This chapter covers the analytical methods developed to characterize ordering phenomena in crystal structures. The chapter gives examples of ordering phenomena and discusses models for long-range ordering, such as the Bragg-Williams-Gorsky (B-W-G) model, and for short-range ordering. Examples of ordering and phase separation due to ordering by the B-W-G model are described. The chapter includes an appendix covering the effect of phase separation inversion type.

This chapter reviews the fundamentals of classical nucleation theory, with application examples. The discussion covers the basic subjects of nucleation, spontaneous nucleation in solution, nucleation by inoculation, and nucleation in solids.

This chapter provides a classification of the types of microstructural changes and transformations and then reviews each type. It presents the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation and explains the thermodynamics of eutectic solidification and eutectoid transformation. An appendix covers growth of eutectoid structure in carburized pearlite.

This chapter describes the basics of energy and entropy and “free energy.” Fundamentals of internal energy U , the enthalpy H , entropy S , free energies G , and F of a substance are presented. The chapter also presents the thermal vibration model to promote a better understanding of the U , S , and F of the crystal. It covers basic concepts of thermodynamics of magnetic transition and discusses the role and the meaning of magnetic transition in iron and steel. The chapter concludes with a general discussion on an amorphous phase from a thermodynamic viewpoint.

This chapter explains the idea of solution theory and the nature of mixed materials. The chapter considers approximation of free energy by the regular solution model and sublattice model. It discusses chemical potential and nonrandom distribution based on the interactions between solute atoms.

This chapter explains the significance of the phase diagram and its use in the development of new materials. The chapter describes the basic rules of heterogeneous equilibrium, presents a comparison between liquidus line and solidus line, and provides information on the solubility curve and the binodal curve.

This chapter considers various behaviors of microstructural interfaces from a thermodynamics viewpoint. It discusses energy of surface and interface, the Gibbs-Thomson Effect, grain-boundary segregation, smooth and rough interfaces, and grain growth.

This chapter provides a detailed discussion on the Brownian motion, diffusion coefficient , and Fick's diffusion laws. It presents a review of solid phase diffusion and discusses the mechanism of diffusion and diffusion coefficient.

This chapter explains the distinction between materials and matter through the concept of microstructure. It presents the history of matter science and the establishment of metallography. The chapter provides an overview of the progress of steel technology, progress in synthetic polymers and ceramics, and establishment and development of materials science.

This chapter contains tables providing reference information on physical constants, unit symbols, SI prefixes, the Greek alphabet, and the unit conversion table.