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doc/Section_commands.html
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@ -363,8 +363,8 @@ full description:
<TR ALIGN="center"><TD ><A HREF = "pair_class2.html">lj/class2/coul/long</A></TD><TD ><A HREF = "pair_lj.html">lj/cut</A></TD><TD ><A HREF = "pair_lj.html">lj/cut/opt</A></TD><TD ><A HREF = "pair_lj.html">lj/cut/coul/cut</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_lj.html">lj/cut/coul/debye</A></TD><TD ><A HREF = "pair_lj.html">lj/cut/coul/long</A></TD><TD ><A HREF = "pair_lj.html">lj/cut/coul/long/tip4p</A></TD><TD ><A HREF = "pair_lj_expand.html">lj/expand</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_lj_smooth.html">lj/smooth</A></TD><TD ><A HREF = "pair_lubricate.html">lubricate</A></TD><TD ><A HREF = "pair_meam.html">meam</A></TD><TD ><A HREF = "pair_morse.html">morse</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_morse.html">morse/opt</A></TD><TD ><A HREF = "pair_soft.html">soft</A></TD><TD ><A HREF = "pair_sw.html">sw</A></TD><TD ><A HREF = "pair_table.html">table</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_tersoff.html">tersoff</A></TD><TD ><A HREF = "pair_yukawa.html">yukawa</A>
<TR ALIGN="center"><TD ><A HREF = "pair_morse.html">morse/opt</A></TD><TD ><A HREF = "pair_resquared.html">resquared</A></TD><TD ><A HREF = "pair_soft.html">soft</A></TD><TD ><A HREF = "pair_sw.html">sw</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_table.html">table</A></TD><TD ><A HREF = "pair_tersoff.html">tersoff</A></TD><TD ><A HREF = "pair_yukawa.html">yukawa</A>
</TD></TR></TABLE></DIV>
<P>These are pair styles contributed by users, which can be used if

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doc/Section_commands.txt
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@ -511,6 +511,7 @@ full description:
"meam"_pair_meam.html,
"morse"_pair_morse.html,
"morse/opt"_pair_morse.html,
"resquared"_pair_resquared.html,
"soft"_pair_soft.html,
"sw"_pair_sw.html,
"table"_pair_table.html,

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doc/pair_coeff.html
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@ -126,6 +126,7 @@ the pair_style command, and coefficients specified by the associated
<LI><A HREF = "pair_meam.html">pair_style meam</A> - modified embedded atom method (MEAM)
<LI><A HREF = "pair_morse.html">pair_style morse</A> - Morse potential
<LI><A HREF = "pair_morse.html">pair_style morse</A> - optimized version of Morse potential
<LI><A HREF = "pair_resquared.html">pair_style resquared</A> - Everaers RE-Squared ellipsoidal potential
<LI><A HREF = "pair_soft.html">pair_style soft</A> - Soft (cosine) potential
<LI><A HREF = "pair_sw.html">pair_style sw</A> - Stillinger-Weber 3-body potential
<LI><A HREF = "pair_table.html">pair_style table</A> - tabulated pair potential

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doc/pair_coeff.txt
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@ -122,6 +122,7 @@ the pair_style command, and coefficients specified by the associated
"pair_style meam"_pair_meam.html - modified embedded atom method (MEAM)
"pair_style morse"_pair_morse.html - Morse potential
"pair_style morse"_pair_morse.html - optimized version of Morse potential
"pair_style resquared"_pair_resquared.html - Everaers RE-Squared ellipsoidal potential
"pair_style soft"_pair_soft.html - Soft (cosine) potential
"pair_style sw"_pair_sw.html - Stillinger-Weber 3-body potential
"pair_style table"_pair_table.html - tabulated pair potential

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<HTML>
<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
</CENTER>
<HR>
<H3>pair_style resquared command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>pair_style resquared cutoff
</PRE>
<UL><LI>cutoff = global cutoff for interactions (distance units)
</UL>
<P><B>Examples:</B>
</P>
<PRE>pair_style resquared 10.0
pair_coeff * * 1.0 1.0 1.7 3.4 3.4 1.0 1.0 1.0
</PRE>
<P><B>Description:</B>
</P>
<P>Style <I>resquared</I> computes the RE-squared anisotropic interaction
<A HREF = "#Everaers">(Everaers,Babadi)</A> between pairs of ellipsoidal and/or
spherical Lennard-Jones particles. For ellipsoidal interactions,
the potential considers the ellipsoid as being comprised of small
spheres of size sigma. LJ particles are a single sphere of size
sigma. The distinction is made to allow the pair style to make
efficient calculations of ellipsoid/solvent interactions.
</P>
<P>Details for the equations used are given in the references below
and <A HREF = "#redoc">this document</A>.
</P>
<P>Use of this pair style requires the NVE, NVT, or NPT fixes
with the <I>asphere</I> extension (e.g. <A HREF = "fix_nve_asphere.html">fix
nve/asphere</A>) in order to integrate particle
rotation. Additionally, <A HREF = "atom_style.html">atom_style ellipsoid</A> should
be used since it defines the rotational state of the ellipsoidal
particles and the <A HREF = "shape.html">shape</A> command should be used to
specify ellipsoid diameters.
</P>
<P>The following coefficients must be defined for each pair of atoms
types via the <A HREF = "pair_coeff.html">pair_coeff</A> command as in the examples
above, or in the data file or restart files read by the
<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
commands:
</P>
<UL><LI>A12 = Energy Prefactor/Hamaker constant (energy units)
<LI>sigma = atomic interaction diameter (distance units)
<LI>epsilon_i_a = relative well depth of type I for side-to-side interactions
<LI>epsilon_i_b = relative well depth of type I for face-to-face interactions
<LI>epsilon_i_c = relative well depth of type I for end-to-end interactions
<LI>epsilon_j_a = relative well depth of type J for side-to-side interactions
<LI>epsilon_j_b = relative well depth of type J for face-to-face interactions
<LI>epsilon_j_c = relative well depth of type J for end-to-end interactions
<LI>cutoff (distance units)
</UL>
<P>The parameters used depend on the type of particles interacting -
ellipsoid or LJ sphere. The type of particle is determined by
the diameters specified with the <A HREF = "shape.html">shape</A>
command. LJ spheres have diameters equal to zero and thus
represent a single particle with size sigma. The epsilon_i_* or
epsilon_j_* parameters are ignored for LJ sphere interactions.
The interactions between two LJ sphere particles are computed
using the standard Lennard-Jones formula.
</P>
<P>A12 specifies the energy prefactor which depends on
the type of particles interacting. For ellipsoid-ellipsoid
interactions, A12 is the Hamaker constant as described in
<A HREF = "#Everaers">(Everaers)</A>. In LJ units:
</P>
<CENTER><IMG SRC = "Eqs/pair_resquared.jpg">
</CENTER>
<P>where rho gives the number density of the spherical particles
composing the ellipsoids and epsilon_LJ determines the
interaction strength of the spherical particles.
</P>
<P>For ellipsoid-LJ sphere interactions, A12 gives the energy
prefactor (see <A HREF = "Eqs/pair_resquared_extra.pdf">here</A> for details:
</P>
<CENTER><IMG SRC = "Eqs/pair_resquared2.jpg">
</CENTER>
<P>For LJ sphere-LJ sphere interactions, A12 is the standard
epsilon used in Lennard-Jones pair styles:
</P>
<CENTER><IMG SRC = "Eqs/pair_resquared3.jpg">
</CENTER>
<P>sigma specifies the diameter of the continuous distribution of
constituent particles within each ellipsoid used to model
the RE-squared potential. Therefore, the effective shape
of an ellipsoid is given by the specified diameters
(see the <A HREF = "shape.html">shape</A> command) plus sigma.
</P>
<P>For large uniform molecules it has been shown that the epsilon_*_*
energy parameters are approximately representable in terms of
local contact curvatures <A HREF = "#Everaers">(Everaers)</A>:
</P>
<CENTER><IMG SRC = "Eqs/pair_resquared4.jpg">
</CENTER>
<P>where a, b, and c give the particle diameters.
</P>
<P>The last coefficient is optional. If not specified, the global
cutoff specified in the pair_style command is used.
</P>
<P>The epsilon_i and epsilon_j coefficients are actually defined for atom
types, not for pairs of atom types. Thus, in a series of pair_coeff
commands, they only need to be specified once for each atom type.
</P>
<P>Specifically, if any of epsilon_i_a, epsilon_i_b, epsilon_i_c are
non-zero, the three values are assigned to atom type I. If all the
epsilon_i values are zero, they are ignored. If any of epsilon_j_a,
epsilon_j_b, epsilon_j_c are non-zero, the three values are assigned
to atom type J. If all three epsilon_i values are zero, they are
ignored. Thus the typical way to define the epsilon_i and epsilon_j
coefficients is to list their values in "pair_coeff I J" commands when
I = J, but set them to 0.0 when I != J. If you do list them when I !=
J, you should insure they are consistent with their values in other
pair_coeff commands.
</P>
<P>Note that if this potential is being used as a sub-style of
<A HREF = "pair_hybrid.html">pair_style hybrid</A>, and there is no "pair_coeff I I"
setting made for RE-squared for a particular type I (because I-I
interactions are computed by another hybrid pair potential), then you
still need to insure the epsilon a,b,c coefficients are assigned to
that type in a "pair_coeff I J" command.
</P>
<HR>
<P><B>Mixing, shift, table, tail correction, per-atom energy/stress,
restart, rRESPA info</B>:
</P>
<P>Automatic mixing is supported only between LJ sphere
pairs due to the different meanings of the energy prefactors used
to calculate the interactions and the implicit dependance of
the ellipsoid-LJ sphere interaction on the equation for the
Hamaker constant presented here. Mixing of sigma and epsilon
followed by calculation of the energy prefactors using the
equations above is recommended.
</P>
<P>This pair styles supports the <A HREF = "pair_modify.html">pair_modify</A> shift
option for the energy of the Lennard-Jones portion of the pair
interaction, but only for sphere-sphere interactions. There is no
shifting performed for ellipsoidal interactions due to the anisotropic
dependence of the interaction.
</P>
<P>The <A HREF = "pair_modify.html">pair_modify</A> table option is not relevant
for this pair style.
</P>
<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A>
tail option for adding long-range tail corrections to energy and
pressure.
</P>
<P>This pair style does not calculate per-atom energy and stress, as used
by the <A HREF = "compute_epair_atom.html">compute epair/atom</A>, <A HREF = "compute_stress_atom.html">compute
stress/atom</A>, and <A HREF = "dump.html">dump custom</A>
commands.
</P>
<P>This pair style writes its information to <A HREF = "restart.html">binary restart
files</A>, so pair_style and pair_coeff commands do not need
to be specified in an input script that reads a restart file.
</P>
<P>This pair style can only be used via the <I>pair</I> keyword of the
<A HREF = "run_style.html">run_style respa</A> command. It does not support the
<I>inner</I>, <I>middle</I>, <I>outer</I> keywords of the <A HREF = "run_style.html">run_style
command</A>.
</P>
<HR>
<P><B>Restrictions:</B>
</P>
<P>This style is part of the "asphere" package. It is only enabled if
LAMMPS was built with that package. See the <A HREF = "Section_start.html#2_3">Making
LAMMPS</A> section for more info.
</P>
<P>The distance-of-closest-approach approximation used by LAMMPS becomes
less accurate when high-aspect ratio ellipsoids are used.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "pair_coeff.html">pair_coeff</A>, <A HREF = "fix_nve_asphere.html">fix nve/asphere</A>,
<A HREF = "compute_temp_asphere.html">compute temp/asphere</A>
</P>
<P><B>Default:</B> none
</P>
<HR>
<A NAME = "Everaers"></A>
<P><B>(Everaers)</B> Everaers and Ejtehadi, Phys Rev E, 67, 041710 (2003).
</P>
<A NAME = "Babadi"></A>
<P><B>(Berardi)</B> Babadi, Ejtehadi, Everaers, J Comp Phys, 219, 770-779 (2006).
</P>
</HTML>

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@ -0,0 +1,194 @@
"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)
:line
pair_style resquared command :h3
[Syntax:]
pair_style resquared cutoff :pre
cutoff = global cutoff for interactions (distance units) :ul
[Examples:]
pair_style resquared 10.0
pair_coeff * * 1.0 1.0 1.7 3.4 3.4 1.0 1.0 1.0 :pre
[Description:]
Style {resquared} computes the RE-squared anisotropic interaction
"(Everaers,Babadi)"_#Everaers between pairs of ellipsoidal and/or
spherical Lennard-Jones particles. For ellipsoidal interactions,
the potential considers the ellipsoid as being comprised of small
spheres of size sigma. LJ particles are a single sphere of size
sigma. The distinction is made to allow the pair style to make
efficient calculations of ellipsoid/solvent interactions.
:link(redoc,Eqs/pair_resquared_extra.pdf)
Details for the equations used are given in the references below
and "this document"_#redoc.
Use of this pair style requires the NVE, NVT, or NPT fixes
with the {asphere} extension (e.g. "fix
nve/asphere"_fix_nve_asphere.html) in order to integrate particle
rotation. Additionally, "atom_style ellipsoid"_atom_style.html should
be used since it defines the rotational state of the ellipsoidal
particles and the "shape"_shape.html command should be used to
specify ellipsoid diameters.
The following coefficients must be defined for each pair of atoms
types via the "pair_coeff"_pair_coeff.html command as in the examples
above, or in the data file or restart files read by the
"read_data"_read_data.html or "read_restart"_read_restart.html
commands:
A12 = Energy Prefactor/Hamaker constant (energy units)
sigma = atomic interaction diameter (distance units)
epsilon_i_a = relative well depth of type I for side-to-side interactions
epsilon_i_b = relative well depth of type I for face-to-face interactions
epsilon_i_c = relative well depth of type I for end-to-end interactions
epsilon_j_a = relative well depth of type J for side-to-side interactions
epsilon_j_b = relative well depth of type J for face-to-face interactions
epsilon_j_c = relative well depth of type J for end-to-end interactions
cutoff (distance units) :ul
The parameters used depend on the type of particles interacting -
ellipsoid or LJ sphere. The type of particle is determined by
the diameters specified with the "shape"_shape.html
command. LJ spheres have diameters equal to zero and thus
represent a single particle with size sigma. The epsilon_i_* or
epsilon_j_* parameters are ignored for LJ sphere interactions.
The interactions between two LJ sphere particles are computed
using the standard Lennard-Jones formula.
A12 specifies the energy prefactor which depends on
the type of particles interacting. For ellipsoid-ellipsoid
interactions, A12 is the Hamaker constant as described in
"(Everaers)"_#Everaers. In LJ units:
:c,image(Eqs/pair_resquared.jpg)
where rho gives the number density of the spherical particles
composing the ellipsoids and epsilon_LJ determines the
interaction strength of the spherical particles.
For ellipsoid-LJ sphere interactions, A12 gives the energy
prefactor (see "here"_Eqs/pair_resquared_extra.pdf for details:
:c,image(Eqs/pair_resquared2.jpg)
For LJ sphere-LJ sphere interactions, A12 is the standard
epsilon used in Lennard-Jones pair styles:
:c,image(Eqs/pair_resquared3.jpg)
sigma specifies the diameter of the continuous distribution of
constituent particles within each ellipsoid used to model
the RE-squared potential. Therefore, the effective shape
of an ellipsoid is given by the specified diameters
(see the "shape"_shape.html command) plus sigma.
For large uniform molecules it has been shown that the epsilon_*_*
energy parameters are approximately representable in terms of
local contact curvatures "(Everaers)"_#Everaers:
:c,image(Eqs/pair_resquared4.jpg)
where a, b, and c give the particle diameters.
The last coefficient is optional. If not specified, the global
cutoff specified in the pair_style command is used.
The epsilon_i and epsilon_j coefficients are actually defined for atom
types, not for pairs of atom types. Thus, in a series of pair_coeff
commands, they only need to be specified once for each atom type.
Specifically, if any of epsilon_i_a, epsilon_i_b, epsilon_i_c are
non-zero, the three values are assigned to atom type I. If all the
epsilon_i values are zero, they are ignored. If any of epsilon_j_a,
epsilon_j_b, epsilon_j_c are non-zero, the three values are assigned
to atom type J. If all three epsilon_i values are zero, they are
ignored. Thus the typical way to define the epsilon_i and epsilon_j
coefficients is to list their values in "pair_coeff I J" commands when
I = J, but set them to 0.0 when I != J. If you do list them when I !=
J, you should insure they are consistent with their values in other
pair_coeff commands.
Note that if this potential is being used as a sub-style of
"pair_style hybrid"_pair_hybrid.html, and there is no "pair_coeff I I"
setting made for RE-squared for a particular type I (because I-I
interactions are computed by another hybrid pair potential), then you
still need to insure the epsilon a,b,c coefficients are assigned to
that type in a "pair_coeff I J" command.
:line
[Mixing, shift, table, tail correction, per-atom energy/stress,
restart, rRESPA info]:
Automatic mixing is supported only between LJ sphere
pairs due to the different meanings of the energy prefactors used
to calculate the interactions and the implicit dependance of
the ellipsoid-LJ sphere interaction on the equation for the
Hamaker constant presented here. Mixing of sigma and epsilon
followed by calculation of the energy prefactors using the
equations above is recommended.
This pair styles supports the "pair_modify"_pair_modify.html shift
option for the energy of the Lennard-Jones portion of the pair
interaction, but only for sphere-sphere interactions. There is no
shifting performed for ellipsoidal interactions due to the anisotropic
dependence of the interaction.
The "pair_modify"_pair_modify.html table option is not relevant
for this pair style.
This pair style does not support the "pair_modify"_pair_modify.html
tail option for adding long-range tail corrections to energy and
pressure.
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 writes its information to "binary restart
files"_restart.html, so pair_style and pair_coeff commands do not need
to be specified 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 of the "run_style
command"_run_style.html.
:line
[Restrictions:]
This style is part of the "asphere" package. It is only enabled if
LAMMPS was built with that package. See the "Making
LAMMPS"_Section_start.html#2_3 section for more info.
The distance-of-closest-approach approximation used by LAMMPS becomes
less accurate when high-aspect ratio ellipsoids are used.
[Related commands:]
"pair_coeff"_pair_coeff.html, "fix nve/asphere"_fix_nve_asphere.html,
"compute temp/asphere"_compute_temp_asphere.html
[Default:] none
:line
:link(Everaers)
[(Everaers)] Everaers and Ejtehadi, Phys Rev E, 67, 041710 (2003).
:link(Babadi)
[(Berardi)] Babadi, Ejtehadi, Everaers, J Comp Phys, 219, 770-779 (2006).

1
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@ -131,6 +131,7 @@ the pair_style command, and coefficients specified by the associated
<LI><A HREF = "pair_meam.html">pair_style meam</A> - modified embedded atom method (MEAM)
<LI><A HREF = "pair_morse.html">pair_style morse</A> - Morse potential
<LI><A HREF = "pair_morse.html">pair_style morse</A> - optimized version of Morse potential
<LI><A HREF = "pair_resquared.html">pair_style resquared</A> - Everaers RE-Squared ellipsoidal potential
<LI><A HREF = "pair_soft.html">pair_style soft</A> - Soft (cosine) potential
<LI><A HREF = "pair_sw.html">pair_style sw</A> - Stillinger-Weber 3-body potential
<LI><A HREF = "pair_table.html">pair_style table</A> - tabulated pair potential

1
doc/pair_style.txt
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@ -127,6 +127,7 @@ the pair_style command, and coefficients specified by the associated
"pair_style meam"_pair_meam.html - modified embedded atom method (MEAM)
"pair_style morse"_pair_morse.html - Morse potential
"pair_style morse"_pair_morse.html - optimized version of Morse potential
"pair_style resquared"_pair_resquared.html - Everaers RE-Squared ellipsoidal potential
"pair_style soft"_pair_soft.html - Soft (cosine) potential
"pair_style sw"_pair_sw.html - Stillinger-Weber 3-body potential
"pair_style table"_pair_table.html - tabulated pair potential

52
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@ -23,14 +23,14 @@ pair_coeff * * SiC.tersoff Si C Si
</PRE>
<P><B>Description:</B>
</P>
<P>The <I>tersoff</I> style computes a 3-body <A HREF = "#Tersoff">Tersoff</A> potential
<P>The <I>tersoff</I> style computes a 3-body <A HREF = "#Tersoff_1">Tersoff</A> potential
for the energy E of a system of atoms as
</P>
<CENTER><IMG SRC = "Eqs/pair_tersoff.jpg">
<CENTER><IMG SRC = "Eqs/pair_tersoff_1.jpg">
</CENTER>
<P>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.
within a cutoff distance = R + D.
</P>
<P>Only a single pair_coeff command is used with the <I>tersoff</I> style
which specifies a Tersoff potential file with parameters for all
@ -66,6 +66,8 @@ above:
<UL><LI>element 1 (the center atom in a 3-body interaction)
<LI>element 2 (the atom bonded to the center atom)
<LI>element 3 (the atom influencing the 1-2 bond in a bond-order sense)
<LI>m
<LI>gamma
<LI>lambda3 (1/distance units)
<LI>c
<LI>d
@ -80,7 +82,7 @@ above:
<LI>A (energy units)
</UL>
<P>The n, beta, lambda2, B, lambda1, and A parameters are only used for
two-body interactions. The lambda3, c, d, and costheta0 parameters
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.
@ -113,6 +115,38 @@ The parameters used only for two-body interactions
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.
</P>
<P>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 <A HREF = "#Albe">Albe
et al.</A> when beta = 1 and m = 1. Tersoff used a slightly
different but equivalent form for alloys, which we will refer to
as <A HREF = "#Tersoff_2">Tersoff_2</A>.
</P>
<P>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:
</P>
<CENTER><IMG SRC = "Eqs/pair_tersoff_2.jpg">
</CENTER>
<P>Values not shown are determined by the first 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.
</P>
<P>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.
</P>
<P>Many thanks to Rutuparna Narulkar, David Farrell, and Xiaowang Zhou for helping clarify
how Tersoff parameters for alloys have been defined in various papers.
</P>
<HR>
<P><B>Mixing, shift, table, tail correction, per-atom energy/stress,
@ -164,8 +198,14 @@ appropriate units if your simulation doesn't use "metal" units.
</P>
<HR>
<A NAME = "Tersoff"></A>
<A NAME = "Tersoff_1"></A>
<P><B>(Tersoff)</B> Tersoff, Phys Rev B, 37, 6991 (1988).
<A NAME = "Albe"></A><B>(Tersoff_1)</B> J. Tersoff, Phys Rev B, 37, 6991 (1988).
<A NAME = "Tersoff_2"></A><B>(Albe)</B> J. Nord, K. Albe, P. Erhartand K. Nordlund, J. Phys.: Condens. Matter, 15, 5649(2003).
<P><B>(Tersoff_2)</B> J. Tersoff, Phys Rev B, 39, 5566 (1989)
</P>
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