forked from lijiext/lammps
244 lines
10 KiB
HTML
244 lines
10 KiB
HTML
<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 tersoff/zbl command
|
||
</H3>
|
||
<P><B>Syntax:</B>
|
||
</P>
|
||
<PRE>pair_style tersoff/zbl
|
||
</PRE>
|
||
<P><B>Examples:</B>
|
||
</P>
|
||
<PRE>pair_style tersoff/zbl
|
||
pair_coeff * * SiC.tersoff.zbl Si C Si
|
||
</PRE>
|
||
<P><B>Description:</B>
|
||
</P>
|
||
<P>The <I>tersoff/zbl</I> style computes a 3-body Tersoff potential
|
||
<A HREF = "#Tersoff_1">(Tersoff_1)</A> with a close-separation pairwise modification
|
||
based on a Coulomb potential and the Ziegler-Biersack-Littmark
|
||
universal screening function <A HREF = "#ZBL">(ZBL)</A>, giving the energy E of a
|
||
system of atoms as
|
||
</P>
|
||
<CENTER><IMG SRC = "Eqs/pair_tersoff_zbl.jpg">
|
||
</CENTER>
|
||
<P>The f_F term is a fermi-like function used to smoothly connect the ZBL
|
||
repulsive potential with the Tersoff potential. There are 2
|
||
parameters used to adjust it: A_F and r_C. A_F controls how "sharp"
|
||
the transition is between the two, and r_C is essentially the cutoff
|
||
for the ZBL potential.
|
||
</P>
|
||
<P>For the ZBL portion, there are two terms. The first is the Coulomb
|
||
repulsive term, with Z1, Z2 as the number of protons in each nucleus,
|
||
e as the electron charge (1 for metal and real units) and epsilon0 as
|
||
the permittivity of vacuum. The second part is the ZBL universal
|
||
screening function, with a0 being the Bohr radius (typically 0.529
|
||
Angstroms), and the remainder of the coefficients provided by the
|
||
original paper. This screening function should be applicable to most
|
||
systems. However, it is only accurate for small separations
|
||
(i.e. less than 1 Angstrom).
|
||
</P>
|
||
<P>For the Tersoff portion, 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.
|
||
</P>
|
||
<P>Only a single pair_coeff command is used with the <I>tersoff/zbl</I> style
|
||
which specifies a Tersoff/ZBL 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:
|
||
</P>
|
||
<UL><LI>filename
|
||
<LI>N element names = mapping of Tersoff/ZBL elements to atom types
|
||
</UL>
|
||
<P>As an example, imagine the SiC.tersoff.zbl file has Tersoff/ZBL 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:
|
||
</P>
|
||
<PRE>pair_coeff * * SiC.tersoff Si Si Si C
|
||
</PRE>
|
||
<P>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/ZBL file. The final C argument maps LAMMPS
|
||
atom type 4 to the C element in the Tersoff/ZBL file. If a mapping
|
||
value is specified as NULL, the mapping is not performed. This can be
|
||
used when a <I>tersoff/zbl</I> potential is used as part of the <I>hybrid</I>
|
||
pair style. The NULL values are placeholders for atom types that will
|
||
be used with other potentials.
|
||
</P>
|
||
<P>Tersoff/ZBL files in the <I>potentials</I> directory of the LAMMPS
|
||
distribution have a ".tersoff.zbl" 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:
|
||
</P>
|
||
<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
|
||
<LI>costheta0 (can be a value < -1 or > 1)
|
||
<LI>n
|
||
<LI>beta
|
||
<LI>lambda2 (1/distance units)
|
||
<LI>B (energy units)
|
||
<LI>R (distance units)
|
||
<LI>D (distance units)
|
||
<LI>lambda1 (1/distance units)
|
||
<LI>A (energy units)
|
||
<LI>Z_i
|
||
<LI>Z_j
|
||
<LI>ZBLcut (distance units)
|
||
<LI>ZBLexpscale (1/distance units)
|
||
</UL>
|
||
<P>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
|
||
Z_i,Z_j, ZBLcut, ZBLexpscale parameters are used in the ZBL repulsive
|
||
portion of the potential and in the Fermi-like function. The
|
||
non-annotated parameters are unitless. The value of m must be 3 or 1.
|
||
</P>
|
||
<P>The Tersoff/ZBL 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.
|
||
</P>
|
||
<P>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.
|
||
</P>
|
||
<P>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.
|
||
</P>
|
||
<P>We chose the above form so as to enable users to define all commonly
|
||
used variants of the Tersoff portion of the 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. Note that in the current Tersoff implementation in LAMMPS,
|
||
m must be specified as either 3 or 1. Tersoff used a slightly
|
||
different but equivalent form for alloys, which we will refer to as
|
||
Tersoff_2 potential <A HREF = "#Tersoff_2">(Tersoff_2)</A>.
|
||
</P>
|
||
<P>LAMMPS parameter values for Tersoff_2 can be obtained as follows:
|
||
gamma = 1, just as for Tersoff_1, but now lambda3 = 0 and the value of
|
||
m has no effect. 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<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.
|
||
</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 parameters 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. Also thanks to Ram Devanathan for
|
||
providing the base ZBL implementation.
|
||
</P>
|
||
<HR>
|
||
|
||
<P><B>Mixing, shift, table, tail correction, restart, rRESPA info</B>:
|
||
</P>
|
||
<P>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.
|
||
</P>
|
||
<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A>
|
||
shift, table, and tail options.
|
||
</P>
|
||
<P>This pair style does not write its information to <A HREF = "restart.html">binary restart
|
||
files</A>, 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.
|
||
</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.
|
||
</P>
|
||
<HR>
|
||
|
||
<P><B>Restrictions:</B>
|
||
</P>
|
||
<P>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 <A HREF = "Section_start.html#2_3">Making LAMMPS</A> section for more info.
|
||
</P>
|
||
<P>This pair style requires the <A HREF = "newton.html">newton</A> setting to be "on"
|
||
for pair interactions.
|
||
</P>
|
||
<P>The Tersoff/ZBL potential files provided with LAMMPS (see the
|
||
potentials directory) are parameterized for metal <A HREF = "units.html">units</A>.
|
||
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.
|
||
</P>
|
||
<P><B>Related commands:</B>
|
||
</P>
|
||
<P><A HREF = "pair_coeff.html">pair_coeff</A>
|
||
</P>
|
||
<P><B>Default:</B> none
|
||
</P>
|
||
<HR>
|
||
|
||
<A NAME = "Tersoff_1"></A>
|
||
|
||
<P><B>(Tersoff_1)</B> J. Tersoff, Phys Rev B, 37, 6991 (1988).
|
||
</P>
|
||
<A NAME = "ZBL"></A>
|
||
|
||
<P><B>(ZBL)</B> J.F. Ziegler, J.P. Biersack, U. Littmark, 'Stopping and Ranges
|
||
of Ions in Matter' Vol 1, 1985, Pergamon Press.
|
||
</P>
|
||
<A NAME = "Albe"></A>
|
||
|
||
<P><B>(Albe)</B> J. Nord, K. Albe, P. Erhartand K. Nordlund, J. Phys.:
|
||
Condens. Matter, 15, 5649(2003).
|
||
</P>
|
||
<A NAME = "Tersoff_2"></A>
|
||
|
||
<P><B>(Tersoff_2)</B> J. Tersoff, Phys Rev B, 39, 5566 (1989)
|
||
</P>
|
||
</HTML>
|