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<li class="toctree-l1"><a class="reference internal" href="Section_intro.html">1. Introduction</a></li>
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<li>compute orientorder/atom command</li>
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<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
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<div class="section" id="compute-orientorder-atom-command">
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<span id="index-0"></span><h1>compute orientorder/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">orientorder</span><span class="o">/</span><span class="n">atom</span> <span class="n">keyword</span> <span class="n">values</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</li>
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<li>orientorder/atom = style name of this compute command</li>
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<li>one or more keyword/value pairs may be appended</li>
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</ul>
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<pre class="literal-block">
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keyword = <em>cutoff</em> or <em>nnn</em> or <em>ql</em>
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<em>cutoff</em> value = distance cutoff
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<em>nnn</em> value = number of nearest neighbors
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<em>degrees</em> values = nlvalues, l1, l2,...
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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">orientorder</span><span class="o">/</span><span class="n">atom</span>
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<span class="n">compute</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">orientorder</span><span class="o">/</span><span class="n">atom</span> <span class="n">degrees</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">6</span> <span class="mi">8</span> <span class="mi">10</span> <span class="mi">12</span> <span class="n">nnn</span> <span class="n">NULL</span> <span class="n">cutoff</span> <span class="mf">1.5</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 a set of bond-orientational
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order parameters <em>Ql</em> for each atom in a group. These order parameters
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were introduced by <a class="reference internal" href="#steinhardt"><span class="std std-ref">Steinhardt et al.</span></a> as a way to
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characterize the local orientational order in atomic structures.
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For each atom, <em>Ql</em> is a real number defined as follows:</p>
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<img alt="_images/orientorder.jpg" class="align-center" src="_images/orientorder.jpg" />
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<p>The first equation defines the spherical harmonic order parameters.
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These are complex number components of the 3D analog of the 2D order
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parameter <em>qn</em>, which is implemented as LAMMPS compute
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<a class="reference internal" href="compute_hexorder_atom.html"><span class="doc">hexorder/atom</span></a>.
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The summation is over the <em>nnn</em> nearest
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neighbors of the central atom.
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The angles theta and phi are the standard spherical polar angles
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defining the direction of the bond vector <em>rij</em>.
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The second equation defines <em>Ql</em>, which is a
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rotationally invariant scalar quantity obtained by summing
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over all the components of degree <em>l</em>.</p>
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<p>The optional keyword <em>cutoff</em> defines the distance cutoff
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used when searching for neighbors. The default value, also
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the maximum allowable value, is the cutoff specified
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by the pair style.</p>
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<p>The optional keyword <em>nnn</em> defines the number of nearest
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neighbors used to calculate <em>Ql</em>. The default value is 12.
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If the value is NULL, then all neighbors up to the
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specified distance cutoff are used.</p>
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<p>The optional keyword <em>degrees</em> defines the list of order parameters to
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be computed. The first argument <em>nlvalues</em> is the number of order
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parameters. This is followed by that number of integers giving the
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degree of each order parameter. Because <em>Q</em>2 and all odd-degree
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order parameters are zero for atoms in cubic crystals
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(see <a class="reference internal" href="#steinhardt"><span class="std std-ref">Steinhardt</span></a>), the default order parameters
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are <em>Q</em>4, <em>Q</em>6, <em>Q</em>8, <em>Q</em>10, and <em>Q</em>12. For the
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FCC crystal with <em>nnn</em>=12, <em>Q</em>4 = sqrt(7/3)/8 = 0.19094....
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The numerical values of all order parameters up to <em>Q</em>12
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for a range of commonly encountered high-symmetry structures are given
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in Table I of <a class="reference internal" href="#mickel"><span class="std std-ref">Mickel et al.</span></a>.</p>
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<p>The value of <em>Ql</em> is set to zero for atoms not in the
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specified compute group, as well as for atoms that have less than
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<em>nnn</em> neighbors within the distance cutoff.</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 (i.e. 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.</p>
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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">If you have a bonded system, then the settings of
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<a class="reference internal" href="special_bonds.html"><span class="doc">special_bonds</span></a> command can remove pairwise
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interactions between atoms in the same bond, angle, or dihedral. This
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is the default setting for the <a class="reference internal" href="special_bonds.html"><span class="doc">special_bonds</span></a>
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command, and means those pairwise interactions do not appear in the
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neighbor list. Because this fix uses the neighbor list, it also means
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those pairs will not be included in the order parameter. This
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difficulty can be circumvented by writing a dump file, and using the
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<a class="reference internal" href="rerun.html"><span class="doc">rerun</span></a> command to compute the order parameter for
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snapshots in the dump file. The rerun script can use a
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<a class="reference internal" href="special_bonds.html"><span class="doc">special_bonds</span></a> command that includes all pairs in
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the neighbor list.</p>
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</div>
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<p><strong>Output info:</strong></p>
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<p>This compute calculates a per-atom array with <em>nlvalues</em> columns, giving the
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<em>Ql</em> values for each atom, which are real numbers on the range 0 <= <em>Ql</em> <= 1.</p>
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<p>These values can be accessed by any command that uses
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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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</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_coord_atom.html"><span class="doc">compute coord/atom</span></a>, <a class="reference internal" href="compute_centro_atom.html"><span class="doc">compute centro/atom</span></a>, <a class="reference internal" href="compute_hexorder_atom.html"><span class="doc">compute hexorder/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 option defaults are <em>cutoff</em> = pair style cutoff, <em>nnn</em> = 12, <em>degrees</em> = 5 4 6 8 9 10 12 i.e. <em>Q</em>4, <em>Q</em>6, <em>Q</em>8, <em>Q</em>10, and <em>Q</em>12.</p>
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<hr class="docutils" />
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<p id="mickel"><span id="steinhardt"></span><strong>(Steinhardt)</strong> P. Steinhardt, D. Nelson, and M. Ronchetti, Phys. Rev. B 28, 784 (1983).</p>
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<p><strong>(Mickel)</strong> W. Mickel, S. C. Kapfer, G. E. Schroeder-Turkand, K. Mecke, J. Chem. Phys. 138, 044501 (2013).</p>
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