# fix orient/eco command

    fix ID group-ID orient/eco u0 eta cutoff orientationsFile

-   ID, group-ID are documented in fix command
-   u0 = energy added to each atom (energy units)
-   eta = cutoff value (usually 0.25)
-   cutoff = cutoff radius for orientation parameter calculation
-   orientationsFile = file that specifies orientation of each grain

## Examples

``` LAMMPS
fix gb all orient/eco 0.08 0.25 3.524 sigma5.ori
```

## Description

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)](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 grain orientation. This fix is designed for
applications in bicrystal system 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)](Ulomek), the
implementation follows the efficient implementation from [(Schratt &
Mohles)](Schratt). The synthetic potential energy added to an atom j is
given by the following formulas

$$\begin{aligned}
w(|\vec{r}_{jk}|) = w_{jk} & = \left\{\begin{array}{lc} \frac{|\vec{r}_{jk}|^{4}}{r_{\mathrm{cut}}^{4}}
  -2\frac{|\vec{r}_{jk}|^{2}}{r_{\mathrm{cut}}^{2}}+1, & |\vec{r}_{jk}|<r_{\mathrm{cut}} \\
   0, & |\vec{r}_{jk}|\ge r_{\mathrm{cut}}
   \end{array}\right. \\
\chi_{j} & = \frac{1}{N}\sum_{l=1}^{3}\left\lbrack\left\vert\psi_{l}^{\mathrm{I}}(\vec{r}_{j})\right\vert^{2}-\left\vert\psi_{l}^{\mathrm{II}}(\vec{r}_{j})\right\vert^{2}\right\rbrack \\
\psi_{l}^{\mathrm{X}}(\vec{r}_{j}) & = \sum_{k\in\mathit{\Gamma}_{j}}w_{jk}\exp\left(\mathrm{i}\vec{r}_{jk}\cdot\vec{q}_{l}^{\mathrm{X}}\right) \\
u(\chi_{j}) & = \frac{u_{0}}{2}\left\{\begin{array}{lc}
1, & \chi_{j}\ge\eta\\
\sin\left(\frac{\pi\chi_{j}}{2\eta}\right), &  -\eta<\chi_{j}<\eta\\
-1, & \chi_{j}\le-\eta
\end{array}\right.
\end{aligned}$$

which are fully explained in [(Ulomek)](Ulomek) and [(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 experience a synthetic force as its
surrounding is that of an oriented single crystal and thermal
fluctuations are masked by the parameter *eta*. Near the grain boundary
however, the gradient is nonzero and synthetic force terms are computed.
The orientationsFile specifies the perfect oriented crystal basis
vectors for the two adjoining crystals. The first three lines (line=row
vector) for the energetically penalized and the last three lines for the
energetically favored grain assuming *u0* is positive. For negative
*u0*, this is reversed. With the *cutoff* parameter, the size of the
region around each atom which is used in the order parameter computation
is defined. The cutoff must be smaller than the interaction range of the
MD potential. It should at least include the nearest neighbor shell. For
high temperatures or low angle grain boundaries, it might be beneficial
to increase the cutoff in order to get a more precise identification of
the atoms surrounding. However, computation time will increase as more
atoms are considered in the order parameter and force computation. It is
also worth noting that the cutoff radius must not exceed the
communication distance for ghost atoms in LAMMPS. With orientationsFile,
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 $\Sigma\langle001\rangle$
mis-orientation 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, still, the order
parameter of the driving force is computed and can be used to track the
grain boundary motion throughout the simulation.

## Restart, fix_modify, output, run start/stop, minimize info

No information about this fix is written to [binary restart
files](restart).

The [fix_modify](fix_modify) *energy* option is supported by this fix to
add the potential energy of atom interactions with the grain boundary
driving force to the global potential energy of the system as part of
[thermodynamic output](thermo_style). The default setting for this fix
is [fix_modify energy no](fix_modify).

This fix calculates a per-atom array with 2 columns, which can be
accessed by indices 1-1 by any command that uses per-atom values from a
fix as input. See the [Howto output](Howto_output) doc page for an
overview of LAMMPS output options.

The first column is the order parameter for each atom; the second is the
thermal masking value for each atom. Both are described above.

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.

## Restrictions

This fix is part of the ORIENT package. It is only enabled if LAMMPS was
built with that package. See the [Build package](Build_package) page for
more info.

## Related commands

[fix_modify](fix_modify)

[fix_orient](fix_orient)

## Default

none

------------------------------------------------------------------------

::: {#Ulomek}
**(Ulomek)** Ulomek, Brien, Foiles, Mohles, Modelling Simul. Mater. Sci.
Eng. 23 (2015) 025007
:::

::: {#Schratt}
**(Schratt & Mohles)** Schratt, Mohles. Comp. Mat. Sci. 182 (2020)
109774
:::

------------------------------------------------------------------------

For illustration purposes, here is an example file that specifies a
$\Sigma=5 \langle 001 \rangle$ tilt grain boundary. This is for a
lattice constant of 3.52 Angstrom:

    sigma5.ori:

    1.671685  0.557228  1.76212
    0.557228 -1.671685  1.76212
    2.228913 -1.114456  0.00000
    0.557228  1.671685  1.76212
    1.671685 -0.557228  1.76212
    2.228913  1.114456  0.00000