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			<div class="section" id="compute-voronoi-atom-command">
			<span id="index-0"></span><h1>compute voronoi/atom command<a class="headerlink" href="#compute-voronoi-atom-command" title="Permalink to this headline">¶</a></h1>
			<div class="section" id="syntax">
			<h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
			<div class="highlight-python"><div class="highlight"><pre>compute ID group-ID voronoi/atom keyword arg ...
			</pre></div>
			</div>
			<ul class="simple">
			<li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
			<li>voronoi/atom = style name of this compute command</li>
			<li>zero or more keyword/value pairs may be appended</li>
			<li>keyword = <em>only_group</em> or <em>surface</em> or <em>radius</em> or <em>edge_histo</em> or <em>edge_threshold</em> or <em>face_threshold</em></li>
			</ul>
			<pre class="literal-block">
			<em>only_group</em> = no arg
			<em>occupation</em> = no arg
			<em>surface</em> arg = sgroup-ID
			sgroup-ID = compute the dividing surface between group-ID and sgroup-ID
			this keyword adds a third column to the compute output
			<em>radius</em> arg = v_r
			v_r = radius atom style variable for a poly-disperse Voronoi tessellation
			<em>edge_histo</em> arg = maxedge
			maxedge = maximum number of Voronoi cell edges to be accounted in the histogram
			<em>edge_threshold</em> arg = minlength
			minlength = minimum length for an edge to be counted
			<em>face_threshold</em> arg = minarea
			minarea = minimum area for a face to be counted
			</pre>
			</div>
			<div class="section" id="examples">
			<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
			<div class="highlight-python"><div class="highlight"><pre>compute 1 all voronoi/atom
			compute 2 precipitate voronoi/atom surface matrix
			compute 3b precipitate voronoi/atom radius v_r
			compute 4 solute voronoi/atom only_group
			</pre></div>
			</div>
			<div class="highlight-python"><div class="highlight"><pre>compute 5 defects voronoi/atom occupation
			</pre></div>
			</div>
			</div>
			<div class="section" id="description">
			<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
			<p>Define a computation that calculates the Voronoi tessellation of the
			atoms in the simulation box. The tessellation is calculated using all
			atoms in the simulation, but non-zero values are only stored for atoms
			in the group.</p>
			<p>By default two quantities per atom are calculated by this compute.
			The first is the volume of the Voronoi cell around each atom. Any
			point in an atom’s Voronoi cell is closer to that atom than any other.
			The second is the number of faces of the Voronoi cell, which is also
			the number of nearest neighbors of the atom in the middle of the cell.</p>
			<hr class="docutils" />
			<p>If the <em>only_group</em> keyword is specified the tessellation is performed
			only with respect to the atoms contained in the compute group. This is
			equivalent to deleting all atoms not contained in the group prior to
			evaluating the tessellation.</p>
			<p>If the <em>surface</em> keyword is specified a third quantity per atom is
			computed: the Voronoi cell surface of the given atom. <em>surface</em> takes
			a group ID as an argument. If a group other than <em>all</em> is specified,
			only the Voronoi cell facets facing a neighbor atom from the specified
			group are counted towards the surface area.</p>
			<p>In the example above, a precipitate embedded in a matrix, only atoms
			at the surface of the precipitate will have non-zero surface area, and
			only the outward facing facets of the Voronoi cells are counted (the
			hull of the precipitate). The total surface area of the precipitate
			can be obtained by running a “reduce sum” compute on c_2[3]</p>
			<p>If the <em>radius</em> keyword is specified with an atom style variable as
			the argument, a poly-disperse Voronoi tessellation is
			performed. Examples for radius variables are</p>
			<div class="highlight-python"><div class="highlight"><pre>variable r1 atom (type==1)0.1+(type==2)0.4
			compute radius all property/atom radius
			variable r2 atom c_radius
			</pre></div>
			</div>
			<p>Here v_r1 specifies a per-type radius of 0.1 units for type 1 atoms
			and 0.4 units for type 2 atoms, and v_r2 accesses the radius property
			present in atom_style sphere for granular models.</p>
			<p>The <em>edge_histo</em> keyword activates the compilation of a histogram of
			number of edges on the faces of the Voronoi cells in the compute
			group. The argument maxedge of the this keyword is the largest number
			of edges on a single Voronoi cell face expected to occur in the
			sample. This keyword adds the generation of a global vector with
			maxedge+1 entries. The last entry in the vector contains the number of
			faces with with more than maxedge edges. Since the polygon with the
			smallest amount of edges is a triangle, entries 1 and 2 of the vector
			will always be zero.</p>
			<p>The <em>edge_threshold</em> and <em>face_threshold</em> keywords allow the
			suppression of edges below a given minimum length and faces below a
			given minimum area. Ultra short edges and ultra small faces can occur
			as artifacts of the Voronoi tessellation. These keywords will affect
			the neighbor count and edge histogram outputs.</p>
			<p>If the <em>occupation</em> keyword is specified the tessellation is only
			performed for the first invocation of the compute and then stored.
			For all following invocations of the compute the number of atoms in
			each Voronoi cell in the stored tessellation is counted. In this mode
			the compute returns a per-atom array with 2 columns. The first column
			is the number of atoms currently in the Voronoi volume defined by this
			atom at the time of the first invocation of the compute (note that the
			atom may have moved significantly). The second column contains the
			total number of atoms sharing the Voronoi cell of the stored
			tessellation at the location of the current atom. Numbers in column
			one can be any positive integer including zero, while column two
			values will always be greater than zero. Column one data can be used
			to locate vacancies (the coordinates are given by the atom coordinates
			at the time step when the compute was first invoked), while column two
			data can be used to identify interstitial atoms.</p>
			<hr class="docutils" />
			<p>The Voronoi calculation is performed by the freely available <a class="reference external" href="http://math.lbl.gov/voro++">Voro++ package</a>, written by Chris Rycroft at UC Berkeley and LBL,
			which must be installed on your system when building LAMMPS for use
			with this compute. See instructions on obtaining and installing the
			Voro++ software in the src/VORONOI/README file.</p>
			<div class="admonition note">
			<p class="first admonition-title">Note</p>
			<p class="last">The calculation of Voronoi volumes is performed by each
			processor for the atoms it owns, and includes the effect of ghost
			atoms stored by the processor. This assumes that the Voronoi cells of
			owned atoms are not affected by atoms beyond the ghost atom cut-off
			distance. This is usually a good assumption for liquid and solid
			systems, but may lead to underestimation of Voronoi volumes in low
			density systems. By default, the set of ghost atoms stored by each
			processor is determined by the cutoff used for
			<a class="reference internal" href="pair_style.html"><em>pair_style</em></a> interactions. The cutoff can be set
			explicitly via the <a class="reference internal" href="comm_modify.html"><em>comm_modify cutoff</em></a> command.</p>
			</div>
			<div class="admonition note">
			<p class="first admonition-title">Note</p>
			<p class="last">The Voro++ package performs its calculation in 3d. This should
			still work for a 2d LAMMPS simulation, to effectively compute Voronoi
			“areas”, so long as the z-dimension of the box is roughly the same (or
			smaller) compared to the separation of the atoms. Typical values for
			the z box dimensions in a 2d LAMMPS model are -0.5 to 0.5, which
			satisfies the criterion for most <a class="reference internal" href="units.html"><em>units</em></a> systems. Note
			that you define the z extent of the simulation box for 2d simulations
			when using the <a class="reference internal" href="create_box.html"><em>create_box</em></a> or
			<a class="reference internal" href="read_data.html"><em>read_data</em></a> commands.</p>
			</div>
			<p><strong>Output info:</strong></p>
			<p>This compute calculates a per-atom array with 2 columns. In regular
			dynamic tessellation mode the first column is the Voronoi volume, the
			second is the neighbor count, as described above (read above for the
			output data in case the <em>occupation</em> keyword is specified).
			These values can be accessed by any command that
			uses 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
			options.</p>
			<p>The Voronoi cell volume will be in distance <a class="reference internal" href="units.html"><em>units</em></a> cubed.</p>
			</div>
			<div class="section" id="restrictions">
			<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
			<p>This compute is part of the VORONOI package. It is only enabled if
			LAMMPS was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
			</div>
			<div class="section" id="related-commands">
			<h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
			<p><a class="reference internal" href="dump.html"><em>dump custom</em></a></p>
			<p><strong>Default:</strong> none</p>
			</div>
			</div>


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