Chapter 62: Crystals, Glass, and Phase Transitions

The frozen regimes—crystal and glass—are the two faces of immobility. In a crystal, immobility coexists with maximal topological order: atoms lock into a periodic lattice, and the defect component d₄ ≫ 0. In a glass, immobility coexists with topological disorder: atoms freeze without long-range order, and d₄ ≈ 0. This chapter develops both regimes from the defect tuple, connects crystal periodicity to T² mode structure, derives band theory as extended molecular orbital theory, and classifies phase transitions by their behavior in the defect phase space D.