Introduction and Outline

In previous chapters, we worked to develop a foundational understanding of the interactions between atoms and molecules using the electrostatic interpretation of the bond. We then developed computational and mathematical models describing the forces acting between two atoms separated in space by some distance. This model - so far using *only* two atoms - already provides us with a strong foundation for exploring how atoms interact when in proximity to each other. It's shown us emergent behaviors such as bond strength, magnitude of thermal vibrations, and thermal expansion. In this chapter, we'll continue with the model, and explore what happens when we move into *materials* systems: assemblies of more than just a few atoms. The outline is as follows:

  • Section 5.3- Bonding in Large(r) Assemblies: Using the interatomic potential models constructed earlier, we'll add more atoms and observe what structures arise when we have more than one atom,
  • Section 5.4 - Emergent Patterns of 2D Structures: We'll quantify and classify new structures, first in 2D, as they arise.
  • Section 5.5 - Patterns in 3D Structures: We'll extend the description that we have in 2D to 3D. These are the assemblies of atoms we observe in bulk crystalline materials.
  • Section 5.6- Navigating 3D Structures - Crystallographic Points: Once we have general descriptions of how assemblies of atoms repeat in 3D space, we'll learn how to navigate these structures by defining points within the context of the unit cell.
  • Section 5.7 - Navigating 3D Structures - Crystallographic Directions: We'll define crystallographic directions within a unit cell.
  • Section 5.8 - Navigating 3D Structures - Crystallographic Planes: We'll define crystallographic planes within a unit cell.
  • Section 5.10 - Working with Common Metallic Crystal Structures: After defining the unit cell and learning how to navigate it, we'll add atoms to create our first crystal structures, starting with rudimentary metal structures.
  • Section 5.11 - Spaces Between the Atoms - Interstitial Sites: It isn't only the positions of the atoms that are important in crystal structures - the empty space between atoms, or interstitial sites - are nearly as important.
  • Section 5.10 - Working with Common Ceramic Crystal Structures: With the tools we develop earlier in the chapter, we'll now discuss common crystalline ceramic structures.
  • Section 5.13 - Degrees of Crystallinity: Finally, we'll define degrees of crystallinity, spanning from amorphous to monocrystalline.
  • Section 5.14 - Feedback and Comments: Please let us know what you think of the chapter by providing feedback in this section.

Outcomes

At the end of this module students should be able to:

  • Predict, model, and interpret what structures arise when larger numbers of atoms or molecules are assembled together.
  • Communicate how atoms assemble into structures by constructing unit cells for regular space-filling atomic assemblies.
  • Create both 2D and 3D crystal structures by translating unit cells and motifs in space.
  • Navigate 2D and 3D crystal structures by identifying crystallographic points, lines, and planes.
  • Understand that there exist symmetry-equivalent points, directions, and planes in crystals and interpret this in context of anisotropic materials behviors.
  • Analyze elemental (only one type of atom) crystal structures (e.g., FCC, BCC, SC) derive atomic positions, densities, unit cell lengths, coordination, and interatomic distances.
  • Identify interstitial positions in crystal structures. Calculate their sizes, positions, and atom-interstitial and interstitial-interstitial distances.