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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</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">compute</span> <span class="n">ID</span> <span class="n">group</span><span class="o">-</span><span class="n">ID</span> <span class="n">centro</span><span class="o">/</span><span class="n">atom</span> <span class="n">lattice</span> <span class="n">keyword</span> <span class="n">value</span> <span class="o">...</span>
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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"><span class="doc">compute</span></a> command
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centro/atom = style name of this compute command
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lattice = <em>fcc</em> or <em>bcc</em> or N = # of neighbors per atom to include</li>
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<li>zero or more keyword/value pairs may be appended</li>
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<li>keyword = <em>axes</em></li>
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</ul>
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<pre class="literal-block">
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<em>axes</em> value = <em>no</em> or <em>yes</em>
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<em>no</em> = do not calulate 3 symmetry axes
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<em>yes</em> = calulate 3 symmetry axes
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</pre>
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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">compute</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">centro</span><span class="o">/</span><span class="n">atom</span> <span class="n">fcc</span>
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</pre></div>
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</div>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">compute</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">centro</span><span class="o">/</span><span class="n">atom</span> <span class="mi">8</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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<p>Define a computation that calculates the centro-symmetry parameter for
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each atom in the group, for either FCC or BCC lattices, depending on
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the choice of the <em>lattice</em> argument. In solid-state systems the
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centro-symmetry parameter is a useful measure of the local lattice
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disorder around an atom and can be used to characterize whether the
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atom is part of a perfect lattice, a local defect (e.g. a dislocation
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or stacking 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 class="std std-ref">(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 of 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>If the keyword <em>axes</em> has the setting <em>yes</em>, then this compute also
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estimates three symmetry axes for each atom’s local neighborhood. The
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first two of these are the vectors joining the two pairs of neighbor
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atoms with smallest contributions to the centrosymmetry parameter,
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i.e. the two most symmetric pairs of atoms. The third vector is
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normal to the first two by the right-hand rule. All three vectors are
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normalized to unit length. For FCC crystals, the first two vectors
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will lie along a <110> direction, while the third vector will lie
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along either a <100> or <111> direction. For HCP crystals, the first
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two vectors will lie along <1000> directions, while the third vector
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will lie along <0001>. This provides a simple way to measure local
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orientation in HCP structures. In general, the <em>axes</em> keyword can be
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used to estimate the orientation of symmetry axes in the neighborhood
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of any atom.</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>By default, this compute calculates the centrosymmetry value for each
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atom as a per-atom vector, which can be accessed by any command that
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uses per-atom values from a compute as input. See <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">Section_howto 15</span></a> for an overview of LAMMPS output
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options.</p>
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<p>If the <em>axes</em> keyword setting is <em>yes</em>, then a per-atom array is
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calculated. The first column is the centrosymmetry parameter. The
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next three columns are the x, y, and z components of the first
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symmetry axis, followed by the second, and third symmetry axes in
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columns 5-7 and 8-10.</p>
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<p>The centrosymmetry values are unitless values >= 0.0. Their magnitude
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depends on the lattice style due to the number of contibuting neighbor
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pairs in the summation in the formula above. And it depends on the
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local defects surrounding the central atom, as described above. For
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the <em>axes yes</em> case, the vector components are also unitless, since
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they represent spatial directions.</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-default"><div class="highlight"><pre><span></span><span class="n">Bulk</span> <span class="n">lattice</span> <span class="o">=</span> <span class="mi">0</span>
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<span class="n">Dislocation</span> <span class="n">core</span> <span class="o">~</span> <span class="mf">1.0</span> <span class="p">(</span><span class="mf">0.5</span> <span class="n">to</span> <span class="mf">1.25</span><span class="p">)</span>
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<span class="n">Stacking</span> <span class="n">faults</span> <span class="o">~</span> <span class="mf">5.0</span> <span class="p">(</span><span class="mf">4.0</span> <span class="n">to</span> <span class="mf">6.0</span><span class="p">)</span>
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<span class="n">Free</span> <span class="n">surface</span> <span class="o">~</span> <span class="mf">23.0</span>
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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-default"><div class="highlight"><pre><span></span><span class="n">Bulk</span> <span class="n">lattice</span> <span class="o">=</span> <span class="mi">0</span>
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<span class="n">Dislocation</span> <span class="n">core</span> <span class="o">~</span> <span class="mf">0.06</span> <span class="p">(</span><span class="mf">0.03</span> <span class="n">to</span> <span class="mf">0.075</span><span class="p">)</span>
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<span class="n">Stacking</span> <span class="n">faults</span> <span class="o">~</span> <span class="mf">0.3</span> <span class="p">(</span><span class="mf">0.24</span> <span class="n">to</span> <span class="mf">0.36</span><span class="p">)</span>
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<span class="n">Free</span> <span class="n">surface</span> <span class="o">~</span> <span class="mf">1.38</span>
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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</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</h2>
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<p><a class="reference internal" href="compute_cna_atom.html"><span class="doc">compute cna/atom</span></a></p>
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</div>
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<div class="section" id="default">
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<h2>Default</h2>
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<p>The default value for the optional keyword is axes = no.</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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