Abrupt phase transitions

This chapter studies abrupt phase transitions, familiar from boiling water, raindrops, snowflake formation, and frost. At these transitions, the properties change abruptly -- the ice cube and the water in which it floats are at the same temperature and pressure, but have quite different densities and rigidities. The chapter studies the coexistence between two phases by matching their free energies, and discover the Maxwell equal-area construction. It examines the barriers to raindrop formation and discovers nucleation and critical droplet theory. It examines how the transition proceeds after nucleation, and discovers coarsening (familiar from the segregation of oil and water in well-shaken salad dressing), dendrites (snowflakes and frost patterns), and martensitic structures (important in steel). Exercises explore nucleation of dislocations, of cracks, and of droplets in the Ising model; complex free energies and nucleation rates; dendrites in surface growth and snowflakes; and martensites, minimizing sequences, and origami.