2006-11-04 01:09:44 +08:00
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<HTML>
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<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>
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<HR>
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<H3>pair_style tersoff command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>pair_style tersoff
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</PRE>
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<P><B>Examples:</B>
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</P>
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<PRE>pair_style tersoff
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pair_coeff * * Si.tersoff Si
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pair_coeff * * SiC.tersoff Si C Si
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>The <I>tersoff</I> style computes a 3-body Tersoff potential
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<A HREF = "#Tersoff_1">(Tersoff_1)</A> for the energy E of a system of atoms as
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</P>
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<CENTER><IMG SRC = "Eqs/pair_tersoff_1.jpg">
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</CENTER>
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<P>where f_R is a two-body term and f_A includes three-body interactions.
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The summations in the formula are over all neighbors J and K of atom I
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within a cutoff distance = R + D.
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</P>
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<P>Only a single pair_coeff command is used with the <I>tersoff</I> style
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which specifies a Tersoff potential file with parameters for all
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needed elements. These are mapped to LAMMPS atom types by specifying
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N additional arguments after the filename in the pair_coeff command,
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where N is the number of LAMMPS atom types:
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</P>
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<UL><LI>filename
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<LI>N element names = mapping of Tersoff elements to atom types
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</UL>
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<P>As an example, imagine the SiC.tersoff file has Tersoff values for Si
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and C. If your LAMMPS simulation has 4 atoms types and you want the
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1st 3 to be Si, and the 4th to be C, you would use the following
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pair_coeff command:
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</P>
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<PRE>pair_coeff * * SiC.tersoff Si Si Si C
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</PRE>
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<P>The 1st 2 arguments must be * * so as to span all LAMMPS atom types.
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The first three Si arguments map LAMMPS atom types 1,2,3 to the Si
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element in the Tersoff file. The final C argument maps LAMMPS atom
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type 4 to the C element in the Tersoff file. If a mapping value is
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specified as NULL, the mapping is not performed. This can be used
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when a <I>tersoff</I> potential is used as part of the <I>hybrid</I> pair style.
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The NULL values are placeholders for atom types that will be used with
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other potentials.
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</P>
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<P>Tersoff files in the <I>potentials</I> directory of the LAMMPS distribution
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have a ".tersoff" suffix. Lines that are not blank or comments
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(starting with #) define parameters for a triplet of elements. The
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parameters in a single entry correspond to coefficients in the formula
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above:
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</P>
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<UL><LI>element 1 (the center atom in a 3-body interaction)
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<LI>element 2 (the atom bonded to the center atom)
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<LI>element 3 (the atom influencing the 1-2 bond in a bond-order sense)
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<LI>m
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<LI>gamma
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<LI>lambda3 (1/distance units)
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<LI>c
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<LI>d
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<LI>costheta0 (can be a value < -1 or > 1)
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<LI>n
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<LI>beta
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<LI>lambda2 (1/distance units)
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<LI>B (energy units)
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<LI>R (distance units)
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<LI>D (distance units)
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<LI>lambda1 (1/distance units)
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<LI>A (energy units)
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</UL>
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<P>The n, beta, lambda2, B, lambda1, and A parameters are only used for
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two-body interactions. The m, gamma, lambda3, c, d, and costheta0
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parameters are only used for three-body interactions. The R and D
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parameters are used for both two-body and three-body interactions. The
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non-annotated parameters are unitless. The value of m must be 3 or 1.
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</P>
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<P>The Tersoff potential file must contain entries for all the elements
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listed in the pair_coeff command. It can also contain entries for
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additional elements not being used in a particular simulation; LAMMPS
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ignores those entries.
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</P>
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<P>For a single-element simulation, only a single entry is required
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(e.g. SiSiSi). For a two-element simulation, the file must contain 8
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entries (for SiSiSi, SiSiC, SiCSi, SiCC, CSiSi, CSiC, CCSi, CCC), that
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specify Tersoff parameters for all permutations of the two elements
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interacting in three-body configurations. Thus for 3 elements, 27
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entries would be required, etc.
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</P>
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<P>As annotated above, the first element in the entry is the center atom
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in a three-body interaction and it is bonded to the 2nd atom and the
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bond is influenced by the 3rd atom. Thus an entry for SiCC means Si
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bonded to a C with another C atom influencing the bond. Thus
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three-body parameters for SiCSi and SiSiC entries will not, in
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general, be the same. The parameters used for the two-body
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interaction come from the entry where the 2nd element is repeated.
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Thus the two-body parameters for Si interacting with C, comes from the
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SiCC entry.
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</P>
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<P>The parameters used for a particular
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three-body interaction come from the entry with the corresponding
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three elements. The parameters used only for two-body interactions
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(n, beta, lambda2, B, lambda1, and A) in entries whose 2nd and 3rd
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element are different (e.g. SiCSi) are not used for anything and can
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be set to 0.0 if desired.
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</P>
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<P>Note that the twobody parameters in entries such as SiCC and CSiSi
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are often the same, due to the common use of symmetric mixing rules,
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but this is not always the case. For example, the beta and n parameters in
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Tersoff_2 <A HREF = "#Tersoff_2">(Tersoff_2)</A> are not symmetric.
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</P>
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<P>We chose the above form so as to enable users to define all commonly
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used variants of the Tersoff potential. In particular, our form
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reduces to the original Tersoff form when m = 3 and gamma = 1, while
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it reduces to the form of <A HREF = "#Albe">Albe et al.</A> when beta = 1 and m = 1.
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Note that in the current Tersoff implementation in LAMMPS, m must be
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specified as either 3 or 1. Tersoff used a slightly different but
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equivalent form for alloys, which we will refer to as Tersoff_2
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potential <A HREF = "#Tersoff_2">(Tersoff_2)</A>.
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</P>
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<P>LAMMPS parameter values for Tersoff_2 can be obtained as follows:
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gamma = 1, just as for Tersoff_1, but now lambda3 = 0 and the value of
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m has no effect. The parameters for species i and j can be calculated
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using the Tersoff_2 mixing rules:
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</P>
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<CENTER><IMG SRC = "Eqs/pair_tersoff_2.jpg">
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</CENTER>
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2009-01-23 02:05:05 +08:00
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<P>Tersoff_2 parameters R and S must be converted to the LAMMPS
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parameters R and D (R is different in both forms), using the following
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relations: R=(R'+S')/2 and D=(S'-R')/2, where the primes indicate the
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Tersoff_2 parameters.
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</P>
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<P>In the potentials directory, the file SiCGe.tersoff provides the
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LAMMPS parameters for Tersoff's various versions of Si, as well as his
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alloy parameters for Si, C, and Ge. This file can be used for pure Si,
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(three different versions), pure C, pure Ge, binary SiC, and binary
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SiGe. LAMMPS will generate an error if this file is used with any
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combination involving C and Ge, since there are no entries for the GeC
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interactions (Tersoff did not publish parameters for this
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cross-interaction.) Tersoff files are also provided for the SiC alloy
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(SiC.tersoff) and the GaN (GaN.tersoff) alloys.
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</P>
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<P>Many thanks to Rutuparna Narulkar, David Farrell, and Xiaowang Zhou
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for helping clarify how Tersoff parameters for alloys have been
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defined in various papers.
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</P>
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2007-06-26 08:03:39 +08:00
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<HR>
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2008-01-22 02:12:34 +08:00
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<P><B>Mixing, shift, table, tail correction, restart, rRESPA info</B>:
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2007-06-26 08:03:39 +08:00
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</P>
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<P>For atom type pairs I,J and I != J, where types I and J correspond to
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two different element types, mixing is performed by LAMMPS as
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described above from values in the potential file.
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</P>
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<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A>
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shift, table, and tail options.
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</P>
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<P>This pair style does not write its information to <A HREF = "restart.html">binary restart
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files</A>, since it is stored in potential files. Thus, you
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need to re-specify the pair_style and pair_coeff commands in an input
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script that reads a restart file.
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</P>
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2007-10-04 08:21:14 +08:00
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<P>This pair style can only be used via the <I>pair</I> keyword of the
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<A HREF = "run_style.html">run_style respa</A> command. It does not support the
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<I>inner</I>, <I>middle</I>, <I>outer</I> keywords.
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</P>
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<HR>
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2006-11-04 01:09:44 +08:00
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<P><B>Restrictions:</B>
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</P>
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<P>This pair style is part of the "manybody" package. It is only enabled
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if LAMMPS was built with that package (which it is by default). See
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the <A HREF = "Section_start.html#2_3">Making LAMMPS</A> section for more info.
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</P>
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<P>This pair style requires the <A HREF = "newton.html">newton</A> setting to be "on"
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for pair interactions.
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</P>
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2007-04-24 00:55:05 +08:00
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<P>The Tersoff potential files provided with LAMMPS (see the potentials
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directory) are parameterized for metal <A HREF = "units.html">units</A>. You can
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use the Tersoff potential with any LAMMPS units, but you would need to
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create your own Tersoff potential file with coefficients listed in the
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appropriate units if your simulation doesn't use "metal" units.
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "pair_coeff.html">pair_coeff</A>
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</P>
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<P><B>Default:</B> none
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</P>
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<HR>
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2007-10-23 05:43:55 +08:00
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<A NAME = "Tersoff_1"></A>
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2007-10-26 00:52:37 +08:00
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<P><B>(Tersoff_1)</B> J. Tersoff, Phys Rev B, 37, 6991 (1988).
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</P>
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<A NAME = "Albe"></A>
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2007-10-23 05:43:55 +08:00
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2008-03-01 09:13:20 +08:00
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<P><B>(Albe)</B> J. Nord, K. Albe, P. Erhart, and K. Nordlund, J. Phys.:
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Condens. Matter, 15, 5649(2003).
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</P>
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<A NAME = "Tersoff_2"></A>
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<P><B>(Tersoff_2)</B> J. Tersoff, Phys Rev B, 39, 5566 (1989)
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</P>
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</HTML>
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