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