy minimization.
@ -124,7 +124,7 @@ Restrictions
""""""""""""
This fix is part of the MISC package. It is only enabled if LAMMPS was
built with that package. See the Making LAMMPS section for more info.
built with that package. See the :doc:`Build package <Build_package>` doc page for more info.
@ -143,7 +143,7 @@ Related commands
.. _Schratt:
**(Schratt)** Schratt, Mohles. Comp. Mat. Sci. 182 (2020) 109774
**(Schratt & Mohles)** Schratt, Mohles. Comp. Mat. Sci. 182 (2020) 109774
----------
@ -153,7 +153,7 @@ Sigma=5 <001> tilt grain boundary.
This is for a lattice constant of 3.52 Angs.
file:
sigma5.ori:
.. parsed-literal::