Update fix_eco_force.rst

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 

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::

\end{eqnarray}

which are fully explained in :ref:`(Ulomek) <Ulomek>`

and `(Schratt & Mohles) <Schratt>`.

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 

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 

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.

""""""""""""

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.

.. _Schratt:

**(Schratt)** Schratt, Mohles. Comp. Mat. Sci. 182 (2020) 109774

**(Schratt & Mohles)** Schratt, Mohles. Comp. Mat. Sci. 182 (2020) 109774

----------

This is for a lattice constant of 3.52 Angs.

file:

sigma5.ori:

.. parsed-literal::