2007-02-10 05:40:32 +08:00
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<HTML>
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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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2007-02-21 08:18:01 +08:00
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<H3>compute centro/atom command
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2007-02-10 05:40:32 +08:00
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</H3>
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<P><B>Syntax:</B>
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</P>
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2010-04-13 23:32:28 +08:00
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<PRE>compute ID group-ID centro/atom lattice
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2007-02-10 05:40:32 +08:00
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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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2010-04-13 23:32:28 +08:00
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<LI>centro/atom = style name of this compute command
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<LI>lattice = <I>fcc</I> or <I>bcc</I> or N = # of neighbors per atom to include
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2007-02-10 05:40:32 +08:00
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</UL>
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<P><B>Examples:</B>
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</P>
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2010-04-13 23:32:28 +08:00
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<PRE>compute 1 all centro/atom fcc
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</PRE>
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<PRE>compute 1 all centro/atom 8
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2007-02-10 05:40:32 +08:00
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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 centro-symmetry parameter for
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2009-01-20 01:17:01 +08:00
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each atom in the group. In solid-state systems the centro-symmetry
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2007-07-03 03:59:42 +08:00
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parameter is a useful measure of the local lattice disorder around an
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atom and can be used to characterize whether the atom is part of a
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perfect lattice, a local defect (e.g. a dislocation or stacking
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fault), or at a surface.
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2007-02-10 05:40:32 +08:00
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</P>
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2007-11-20 23:37:16 +08:00
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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.
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</P>
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2007-02-10 05:40:32 +08:00
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<P>This parameter is computed using the following formula from
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<A HREF = "#Kelchner">(Kelchner)</A>
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</P>
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<CENTER><IMG SRC = "Eqs/centro_symmetry.jpg">
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</CENTER>
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2010-04-13 23:32:28 +08:00
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<P>where the <I>N</I> nearest neighbors or 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.
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</P>
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<P><I>N</I> 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 <I>fcc</I> or <I>bcc</I> is used, <I>N</I> is set to 12 and 8
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respectively. More generally, <I>N</I> can be set to a positive, even
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integer.
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</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 <I>N</I> neighbors (within
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the potential cutoff), then its centro-symmetry parameter is set to
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0.0.
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</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 <I>N</I> neighbors used in this calculation.
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2007-02-10 05:40:32 +08:00
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</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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2007-02-10 05:40:32 +08:00
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is dumped). Thus it can be inefficient to compute/dump this quantity
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2009-01-20 01:17:01 +08:00
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too frequently or to have multiple compute/dump commands, each with a
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2007-02-10 05:40:32 +08:00
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<I>centro/atom</I> style.
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</P>
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2008-01-04 08:56:10 +08:00
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<P><B>Output info:</B>
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</P>
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2009-12-05 05:04:00 +08:00
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<P>This compute calculates a per-atom vector, which can be accessed by
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any command that uses per-atom values from a compute as input. See
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<A HREF = "Section_howto.html#4_15">this section</A> for an overview of LAMMPS
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output options.
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2008-01-04 08:56:10 +08:00
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</P>
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2010-04-13 23:32:28 +08:00
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<P>The per-atom vector values are unitless values >= 0.0. Their
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magnitude depends on the lattice style due to the number of
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contibuting neighbor pairs in the summation in the formula above. And
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it depends on the local defects surrounding the central atom, as
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described above.
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</P>
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2010-04-29 00:44:36 +08:00
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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):
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</P>
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<PRE>Bulk lattice = 0
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Dislocation core ~ 1.0 (0.5 to 1.25)
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Stacking faults ~ 5.0 (4.0 to 6.0)
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Free surface ~ 23.0
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</PRE>
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<P>These values are *not* normalized by the square of the lattice
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parameter. If they were, normalized values would be:
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</P>
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<PRE>Bulk lattice = 0
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Dislocation core ~ 0.06 (0.03 to 0.075)
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Stacking faults ~ 0.3 (0.24 to 0.36)
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Free surface ~ 1.38
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</PRE>
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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.
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</P>
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2007-02-10 05:40:32 +08:00
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<P><B>Restrictions:</B> none
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</P>
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2009-01-20 01:17:01 +08:00
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "compute_cna_atom.html">compute cna/atom</A>
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2007-02-10 05:40:32 +08:00
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</P>
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<P><B>Default:</B> none
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</P>
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<HR>
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<A NAME = "Kelchner"></A>
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<P><B>(Kelchner)</B> Kelchner, Plimpton, Hamilton, Phys Rev B, 58, 11085 (1998).
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</P>
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</HTML>
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