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<div class="section" id="pair-style-eam-command">
<span id="index-0"></span><h1>pair_style eam command</h1>
</div>
<div class="section" id="pair-style-eam-gpu-command">
<h1>pair_style eam/gpu command</h1>
</div>
<div class="section" id="pair-style-eam-kk-command">
<h1>pair_style eam/kk command</h1>
</div>
<div class="section" id="pair-style-eam-omp-command">
<h1>pair_style eam/omp command</h1>
</div>
<div class="section" id="pair-style-eam-opt-command">
<h1>pair_style eam/opt command</h1>
</div>
<div class="section" id="pair-style-eam-alloy-command">
<h1>pair_style eam/alloy command</h1>
</div>
<div class="section" id="pair-style-eam-alloy-gpu-command">
<h1>pair_style eam/alloy/gpu command</h1>
</div>
<div class="section" id="pair-style-eam-alloy-kk-command">
<h1>pair_style eam/alloy/kk command</h1>
</div>
<div class="section" id="pair-style-eam-alloy-omp-command">
<h1>pair_style eam/alloy/omp command</h1>
</div>
<div class="section" id="pair-style-eam-alloy-opt-command">
<h1>pair_style eam/alloy/opt command</h1>
</div>
<div class="section" id="pair-style-eam-cd-command">
<h1>pair_style eam/cd command</h1>
</div>
<div class="section" id="pair-style-eam-cd-omp-command">
<h1>pair_style eam/cd/omp command</h1>
</div>
<div class="section" id="pair-style-eam-fs-command">
<h1>pair_style eam/fs command</h1>
</div>
<div class="section" id="pair-style-eam-fs-gpu-command">
<h1>pair_style eam/fs/gpu command</h1>
</div>
<div class="section" id="pair-style-eam-fs-kk-command">
<h1>pair_style eam/fs/kk command</h1>
</div>
<div class="section" id="pair-style-eam-fs-omp-command">
<h1>pair_style eam/fs/omp command</h1>
</div>
<div class="section" id="pair-style-eam-fs-opt-command">
<h1>pair_style eam/fs/opt command</h1>
<div class="section" id="syntax">
<h2>Syntax</h2>
<pre class="literal-block">
pair_style style
</pre>
<ul class="simple">
<li>style = <em>eam</em> or <em>eam/alloy</em> or <em>eam/cd</em> or <em>eam/fs</em></li>
</ul>
</div>
<div class="section" id="examples">
<h2>Examples</h2>
<pre class="literal-block">
pair_style eam
pair_coeff * * cuu3
pair_coeff 1*3 1*3 niu3.eam
</pre>
<pre class="literal-block">
pair_style eam/alloy
pair_coeff * * ../potentials/NiAlH_jea.eam.alloy Ni Al Ni Ni
</pre>
<pre class="literal-block">
pair_style eam/cd
pair_coeff * * ../potentials/FeCr.cdeam Fe Cr
</pre>
<pre class="literal-block">
pair_style eam/fs
pair_coeff * * NiAlH_jea.eam.fs Ni Al Ni Ni
</pre>
</div>
<div class="section" id="description">
<h2>Description</h2>
<p>Style <em>eam</em> computes pairwise interactions for metals and metal alloys
using embedded-atom method (EAM) potentials <a class="reference internal" href="pair_polymorphic.html#daw"><span class="std std-ref">(Daw)</span></a>. The total
energy Ei of an atom I is given by</p>
<img alt="_images/pair_eam.jpg" class="align-center" src="_images/pair_eam.jpg" />
<p>where F is the embedding energy which is a function of the atomic
electron density rho, phi is a pair potential interaction, and alpha
and beta are the element types of atoms I and J. The multi-body
nature of the EAM potential is a result of the embedding energy term.
Both summations in the formula are over all neighbors J of atom I
within the cutoff distance.</p>
<p>The cutoff distance and the tabulated values of the functionals F,
rho, and phi are listed in one or more files which are specified by
the <a class="reference internal" href="pair_coeff.html"><span class="doc">pair_coeff</span></a> command. These are ASCII text files
in a DYNAMO-style format which is described below. DYNAMO was the
original serial EAM MD code, written by the EAM originators. Several
DYNAMO potential files for different metals are included in the
&#8220;potentials&#8221; directory of the LAMMPS distribution. All of these files
are parameterized in terms of LAMMPS <a class="reference internal" href="units.html"><span class="doc">metal units</span></a>.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">The <em>eam</em> style reads single-element EAM potentials in the
DYNAMO <em>funcfl</em> format. Either single element or alloy systems can be
modeled using multiple <em>funcfl</em> files and style <em>eam</em>. For the alloy
case LAMMPS mixes the single-element potentials to produce alloy
potentials, the same way that DYNAMO does. Alternatively, a single
DYNAMO <em>setfl</em> file or Finnis/Sinclair EAM file can be used by LAMMPS
to model alloy systems by invoking the <em>eam/alloy</em> or <em>eam/cd</em> or
<em>eam/fs</em> styles as described below. These files require no mixing
since they specify alloy interactions explicitly.</p>
</div>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">Note that unlike for other potentials, cutoffs for EAM
potentials are not set in the pair_style or pair_coeff command; they
are specified in the EAM potential files themselves. Likewise, the
EAM potential files list atomic masses; thus you do not need to use
the <a class="reference internal" href="mass.html"><span class="doc">mass</span></a> command to specify them.</p>
</div>
<p>There are several WWW sites that distribute and document EAM
potentials stored in DYNAMO or other formats:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">http</span><span class="p">:</span><span class="o">//</span><span class="n">www</span><span class="o">.</span><span class="n">ctcms</span><span class="o">.</span><span class="n">nist</span><span class="o">.</span><span class="n">gov</span><span class="o">/</span><span class="n">potentials</span>
<span class="n">http</span><span class="p">:</span><span class="o">//</span><span class="n">cst</span><span class="o">-</span><span class="n">www</span><span class="o">.</span><span class="n">nrl</span><span class="o">.</span><span class="n">navy</span><span class="o">.</span><span class="n">mil</span><span class="o">/</span><span class="n">ccm6</span><span class="o">/</span><span class="n">ap</span>
<span class="n">http</span><span class="p">:</span><span class="o">//</span><span class="n">enpub</span><span class="o">.</span><span class="n">fulton</span><span class="o">.</span><span class="n">asu</span><span class="o">.</span><span class="n">edu</span><span class="o">/</span><span class="n">cms</span><span class="o">/</span><span class="n">potentials</span><span class="o">/</span><span class="n">main</span><span class="o">/</span><span class="n">main</span><span class="o">.</span><span class="n">htm</span>
</pre></div>
</div>
<p>These potentials should be usable with LAMMPS, though the alternate
formats would need to be converted to the DYNAMO format used by LAMMPS
and described on this page. The NIST site is maintained by Chandler
Becker (cbecker at nist.gov) who is good resource for info on
interatomic potentials and file formats.</p>
<hr class="docutils" />
<p>For style <em>eam</em>, potential values are read from a file that is in the
DYNAMO single-element <em>funcfl</em> format. If the DYNAMO file was created
by a Fortran program, it cannot have &#8220;D&#8221; values in it for exponents.
C only recognizes &#8220;e&#8221; or &#8220;E&#8221; for scientific notation.</p>
<p>Note that unlike for other potentials, cutoffs for EAM potentials are
not set in the pair_style or pair_coeff command; they are specified in
the EAM potential files themselves.</p>
<p>For style <em>eam</em> a potential file must be assigned to each I,I pair of
atom types by using one or more pair_coeff commands, each with a
single argument:</p>
<ul class="simple">
<li>filename</li>
</ul>
<p>Thus the following command</p>
<pre class="literal-block">
pair_coeff *2 1*2 cuu3.eam
</pre>
<p>will read the cuu3 potential file and use the tabulated Cu values for
F, phi, rho that it contains for type pairs 1,1 and 2,2 (type pairs
1,2 and 2,1 are ignored). See the <a class="reference internal" href="pair_coeff.html"><span class="doc">pair_coeff</span></a> doc
page for alternate ways to specify the path for the potential file.
In effect, this makes atom types 1 and 2 in LAMMPS be Cu atoms.
Different single-element files can be assigned to different atom types
to model an alloy system. The mixing to create alloy potentials for
type pairs with I != J is done automatically the same way that the
serial DYNAMO code originally did it; you do not need to specify
coefficients for these type pairs.</p>
<p><em>Funcfl</em> files in the <em>potentials</em> directory of the LAMMPS
distribution have an &#8221;.eam&#8221; suffix. A DYNAMO single-element <em>funcfl</em>
file is formatted as follows:</p>
<ul class="simple">
<li>line 1: comment (ignored)</li>
<li>line 2: atomic number, mass, lattice constant, lattice type (e.g. FCC)</li>
<li>line 3: Nrho, drho, Nr, dr, cutoff</li>
</ul>
<p>On line 2, all values but the mass are ignored by LAMMPS. The mass is
in mass <a class="reference internal" href="units.html"><span class="doc">units</span></a>, e.g. mass number or grams/mole for metal
units. The cubic lattice constant is in Angstroms. On line 3, Nrho
and Nr are the number of tabulated values in the subsequent arrays,
drho and dr are the spacing in density and distance space for the
values in those arrays, and the specified cutoff becomes the pairwise
cutoff used by LAMMPS for the potential. The units of dr are
Angstroms; I&#8217;m not sure of the units for drho - some measure of
electron density.</p>
<p>Following the three header lines are three arrays of tabulated values:</p>
<ul class="simple">
<li>embedding function F(rho) (Nrho values)</li>
<li>effective charge function Z(r) (Nr values)</li>
<li>density function rho(r) (Nr values)</li>
</ul>
<p>The values for each array can be listed as multiple values per line,
so long as each array starts on a new line. For example, the
individual Z(r) values are for r = 0,dr,2*dr, ... (Nr-1)*dr.</p>
<p>The units for the embedding function F are eV. The units for the
density function rho are the same as for drho (see above, electron
density). The units for the effective charge Z are &#8220;atomic charge&#8221; or
sqrt(Hartree * Bohr-radii). For two interacting atoms i,j this is used
by LAMMPS to compute the pair potential term in the EAM energy
expression as r*phi, in units of eV-Angstroms, via the formula</p>
<pre class="literal-block">
r*phi = 27.2 * 0.529 * Zi * Zj
</pre>
<p>where 1 Hartree = 27.2 eV and 1 Bohr = 0.529 Angstroms.</p>
<hr class="docutils" />
<p>Style <em>eam/alloy</em> computes pairwise interactions using the same
formula as style <em>eam</em>. However the associated
<a class="reference internal" href="pair_coeff.html"><span class="doc">pair_coeff</span></a> command reads a DYNAMO <em>setfl</em> file
instead of a <em>funcfl</em> file. <em>Setfl</em> files can be used to model a
single-element or alloy system. In the alloy case, as explained
above, <em>setfl</em> files contain explicit tabulated values for alloy
interactions. Thus they allow more generality than <em>funcfl</em> files for
modeling alloys.</p>
<p>For style <em>eam/alloy</em>, potential values are read from a file that is
in the DYNAMO multi-element <em>setfl</em> format, except that element names
(Ni, Cu, etc) are added to one of the lines in the file. If the
DYNAMO file was created by a Fortran program, it cannot have &#8220;D&#8221;
values in it for exponents. C only recognizes &#8220;e&#8221; or &#8220;E&#8221; for
scientific notation.</p>
<p>Only a single pair_coeff command is used with the <em>eam/alloy</em> style
which specifies a DYNAMO <em>setfl</em> file, which contains information for
M 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>
<li>N element names = mapping of <em>setfl</em> elements to atom types</li>
</ul>
<p>As an example, the potentials/NiAlH_jea.eam.alloy file is a <em>setfl</em>
file which has tabulated EAM values for 3 elements and their alloy
interactions: Ni, Al, and H. See the <a class="reference internal" href="pair_coeff.html"><span class="doc">pair_coeff</span></a> doc
page for alternate ways to specify the path for the potential file.
If your LAMMPS simulation has 4 atoms types and you want the 1st 3 to
be Ni, and the 4th to be Al, you would use the following pair_coeff
command:</p>
<pre class="literal-block">
pair_coeff * * NiAlH_jea.eam.alloy Ni Ni Ni Al
</pre>
<p>The 1st 2 arguments must be * * so as to span all LAMMPS atom types.
The first three Ni arguments map LAMMPS atom types 1,2,3 to the Ni
element in the <em>setfl</em> file. The final Al argument maps LAMMPS atom
type 4 to the Al element in the <em>setfl</em> file. Note that there is no
requirement that your simulation use all the elements specified by the
<em>setfl</em> file.</p>
<p>If a mapping value is specified as NULL, the mapping is not performed.
This can be used when an <em>eam/alloy</em> potential is used as part of the
<em>hybrid</em> pair style. The NULL values are placeholders for atom types
that will be used with other potentials.</p>
<p><em>Setfl</em> files in the <em>potentials</em> directory of the LAMMPS distribution
have an &#8221;.eam.alloy&#8221; suffix. A DYNAMO multi-element <em>setfl</em> file is
formatted as follows:</p>
<ul class="simple">
<li>lines 1,2,3 = comments (ignored)</li>
<li>line 4: Nelements Element1 Element2 ... ElementN</li>
<li>line 5: Nrho, drho, Nr, dr, cutoff</li>
</ul>
<p>In a DYNAMO <em>setfl</em> file, line 4 only lists Nelements = the # of
elements in the <em>setfl</em> file. For LAMMPS, the element name (Ni, Cu,
etc) of each element must be added to the line, in the order the
elements appear in the file.</p>
<p>The meaning and units of the values in line 5 is the same as for the
<em>funcfl</em> file described above. Note that the cutoff (in Angstroms) is
a global value, valid for all pairwise interactions for all element
pairings.</p>
<p>Following the 5 header lines are Nelements sections, one for each
element, each with the following format:</p>
<ul class="simple">
<li>line 1 = atomic number, mass, lattice constant, lattice type (e.g. FCC)</li>
<li>embedding function F(rho) (Nrho values)</li>
<li>density function rho(r) (Nr values)</li>
</ul>
<p>As with the <em>funcfl</em> files, only the mass (in mass <a class="reference internal" href="units.html"><span class="doc">units</span></a>,
e.g. mass number or grams/mole for metal units) is used by LAMMPS from
the 1st line. The cubic lattice constant is in Angstroms. The F and
rho arrays are unique to a single element and have the same format and
units as in a <em>funcfl</em> file.</p>
<p>Following the Nelements sections, Nr values for each pair potential
phi(r) array are listed for all i,j element pairs in the same format
as other arrays. Since these interactions are symmetric (i,j = j,i)
only phi arrays with i &gt;= j are listed, in the following order: i,j =
(1,1), (2,1), (2,2), (3,1), (3,2), (3,3), (4,1), ..., (Nelements,
Nelements). Unlike the effective charge array Z(r) in <em>funcfl</em> files,
the tabulated values for each phi function are listed in <em>setfl</em> files
directly as r*phi (in units of eV-Angstroms), since they are for atom
pairs.</p>
<hr class="docutils" />
<p>Style <em>eam/cd</em> is similar to the <em>eam/alloy</em> style, except that it
computes alloy pairwise interactions using the concentration-dependent
embedded-atom method (CD-EAM). This model can reproduce the enthalpy
of mixing of alloys over the full composition range, as described in
<a class="reference internal" href="#stukowski"><span class="std std-ref">(Stukowski)</span></a>.</p>
<p>The pair_coeff command is specified the same as for the <em>eam/alloy</em>
style. However the DYNAMO <em>setfl</em> file must has two
lines added to it, at the end of the file:</p>
<ul class="simple">
<li>line 1: Comment line (ignored)</li>
<li>line 2: N Coefficient0 Coefficient1 ... CoeffincientN</li>
</ul>
<p>The last line begins with the degree <em>N</em> of the polynomial function
<em>h(x)</em> that modifies the cross interaction between A and B elements.
Then <em>N+1</em> coefficients for the terms of the polynomial are then
listed.</p>
<p>Modified EAM <em>setfl</em> files used with the <em>eam/cd</em> style must contain
exactly two elements, i.e. in the current implementation the <em>eam/cd</em>
style only supports binary alloys. The first and second elements in
the input EAM file are always taken as the <em>A</em> and <em>B</em> species.</p>
<p><em>CD-EAM</em> files in the <em>potentials</em> directory of the LAMMPS
distribution have a &#8221;.cdeam&#8221; suffix.</p>
<hr class="docutils" />
<p>Style <em>eam/fs</em> computes pairwise interactions for metals and metal
alloys using a generalized form of EAM potentials due to Finnis and
Sinclair <a class="reference internal" href="#finnis"><span class="std std-ref">(Finnis)</span></a>. The total energy Ei of an atom I is
given by</p>
<img alt="_images/pair_eam_fs.jpg" class="align-center" src="_images/pair_eam_fs.jpg" />
<p>This has the same form as the EAM formula above, except that rho is
now a functional specific to the atomic types of both atoms I and J,
so that different elements can contribute differently to the total
electron density at an atomic site depending on the identity of the
element at that atomic site.</p>
<p>The associated <a class="reference internal" href="pair_coeff.html"><span class="doc">pair_coeff</span></a> command for style <em>eam/fs</em>
reads a DYNAMO <em>setfl</em> file that has been extended to include
additional rho_alpha_beta arrays of tabulated values. A discussion of
how FS EAM differs from conventional EAM alloy potentials is given in
<a class="reference internal" href="#ackland1"><span class="std std-ref">(Ackland1)</span></a>. An example of such a potential is the same
author&#8217;s Fe-P FS potential <a class="reference internal" href="#ackland2"><span class="std std-ref">(Ackland2)</span></a>. Note that while FS
potentials always specify the embedding energy with a square root
dependence on the total density, the implementation in LAMMPS does not
require that; the user can tabulate any functional form desired in the
FS potential files.</p>
<p>For style <em>eam/fs</em>, the form of the pair_coeff command is exactly the
same as for style <em>eam/alloy</em>, e.g.</p>
<pre class="literal-block">
pair_coeff * * NiAlH_jea.eam.fs Ni Ni Ni Al
</pre>
<p>where there are N additional arguments after the filename, where N is
the number of LAMMPS atom types. See the <a class="reference internal" href="pair_coeff.html"><span class="doc">pair_coeff</span></a>
doc page for alternate ways to specify the path for the potential
file. The N values determine the mapping of LAMMPS atom types to EAM
elements in the file, as described above for style <em>eam/alloy</em>. As
with <em>eam/alloy</em>, if a mapping value is NULL, the mapping is not
performed. This can be used when an <em>eam/fs</em> potential is used as
part of the <em>hybrid</em> pair style. The NULL values are used as
placeholders for atom types that will be used with other potentials.</p>
<p>FS EAM files include more information than the DYNAMO <em>setfl</em> format
files read by <em>eam/alloy</em>, in that i,j density functionals for all
pairs of elements are included as needed by the Finnis/Sinclair
formulation of the EAM.</p>
<p>FS EAM files in the <em>potentials</em> directory of the LAMMPS distribution
have an &#8221;.eam.fs&#8221; suffix. They are formatted as follows:</p>
<ul class="simple">
<li>lines 1,2,3 = comments (ignored)</li>
<li>line 4: Nelements Element1 Element2 ... ElementN</li>
<li>line 5: Nrho, drho, Nr, dr, cutoff</li>
</ul>
<p>The 5-line header section is identical to an EAM <em>setfl</em> file.</p>
<p>Following the header are Nelements sections, one for each element I,
each with the following format:</p>
<ul class="simple">
<li>line 1 = atomic number, mass, lattice constant, lattice type (e.g. FCC)</li>
<li>embedding function F(rho) (Nrho values)</li>
<li>density function rho(r) for element I at element 1 (Nr values)</li>
<li>density function rho(r) for element I at element 2</li>
<li>...</li>
<li>density function rho(r) for element I at element Nelement</li>
</ul>
<p>The units of these quantities in line 1 are the same as for <em>setfl</em>
files. Note that the rho(r) arrays in Finnis/Sinclair can be
asymmetric (i,j != j,i) so there are Nelements^2 of them listed in the
file.</p>
<p>Following the Nelements sections, Nr values for each pair potential
phi(r) array are listed in the same manner (r*phi, units of
eV-Angstroms) as in EAM <em>setfl</em> files. Note that in Finnis/Sinclair,
the phi(r) arrays are still symmetric, so only phi arrays for i &gt;= j
are listed.</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
functionally the same as the corresponding style without the suffix.
They have been optimized to run faster, depending on your available
hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><span class="doc">Section_accelerate</span></a>
of the manual. The accelerated styles take the same arguments and
should produce the same results, except for round-off and precision
issues.</p>
<p>These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,
USER-OMP and OPT packages, respectively. They are only enabled if
LAMMPS was built with those packages. 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>You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span class="std std-ref">-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
use the <a class="reference internal" href="suffix.html"><span class="doc">suffix</span></a> command in your input script.</p>
<p>See <a class="reference internal" href="Section_accelerate.html"><span class="doc">Section_accerlate</span></a> of the manual for more
instructions on how to use the accelerated styles effectively.</p>
<hr class="docutils" />
<p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</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 with the individual styles. You never need to specify
a pair_coeff command with I != J arguments for the eam styles.</p>
<p>This pair style does not support the <a class="reference internal" href="pair_modify.html"><span class="doc">pair_modify</span></a>
shift, table, and tail options.</p>
<p>The eam pair styles do not write their information to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>, since it is stored in tabulated 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>The eam pair styles can only be used via the <em>pair</em> keyword of the
<a class="reference internal" href="run_style.html"><span class="doc">run_style respa</span></a> command. They do not support the
<em>inner</em>, <em>middle</em>, <em>outer</em> keywords.</p>
</div>
<hr class="docutils" />
<div class="section" id="restrictions">
<h2>Restrictions</h2>
<p>All of these styles except the <em>eam/cd</em> style are part of the MANYBODY
package. They are only enabled 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>The <em>eam/cd</em> style is part of the USER-MISC package and also requires
the MANYBODY package. It is only enabled if LAMMPS was built with
those packages. 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>
</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="ackland1"><strong>(Ackland1)</strong> Ackland, Condensed Matter (2005).</p>
<p id="ackland2"><strong>(Ackland2)</strong> Ackland, Mendelev, Srolovitz, Han and Barashev, Journal
of Physics: Condensed Matter, 16, S2629 (2004).</p>
<p id="daw"><strong>(Daw)</strong> Daw, Baskes, Phys Rev Lett, 50, 1285 (1983).
Daw, Baskes, Phys Rev B, 29, 6443 (1984).</p>
<p id="finnis"><strong>(Finnis)</strong> Finnis, Sinclair, Philosophical Magazine A, 50, 45 (1984).</p>
<p id="stukowski"><strong>(Stukowski)</strong> Stukowski, Sadigh, Erhart, Caro; Modeling Simulation
Materials Science &amp; Engineering, 7, 075005 (2009).</p>
</div>
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