Syntax:
compute ID group-ID hexorder/atom keyword values ...
n value = degree of order parameter
Examples:
compute 1 all hexorder/atom compute 1 all hexorder/atom n 4
Description:
Define a computation that calculates qn the bond-orientational order parameter for each atom in a group. The hexatic (n = 6) order parameter was introduced by Nelson and Halperin as a way to detect hexagonal symmetry in two-dimensional systems. For each atom, qn is a complex number (stored as two real numbers) defined as follows:
where the sum is over the n nearest neighbors of the central atom. The angle theta is formed by the bond vector rij and the x axis. theta is calculated only using the x and y components, whereas the distance from the central atom is calculated using all three x, y, and z components of the bond vector. Neighbor atoms not in the group are included in the order parameter of atoms in the group.
The optional keyword n sets the degree of the order parameter. The default value is 6. For a perfect hexagonal lattice, q6 = exp(6 i phi) for all atoms, where the constant 0 < phi < pi/3 depends only on the orientation of the lattice relative to the x axis. In an isotropic liquid, local neighborhoods may still exhibit weak hexagonal symmetry, but because the orientational correlation decays quickly with distance, the value of phi will be different for different atoms, and |<q6>| << 1.
The value of qn will be zero for atoms not in the specified compute group. If the atom has less than n neighbors (within the potential cutoff), then qn is set to zero.
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.
IMPORTANT NOTE: If you have a bonded system, then the settings of special_bonds command can remove pairwise interactions between atoms in the same bond, angle, or dihedral. This is the default setting for the 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. One way to get around this, is to write a dump file, and use the rerun command to compute the order parameter for snapshots in the dump file. The rerun script can use a special_bonds command that includes all pairs in the neighbor list.
Output info:
This compute calculates a per-atom array with 2 columns, giving the real and imaginary parts of qn, respectively.
These values can be accessed by any command that uses per-atom values from a compute as input. See Section_howto 15 for an overview of LAMMPS output options.
The per-atom array contain pairs of numbers representing the real and imaginary parts of qn, a complex number subject to the constraint |qn| <= 1.
Restrictions: none
Related commands:
compute coord/atom, compute centro/atom
Default:
The option default is n = 6.
(Nelson) Nelson, Halperin, Phys Rev B, 19, 2457 (1979).