Merge pull request #271 from akohlmey/tersoff-modc

\documentclass[12pt]{article}

\pagestyle{empty}

\begin{document}

\begin{eqnarray*}

  V_{ij}  & =  & f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) + c_0 \right]

\end{eqnarray*}

\end{document}

:line

pair_style tersoff/mod command :h3

pair_style tersoff/mod/c command :h3

pair_style tersoff/mod/gpu command :h3

pair_style tersoff/mod/kk command :h3

pair_style tersoff/mod/omp command :h3

pair_style tersoff/mod/c/omp command :h3

[Syntax:]

pair_style tersoff/mod :pre

pair_style tersoff/mod/c :pre

[Examples:]

pair_style tersoff/mod

pair_coeff * * Si.tersoff.mod Si Si :pre

pair_style tersoff/mod/c

pair_coeff * * Si.tersoff.modc Si Si :pre

[Description:]

The {tersoff/mod} style computes a bond-order type interatomic

potential "(Kumagai)"_#Kumagai based on a 3-body Tersoff potential

"(Tersoff_1)"_#Tersoff_1, "(Tersoff_2)"_#Tersoff_2 with modified

cutoff function and angular-dependent term, giving the energy E of a

system of atoms as

The {tersoff/mod} and {tersoff/mod/c} styles computes a bond-order type

interatomic potential "(Kumagai)"_#Kumagai based on a 3-body Tersoff

potential "(Tersoff_1)"_#Tersoff_1, "(Tersoff_2)"_#Tersoff_2 with

modified cutoff function and angular-dependent term, giving the energy

E of a system of atoms as

:c,image(Eqs/pair_tersoff_mod.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.

The {tersoff/mod/c} style differs from {tersoff/mod} only in the

formulation of the V_ij term, where it contains an additional c0 term.

:c,image(Eqs/pair_tersoff_mod_c.jpg)

The modified cutoff function f_C proposed by "(Murty)"_#Murty and

having a continuous second-order differential is employed. The

potentials.

Tersoff/MOD file in the {potentials} directory of the LAMMPS

distribution have a ".tersoff.mod" 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:

distribution have a ".tersoff.mod" suffix. Potential files for the

{tersoff/mod/c} style have the suffix ".tersoff.modc". 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 formulae above:

element 1 (the center atom in a 3-body interaction)

element 2 (the atom bonded to the center atom)

c2

c3

c4

c5 :ul

c5

c0 (energy units, tersoff/mod/c only):ul

The n, eta, lambda2, B, lambda1, and A parameters are only used for

two-body interactions.  The beta, alpha, c1, c2, c3, c4, c5, h

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.

parameters are used for both two-body and three-body interactions.

The c0 term applies to {tersoff/mod/c} only. The non-annotated

parameters are unitless.

The Tersoff/MOD potential file must contain entries for all the elements

listed in the pair_coeff command.  It can also contain entries for

neigh_modify    every 1 delay 10 check yes

run             100

# Test Tersoff/Mod model for Si

clear

read_restart	restart.equil

pair_style      tersoff/mod

pair_coeff 	* * Si.tersoff.mod Si Si Si Si Si Si Si Si

thermo          10

fix             1 all nvt temp $t $t 0.1

fix_modify 	1 energy yes

timestep        1.0e-3

neighbor        1.0 bin

neigh_modify    every 1 delay 10 check yes

run             100

# Test Tersoff/Mod/C model for Si

clear

read_restart	restart.equil

pair_style      tersoff/mod/c

pair_coeff 	* * Si.tersoff.modc Si Si Si Si Si Si Si Si

thermo          10

fix             1 all nvt temp $t $t 0.1

fix_modify 	1 energy yes

timestep        1.0e-3

neighbor        1.0 bin

neigh_modify    every 1 delay 10 check yes

run             100

# DATE: 2016-11-09 CONTRIBUTOR: Ganga P Purja Pun (George Mason University, Fairfax) CITATION: Unknown

#

# Format:

# element1 element2 element3

# beta alpha h eta

# beta_ters lam2 B R D lam1 A

# n c1 c2 c3 c4 c5 C

Si Si Si 3.00000000 1.80536502 -0.38136087 2.16152496

1 1.39343356 117.78072440 2.87478837 0.33090566 3.18011795 3198.51383127

1.98633876 0.20123243 614230.04310619 996439.09714140 3.33560562 25.20963770 -0.00592042