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         xml:id="particles.modifiers.centrosymmetry"
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  <title>Centrosymmetry parameter</title>

  <para>
    <informalfigure><screenshot><mediaobject><imageobject>
       <imagedata fileref="images/modifiers/centrosymmetry_panel.png" format="PNG" />
    </imageobject></mediaobject></screenshot></informalfigure>
      
  This modifier calculates the centro-symmetry parameter of each particle [<link
  xlink:href="http://link.aps.org/doi/10.1103/PhysRevB.58.11085">Kelchner, Plimpton, Hamilton, Phys Rev B, 58, 11085 (1998)</link>].
  In solid-state systems the centro-symmetry parameter is a useful measure of the local 
  lattice disorder around an atom and can be used to characterize whether the atom is 
  part of a perfect lattice, a local defect (e.g. a dislocation or stacking fault), or at a surface.
  </para>
  
  <para>
    OVITO uses the same <link xlink:href="http://lammps.sandia.gov/doc/compute_centro_atom.html">algorithm as LAMMPS</link>
    to calculate the centro-symmetry parameter.
  </para>
  
  <para>
    The modifier needs to know the number of neighbors that should be taken into account for the computation of the centrosymmetry value.
    It should correspond to the number of nearest neighbors in the underlying lattice of atoms. 
    For fcc and bcc lattices, it should be set to 12 and 8 respectively. More generally, the parameter can be set to a positive, even integer.
  </para>
  
  <para>
    For an atom on a lattice site, surrounded by atoms on a perfect lattice, 
    the centro-symmetry parameter will be zero. It will be near zero for small thermal perturbations 
    of a perfect lattice. At a point defect the symmetry is broken, and the parameter 
    will be a larger positive value. An atom at a surface will have a large positive parameter too.
  </para>
  
  <para>
    Note that this modifier requires access to the complete set of particles to perform the analysis. It should therefore be placed at the 
    beginning of the processing pipeline, preceding any modifiers that delete particles.
  </para>
  
  <para>
    After you have computed the centro-symmetry parameter (CSP) values with this analysis modifier, you can use the 
    <link linkend="particles.modifiers.color_coding">Color Coding</link> modifier to color atoms according to their CSP value.
    Or you can use the <link linkend="particles.modifiers.expression_select">Expression Select</link> modifier to select atoms 
    having a low CSP value. These undisturbed atoms can then be hidden using the <link linkend="particles.modifiers.delete_selected_particles">Delete Selected Particles</link>
    modifier to reveal crystal defect atoms.
  </para>
  
</section>
