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@ -129,10 +129,30 @@
</div>
<div class="section" id="pair-style-vashishta-omp-command">
<h1>pair_style vashishta/omp command</h1>
</div>
<div class="section" id="pair-style-vashishta-table-command">
<h1>pair_style vashishta/table command</h1>
</div>
<div class="section" id="pair-style-vashishta-table-omp-command">
<h1>pair_style vashishta/table/omp command</h1>
<div class="section" id="syntax">
<h2>Syntax</h2>
<pre class="literal-block">
pair_style vashishta
pair_style style args
</pre>
<ul class="simple">
<li>style = <em>vashishta</em> or <em>vashishta/table</em> or <em>vashishta/omp</em> or <em>vashishta/table/omp</em></li>
<li>args = list of arguments for a particular style</li>
</ul>
<pre class="literal-block">
<em>vashishta</em> args = none
<em>vashishta/omp</em> args = none
<em>vashishta/table</em> args = Ntable cutinner
Ntable = # of tabulation points
cutinner = tablulate from cutinner to cutoff
<em>vashishta/table/omp</em> args = Ntable cutinner
Ntable = # of tabulation points
cutinner = tablulate from cutinner to cutoff
</pre>
</div>
<div class="section" id="examples">
@ -141,17 +161,20 @@ pair_style vashishta
pair_style vashishta
pair_coeff * * SiC.vashishta Si C
</pre>
<pre class="literal-block">
pair_style vashishta/table 100000 0.2
pair_coeff * * SiC.vashishta Si C
</pre>
</div>
<div class="section" id="description">
<h2>Description</h2>
<p>The <em>vashishta</em> style computes the combined 2-body and 3-body
family of potentials developed in the group of Vashishta and
co-workers. By combining repulsive, screened Coulombic,
screened charge-dipole, and dispersion interactions with a
bond-angle energy based on the Stillinger-Weber potential,
this potential has been used to describe a variety of inorganic
compounds, including SiO2 <a class="reference internal" href="#vashishta1990"><span class="std std-ref">Vashishta1990</span></a>,
SiC <a class="reference internal" href="#vashishta2007"><span class="std std-ref">Vashishta2007</span></a>,
<p>The <em>vashishta</em> and <em>vashishta/table</em> styles compute the combined
2-body and 3-body family of potentials developed in the group of
Vashishta and co-workers. By combining repulsive, screened Coulombic,
screened charge-dipole, and dispersion interactions with a bond-angle
energy based on the Stillinger-Weber potential, this potential has
been used to describe a variety of inorganic compounds, including SiO2
<a class="reference internal" href="#vashishta1990"><span class="std std-ref">Vashishta1990</span></a>, SiC <a class="reference internal" href="#vashishta2007"><span class="std std-ref">Vashishta2007</span></a>,
and InP <a class="reference internal" href="#branicio2009"><span class="std std-ref">Branicio2009</span></a>.</p>
<p>The potential for the energy U of a system of atoms is</p>
<img alt="_images/pair_vashishta.jpg" class="align-center" src="_images/pair_vashishta.jpg" />
@ -163,10 +186,20 @@ tilted by a linear function so that the energy and force are
both zero at <em>rc</em>. The summation over three-body terms
is over all neighbors J and K within a cut-off distance = <em>r0</em>,
where the exponential screening function becomes zero.</p>
<p>Only a single pair_coeff command is used with the <em>vashishta</em> style which
specifies a Vashishta 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,
<p>The <em>vashishta</em> style computes these formulas analytically. The
<em>vashishta/table</em> style tabulates the analytic values for <em>Ntable</em>
points from cutinner to the cutoff of the potential. The points are
equally spaced in R^2 space from cutinner^2 to cutoff^2. For the
two-body term in the above equation, a linear interpolation for each
pairwise distance between adjacent points in the table. In practice
the tabulated version can run 3-5x faster than the analytic version
with with moderate to little loss of accuracy for Ntable values
between 10000 and 1000000. It is not recommended to use less than
5000 tabulation points.</p>
<p>Only a single pair_coeff command is used with either style which
specifies a Vashishta 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 class="simple">
<li>filename</li>
@ -213,56 +246,49 @@ and three-body coefficients in the formulae above:</p>
<li>C</li>
<li>costheta0</li>
</ul>
<p>The non-annotated parameters are unitless.
The Vashishta 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 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>Depending on the particular version of the Vashishta potential,
the values of these parameters may be keyed to the identities of
zero, one, two, or three elements.
In order to make the input file format unambiguous, general,
and simple to code,
LAMMPS uses a slightly confusing method for specifying parameters.
All parameters are divided into two classes: two-body and three-body.
Two-body and three-body parameters are handled differently,
as described below.
The two-body parameters are H, eta, lambda1, D, lambda4, W, rc, gamma, and r0.
They appear in the above formulae with two subscripts.
The parameters Zi and Zj are also classified as two-body parameters,
even though they only have 1 subscript.
The three-body parameters are B, C, costheta0.
They appear in the above formulae with three subscripts.
Two-body and three-body parameters are handled differently,
as described below.</p>
<p>The first element in each entry is the center atom
in a three-body interaction, while the second and third elements
are two neighbor atoms. Three-body parameters for a central atom I
and two neighbors J and K are taken from the IJK entry.
Note that even though three-body parameters do not depend on the order of
J and K, LAMMPS stores three-body parameters for both IJK and IKJ.
The user must ensure that these values are equal.
Two-body parameters for an atom I interacting with atom J are taken from
the IJJ entry, where the 2nd and 3rd
elements are the same. Thus the two-body parameters
for Si interacting with C come from the SiCC entry. Note that even
though two-body parameters (except possibly gamma and r0 in U3)
do not depend on the order of the two elements,
LAMMPS will get the Si-C value from the SiCC entry
and the C-Si value from the CSiSi entry. The user must ensure
that these values are equal. Two-body parameters appearing
in entries where the 2nd and 3rd elements are different are
stored but never used. It is good practice to enter zero for
these values. Note that the three-body function U3 above
contains the two-body parameters gamma and r0. So U3 for a
central C atom bonded to an Si atom and a second C atom
will take three-body parameters from the CSiC entry, but
<p>The non-annotated parameters are unitless. The Vashishta 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 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>Depending on the particular version of the Vashishta potential, the
values of these parameters may be keyed to the identities of zero,
one, two, or three elements. In order to make the input file format
unambiguous, general, and simple to code, LAMMPS uses a slightly
confusing method for specifying parameters. All parameters are
divided into two classes: two-body and three-body. Two-body and
three-body parameters are handled differently, as described below.
The two-body parameters are H, eta, lambda1, D, lambda4, W, rc, gamma,
and r0. They appear in the above formulae with two subscripts. The
parameters Zi and Zj are also classified as two-body parameters, even
though they only have 1 subscript. The three-body parameters are B,
C, costheta0. They appear in the above formulae with three
subscripts. Two-body and three-body parameters are handled
differently, as described below.</p>
<p>The first element in each entry is the center atom in a three-body
interaction, while the second and third elements are two neighbor
atoms. Three-body parameters for a central atom I and two neighbors J
and K are taken from the IJK entry. Note that even though three-body
parameters do not depend on the order of J and K, LAMMPS stores
three-body parameters for both IJK and IKJ. The user must ensure that
these values are equal. Two-body parameters for an atom I interacting
with atom J are taken from the IJJ entry, where the 2nd and 3rd
elements are the same. Thus the two-body parameters for Si interacting
with C come from the SiCC entry. Note that even though two-body
parameters (except possibly gamma and r0 in U3) do not depend on the
order of the two elements, LAMMPS will get the Si-C value from the
SiCC entry and the C-Si value from the CSiSi entry. The user must
ensure that these values are equal. Two-body parameters appearing in
entries where the 2nd and 3rd elements are different are stored but
never used. It is good practice to enter zero for these values. Note
that the three-body function U3 above contains the two-body parameters
gamma and r0. So U3 for a central C atom bonded to an Si atom and a
second C atom will take three-body parameters from the CSiC entry, but
two-body parameters from the CCC and CSiSi entries.</p>
<hr class="docutils" />
<p>Styles with a <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
@ -302,20 +328,23 @@ if LAMMPS was built with that package (which it is by default). See
the <a class="reference internal" href="Section_start.html#start-3"><span class="std std-ref">Making LAMMPS</span></a> section for more info.</p>
<p>This pair style requires the <a class="reference internal" href="newton.html"><span class="doc">newton</span></a> setting to be &#8220;on&#8221;
for pair interactions.</p>
<p>The Vashishta potential files provided with LAMMPS (see the
potentials directory) are parameterized for metal <a class="reference internal" href="units.html"><span class="doc">units</span></a>.
You can use the Vashishta potential with any LAMMPS units, but you would need
to create your own Vashishta potential file with coefficients listed in the
appropriate units if your simulation doesn&#8217;t use &#8220;metal&#8221; units.</p>
<p>The Vashishta potential files provided with LAMMPS (see the potentials
directory) are parameterized for metal <a class="reference internal" href="units.html"><span class="doc">units</span></a>. You can
use the Vashishta potential with any LAMMPS units, but you would need
to create your own Vashishta potential file with coefficients listed
in the appropriate units if your simulation doesn&#8217;t use &#8220;metal&#8221; units.</p>
</div>
<div class="section" id="related-commands">
<h2>Related commands</h2>
<p><a class="reference internal" href="pair_coeff.html"><span class="doc">pair_coeff</span></a></p>
<p><strong>Default:</strong> none</p>
<hr class="docutils" />
<p id="vashishta1990"><strong>(Vashishta1990)</strong> P. Vashishta, R. K. Kalia, J. P. Rino, Phys. Rev. B 41, 12197 (1990).</p>
<p id="vashishta2007"><strong>(Vashishta2007)</strong> P. Vashishta, R. K. Kalia, A. Nakano, J. P. Rino. J. Appl. Phys. 101, 103515 (2007).</p>
<p id="branicio2009"><strong>(Branicio2009)</strong> Branicio, Rino, Gan and Tsuzuki, J. Phys Condensed Matter 21 (2009) 095002</p>
<p id="vashishta1990"><strong>(Vashishta1990)</strong> P. Vashishta, R. K. Kalia, J. P. Rino, Phys. Rev. B
41, 12197 (1990).</p>
<p id="vashishta2007"><strong>(Vashishta2007)</strong> P. Vashishta, R. K. Kalia, A. Nakano,
J. P. Rino. J. Appl. Phys. 101, 103515 (2007).</p>
<p id="branicio2009"><strong>(Branicio2009)</strong> Branicio, Rino, Gan and Tsuzuki, J. Phys Condensed
Matter 21 (2009) 095002</p>
</div>
</div>