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<div class="section" id="pair-style-meam-command">
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<span id="index-0"></span><h1>pair_style meam command</h1>
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<div class="section" id="syntax">
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<h2>Syntax</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">pair_style</span> <span class="n">meam</span>
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</pre></div>
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</div>
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</div>
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<div class="section" id="examples">
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<h2>Examples</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">pair_style</span> <span class="n">meam</span>
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<span class="n">pair_coeff</span> <span class="o">*</span> <span class="o">*</span> <span class="o">../</span><span class="n">potentials</span><span class="o">/</span><span class="n">library</span><span class="o">.</span><span class="n">meam</span> <span class="n">Si</span> <span class="o">../</span><span class="n">potentials</span><span class="o">/</span><span class="n">si</span><span class="o">.</span><span class="n">meam</span> <span class="n">Si</span>
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<span class="n">pair_coeff</span> <span class="o">*</span> <span class="o">*</span> <span class="o">../</span><span class="n">potentials</span><span class="o">/</span><span class="n">library</span><span class="o">.</span><span class="n">meam</span> <span class="n">Ni</span> <span class="n">Al</span> <span class="n">NULL</span> <span class="n">Ni</span> <span class="n">Al</span> <span class="n">Ni</span> <span class="n">Ni</span>
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</pre></div>
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</div>
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</div>
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<div class="section" id="description">
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<h2>Description</h2>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">The behavior of the MEAM potential for alloy systems has changed
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as of November 2010; see description below of the mixture_ref_t
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parameter</p>
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</div>
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<p>Style <em>meam</em> computes pairwise interactions for a variety of materials
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using modified embedded-atom method (MEAM) potentials
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<a class="reference internal" href="#baskes"><span class="std std-ref">(Baskes)</span></a>. Conceptually, it is an extension to the original
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<a class="reference internal" href="pair_eam.html"><span class="doc">EAM potentials</span></a> which adds angular forces. It is
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thus suitable for modeling metals and alloys with fcc, bcc, hcp and
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diamond cubic structures, as well as covalently bonded materials like
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silicon and carbon.</p>
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<p>In the MEAM formulation, the total energy E of a system of atoms is
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given by:</p>
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<img alt="_images/pair_meam.jpg" class="align-center" src="_images/pair_meam.jpg" />
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<p>where F is the embedding energy which is a function of the atomic
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electron density rho, and phi is a pair potential interaction. The
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pair interaction is summed over all neighbors J of atom I within the
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cutoff distance. As with EAM, the multi-body nature of the MEAM
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potential is a result of the embedding energy term. Details of the
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computation of the embedding and pair energies, as implemented in
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LAMMPS, are given in <a class="reference internal" href="#gullet"><span class="std std-ref">(Gullet)</span></a> and references therein.</p>
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<p>The various parameters in the MEAM formulas are listed in two files
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which are specified by the <a class="reference internal" href="pair_coeff.html"><span class="doc">pair_coeff</span></a> command.
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These are ASCII text files in a format consistent with other MD codes
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that implement MEAM potentials, such as the serial DYNAMO code and
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Warp. Several MEAM potential files with parameters for different
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materials are included in the “potentials” directory of the LAMMPS
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distribution with a ”.meam” suffix. All of these are parameterized in
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terms of LAMMPS <a class="reference internal" href="units.html"><span class="doc">metal units</span></a>.</p>
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<p>Note that unlike for other potentials, cutoffs for MEAM potentials are
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not set in the pair_style or pair_coeff command; they are specified in
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the MEAM potential files themselves.</p>
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<p>Only a single pair_coeff command is used with the <em>meam</em> style which
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specifies two MEAM files and the element(s) to extract information
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for. The MEAM elements are mapped to LAMMPS atom types by specifying
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N additional arguments after the 2nd filename in the pair_coeff
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command, where N is the number of LAMMPS atom types:</p>
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<ul class="simple">
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<li>MEAM library file</li>
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<li>Elem1, Elem2, ...</li>
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<li>MEAM parameter file</li>
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<li>N element names = mapping of MEAM elements to atom types</li>
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</ul>
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<p>See the <a class="reference internal" href="pair_coeff.html"><span class="doc">pair_coeff</span></a> doc page for alternate ways
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to specify the path for the potential files.</p>
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<p>As an example, the potentials/library.meam file has generic MEAM
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settings for a variety of elements. The potentials/sic.meam file has
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specific parameter settings for a Si and C alloy system. If your
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LAMMPS simulation has 4 atoms types and you want the 1st 3 to be Si,
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and the 4th to be C, you would use the following pair_coeff command:</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">pair_coeff</span> <span class="o">*</span> <span class="o">*</span> <span class="n">library</span><span class="o">.</span><span class="n">meam</span> <span class="n">Si</span> <span class="n">C</span> <span class="n">sic</span><span class="o">.</span><span class="n">meam</span> <span class="n">Si</span> <span class="n">Si</span> <span class="n">Si</span> <span class="n">C</span>
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</pre></div>
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</div>
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<p>The 1st 2 arguments must be * * so as to span all LAMMPS atom types.
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The two filenames are for the library and parameter file respectively.
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The Si and C arguments (between the file names) are the two elements
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for which info will be extracted from the library file. The first
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three trailing Si arguments map LAMMPS atom types 1,2,3 to the MEAM Si
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element. The final C argument maps LAMMPS atom type 4 to the MEAM C
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element.</p>
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<p>If the 2nd filename is specified as NULL, no parameter file is read,
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which simply means the generic parameters in the library file are
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used. Use of the NULL specification for the parameter file is
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discouraged for systems with more than a single element type
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(e.g. alloys), since the parameter file is expected to set element
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interaction terms that are not captured by the information in the
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library file.</p>
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<p>If a mapping value is specified as NULL, the mapping is not performed.
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This can be used when a <em>meam</em> potential is used as part of the
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<em>hybrid</em> pair style. The NULL values are placeholders for atom types
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that will be used with other potentials.</p>
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<p>The MEAM library file provided with LAMMPS has the name
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potentials/library.meam. It is the “meamf” file used by other MD
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codes. Aside from blank and comment lines (start with #) which can
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appear anywhere, it is formatted as a series of entries, each of which
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has 19 parameters and can span multiple lines:</p>
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<p>elt, lat, z, ielement, atwt, alpha, b0, b1, b2, b3, alat, esub, asub,
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t0, t1, t2, t3, rozero, ibar</p>
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<p>The “elt” and “lat” parameters are text strings, such as elt = Si or
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Cu and lat = dia or fcc. Because the library file is used by Fortran
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MD codes, these strings may be enclosed in single quotes, but this is
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not required. The other numeric parameters match values in the
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formulas above. The value of the “elt” string is what is used in the
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pair_coeff command to identify which settings from the library file
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you wish to read in. There can be multiple entries in the library
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file with the same “elt” value; LAMMPS reads the 1st matching entry it
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finds and ignores the rest.</p>
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<p>Other parameters in the MEAM library file correspond to single-element
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potential parameters:</p>
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<pre class="literal-block">
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lat = lattice structure of reference configuration
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z = number of nearest neighbors in the reference structure
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ielement = atomic number
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atwt = atomic weight
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alat = lattice constant of reference structure
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esub = energy per atom (eV) in the reference structure at equilibrium
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asub = "A" parameter for MEAM (see e.g. <a class="reference internal" href="#baskes"><span class="std std-ref">(Baskes)</span></a>)
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</pre>
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<p>The alpha, b0, b1, b2, b3, t0, t1, t2, t3 parameters correspond to the
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standard MEAM parameters in the literature <a class="reference internal" href="#baskes"><span class="std std-ref">(Baskes)</span></a> (the b
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parameters are the standard beta parameters). The rozero parameter is
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an element-dependent density scaling that weights the reference
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background density (see e.g. equation 4.5 in <a class="reference internal" href="#gullet"><span class="std std-ref">(Gullet)</span></a>) and
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is typically 1.0 for single-element systems. The ibar parameter
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selects the form of the function G(Gamma) used to compute the electron
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density; options are</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span> <span class="mi">0</span> <span class="o">=></span> <span class="n">G</span> <span class="o">=</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">Gamma</span><span class="p">)</span>
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<span class="mi">1</span> <span class="o">=></span> <span class="n">G</span> <span class="o">=</span> <span class="n">exp</span><span class="p">(</span><span class="n">Gamma</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
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<span class="mi">2</span> <span class="o">=></span> <span class="ow">not</span> <span class="n">implemented</span>
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<span class="mi">3</span> <span class="o">=></span> <span class="n">G</span> <span class="o">=</span> <span class="mi">2</span><span class="o">/</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">Gamma</span><span class="p">))</span>
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<span class="mi">4</span> <span class="o">=></span> <span class="n">G</span> <span class="o">=</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">Gamma</span><span class="p">)</span>
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<span class="o">-</span><span class="mi">5</span> <span class="o">=></span> <span class="n">G</span> <span class="o">=</span> <span class="o">+-</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">Gamma</span><span class="p">))</span>
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</pre></div>
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</div>
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<p>If used, the MEAM parameter file contains settings that override or
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complement the library file settings. Examples of such parameter
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files are in the potentials directory with a ”.meam” suffix. Their
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format is the same as is read by other Fortran MD codes. Aside from
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blank and comment lines (start with #) which can appear anywhere, each
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line has one of the following forms. Each line can also have a
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trailing comment (starting with #) which is ignored.</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">keyword</span> <span class="o">=</span> <span class="n">value</span>
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<span class="n">keyword</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="o">=</span> <span class="n">value</span>
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<span class="n">keyword</span><span class="p">(</span><span class="n">I</span><span class="p">,</span><span class="n">J</span><span class="p">)</span> <span class="o">=</span> <span class="n">value</span>
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<span class="n">keyword</span><span class="p">(</span><span class="n">I</span><span class="p">,</span><span class="n">J</span><span class="p">,</span><span class="n">K</span><span class="p">)</span> <span class="o">=</span> <span class="n">value</span>
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</pre></div>
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</div>
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<p>The recognized keywords are as follows:</p>
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<p>Ec, alpha, rho0, delta, lattce, attrac, repuls, nn2, Cmin, Cmax, rc, delr,
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augt1, gsmooth_factor, re</p>
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<p>where</p>
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<pre class="literal-block">
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rc = cutoff radius for cutoff function; default = 4.0
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delr = length of smoothing distance for cutoff function; default = 0.1
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rho0(I) = relative density for element I (overwrites value
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read from meamf file)
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Ec(I,J) = cohesive energy of reference structure for I-J mixture
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delta(I,J) = heat of formation for I-J alloy; if Ec_IJ is input as
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zero, then LAMMPS sets Ec_IJ = (Ec_II + Ec_JJ)/2 - delta_IJ
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alpha(I,J) = alpha parameter for pair potential between I and J (can
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be computed from bulk modulus of reference structure
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re(I,J) = equilibrium distance between I and J in the reference
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structure
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Cmax(I,J,K) = Cmax screening parameter when I-J pair is screened
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by K (I<=J); default = 2.8
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Cmin(I,J,K) = Cmin screening parameter when I-J pair is screened
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by K (I<=J); default = 2.0
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lattce(I,J) = lattice structure of I-J reference structure:
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dia = diamond (interlaced fcc for alloy)
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fcc = face centered cubic
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bcc = body centered cubic
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dim = dimer
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b1 = rock salt (NaCl structure)
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hcp = hexagonal close-packed
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c11 = MoSi2 structure
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l12 = Cu3Au structure (lower case L, followed by 12)
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b2 = CsCl structure (interpenetrating simple cubic)
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nn2(I,J) = turn on second-nearest neighbor MEAM formulation for
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I-J pair (see for example <a class="reference internal" href="#lee"><span class="std std-ref">(Lee)</span></a>).
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0 = second-nearest neighbor formulation off
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1 = second-nearest neighbor formulation on
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default = 0
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attrac(I,J) = additional cubic attraction term in Rose energy I-J pair potential
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default = 0
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repuls(I,J) = additional cubic repulsive term in Rose energy I-J pair potential
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default = 0
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zbl(I,J) = blend the MEAM I-J pair potential with the ZBL potential for small
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atom separations <a class="reference internal" href="pair_tersoff_zbl.html#zbl"><span class="std std-ref">(ZBL)</span></a>
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default = 1
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gsmooth_factor = factor determining the length of the G-function smoothing
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region; only significant for ibar=0 or ibar=4.
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99.0 = short smoothing region, sharp step
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0.5 = long smoothing region, smooth step
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default = 99.0
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augt1 = integer flag for whether to augment t1 parameter by
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3/5*t3 to account for old vs. new meam formulations;
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0 = don't augment t1
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1 = augment t1
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default = 1
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ialloy = integer flag to use alternative averaging rule for t parameters,
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for comparison with the DYNAMO MEAM code
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0 = standard averaging (matches ialloy=0 in DYNAMO)
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1 = alternative averaging (matches ialloy=1 in DYNAMO)
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2 = no averaging of t (use single-element values)
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default = 0
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mixture_ref_t = integer flag to use mixture average of t to compute the background
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reference density for alloys, instead of the single-element values
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(see description and warning elsewhere in this doc page)
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0 = do not use mixture averaging for t in the reference density
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1 = use mixture averaging for t in the reference density
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default = 0
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erose_form = integer value to select the form of the Rose energy function
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(see description below).
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default = 0
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emb_lin_neg = integer value to select embedding function for negative densities
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0 = F(rho)=0
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1 = F(rho) = -asub*esub*rho (linear in rho, matches DYNAMO)
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default = 0
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bkgd_dyn = integer value to select background density formula
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0 = rho_bkgd = rho_ref_meam(a) (as in the reference structure)
|
|
1 = rho_bkgd = rho0_meam(a)*Z_meam(a) (matches DYNAMO)
|
|
default = 0
|
|
</pre>
|
|
<p>Rc, delr, re are in distance units (Angstroms in the case of metal
|
|
units). Ec and delta are in energy units (eV in the case of metal
|
|
units).</p>
|
|
<p>Each keyword represents a quantity which is either a scalar, vector,
|
|
2d array, or 3d array and must be specified with the correct
|
|
corresponding array syntax. The indices I,J,K each run from 1 to N
|
|
where N is the number of MEAM elements being used.</p>
|
|
<p>Thus these lines</p>
|
|
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">rho0</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">=</span> <span class="mf">2.25</span>
|
|
<span class="n">alpha</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="o">=</span> <span class="mf">4.37</span>
|
|
</pre></div>
|
|
</div>
|
|
<p>set rho0 for the 2nd element to the value 2.25 and set alpha for the
|
|
alloy interaction between elements 1 and 2 to 4.37.</p>
|
|
<p>The augt1 parameter is related to modifications in the MEAM
|
|
formulation of the partial electron density function. In recent
|
|
literature, an extra term is included in the expression for the
|
|
third-order density in order to make the densities orthogonal (see for
|
|
example <a class="reference internal" href="pair_polymorphic.html#wang"><span class="std std-ref">(Wang)</span></a>, equation 3d); this term is included in the
|
|
MEAM implementation in lammps. However, in earlier published work
|
|
this term was not included when deriving parameters, including most of
|
|
those provided in the library.meam file included with lammps, and to
|
|
account for this difference the parameter t1 must be augmented by
|
|
3/5*t3. If augt1=1, the default, this augmentation is done
|
|
automatically. When parameter values are fit using the modified
|
|
density function, as in more recent literature, augt1 should be set to
|
|
0.</p>
|
|
<p>The mixture_ref_t parameter is available to match results with those
|
|
of previous versions of lammps (before January 2011). Newer versions
|
|
of lammps, by default, use the single-element values of the t
|
|
parameters to compute the background reference density. This is the
|
|
proper way to compute these parameters. Earlier versions of lammps
|
|
used an alloy mixture averaged value of t to compute the background
|
|
reference density. Setting mixture_ref_t=1 gives the old behavior.
|
|
WARNING: using mixture_ref_t=1 will give results that are demonstrably
|
|
incorrect for second-neighbor MEAM, and non-standard for
|
|
first-neighbor MEAM; this option is included only for matching with
|
|
previous versions of lammps and should be avoided if possible.</p>
|
|
<p>The parameters attrac and repuls, along with the integer selection
|
|
parameter erose_form, can be used to modify the Rose energy function
|
|
used to compute the pair potential. This function gives the energy of
|
|
the reference state as a function of interatomic spacing. The form of
|
|
this function is:</p>
|
|
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">astar</span> <span class="o">=</span> <span class="n">alpha</span> <span class="o">*</span> <span class="p">(</span><span class="n">r</span><span class="o">/</span><span class="n">re</span> <span class="o">-</span> <span class="mf">1.</span><span class="n">d0</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="n">erose_form</span> <span class="o">=</span> <span class="mi">0</span><span class="p">:</span> <span class="n">erose</span> <span class="o">=</span> <span class="o">-</span><span class="n">Ec</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">astar</span><span class="o">+</span><span class="n">a3</span><span class="o">*</span><span class="p">(</span><span class="n">astar</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">r</span><span class="o">/</span><span class="n">re</span><span class="p">))</span><span class="o">*</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">astar</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="n">erose_form</span> <span class="o">=</span> <span class="mi">1</span><span class="p">:</span> <span class="n">erose</span> <span class="o">=</span> <span class="o">-</span><span class="n">Ec</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">astar</span><span class="o">+</span><span class="p">(</span><span class="o">-</span><span class="n">attrac</span><span class="o">+</span><span class="n">repuls</span><span class="o">/</span><span class="n">r</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="n">astar</span><span class="o">**</span><span class="mi">3</span><span class="p">))</span><span class="o">*</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">astar</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="n">erose_form</span> <span class="o">=</span> <span class="mi">2</span><span class="p">:</span> <span class="n">erose</span> <span class="o">=</span> <span class="o">-</span><span class="n">Ec</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span><span class="n">astar</span> <span class="o">+</span> <span class="n">a3</span><span class="o">*</span><span class="p">(</span><span class="n">astar</span><span class="o">**</span><span class="mi">3</span><span class="p">))</span><span class="o">*</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">astar</span><span class="p">)</span>
|
|
<span class="n">a3</span> <span class="o">=</span> <span class="n">repuls</span><span class="p">,</span> <span class="n">astar</span> <span class="o"><</span> <span class="mi">0</span>
|
|
<span class="n">a3</span> <span class="o">=</span> <span class="n">attrac</span><span class="p">,</span> <span class="n">astar</span> <span class="o">>=</span> <span class="mi">0</span>
|
|
</pre></div>
|
|
</div>
|
|
<p>Most published MEAM parameter sets use the default values attrac=repulse=0.
|
|
Setting repuls=attrac=delta corresponds to the form used in several
|
|
recent published MEAM parameter sets, such as <a class="reference internal" href="#valone"><span class="std std-ref">(Valone)</span></a></p>
|
|
<div class="admonition note">
|
|
<p class="first admonition-title">Note</p>
|
|
<p class="last">The default form of the erose expression in LAMMPS was corrected
|
|
in March 2009. The current version is correct, but may show different
|
|
behavior compared with earlier versions of lammps with the attrac
|
|
and/or repuls parameters are non-zero. To obtain the previous default
|
|
form, use erose_form = 1 (this form does not seem to appear in the
|
|
literature). An alternative form (see e.g. <a class="reference internal" href="#lee2"><span class="std std-ref">(Lee2)</span></a>) is
|
|
available using erose_form = 2.</p>
|
|
</div>
|
|
<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 with
|
|
user-specifiable parameters as described above. You never need to
|
|
specify a pair_coeff command with I != J arguments for this style.</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>This pair style does not write its information to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></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 <em>pair</em> keyword of the
|
|
<a class="reference internal" href="run_style.html"><span class="doc">run_style respa</span></a> command. It does 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>This style is part of the MEAM package. It is only enabled if LAMMPS
|
|
was built with that package, which also requires the MEAM library be
|
|
built and linked with LAMMPS. 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>, <a class="reference internal" href="pair_eam.html"><span class="doc">pair_style eam</span></a>,
|
|
<a class="reference internal" href="pair_meam_spline.html"><span class="doc">pair_style meam/spline</span></a></p>
|
|
<p><strong>Default:</strong> none</p>
|
|
<hr class="docutils" />
|
|
<p id="baskes"><strong>(Baskes)</strong> Baskes, Phys Rev B, 46, 2727-2742 (1992).</p>
|
|
<p id="gullet"><strong>(Gullet)</strong> Gullet, Wagner, Slepoy, SANDIA Report 2003-8782 (2003).
|
|
This report may be accessed on-line via <a class="reference external" href="http://infoserve.sandia.gov/sand_doc/2003/038782.pdf">this link</a>.</p>
|
|
<p id="lee"><strong>(Lee)</strong> Lee, Baskes, Phys. Rev. B, 62, 8564-8567 (2000).</p>
|
|
<p id="lee2"><strong>(Lee2)</strong> Lee, Baskes, Kim, Cho. Phys. Rev. B, 64, 184102 (2001).</p>
|
|
<p id="valone"><strong>(Valone)</strong> Valone, Baskes, Martin, Phys. Rev. B, 73, 214209 (2006).</p>
|
|
<p id="wang"><strong>(Wang)</strong> Wang, Van Hove, Ross, Baskes, J. Chem. Phys., 121, 5410 (2004).</p>
|
|
<p id="zbl"><strong>(ZBL)</strong> J.F. Ziegler, J.P. Biersack, U. Littmark, “Stopping and Ranges
|
|
of Ions in Matter”, Vol 1, 1985, Pergamon Press.</p>
|
|
</div>
|
|
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|
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