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<li>compute hexorder/atom command</li>
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<div class="section" id="compute-hexorder-atom-command">
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<span id="index-0"></span><h1>compute hexorder/atom command<a class="headerlink" href="#compute-hexorder-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 hexorder/atom keyword values ...
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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>hexorder/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>degree</em> or <em>nnn</em> or <em>cutoff</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>degree</em> value = degree <em>n</em> of order parameter
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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<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 hexorder/atom
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compute 1 all hexorder/atom degree 4 nnn 4 cutoff 1.2
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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 <em>qn</em> the bond-orientational
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order parameter for each atom in a group. The hexatic (<em>n</em> = 6) order
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parameter was introduced by <a class="reference internal" href="#nelson"><span>Nelson and Halperin</span></a> as a way to detect
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hexagonal symmetry in two-dimensional systems. For each atom, <em>qn</em>
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is a complex number (stored as two real numbers) defined as follows:</p>
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<img alt="_images/hexorder.jpg" class="align-center" src="_images/hexorder.jpg" />
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<p>where the sum is over the <em>nnn</em> nearest neighbors
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of the central atom. The angle theta
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is formed by the bond vector rij and the <em>x</em> axis. theta is calculated
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only using the <em>x</em> and <em>y</em> components, whereas the distance from the
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central atom is calculated using all three
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<em>x</em>, <em>y</em>, and <em>z</em> components of the bond vector.
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Neighbor atoms not in the group
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are included in the order parameter of atoms in the group.</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>qn</em>. The default value is 6.
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If the value is NULL, then all neighbors up to the
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distance cutoff are used.</p>
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<p>The optional keyword <em>degree</em> sets the degree <em>n</em> of the order parameter.
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The default value is 6. For a perfect hexagonal lattice with
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<em>nnn</em> = 6,
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<em>q*6 = exp(6 i phi) for all atoms, where the constant 0 < phi < pi/3
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depends only on the orientation of the lattice relative to the *x</em> axis.
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In an isotropic liquid, local neighborhoods may still exhibit
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weak hexagonal symmetry, but because the orientational correlation
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decays quickly with distance, the value of phi will be different for
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different atoms, and so when <a href="#id1"><span class="problematic" id="id2">*</span></a>q*6 is averaged over all the atoms
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in the system, <a href="#id3"><span class="problematic" id="id4">|<*q*6>|</span></a> << 1.</p>
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<p>The value of <em>qn</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"><em>special_bonds</em></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"><em>special_bonds</em></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"><em>rerun</em></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"><em>special_bonds</em></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 2 columns, giving the
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real and imaginary parts <em>qn</em>, a complex number restricted to the
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unit disk of the complex plane i.e. Re(<em>qn</em>)^2 + Im(<em>qn</em>)^2 <= 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>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<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_orientorder_atom.html"><em>compute orientorder/atom</em></a>, <a class="reference internal" href="compute_coord_atom.html"><em>compute coord/atom</em></a>, <a class="reference internal" href="compute_centro_atom.html"><em>compute centro/atom</em></a></p>
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</div>
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<div class="section" id="default">
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<h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
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<p>The option defaults are <em>cutoff</em> = pair style cutoff, <em>nnn</em> = 6, <em>degree</em> = 6</p>
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<hr class="docutils" />
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<p id="nelson"><strong>(Nelson)</strong> Nelson, Halperin, Phys Rev B, 19, 2457 (1979).</p>
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