lammps/doc/pair_tersoff.txt

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pair_style tersoff command :h3

[Syntax:]

pair_style tersoff :pre

[Examples:]

pair_style tersoff
pair_coeff * * si.tersoff Si
pair_coeff * * SiC.tersoff Si C Si :pre

[Description:]

The {tersoff} style computes a 3-body Tersoff potential
"(Tersoff_1)"_#Tersoff_1 for the energy E of a system of atoms as

:c,image(Eqs/pair_tersoff_1.jpg)

where f_R is a two-body term and f_A includes three-body interactions.
The summations in the formula are over all neighbors J and K of atom I
within a cutoff distance = R + D. 

Only a single pair_coeff command is used with the {tersoff} style
which specifies a Tersoff 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 Tersoff elements to atom types :ul

As an example, imagine the SiC.tersoff file has Tersoff values for Si
and C.  If your LAMMPS simulation has 4 atoms types and you want the
1st 3 to be Si, and the 4th to be C, you would use the following
pair_coeff command:

pair_coeff * * SiC.tersoff Si Si Si C :pre

The 1st 2 arguments must be * * so as to span all LAMMPS atom types.
The first three Si arguments map LAMMPS atom types 1,2,3 to the Si
element in the Tersoff file.  The final C argument maps LAMMPS atom
type 4 to the C element in the Tersoff file.  If a mapping value is
specified as NULL, the mapping is not performed.  This can be used
when a {tersoff} 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.

Tersoff files in the {potentials} directory of the LAMMPS distribution
have a ".tersoff" suffix.  Lines that are not blank or comments
(starting with #) define parameters for a triplet of elements.  The
parameters in a single entry correspond to coefficients in the formula
above:

element 1 (the center atom in a 3-body interaction)
element 2 (the atom bonded to the center atom)
element 3 (the atom influencing the 1-2 bond in a bond-order sense)
m
gamma
lambda3 (1/distance units)
c
d
costheta0 (can be a value < -1 or > 1)
n
beta
lambda2 (1/distance units)
B (energy units)
R (distance units)
D (distance units)
lambda1 (1/distance units)
A (energy units) :ul

The n, beta, lambda2, B, lambda1, and A parameters are only used for
two-body interactions.  The m, gamma, lambda3, c, d, and costheta0 parameters
are only used for three-body interactions. The R and D parameters 
are used for both two-body and three-body interactions. The 
non-annotated parameters are unitless.

The Tersoff potential file must contain entries for all the elements
listed in the pair_coeff command.  It can also contain entries for
additional elements not being used in a particular simulation; LAMMPS
ignores those entries.

For a single-element simulation, only a single entry is required
(e.g. SiSiSi).  For a two-element simulation, the file must contain 8
entries (for SiSiSi, SiSiC, SiCSi, SiCC, CSiSi, CSiC, CCSi, CCC), that
specify Tersoff parameters for all permutations of the two elements
interacting in three-body configurations.  Thus for 3 elements, 27
entries would be required, etc.

As annotated above, the first element in the entry is the center atom
in a three-body interaction and it is bonded to the 2nd atom and the
bond is influenced by the 3rd atom.  Thus an entry for SiCC means Si
bonded to a C with another C atom influencing the bond.  Thus
three-body parameters for SiCSi and SiSiC entries will not, in
general, be the same.  The parameters used for the two-body
interaction come from the entry where the 2nd element is repeated.
Thus the two-body parameters for Si interacting with C, comes from the
SiCC entry.  By symmetry, the twobody parameters in the SiCC and CSiSi
entries should thus be the same.  The parameters used for a particular
three-body interaction come from the entry with the corresponding
three elements.  The parameters used only for two-body interactions
(n, beta, lambda2, B, lambda1, and A) in entries whose 2nd and 3rd
element are different (e.g. SiCSi) are not used for anything and can
be set to 0.0 if desired.

We chose the above form so as to enable users to define all commonly
used variants of the Tersoff potential.  In particular, our form
reduces to the original Tersoff form when m = 3 and gamma = 1, while
it reduces to the form of "Albe et al."_#Albe when beta = 1 and m = 1.
Tersoff used a slightly different but equivalent form for alloys,
which we will refer to as Tersoff_2 potential
"(Tersoff_2)"_#Tersoff_2.

LAMMPS parameter values for Tersoff_2 can be obtained as follows. 
The parameters for species i and j can be calculated 
using the Tersoff_2 mixing rules:

:c,image(Eqs/pair_tersoff_2.jpg)

Values not shown are determined by the first<73>atom type. Finally, the
Tersoff_2 parameters R and S must be converted to the LAMMPS
parameters R and D (R is different in both forms), using the following
relations: R=(R'+S')/2 and D=(S'-R')/2, where the primes indicate the
Tersoff_2 parameters.

In the potentials directory, the file SiCGe.tersoff provides the
LAMMPS parameters for Tersoff's various versions of Si, as well as his
alloy paramters for Si, C, and Ge. This file can be used for pure Si,
(three different versions), pure C, pure Ge, binary SiC, and binary
SiGe.  LAMMPS will generate an error if this file is used with any
combination involving C and Ge, since there are no entries for the GeC
interactions (Tersoff did not publish parameters for this
cross-interaction.)  Tersoff files are also provided for the SiC alloy
(SiC.tersoff) and the GaN (GaN.tersoff) alloys.

Many thanks to Rutuparna Narulkar, David Farrell, and Xiaowang Zhou
for helping clarify how Tersoff parameters for alloys have been
defined in various papers.

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[Mixing, shift, table, tail correction, per-atom energy/stress,
restart, rRESPA info]:

For atom type pairs I,J and I != J, where types I and J correspond to
two different element types, mixing is performed by LAMMPS as
described above from values in the potential file.

This pair style does not support the "pair_modify"_pair_modify.html
shift, table, and tail options.

This pair style does not calculate per-atom energy and stress, as used
by the "compute epair/atom"_compute_epair_atom.html, "compute
stress/atom"_compute_stress_atom.html, and "dump custom"_dump.html
commands.

This pair style does not write its information to "binary restart
files"_restart.html, since it is stored in potential files.  Thus, you
need to re-specify the pair_style and pair_coeff commands in an input
script that reads a restart file.

This pair style can only be used via the {pair} keyword of the
"run_style respa"_run_style.html command.  It does not support the
{inner}, {middle}, {outer} keywords.

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[Restrictions:]

This pair style is part of the "manybody" package.  It is only enabled
if LAMMPS was built with that package (which it is by default).  See
the "Making LAMMPS"_Section_start.html#2_3 section for more info.

This pair style requires the "newton"_newton.html setting to be "on"
for pair interactions.

The Tersoff potential files provided with LAMMPS (see the potentials
directory) are parameterized for metal "units"_units.html.  You can
use the Tersoff potential with any LAMMPS units, but you would need to
create your own Tersoff potential file with coefficients listed in the
appropriate units if your simulation doesn't use "metal" units.

[Related commands:]

"pair_coeff"_pair_coeff.html

[Default:] none

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:link(Tersoff_1)
[(Tersoff_1)] J. Tersoff, Phys Rev B, 37, 6991 (1988).

:link(Albe)
[(Albe)] J. Nord, K. Albe, P. Erhartand K. Nordlund, J. Phys.:
Condens. Matter, 15, 5649(2003).

:link(Tersoff_2)
[(Tersoff_2)] J. Tersoff, Phys Rev B, 39, 5566 (1989)