Introduction and Outline

Through the previous chapters we've worked to investigate structure by starting with bonding, discovering how interatomic interactions lead to regular crystal structures, learning how to describe and navigate crystals, and showing how the spaces between atoms in crystals can be important.

Now, we'll explore a certain type of deviation from perfect crystalline structures. We call these deviations - examples of which are shown in Figure 6.2.1 - defects or imperfections. This importance of this topic is often best introduced to introductory MSE students using the succinct words of the late British physicist Charles Frank:

Crystals are like people: it is the defects in them that make them interesting.

As seen in Figure 6.2.1, there are many types of defects in crystals. We typically first classify these by their dimensionality: point, line, plane, and volume defects (line and plane defects will be covered in Chapter 11). All of these structural defects have tremendous impacts on nearly every property a material can have. They impact mechanical strength, electrical resistivity, color, chemical reactivity... you name it.

In particular, the tiny defects at "points" in crystals can have huge impacts on technology and society - and (this isn't hyperbole) they're the reason that steel is strong, rubies are red, and your tap water is fluoridated (at least in the US). If you were paying attention to the news about the possible discovery of a room-temperature semiconductor in the summer of 2023, you may be surprised to learn that the (defected) positioning of the Cu in the material's structure was proposed to be central to the purported high-temperature superconducting behavior (S. Griffin, arxiv, 2023), although this remains up to debate.

So, we'll first focus on the point defects: deviations from perfection within a crystalline lattice that occur at lattice points within the crystal. These might be missing atoms (e.g., a vacant lattice site in a silicon crystal), atoms positioned in interstitial sites (i.e., a carbon atom sitting in an iron octahedral site), or atoms substituting for atoms in a crystal (e.g., a Ni atom substituting for a Cu atom in a Cu crystal.

These defects or imperfections in crystals are considered a core topic in MSE - something that the discipline claims to be fundamental to materials science itself. Nearly every student that studies MSE takes one or more courses simply on the thermodynamics of these types of defects because of the heavy influence they have on materials properties and the role they play in materials design. The outline is below.

Outline

• Section 6.3 - Small Imperfections, Big Impacts: A missing or misplaced atom within a lattice may seem like a small thing, but the implications influence almost every facet of our daily lives. We'll start with a story about a major consequence of a small defect.
• Section 6.4 - Vacancy Exploration: Computational models tell us a lot about the behavior of defects. Here, we'll build on the computational models we've used previously (i.e., molecular dynamics) to explore the vacancy.
• Section 6.4 - Substitutional Impurity Exploration: A second type of point defect is a substitutional impurity - a common impurity that we need to consider when thinking about the mixing of elements to make compounds or alloys.
• Section 6.6 - Interstitial Defect Exploration: The last type of point defect we'll discuss is an interstitial defect, in which an atom is positioned in an interstitial site.
• Section 6.7 - Classification of Point Defects: We'll review and classificy these four different types of simple point defects and introduce a nomenclature that allows us to discuss them efficiently called Kröger-Vink notation.
• Section 6.7 - Feedback and Comments: Please let us know what you think of the chapter by providing feedback in this section.

Note, for this chapter we explore the basic way to classify and describe point defects, then exploring the implications of their existence on crystal structures. We'll then use these point defects to investigate atomic diffusion in solids - the topic of Chapter 7. We'll return, then, to a more in-depth study of the important vacancy defect in Chapter 8.

Outcomes

• Classify different point defects and discuss their influence on crystal structure.
• Use Kröger–Vink notation to communicate about types of point defects.
• Use computational and geometric models to determine that the strain (atomic displacement) and strain energy induced from different types of point defects structures.
• Consider the consequences of the existence of point defects on structural stability.