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.

Presents functional integral methods of quantum many-body theory. Starting with Feynman’s path integral, it develops functional integrals of partition functions in imaginary time and extends these techniques to many-body systems. It expands the formulation in the coherent-state basis, and describes the application of the Hubbard–Stratononvich transformation and the saddle-point approximation.

Deals with magnetism in itinerant systems. It starts with the Stoner mean-field theory, as derived from a simple Hubbard model, and Stoner excitations and spin-waves obtained with the aid of RPA. The concept of nesting and spin-density waves is then discussed. This is followed by a detailed presentation of Anderson’s magnetic impurity model and its relation to the Kondo model through the Schrieffer–Wolff transformation. Finally, a detailed account of the Kondo effect and the Kondo resonance is given.

Covers linear response from the one-electron viewpoint, including causality and the Kramers–Kronig relation. It develops the Kubo conductivity formula with special reference to the quantum Hall effect. The longitudinal and transverse dielectric functions are derived, and the ideas of intraband and interband, both direct and indirect, optical transitions are discussed.