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<title>compute centro/atom command — LAMMPS 15 May 2015 version documentation</title>
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<li>compute centro/atom command</li>
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<div class="section" id="compute-centro-atom-command">
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<span id="index-0"></span><h1>compute centro/atom command<a class="headerlink" href="#compute-centro-atom-command" title="Permalink to this headline">¶</a></h1>
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<div class="section" id="syntax">
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<h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
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<div class="highlight-python"><div class="highlight"><pre>compute ID group-ID centro/atom lattice
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</pre></div>
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</div>
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<ul class="simple">
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<li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
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<li>centro/atom = style name of this compute command</li>
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<li>lattice = <em>fcc</em> or <em>bcc</em> or N = # of neighbors per atom to include</li>
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</ul>
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</div>
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<div class="section" id="examples">
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<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
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<div class="highlight-python"><div class="highlight"><pre>compute 1 all centro/atom fcc
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</pre></div>
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</div>
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<div class="highlight-python"><div class="highlight"><pre>compute 1 all centro/atom 8
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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<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
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<p>Define a computation that calculates the centro-symmetry parameter for
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each atom in the group. In solid-state systems the centro-symmetry
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parameter is a useful measure of the local lattice disorder around an
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atom and can be used to characterize whether the atom is part of a
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perfect lattice, a local defect (e.g. a dislocation or stacking
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fault), or at a surface.</p>
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<p>The value of the centro-symmetry parameter will be 0.0 for atoms not
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in the specified compute group.</p>
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<p>This parameter is computed using the following formula from
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<a class="reference internal" href="#kelchner"><span>(Kelchner)</span></a></p>
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<img alt="_images/centro_symmetry.jpg" class="align-center" src="_images/centro_symmetry.jpg" />
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<p>where the <em>N</em> nearest neighbors or each atom are identified and Ri and
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Ri+N/2 are vectors from the central atom to a particular pair of
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nearest neighbors. There are N*(N-1)/2 possible neighbor pairs that
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can contribute to this formula. The quantity in the sum is computed
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for each, and the N/2 smallest are used. This will typically be for
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pairs of atoms in symmetrically opposite positions with respect to the
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central atom; hence the i+N/2 notation.</p>
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<p><em>N</em> is an input parameter, which should be set to correspond to the
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number of nearest neighbors in the underlying lattice of atoms. If
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the keyword <em>fcc</em> or <em>bcc</em> is used, <em>N</em> is set to 12 and 8
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respectively. More generally, <em>N</em> can be set to a positive, even
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integer.</p>
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<p>For an atom on a lattice site, surrounded by atoms on a perfect
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lattice, the centro-symmetry parameter will be 0. It will be near 0
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for small thermal perturbations of a perfect lattice. If a point
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defect exists, the symmetry is broken, and the parameter will be a
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larger positive value. An atom at a surface will have a large
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positive parameter. If the atom does not have <em>N</em> neighbors (within
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the potential cutoff), then its centro-symmetry parameter is set to
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0.0.</p>
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<p>Only atoms within the cutoff of the pairwise neighbor list are
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considered as possible neighbors. Atoms not in the compute group are
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included in the <em>N</em> neighbors used in this calculation.</p>
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<p>The neighbor list needed to compute this quantity is constructed each
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time the calculation is performed (e.g. each time a snapshot of atoms
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is dumped). Thus it can be inefficient to compute/dump this quantity
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too frequently or to have multiple compute/dump commands, each with a
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<em>centro/atom</em> style.</p>
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<p><strong>Output info:</strong></p>
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<p>This compute calculates a per-atom vector, which can be accessed by
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any command that uses per-atom values from a compute as input. See
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<a class="reference internal" href="Section_howto.html#howto-15"><span>Section_howto 15</span></a> for an overview of
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LAMMPS output options.</p>
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<p>The per-atom vector values are unitless values >= 0.0. Their
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magnitude depends on the lattice style due to the number of
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contibuting neighbor pairs in the summation in the formula above. And
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it depends on the local defects surrounding the central atom, as
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described above.</p>
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<p>Here are typical centro-symmetry values, from a a nanoindentation
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simulation into gold (FCC). These were provided by Jon Zimmerman
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(Sandia):</p>
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<div class="highlight-python"><div class="highlight"><pre>Bulk lattice = 0
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Dislocation core ~ 1.0 (0.5 to 1.25)
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Stacking faults ~ 5.0 (4.0 to 6.0)
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Free surface ~ 23.0
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</pre></div>
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</div>
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<p>These values are <em>not</em> normalized by the square of the lattice
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parameter. If they were, normalized values would be:</p>
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<div class="highlight-python"><div class="highlight"><pre>Bulk lattice = 0
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Dislocation core ~ 0.06 (0.03 to 0.075)
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Stacking faults ~ 0.3 (0.24 to 0.36)
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Free surface ~ 1.38
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</pre></div>
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</div>
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<p>For BCC materials, the values for dislocation cores and free surfaces
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would be somewhat different, due to their being only 8 neighbors instead
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of 12.</p>
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</div>
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<div class="section" id="restrictions">
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<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
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<blockquote>
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<div>none</div></blockquote>
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</div>
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<div class="section" id="related-commands">
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<h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
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<p><a class="reference internal" href="compute_cna_atom.html"><em>compute cna/atom</em></a></p>
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<p><strong>Default:</strong> none</p>
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<hr class="docutils" />
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<p id="kelchner"><strong>(Kelchner)</strong> Kelchner, Plimpton, Hamilton, Phys Rev B, 58, 11085 (1998).</p>
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