Defects are distortions from a regular crystal packing. They are not periodic, but instead appear randomly distributed across the structure. While defects do not usually sit on the convex hull, they are often kinetically stable.

Point Defects

Probably the simplest example of a defect, point defects occur at a single atomic site. There are three main categories:

• Vacancies are atoms which are missing from a structure.
• Substitutional defects are atomic sites which are occupied by a different atom than usual.
• Interstitial defects are sites which contain an atom but are usually vacant

In addition to above, Frenkel defects are a special case where an atom has relocated from one site to another nearby usually-vacant site. Frenkel defects are therefore compromised of a vacancy and a neighbouring interstitial defect.

Properties

Defects appearing in small enough concentrations that they have no significant impact on a crystal‘s overall geometry or chemical properties. They do, however, play a significant role in excited-state properties such as single photon emission. A discussion of excited-state properties is beyond the scope of this site.

Modelling

Critically, defects are rare anomalies in periodic structures. One must be conscious that unit cell dimensions that are appropriate for modelling a pristine crystal may not be suitable for defect modelling. The environment around a defect should be treated as if it is pristine, and this requires a “large” unit cell. Ideally, there will be no perceptible interaction between defects in periodic images. Where possible, I recommend 10-20 Å between defects, but you should converge the lattice parameters for your particular system, particularly if you intend to model excited-state properties. Furthermore, when performing geometry optimisations on your defected cells, your lattice parameters should be fixed to those of the pristine crystal as your defect is imagined to be embedded in an infinite pristine crystal, which would constrain the geometry of the atoms immediately surrounding your defect. Notably, this will strain your cell and increase the defect energy. If your energy rankings are important, and your defects are somewhat significant, you may need an even larger unit cell than expected so as to minimise strain.

Structure Prediction

The first step in predicting defects is to have an optimised unit cell for the pristine crystal. As per convention, your unit cell will probably be a minimum (or near-minimum) representation of the crystal structure, and therefore you will want to build a supercell to mitigate defect-defect interactions (as described above). Critically, you will also need your cell to be in P1 as you likely only want one defect per unit cell.

To generate initial candidate defect structures, the best approach may depend on the complexity of the defects you wish to introduce. For single-atom point defects, consider manually introducing the defects. For vacancies, this is as simple as deleting atoms, and for substitutional defects, it is as simple as changing the label on an atom. Interstitial defects are slightly more challenging; you will need to add a new atom, and select “sensible” coordinates. For more complex defects, consider a RSS approach, which randomly removes and adds atoms to the cell. After generating candidate defect structures, you may geometry optimise the structure, as per usual, with the exception that the cell lattice parameters should be constrained to those of the pristine cell.