2013-01-26 00:33:10 +08:00
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<HR>
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<H3>compute voronoi/atom command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>compute ID group-ID voronoi/atom keyword arg ...
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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
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<LI>voronoi/atom = style name of this compute command
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2013-07-26 23:13:02 +08:00
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<LI>zero or more keyword/value pairs may be appended
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2013-07-26 07:57:01 +08:00
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<LI>keyword = <I>only_group</I> or <I>surface</I> or <I>radius</I> or <I>edge_histo</I> or <I>edge_threshold</I> or <I>face_threshold</I>
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2013-07-26 23:13:02 +08:00
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<PRE> <I>only_group</I> = no arg
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<I>occupation</I> = no arg
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<I>surface</I> arg = sgroup-ID
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sgroup-ID = compute the dividing surface between group-ID and sgroup-ID
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this keyword adds a third column to the compute output
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<I>radius</I> arg = v_r
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v_r = radius atom style variable for a poly-disperse Voronoi tessellation
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<I>edge_histo</I> arg = maxedge
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maxedge = maximum number of Voronoi cell edges to be accounted in the histogram
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<I>edge_threshold</I> arg = minlength
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minlength = minimum length for an edge to be counted
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<I>face_threshold</I> arg = minarea
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minarea = minimum area for a face to be counted
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</PRE>
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2013-01-26 00:33:10 +08:00
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>compute 1 all voronoi/atom
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compute 2 precipitate voronoi/atom surface matrix
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compute 3b precipitate voronoi/atom radius v_r
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compute 4 solute voronoi/atom only_group
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</PRE>
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<PRE>compute 5 defects voronoi/atom occupation
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Define a computation that calculates the Voronoi tessellation of the
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atoms in the simulation box. The tessellation is calculated using all
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atoms in the simulation, but non-zero values are only stored for atoms
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in the group.
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</P>
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<P>By default two quantities per atom are calculated by this compute.
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The first is the volume of the Voronoi cell around each atom. Any
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point in an atom's Voronoi cell is closer to that atom than any other.
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The second is the number of faces of the Voronoi cell, which is also
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the number of nearest neighbors of the atom in the middle of the cell.
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</P>
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<HR>
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<P>If the <I>only_group</I> keyword is specified the tessellation is performed
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only with respect to the atoms contained in the compute group. This is
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equivalent to deleting all atoms not contained in the group prior to
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evaluating the tessellation.
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</P>
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<P>If the <I>surface</I> keyword is specified a third quantity per atom is
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computed: the Voronoi cell surface of the given atom. <I>surface</I> takes
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a group ID as an argument. If a group other than <I>all</I> is specified,
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only the Voronoi cell facets facing a neighbor atom from the specified
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group are counted towards the surface area.
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</P>
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<P>In the example above, a precipitate embedded in a matrix, only atoms
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at the surface of the precipitate will have non-zero surface area, and
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only the outward facing facets of the Voronoi cells are counted (the
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hull of the precipitate). The total surface area of the precipitate
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can be obtained by running a "reduce sum" compute on c_2[3]
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</P>
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<P>If the <I>radius</I> keyword is specified with an atom style variable as
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the argument, a poly-disperse Voronoi tessellation is
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performed. Examples for radius variables are
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</P>
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<PRE>variable r1 atom (type==1)*0.1+(type==2)*0.4
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compute radius all property/atom radius
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variable r2 atom c_radius
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</PRE>
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<P>Here v_r1 specifies a per-type radius of 0.1 units for type 1 atoms
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and 0.4 units for type 2 atoms, and v_r2 accesses the radius property
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present in atom_style sphere for granular models.
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</P>
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<P>The <I>edge_histo</I> keyword activates the compilation of a histogram of
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number of edges on the faces of the Voronoi cells in the compute
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group. The argument maxedge of the this keyword is the largest number
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of edges on a single Voronoi cell face expected to occur in the
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sample. This keyword adds the generation of a global vector with
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maxedge+1 entries. The last entry in the vector contains the number of
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faces with with more than maxedge edges. Since the polygon with the
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smallest amount of edges is a triangle, entries 1 and 2 of the vector
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will always be zero.
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</P>
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<P>The <I>edge_threshold</I> and <I>face_threshold</I> keywords allow the
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suppression of edges below a given minimum length and faces below a
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given minimum area. Ultra short edges and ultra small faces can occur
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as artifacts of the Voronoi tessellation. These keywords will affect
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the neighbor count and edge histogram outputs.
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</P>
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<P>If the <I>occupation</I> keyword is specified the tessellation is only
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performed for the first invocation of the compute and then stored.
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For all following invocations of the compute the number of atoms in
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each Voronoi cell in the stored tessellation is counted. In this mode
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the compute returns a per-atom array with 2 columns. The first column
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2014-04-30 06:23:31 +08:00
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is the number of atoms currently in the Voronoi volume defined by this
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atom at the time of the first invocation of the compute (note that the
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atom may have moved significantly). The second column contains the
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total number of atoms sharing the Voronoi cell of the stored
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tessellation at the location of the current atom. Numbers in column
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one can be any positive integer including zero, while column two
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values will always be greater than zero. Column one data can be used
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to locate vacancies (the coordinates are given by the atom coordinates
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at the time step when the compute was first invoked), while column two
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data can be used to identify interstitial atoms.
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</P>
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<HR>
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2013-01-26 00:33:10 +08:00
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<P>The Voronoi calculation is performed by the freely available <A HREF = "http://math.lbl.gov/voro++">Voro++
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package</A>, written by Chris Rycroft at UC Berkeley and LBL,
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which must be installed on your system when building LAMMPS for use
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with this compute. See instructions on obtaining and installing the
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Voro++ software in the src/VORONOI/README file.
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</P>
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<P>IMPORTANT NOTE: The calculation of Voronoi volumes is performed by
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each processor for the atoms it owns, and includes the effect of ghost
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atoms stored by the processor. This assumes that the Voronoi cells of
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owned atoms are not affected by atoms beyond the ghost atom cut-off
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distance. This is usually a good assumption for liquid and solid
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systems, but may lead to underestimation of Voronoi volumes in low
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density systems. By default, the set of ghost atoms stored by each
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processor is determined by the cutoff used for
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<A HREF = "pair_style.html">pair_style</A> interactions. The cutoff can be set
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explicitly via the <A HREF = "communicate.html">communicate cutoff</A> command.
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</P>
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2013-02-15 07:59:38 +08:00
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<P>IMPORTANT NOTE: The Voro++ package performs its calculation in 3d.
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This should still work for a 2d LAMMPS simulation, to effectively
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compute Voronoi "areas", so long as the z-dimension of the box is
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roughly the same (or smaller) compared to the separation of the atoms.
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Typical values for the z box dimensions in a 2d LAMMPS model are -0.5
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to 0.5, which satisfies the criterion for most <A HREF = "units.html">units</A>
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systems. Note that you define the z extent of the simulation box for
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2d simulations when using the <A HREF = "create_box.html">create_box</A> or
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<A HREF = "read_data.html">read_data</A> commands.
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</P>
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<P><B>Output info:</B>
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</P>
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<P>This compute calculates a per-atom array with 2 columns. In regular
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dynamic tessellation mode the first column is the Voronoi volume, the
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second is the neighbor count, as described above (read above for the
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output data in case the <I>occupation</I> keyword is specified).
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These values can be accessed by any command that
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uses per-atom values from a compute as input. See <A HREF = "Section_howto.html#howto_15">Section_howto
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15</A> for an overview of LAMMPS output
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options.
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</P>
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<P>The Voronoi cell volume will be in distance <A HREF = "units.html">units</A> cubed.
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</P>
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<P><B>Restrictions:</B>
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</P>
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<P>This compute is part of the VORONOI package. It is only enabled if
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LAMMPS was built with that package. See the <A HREF = "Section_start.html#start_3">Making
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LAMMPS</A> section for more info.
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "dump.html">dump custom</A>
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</P>
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<P><B>Default:</B> none
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</P>
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</HTML>
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