git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@14950 f3b2605a-c512-4ea7-a41b-209d697bcdaa

doc/html/_sources/compute_orientorder_atom.txt

@@ -0,0 +1,144 @@
+.. index:: compute orientorder/atom
+
+compute orientorder/atom command
+================================
+
+Syntax
+""""""
+
+.. parsed-literal::
+
+   compute ID group-ID orientorder/atom keyword values ...
+
+* ID, group-ID are documented in :doc:`compute <compute>` command
+* orientorder/atom = style name of this compute command
+* one or more keyword/value pairs may be appended
+.. parsed-literal::
+
+   keyword = *cutoff* or *nnn* or *ql* 
+     *cutoff* value = distance cutoff
+     *nnn* value = number of nearest neighbors
+     *degrees* values = nlvalues, l1, l2,...
+
+
+
+Examples
+""""""""
+
+.. parsed-literal::
+
+   compute 1 all orientorder/atom 
+   compute 1 all orientorder/atom degrees 5 4 6 8 10 12 nnn NULL cutoff 1.5
+
+Description
+"""""""""""
+
+Define a computation that calculates a set of bond-orientational 
+order parameters *Ql* for each atom in a group. These order parameters
+were introduced by :ref:`Steinhardt et al. <Steinhardt>` as a way to
+characterize the local orientational order in atomic structures. 
+For each atom, *Ql* is a real number defined as follows:
+
+.. image:: Eqs/orientorder.jpg
+   :align: center
+
+The first equation defines the spherical harmonic order parameters. 
+These are complex number components of the 3D analog of the 2D order 
+parameter *qn*\ , which is implemented as LAMMPS compute 
+:doc:`hexorder/atom <compute_hexorder_atom>`. 
+The summation is over the *nnn* nearest 
+neighbors of the central atom. 
+The angles theta and phi are the standard spherical polar angles 
+defining the direction of the bond vector *rij*\ .
+The second equation defines *Ql*\ , which is a
+rotationally invariant scalar quantity obtained by summing 
+over all the components of degree *l*\ .
+
+The optional keyword *cutoff* defines the distance cutoff
+used when searching for neighbors. The default value, also
+the maximum allowable value, is the cutoff specified
+by the pair style.
+
+The optional keyword *nnn* defines the number of nearest
+neighbors used to calculate *Ql*\ . The default value is 12.
+If the value is NULL, then all neighbors up to the 
+specified distance cutoff are used.
+
+The optional keyword *degrees* defines the list of order parameters to
+be computed.  The first argument *nlvalues* is the number of order 
+parameters. This is followed by that number of integers giving the
+degree of each order parameter. Because *Q*\ 2 and all odd-degree 
+order parameters are zero for atoms in cubic crystals 
+(see :ref:`Steinhardt <Steinhardt>`), the default order parameters
+are *Q*\ 4, *Q*\ 6, *Q*\ 8, *Q*\ 10, and *Q*\ 12. For the
+FCC crystal with *nnn*\ =12, *Q*\ 4 = sqrt(7/3)/8 = 0.19094....
+The numerical values of all order parameters up to *Q*\ 12
+for a range of commonly encountered high-symmetry structures are given 
+in Table I of :ref:`Mickel et al. <Mickel>`.
+
+The value of *Ql* is set to zero for atoms not in the
+specified compute group, as well as for atoms that have less than 
+*nnn* neighbors within the distance cutoff.
+
+The neighbor list needed to compute this quantity is constructed each
+time the calculation is performed (i.e. each time a snapshot of atoms
+is dumped).  Thus it can be inefficient to compute/dump this quantity
+too frequently.
+
+.. note::
+
+   If you have a bonded system, then the settings of
+   :doc:`special_bonds <special_bonds>` command can remove pairwise
+   interactions between atoms in the same bond, angle, or dihedral.  This
+   is the default setting for the :doc:`special_bonds <special_bonds>`
+   command, and means those pairwise interactions do not appear in the
+   neighbor list.  Because this fix uses the neighbor list, it also means
+   those pairs will not be included in the order parameter.  This
+   difficulty can be circumvented by writing a dump file, and using the
+   :doc:`rerun <rerun>` command to compute the order parameter for
+   snapshots in the dump file.  The rerun script can use a
+   :doc:`special_bonds <special_bonds>` command that includes all pairs in
+   the neighbor list.
+
+**Output info:**
+
+This compute calculates a per-atom array with *nlvalues* columns, giving the
+*Ql* values for each atom, which are real numbers on the range 0 <= *Ql* <= 1.
+
+These values can be accessed by any command that uses
+per-atom values from a compute as input.  See :ref:`Section_howto 15 <howto_15>` for an overview of LAMMPS output
+options.
+
+Restrictions
+""""""""""""
+ none
+
+Related commands
+""""""""""""""""
+
+:doc:`compute coord/atom <compute_coord_atom>`, :doc:`compute centro/atom <compute_centro_atom>`, :doc:`compute hexorder/atom <compute_hexorder_atom>`
+
+Default
+"""""""
+
+The option defaults are *cutoff* = pair style cutoff, *nnn* = 12, *degrees* = 5 4 6 8 9 10 12 i.e. *Q*\ 4, *Q*\ 6, *Q*\ 8, *Q*\ 10, and *Q*\ 12.
+
+
+----------
+
+
+.. _Steinhardt:
+
+
+
+.. _Mickel:
+
+**(Steinhardt)** P. Steinhardt, D. Nelson, and M. Ronchetti, Phys. Rev. B 28, 784 (1983).
+
+
+**(Mickel)** W. Mickel, S. C. Kapfer, G. E. Schroeder-Turkand, K. Mecke, J. Chem. Phys. 138, 044501 (2013).
+
+
+.. _lws: http://lammps.sandia.gov
+.. _ld: Manual.html
+.. _lc: Section_commands.html#comm