Diffusionless transformations occur when atoms in a crystal move cooperatively and nearly simultaneously, distorting the crystal into a new shape. The martensite transformation is the most famous diffusionless transformation, owing to its importance in steel metallurgy. In a martensitic transformation the change in crystal structure occurs by shears and dilatations, and the atom displacements accommodate the shape of the new crystal. The atoms do not move with independent degrees of freedom, so the change in configurational entropy is negligible or small. The entropy of a martensitic transformation is primarily vibrational (sometimes with electronic entropy, or magnetic entropy for many iron alloys). This chapter begins with a review of dislocations, and how their glide motions can give crystallographic shear. Some macroscopic and microscopic features of martensite are then described, followed by a two-dimensional analog for a crystallographic theory that predicts the martensite “habit plane” (the orientation of a martensite plate in its parent crystal). Displacive phase transitions are explained more formally with Landau theories having anharmonic potentials and vibrational entropy. Phonons are discussed from the viewpoint of soft modes and instabilities of bcc structures that may be relevant to diffusionless transformations.

Phase transformations often begin by nucleation, where a small but distinct volume of material forms with a structure and composition that differ from those of the parent phase. An unfavorable surface bounds the new phase, giving rise to a barrier that must be overcome before thefluctuation in structure and composition can become a stable, growing region of new phase. Chapter 4 develops the thermodynamics of forming a nucleus, with emphasis on the characteristic size and undercooling that are required. Homogeneous and heterogeneous nucleation are explained. The temperature dependence of nucleation is explained. The time dependence of nucleation is discussed in terms of the shape of the free energy barrier that must be crossed by a growing nucleus. There is some discussion of nucleation in multicomponent alloys.

Here nanomaterials are defined as materials with structural features of approximately 10 nm or smaller, i.e., tens of atoms across. Unique physical properties of nanomaterials originate from one or two of their essential features: (1) nanomaterials have high surface-to-volume ratios, and a large fraction of atoms located at, or near, surfaces; (2) nanomaterials confine electrons, phonons, excitons, or polarons to relatively small volumes, altering their energies. Chapter 20 focuses on the thermodynamic functions of nanostructures that determine whether a nanostructure can be synthesized, or if a nanostructure is adequately stable at a modest temperature. The internal energy of nanomaterials is increased by the surfaces, interfaces, or large composition gradients. A nanostructured material generally has a higher entropy than bulk material, however, and at finite temperature the entropy contribution to the free energy can help to offset the higher internal energy term in the free energy F = E – TS. Chapter 20 discusses the structure of nanomaterials, the thermodynamics of interfaces in nanostructures, electron states in nanostructures, and the entropy of nanostructures.

This chapter introduces key concepts that are developed in this textbook. It describes the concept of microstructure and other features of materials that undergo interesting changes with temperature or pressure. These changes are motivated by the thermodynamic free energy, but require a kinetic mechanism for atoms to move. Chemical unmixing and ordering on a crystal lattice are described, and the kinetics of diffusion by vacancies is explained. The free energy is used to explain melting. A summary of essential aspects of thermodynamics and kinetics is given at the end of the chapter, including basic ideas of statistical mechanics and the kinetic master equation.

The structures and dynamics of surfaces affects the chemical reactivity and growth characteristics of materials. Chapter 11 describes atomistic structures of surfaces of crystalline materials, and describes how a crystal may grow by adding atoms to its surface. Most inorganic materials are polycrystalline aggregates, and their crystals of different orientation make contact at “grain boundaries.” Some features of atom arrangements at grain boundaries are explained, as are some aspects of the energetics and thermodynamics of grain boundaries. Grain boundaries alter both the internal energy and the entropy of materials. Surface energy varies with crystallographic orientation, and this affects the equilibrium shape of a crystal. The interaction of gas atoms with a surface, specifically the topic of gas physisorption, is presented.

Chapter 12 discusses the enthalpy and entropy of solid and liquid phases near the melting temperature Tm, and highlights rules of thumb, such as the tendency for the entropy of melting to be similar for different materials. Correlations between Tm and the amplitude of thermal displacements of atoms (“Lindemann rule”), and between Tm and the bulk modulus are presented, but these correlations are semiquantitative at best. Richard's rule for the entropy of melting is more robust. Interface behavior during melting is covered in more detail, including premelting. At a temperature well below Tm, a glass undergoes a type of melting called a “glass transition” which is discussed in more detail in this chapter.Some features of melting in two dimensions are described, which are quite different from melting in three dimensions.

There is a marked kinetic asymmetry between melting and solidification -- the two are quite different as phase transformations. Solidification can occur by different mechanisms that create very different solid microstructures. This chapter emphasizes processes at the solid-liquid interface during solidification, and the microstructure and solute distributions in the newly formed solid. During solidification, a solid-liquid interface moves forward as the liquid is consumed, and the velocity of the interface increases with the rate of heat extraction. Instabilities set in even at relatively small velocity, however, and a flat interface evolves into finger-like columns or tree-like dendrites of growing solid. This instability is driven by the release of latent heat and the partitioning of solute atoms at the solid-liquid interface. Finger-like solids have more surface area, so countering the instability is surface energy. Solidification involves the evolution of several coupled fields. Crystallographic orientation of the growing solid phase is also important for the growth rate and surface energy.

Chapter 15 develops further the concepts underlying precipitation phase transformations that were started in Chapter 14. Atoms move across an interface as one of the phases grows at the expense of the other. The interface, an essential feature of having two adjacent phases, has an atomic structure and chemical composition that are set by local thermodynamic equilibrium, but interface velocity constrains this equilibrium. Interactions of solute atoms with the interface can slow the interface velocity by "solute drag." When an interface moves at a high velocity, chemical equilibration by solute atoms does not occur in the short time when the interface passes by. These issues also pertain to rapid solidification, and extend the ideas of Chapter 13. Solid–solid phase transformations also require consideration of elastic energy and how it evolves during the phase transformation. The balance between surface energy, elastic energy, and chemical free energy is altered as a precipitate grows larger, so the optimal shape of the precipitate changes as it grows. The chapter ends with some discussion of the elastic energy of interstitial solid solutions and metal hydrides.

Introduces the idea of second quantized operators in the many-particle domain, Fock spaces, field operators, and vacuum states, and outlines how canonical transformations can be applied to solve many-body problems. Coherent states, as eigenstates of the annihilation operator, including the development of Grassmann’s algebra and calculus for fermions, are presented.

Derives the spin–orbit interaction from the Dirac equation and discusses its manifestations in electronic structure using the k · p method. The Dresselhaus and Rashba Hamiltonians are developed.

Delineates how the ideas of topological equivalence and adiabatic continuity lead to the emergence of distinct classes of insulator Hamiltonians, and how this, in turn, leads to bulk-boundary correspondence – the connection between bulk topological invariants and edge or surface states. Classification of topologically nontrivial and trivial phases, based on fundamental discrete symmetries and dimensionality, the “tenfold way," is explained. Mapping of d-dimensional Brillouin zones onto a d-dimensional Brillouin torus and Bloch Hamiltonians are defined. and construction of Bloch bundles on the torus base manifold is outlined. Time-reversal symmetry, Kramers’ band degeneracy, “time-reversal invariant momenta,” and the implied vanishing of Berry’s curvature are delineated. The integer quantum Hall effect and the modern theory of polarization are discussed in detail. Z2 topological invariant is derived using the sewing matrix, time-reversal polarization and the non-Abelian Berry connection.

Summarizes elementary building blocks of solid-state physics, including the Born–Oppenheimer approximation. It also reviews time-reversal symmetry and its implications.

Provides detailed analysis of mechanisms of exchange coupling: direct or potential exchange, kinetic exchange, superexchange, polarization exchange, Dzialoshinskii–Moriya, double exchange, and RKKY. The effect of crystal fields and the single-site anisotropy are also discussed.