From fdc1520330983ff373758f5aa85048545b2d528a Mon Sep 17 00:00:00 2001 From: sjplimp Date: Wed, 1 Oct 2008 15:02:48 +0000 Subject: [PATCH] git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@2122 f3b2605a-c512-4ea7-a41b-209d697bcdaa --- doc/Eqs/pair_tersoff_zbl.jpg | Bin 0 -> 37457 bytes doc/Eqs/pair_tersoff_zbl.tex | 33 +++++ doc/Section_commands.html | 2 +- doc/Section_commands.txt | 1 + doc/pair_coeff.html | 3 +- doc/pair_coeff.txt | 3 +- doc/pair_style.html | 1 + doc/pair_style.txt | 1 + doc/pair_tersoff.html | 4 +- doc/pair_tersoff.txt | 4 +- doc/pair_tersoff_zbl.html | 243 +++++++++++++++++++++++++++++++++++ doc/pair_tersoff_zbl.txt | 234 +++++++++++++++++++++++++++++++++ 12 files changed, 522 insertions(+), 7 deletions(-) create mode 100644 doc/Eqs/pair_tersoff_zbl.jpg create mode 100644 doc/Eqs/pair_tersoff_zbl.tex create mode 100644 doc/pair_tersoff_zbl.html create mode 100644 doc/pair_tersoff_zbl.txt diff --git a/doc/Eqs/pair_tersoff_zbl.jpg b/doc/Eqs/pair_tersoff_zbl.jpg 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--git a/doc/Eqs/pair_tersoff_zbl.tex b/doc/Eqs/pair_tersoff_zbl.tex new file mode 100644 index 0000000000..4accac098e --- /dev/null +++ b/doc/Eqs/pair_tersoff_zbl.tex @@ -0,0 +1,33 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + E & = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\ + V_{ij} & = & (1 - f_F(r_{ij})) V^{ZBL}_{ij} + f_F(r_{ij}) V^{Tersoff}_{ij} \\ +f_F(r_{ij}) & = & \frac{1}{1 + e^{-A_F(r_{ij} - r_C)}}\\ + \\ + \\ + V^{ZBL}_{ij} & = & \frac{1}{4\pi\epsilon_0} \frac{Z_1 Z_2 \,e^2}{r_{ij}} \phi(r_{ij}/a) \\ + a & = & \frac{0.8854\,a_0}{Z_{1}^{0.23} + Z_{2}^{0.23}}\\ + \phi(x) & = & 0.1818e^{-3.2x} + 0.5099e^{-0.9423x} + 0.2802e^{-0.4029x} + 0.02817e^{-0.2016x}\\ + \\ + \\ + V^{Tersoff}_{ij} & = & f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right] \\ + f_C(r) & = & \left\{ \begin{array} {r@{\quad:\quad}l} + 1 & r < R - D \\ + \frac{1}{2} - \frac{1}{2} \sin \left( \frac{\pi}{2} \frac{r-R}{D} \right) & + R-D < r < R + D \\ + 0 & r > R + D + \end{array} \right. \\ + f_R(r) & = & A \exp (-\lambda_1 r) \\ + f_A(r) & = & -B \exp (-\lambda_2 r) \\ + b_{ij} & = & \left( 1 + \beta^n {\zeta_{ij}}^n \right)^{-\frac{1}{2n}} \\ + \zeta_{ij} & = & \sum_{k \neq i,j} f_C(r_{ik}) g(\theta_{ijk}) + \exp \left[ {\lambda_3}^3 (r_{ij} - r_{ik})^m \right] \\ + g(\theta) & = & \gamma_{ijk} \left( 1 + \frac{c^2}{d^2} - + \frac{c^2}{\left[ d^2 + + (\cos \theta - \cos \theta_0)^2\right]} \right) +\end{eqnarray*} + +\end{document} diff --git a/doc/Section_commands.html b/doc/Section_commands.html index 80ac76b039..da2fdbdeab 100644 --- a/doc/Section_commands.html +++ b/doc/Section_commands.html @@ -373,7 +373,7 @@ full description: lj/expandlj/gromacslj/gromacs/coul/gromacslj/smooth lubricatemeammorsemorse/opt resquaredperi/pmbsoftsw -tabletersoffyukawa +tabletersofftersoff/zblyukawa

These are pair styles contributed by users, which can be used if diff --git a/doc/Section_commands.txt b/doc/Section_commands.txt index 01c1f40476..128cd551b4 100644 --- a/doc/Section_commands.txt +++ b/doc/Section_commands.txt @@ -532,6 +532,7 @@ full description: "sw"_pair_sw.html, "table"_pair_table.html, "tersoff"_pair_tersoff.html, +"tersoff/zbl"_pair_tersoff_zbl.html, "yukawa"_pair_yukawa.html :tb(c=4,ea=c) These are pair styles contributed by users, which can be used if diff --git a/doc/pair_coeff.html b/doc/pair_coeff.html index 61c4f7840f..5b7c071ef4 100644 --- a/doc/pair_coeff.html +++ b/doc/pair_coeff.html @@ -96,7 +96,7 @@ the pair_style command, and coefficients specified by the associated

  • pair_style coul/cut - cutoff Coulombic potential
  • pair_style coul/debye - cutoff Coulombic potential with Debye screening
  • pair_style coul/long - long-range Coulombic potential -
  • pair_style dipole/cut - point dipoles with cutoff +
  • pair_style dipole/cut - point dipoles with cutoff
  • pair_style dpd - dissipative particle dynamics (DPD)
  • pair_style eam - embedded atom method (EAM)
  • pair_style eam/opt - optimized version of EAM @@ -135,6 +135,7 @@ the pair_style command, and coefficients specified by the associated
  • pair_style sw - Stillinger-Weber 3-body potential
  • pair_style table - tabulated pair potential
  • pair_style tersoff - Tersoff 3-body potential +
  • pair_style tersoff/zbl - Tersoff/ZBL 3-body potential
  • pair_style yukawa - Yukawa potential

    There are also additional pair styles submitted by users which are diff --git a/doc/pair_coeff.txt b/doc/pair_coeff.txt index 293f4cde8e..60913fed19 100644 --- a/doc/pair_coeff.txt +++ b/doc/pair_coeff.txt @@ -92,7 +92,7 @@ the pair_style command, and coefficients specified by the associated "pair_style coul/cut"_pair_coul.html - cutoff Coulombic potential "pair_style coul/debye"_pair_coul.html - cutoff Coulombic potential with Debye screening "pair_style coul/long"_pair_coul.html - long-range Coulombic potential -"pair_style dipole/cut"_pair_dpd.html - point dipoles with cutoff +"pair_style dipole/cut"_pair_dipole.html - point dipoles with cutoff "pair_style dpd"_pair_dpd.html - dissipative particle dynamics (DPD) "pair_style eam"_pair_eam.html - embedded atom method (EAM) "pair_style eam/opt"_pair_eam.html - optimized version of EAM @@ -131,6 +131,7 @@ the pair_style command, and coefficients specified by the associated "pair_style sw"_pair_sw.html - Stillinger-Weber 3-body potential "pair_style table"_pair_table.html - tabulated pair potential "pair_style tersoff"_pair_tersoff.html - Tersoff 3-body potential +"pair_style tersoff/zbl"_pair_tersoff.html - Tersoff/ZBL 3-body potential "pair_style yukawa"_pair_yukawa.html - Yukawa potential :ul There are also additional pair styles submitted by users which are diff --git a/doc/pair_style.html b/doc/pair_style.html index 3b63836388..69ae43307b 100644 --- a/doc/pair_style.html +++ b/doc/pair_style.html @@ -137,6 +137,7 @@ the pair_style command, and coefficients specified by the associated

  • pair_style sw - Stillinger-Weber 3-body potential
  • pair_style table - tabulated pair potential
  • pair_style tersoff - Tersoff 3-body potential +
  • pair_style tersoff/zbl - Tersoff/ZBL 3-body potential
  • pair_style yukawa - Yukawa potential

    There are also additional pair styles submitted by users which are diff --git a/doc/pair_style.txt b/doc/pair_style.txt index 35c0f2bf0b..f96bc89f84 100644 --- a/doc/pair_style.txt +++ b/doc/pair_style.txt @@ -133,6 +133,7 @@ the pair_style command, and coefficients specified by the associated "pair_style sw"_pair_sw.html - Stillinger-Weber 3-body potential "pair_style table"_pair_table.html - tabulated pair potential "pair_style tersoff"_pair_tersoff.html - Tersoff 3-body potential +"pair_style tersoff/zbl"_pair_tersoff.html - Tersoff/ZBL 3-body potential "pair_style yukawa"_pair_yukawa.html - Yukawa potential :ul There are also additional pair styles submitted by users which are diff --git a/doc/pair_tersoff.html b/doc/pair_tersoff.html index b7dc86acf9..fbfbfdf5cd 100644 --- a/doc/pair_tersoff.html +++ b/doc/pair_tersoff.html @@ -18,7 +18,7 @@

    Examples: 

    pair_style tersoff
-pair_coeff * * si.tersoff Si
+pair_coeff * * Si.tersoff Si
 pair_coeff * * SiC.tersoff Si C Si

    Description: @@ -124,7 +124,7 @@ 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 (Tersoff_2).

    -

    LAMMPS parameter values for Tersoff_2 can be obtained as follows. +

    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: diff --git a/doc/pair_tersoff.txt b/doc/pair_tersoff.txt index 85cf3831aa..1325f7618e 100644 --- a/doc/pair_tersoff.txt +++ b/doc/pair_tersoff.txt @@ -15,7 +15,7 @@ pair_style tersoff :pre [Examples:] pair_style tersoff -pair_coeff * * si.tersoff Si +pair_coeff * * Si.tersoff Si pair_coeff * * SiC.tersoff Si C Si :pre [Description:] @@ -121,7 +121,7 @@ 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 "(Tersoff_2)"_#Tersoff_2. -LAMMPS parameter values for Tersoff_2 can be obtained as follows. +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: diff --git a/doc/pair_tersoff_zbl.html b/doc/pair_tersoff_zbl.html new file mode 100644 index 0000000000..5c32d6079e --- /dev/null +++ b/doc/pair_tersoff_zbl.html @@ -0,0 +1,243 @@ + +

    LAMMPS WWW Site - LAMMPS Documentation - LAMMPS Commands +
    + + + + + + +
    + +

    pair_style tersoff/zbl command +

    +

    Syntax: +

    +
    pair_style tersoff/zbl 
+
    +

    Examples: +

    +
    pair_style tersoff/zbl
+pair_coeff * * SiC.tersoff.zbl Si C Si 
+
    +

    Description: +

    +

    The tersoff/zbl style computes a 3-body Tersoff potential +(Tersoff_1) with a close-separation pairwise modification +based on a Coulomb potential and the Ziegler-Biersack-Littmark +universal screening function (ZBL), giving the energy E of a +system of atoms as +

    +
    +
    +

    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. +

    +

    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). +

    +

    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. +

    +

    Only a single pair_coeff command is used with the tersoff/zbl 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: +

    +
    • filename +
    • N element names = mapping of Tersoff/ZBL elements to atom types +
    +

    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: +

    +
    pair_coeff * * SiC.tersoff Si Si Si C 
+
    +

    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 tersoff/zbl 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/ZBL files in the potentials 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: +

    +
    • 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) +
    • Z_i +
    • Z_j +
    • ZBLcut (distance units) +
    • ZBLexpscale (1/distance units) +
    +

    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. +

    +

    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. +

    +

    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 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 Albe et al. 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 (Tersoff_2). +

    +

    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: +

    +
    +
    +

    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. +

    +

    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. +

    +

    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. +

    +
    + +

    Mixing, shift, table, tail correction, 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 +shift, table, and tail options. +

    +

    This pair style does not write its information to binary restart +files, 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 command. It does not support the +inner, middle, outer keywords. +

    +
    + +

    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 for more info. +

    +

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

    +

    The Tersoff/ZBL potential files provided with LAMMPS (see the +potentials directory) are parameterized for metal units. +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 +

    +

    Default: none +

    +
    + + + +

    (Tersoff_1) J. Tersoff, Phys Rev B, 37, 6991 (1988). +

    + + +

    (ZBL) J.F. Ziegler, J.P. Biersack, U. Littmark, 'Stopping and Ranges +of Ions in Matter' Vol 1, 1985, Pergamon Press. +

    + + +

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

    + + +

    (Tersoff_2) J. Tersoff, Phys Rev B, 39, 5566 (1989) +

    + diff --git a/doc/pair_tersoff_zbl.txt b/doc/pair_tersoff_zbl.txt new file mode 100644 index 0000000000..7f1b95541f --- /dev/null +++ b/doc/pair_tersoff_zbl.txt @@ -0,0 +1,234 @@ +"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 tersoff/zbl command :h3 + +[Syntax:] + +pair_style tersoff/zbl :pre + +[Examples:] + +pair_style tersoff/zbl +pair_coeff * * SiC.tersoff.zbl Si C Si :pre + +[Description:] + +The {tersoff/zbl} style computes a 3-body Tersoff potential +"(Tersoff_1)"_#Tersoff_1 with a close-separation pairwise modification +based on a Coulomb potential and the Ziegler-Biersack-Littmark +universal screening function "(ZBL)"_#ZBL, giving the energy E of a +system of atoms as + +:c,image(Eqs/pair_tersoff_zbl.jpg) + +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. + +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). + +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. + +Only a single pair_coeff command is used with the {tersoff/zbl} 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: + +filename +N element names = mapping of Tersoff/ZBL elements to atom types :ul + +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: + +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/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 {tersoff/zbl} 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/ZBL files in the {potentials} 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: + +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) +Z_i +Z_j +ZBLcut (distance units) +ZBLexpscale (1/distance 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 +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. + +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. + +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 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 "Albe et al."_#Albe 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 "(Tersoff_2)"_#Tersoff_2. + +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: + +:c,image(Eqs/pair_tersoff_2.jpg) + +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. + +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. + +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. + +:line + +[Mixing, shift, table, tail correction, 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 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. + +:line + +[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/ZBL 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 + +:line + +:link(Tersoff_1) +[(Tersoff_1)] J. Tersoff, Phys Rev B, 37, 6991 (1988). + +:link(ZBL) +[(ZBL)] J.F. Ziegler, J.P. Biersack, U. Littmark, 'Stopping and Ranges +of Ions in Matter' Vol 1, 1985, Pergamon Press. + +: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)