Chapter 30: Internal Geometry of Crystals

The discussion distinguishes between major types of chemical bonding in solids, explaining ionic bonds (as found in sodium chloride) resulting from electron transfer, covalent bonds (as in diamond) involving electron sharing, and metallic bonds, characterized by valence electrons that are not localized, which explains the high electrical conductivity of metals. To define the repeating atomic arrangement, the chapter uses a two-dimensional "wallpaper" pattern analogy to introduce concepts like the unit cell and periodicity. Expanding to three dimensions, the text describes crystal lattices, focusing on common arrangements like the body-centered cubic and face-centered cubic structures, which are related to efficient close-packing of spheres. A critical exploration of symmetry demonstrates why only specific rotational symmetries—namely one, two, three, four, and six-fold—are possible for a repeating pattern or lattice, leading to the classification of three-dimensional crystals into seven basic systems (including triclinic, hexagonal, and cubic). These internal symmetries dictate the macroscopic physical properties of the crystal, such as its response to polarization and stress. Crucially, the chapter addresses the apparent paradox of metal strength: although the chemical bonds are inherently strong, real metals are often "soft" because they contain dislocations, which are line defects. These defects move easily under stress, facilitating slip and plastic deformation, explaining why imperfect crystals deform far more readily than theoretically perfect ones would. Finally, the mechanics of grain boundaries, dislocations, and recrystallization are visually simulated using the Bragg-Nye bubble raft model, a two-dimensional analogue where floating soap bubbles represent atoms in a lattice.