.. index:: pair_style meam/sw/spline

pair_style meam/sw/spline command
=================================

Syntax
""""""

.. code-block:: LAMMPS

   pair_style meam/sw/spline

Examples
""""""""

.. code-block:: LAMMPS

   pair_style meam/sw/spline
   pair_coeff * * Ti.meam.sw.spline Ti
   pair_coeff * * Ti.meam.sw.spline Ti Ti Ti

Description
"""""""""""

The *meam/sw/spline* style computes pairwise interactions for metals
using a variant of modified embedded-atom method (MEAM) potentials
:ref:`(Lenosky) <Lenosky2>` with an additional Stillinger-Weber (SW) term
:ref:`(Stillinger) <Stillinger1>` in the energy.  This form of the potential
was first proposed by Nicklas, Fellinger, and Park
:ref:`(Nicklas) <Nicklas>`.  We refer to it as MEAM+SW.  The total energy E
is given by

.. math::

   E & = E_{MEAM} + E_{SW} \\
   E_{MEAM} & =  \sum _{IJ} \phi (r_{IJ}) + \sum _{I} U(\rho _I) \\
   E_{SW} & =  \sum _{I} \sum _{JK} F(r_{IJ}) \, F(r_{IK}) \, G(\cos(\theta _{JIK})) \\
   \rho _I & = \sum _J \rho(r_{IJ}) + \sum _{JK} f(r_{IJ}) \, f(r_{IK}) \, g(\cos(\theta _{JIK}))

where :math:`\rho_I` is the density at atom I, :math:`\theta_{JIK}` is
the angle between atoms J, I, and K centered on atom I. The seven
functions :math:`\phi, F, G, U, \rho, f,` and *g* are represented by
cubic splines.

The cutoffs and the coefficients for these spline functions are listed
in a parameter file which is specified by the
:doc:`pair_coeff <pair_coeff>` command.  Parameter files for different
elements are included in the "potentials" directory of the LAMMPS
distribution and have a ".meam.sw.spline" file suffix.  All of these
files are parameterized in terms of LAMMPS :doc:`metal units <units>`.

Note that unlike for other potentials, cutoffs for spline-based
MEAM+SW potentials are not set in the pair_style or pair_coeff
command; they are specified in the potential files themselves.

Unlike the EAM pair style, which retrieves the atomic mass from the
potential file, the spline-based MEAM+SW potentials do not include
mass information; thus you need to use the :doc:`mass <mass>` command to
specify it.

Only a single pair_coeff command is used with the meam/sw/spline style
which specifies a potential file with parameters for all needed
elements.  These are mapped to LAMMPS atom types by specifying N
additional arguments after the filename in the pair_coeff command,
where N is the number of LAMMPS atom types:

* filename
* N element names = mapping of spline-based MEAM+SW elements to atom types

See the :doc:`pair_coeff <pair_coeff>` doc page for alternate ways
to specify the path for the potential file.

As an example, imagine the Ti.meam.sw.spline file has values for Ti.
If your LAMMPS simulation has 3 atoms types and they are all to be
treated with this potential, you would use the following pair_coeff
command:

.. code-block:: LAMMPS

   pair_coeff * * Ti.meam.sw.spline Ti Ti Ti

The first 2 arguments must be \* \* so as to span all LAMMPS atom types.
The three Ti arguments map LAMMPS atom types 1,2,3 to the Ti element
in the potential file. If a mapping value is specified as NULL, the
mapping is not performed. This can be used when a *meam/sw/spline*
potential is used as part of the hybrid pair style. The NULL values
are placeholders for atom types that will be used with other
potentials.

.. note::

   The *meam/sw/spline* style currently supports only
   single-element MEAM+SW potentials.  It may be extended for alloy
   systems in the future.

Example input scripts that use this pair style are provided
in the examples/USER/misc/meam_sw_spline directory.

----------

**Mixing, shift, table, tail correction, restart, rRESPA info**\ :

The pair style does not support multiple element types or mixing.
It has been designed for pure elements only.

This pair style does not support the :doc:`pair_modify <pair_modify>`
shift, table, and tail options.

The *meam/sw/spline* pair style does not write its information to
:doc:`binary restart files <restart>`, since it is stored in an external
potential parameter file.  Thus, you need to re-specify the pair_style
and pair_coeff commands in an input script that reads a restart file.

The *meam/sw/spline* pair style can only be used via the *pair*
keyword of the :doc:`run_style respa <run_style>` command.  They do not
support the *inner*\ , *middle*\ , *outer* keywords.

----------

Restrictions
""""""""""""

This pair style requires the :doc:`newton <newton>` setting to be "on"
for pair interactions.

This pair style is only enabled if LAMMPS was built with the USER-MISC
package.  See the :doc:`Build package <Build_package>` doc page for more
info.

Related commands
""""""""""""""""

:doc:`pair_coeff <pair_coeff>`, :doc:`pair_style meam/c <pair_meamc>`,
:doc:`pair_style meam/spline <pair_meam_spline>`

**Default:** none

----------

.. _Lenosky2:

**(Lenosky)** Lenosky, Sadigh, Alonso, Bulatov, de la Rubia, Kim, Voter,
Kress, Modell. Simul. Mater. Sci. Eng. 8, 825 (2000).

.. _Stillinger1:

**(Stillinger)** Stillinger, Weber, Phys. Rev. B 31, 5262 (1985).

.. _Nicklas:

**(Nicklas)**
The spline-based MEAM+SW format was first devised and used to develop
potentials for bcc transition metals by Jeremy Nicklas, Michael Fellinger,
and Hyoungki Park at The Ohio State University.
