Classification of Point Defects
For any crystal comprised of regular arrays atoms (i.e. metals and ceramics), we can essentially define two types of sites in a unit cell when the crystal is perfect:
- The positions occupied by atoms - an atomic site.
- The positions of the interstitial sites.
It makes sense, then, that we could classify point defects based on whether the defect is at an atomic site or an interstitial site.
Let's consider this with our simple cubic crystal structure of Po, as shown in Figure 6.7.1. We have one set of symmetry-equivalent sites shown that have atoms: the corners of the unit cell ($qrs = 000$). We also have a cubic interstitial site at the body-center position $qrs = \frac{1}{2}\frac{1}{2}\frac{1}{2}$.
Figure 6.7.1 The simple cubic crystal structure.
Now, let's imagine the types of defects that can occur at each of these positions:
- We could have a missing Po atom: a "vacant" site or a vacancy.
- We could have a Po atom sit on the cubic interstitial site: a self-interstitial, because the crystal's constituent atoms (Po) are sitting in its own interstitial sites.
- We could have a foreign atom (e.g. Pb) substitute for the Po atom: a substitutional impurity.
- We could have foreign atom (e.g Pb) occupy the cubic interstitial site: a interstitial impurity.
We can see a systematic structure in the classification of the point defects: either there is a defect at an atomic or interstitial site that doesn't require an external source (i.e., the defect is intrinsic to the crystal), or there is a defect at an atomic or interstitial site that is foreign, (or extrinsic) to the host crystal itself. These point defects are summarized in the table below and in Figure 6.7.2:
| Intrinsic | Extrinsic | |
|---|---|---|
| Atomic Site | Vacancy | Substitutional Impurity |
| Interstitial Site | Self-interstitial | Interstitial Impurity |
Figure 6.7.2 Various types of point defects, organized into their sub-classifications (extrinsic/extrinsic and atomic/interstitial site). We also denote the generalized Kroger-Vink notation for the defect where $\text{h}$ and $\text{i}$ denote host atoms/site and interstitial site, respectively. $\text{x}$ denotes an impurity atom.
We can also devise a notation to more succinctly communicate the type of point defect we have. Two Dutch scientists proposed such a notation to better understand point defects (and their interactions) in the 1950s, which was later termed Kröger–Vink notation. Here, we'll introduct a simplified form of this notation that tells us about the character of the defect $\text{x}$ located on some site $\text{s}$, written as $\text{x}_{\text{s}}$. The type of defect, $\text{x}$ can be a vacancy, the host crystal's atoms, or a foreign atom. $\text{s}$ can be the site of the host atoms or an interstitial site. Generic notation for each configuration shown in Figure 6.7.2:
- Vacancy: $\text{v}_\text{h}$, a host atom site which is vacant, or missing an atom.
- Self-interstitial: $\text{h}_\text{i}$, an interstitial site which is occupied by the host atom.
- Substitutional Impurity: $\text{x}_\text{h}$, an impurity sitting on a host atom site.
- Interstitial Impurity: $\text{x}_\text{i}$, an impurity sitting in an interstitial site.
Now, consider the simple cubic Pu crystal and complete Exercise 6.7.1.