Wigner-Seitz defect analysis

This analysis modifier identifies point defects and counts vacancies and interstitials in a crystal using the so-called Wigner-Seitz cell method.

The Wigner-Seitz cell method works as follows: We assume that there exist two configurations of the atomistic system. One is the reference state, which is defect-free (typically a perfect crystal lattice). The other is the displaced configuration, which represents the defective state of the crystal to be analyzed. Here, some atoms have been displaced from their original sites.

Each atomic site in the reference configuration defines the center of a Wigner-Seitz cell (also called Voronoi cell), which is the spatial region that belongs to that site. Any atom (from the displaced configuration) that is located within the Wigner-Seitz cell of a reference site is said to occupy that site. The analysis modifier basically counts the number of atoms from the displaced configuration that occupy each site from the reference configuration. Typically, sites are occupied by exactly one atom each. However, some sites may by occupied by zero atoms (then we call it a vacancy) or by more than one atom (then we call the excess atoms interstitials).

The modifier outputs the number of atoms sitting on each site as a new particle property named Occupancy. This property allows to subsequently filter out normal sites and show only defective sites (e.g. by using the Expression Select modifier). Furthermore, the modifier reports two global quantities:

Number of vacancies

This is the total number of sites in the reference configuration which are not occupied by any atom in the displaced configuration (sites with occupancy=0).

Number of interstitials

This is the total number of excess atoms, summed over all sites of the reference configuration. A site with occupancy=2 has one excess atom. A site with occupancy=3 has two excess atoms, and so forth.

The number of atoms in the reference configuration and in the displaced configuration do not have to be the same. However, if the two configurations do contain the same number of atoms, then the number of vacancies and the number of interstitials reported by the modifier will be equal. That is because, in this case, the sum over all occupancy numbers is equal to the number of sites in the reference configuration.

The modifier loads the reference configuration from a separate input file. Use the "Reference: External file" panel to pick the file containing the reference particle positions, which define the defect-free state of the crystal. The displaced configuration is given by the particle dataset to which the Wigner-Seitz modifier is being applied.

IMPORTANT NOTE: After performing the analysis this modifier throws away the displaced configuration and completely replaces it with the reference configuration loaded from the external file. Thus, as an effect of applying the Wigner-Seitz modifier you will now see the reference configuration (defect-free crystal) instead of the displaced configuration (defective crystal) which you applied it to. This makes sense because the computed occupancy numbers apply to the atomic sites of the reference configuration, not to the atoms of the defective crystal. Keep in mind that the modifier only computes the number of atoms that occupy each site. It does not tell you which atom from the defective configuration occupies which site.

However, if more specific information is needed, the modifier provides the Output per-type occupancies option. If actived, the modifer breaks down the occupancy number of each site into per-type counts. Thus, if your displaced configuration contains atoms of different types, then this allows you to determine how many atoms of each type occupy each site in the ideal reference crystal. The per-type occupancy numbers are output as vector components of the Occupancy particle property. For example, the property component Occupancy.1 contains the number of atoms of type 1 that occupy a site.

This allows you to identify specific types of point defects, e.g. vacancies or antisites. OVITO's particle selection tools, in particular the Expression Select modifier, can be used to select the sites that meet specific criteria, for example A-sites that are occupied by a B-atom. You can find a detailed example of how to also accomplish this selection using the Python Script modifier in the scripting documentation of the Wigner-Seitz modifier.

Parameters

Eliminate homogeneous cell deformation

This option lets the modifier first rescale the simulation cell of the displaced configuration including all particle positions to match the cell shape of the reference configuration before performing the Wigner-Seitz analysis. This effectively eliminates any macroscopic, homogeneous deformation of the simulation cell, and the atomic displacements will reflect only the internal motion of particles.

Output per-type occupancies

If this option is active, the modifier outputs per-type occupancy numbers as explained above.

Fixed reference configuration

If this option is active, the selected animation frame from the reference simulation sequence is used as a fixed reference to perform the analysis. This is the default mode.

Relative to current frame

If this option is active, then a changing reference configuration is used for the analysis. The frame offset controls the distance between reference and current frame and can be negative or positive. If it is negative, then the reference frame precedes the current frame in the simulation sequence. Note that the analysis will not be performed for frames for which the reference frame is negative or out of range.

Implementation detail

The Wigner-Seitz cell of a site is by definition the locus of points in space that are closer to that site than to any of the other sites. Note, however, that the modifier never has to compute the shape of the Wigner-Seitz cells explicitly to perform the analysis. It rather determines the closest site from the reference configuration for each atom of the displaced configuration. The occupancy counter of that site is then incremented by one.