Understanding Solids E-Book

Richard J. D. Tilley

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 1257

Veröffentlichungsjahr: 2021

Beschreibung

Explore a comprehensive and illuminating introductory text to the science of solid materials from a leading voice in the field

The newly revised Third Edition of Understanding Solids: The Science of Materials delivers a complete yet concise treatment of the basic properties and chemical and physical behaviors of solid materials. Following a completely revised opening set of chapters in which the basic properties of solids—including atomic structure, chemical bonding, crystallography, and phase relationships—are discussed, the book goes on to describe new developments in the areas of batteries and fuel cells, perovskite solar cells, lighting and displays, nanoparticles, whiskers, and sheets.

The distinguished author has also added sections about organic framework structures, superionic conductors, mechanochemistry, bi-layer graphene, hologram formation and recording, and the optics of nanoparticle arrays and thermochromic materials. Each chapter includes a Further Reading section to help students accumulate additional knowledge on the topic within and new problems have been added throughout the book. Readers will also enjoy the inclusion of:

• A thorough introduction to the states of aggregation, including atoms and bonding, microstructures and phase relationships, and crystal structures and defects
• A comprehensive overview of different categories of solids, including metals, crystalline silicates, inorganic ceramics, and silicate glasses
• An exploration of reactions and transformations, including diffusion and ionic conductivity, phase transformations, and phase reactions
• A treatment of oxidation and reduction, including galvanic cells and chemical analysis

Perfect for undergraduate students in sciences, engineering, and technology, Understanding Solids: The Science of Materials will also earn a place in the libraries of anyone seeking a thoroughly up to date, one-stop reference to the science of solid materials.

Leseprobe

Table of Contents

Cover

Title Page

Copyright

Preface

About the Companion Website

Part I: States of Aggregation

1 Atoms and Bonding

1.1 The Electron Structure of Atoms

1.2 Ionic Bonding

1.3 Covalent Bonding

1.4 Metallic Bonding

1.5 Weak Chemical Bonds

1.6 Computation of Material Properties

Further Reading

Problems and Exercises

Note

2 Microstructures and Phase Relationships

2.1 Macrostructure, Microstructure, and Nanostructure

2.2 The Development of Microstructures

2.3 Phase Diagrams

2.4 Ternary Systems

Reference

Further Reading

Problems and Exercises

3 Crystal Structures and Defects

3.1 Crystal Geometry

3.2 Crystal Structures

3.3 Crystal Planes and Directions

3.4 Crystal Density

3.5 Structural Relationships

3.6 Point Defects

3.7 Linear, Planar, and Volume defects

Reference

Further Reading

Problems and Exercises

Notes

4 Solids: Overview

4.1 Metals

4.2 Crystalline Silicates and Inorganic Ceramic Materials

4.3 Silicate Glasses

4.4 Polymers and Organic Materials

4.5 Composite Materials

Reference

Further Reading

Problems and Exercises

Notes

Part II: Reactions and Transformations

5 Diffusion and Ionic Conductivity

5.1 Self‐Diffusion and Tracer Diffusion

5.2 Non‐steady‐state and Steady‐State Diffusion

5.3 Temperature Variation of Diffusion Coefficient

5.4 The Effect of Impurities

5.5 Random Walk Diffusion

5.6 Diffusion in Solids

5.7 Self‐Diffusion in One Dimension

5.8 Self‐Diffusion in Crystals

5.9 The Arrhenius Equation and Point Defects

5.10 Correlation Factors for Self‐Diffusion

5.11 Ionic Conductivity

5.12 The Relationship Between Ionic Conductivity and Diffusion Coefficient

5.13 Superionic Conductors

Reference

Further Reading

Superionic Conductors: See Also References Therein:

Problems and Exercises

Note

6 Phase Transformations and Reactions

6.1 Sintering

6.2 Phase Transitions

6.3 Displacive and Reconstructive Transitions

6.4 Order–Disorder Transitions

6.5 Martensitic Transformations

6.6 Phase Diagrams and Microstructures

6.7 High Temperature Oxidation of Metals

6.8 Solid‐State Reactions

Further Reading

Problems and Exercises

7 Oxidation and Reduction

7.1 Galvanic Cells

7.2 Chemical Analysis Using Galvanic Cells

7.3 Batteries

7.4 Corrosion

7.5 Electrolysis

7.6 Pourbaix Diagrams

Reference

Further Reading

Problems and Exercises

Notes

Part III: Physical Properties

8 Mechanical Properties of Solids

8.1 Strength and Hardness

8.2 Elastic Moduli

8.3 Deformation and Fracture

8.4 Time‐Dependent Properties

8.5 Nanoscale Properties

8.6 Composite Materials

Further Reading

Problems and Exercises

9 Insulating Solids

9.1 Dielectrics

9.2 Piezoelectrics, Pyroelectrics, and Ferroelectrics

9.3 Ferroelectrics

Reference

Further Reading

Problems and Exercises

Note

10 Magnetic Solids

10.1 Magnetic Materials

10.2 Paramagnetic Materials

10.3 Ferromagnetic Materials

10.4 Antiferromagnetic Materials and Superexchange

10.5 Ferrimagnetic Materials

10.6 Nanostructures

10.7 Magnetic Defects

Further Reading

Problems and Exercises

Note

11 Electronic Conductivity in Solids

11.1 Metals

11.2 Semiconductors

11.3 Metal–Insulator Transitions

11.4 Conducting Polymers

11.5 Superconductivity

11.6 Nanostructures and Quantum Confinement of Electrons

Further Reading

Problems and Exercises

Notes

12 Optical Aspects of Solids

12.1 Light

12.2 Sources of Light

12.3 Refraction

12.4 Reflection

12.5 Scattering and Attenuation

12.6 Diffraction

12.7 Fibre Optics

12.8 Energy Conversion

12.9 Nanostructures

Further Reading

Problems and Exercises

Notes

13 Thermal Properties of Solids

13.1 Heat Capacity

13.2 Thermal Conductivity

13.3 Expansion and Contraction

13.4 Thermoelectric Effects

13.5 The Magnetocaloric Effect

13.6 Thermochromic Effects

References

Further Reading

Problems and Exercises

Note

Part IV: Nuclear Properties of Solids

14 Radioactivity and Nuclear Reactions

14.1 Radioactivity

14.2 Artificial Radioactive Atoms

14.3 Nuclear Decay

14.4 Nuclear Energy

14.5 Nuclear Waste

Further Reading

Problems and Exercises

Appendix A: Periodic Table

Appendix B: Energy Levels and Terms of Many‐Electron Atoms

B.1 Derivation of Atomic Terms

B.2 The Ground State Term of an Atom

B.3 Energy Levels of Many Electron Atoms

Index

End User License Agreement

List of Tables

Chapter 1

Table 1.1 Orbitals of hydrogen‐like atoms.

Table 1.2 Reduced Madelung constants,

α

.

Table 1.3 The geometry of some hybrid orbitals.

Table 1.4 The electron configurations of some homonuclear diatomic molecules.

Table 1.5 Bonds between atoms, ions, and molecules.

Chapter 3

Table 3.1 The crystal systems.

Table 3.2 Interplanar spacing and unit cell volume.

Table 3.3 Structures in terms of anion packing.

Table 3.4 The formation enthalpy of Schottky defects in alkali halide compoun...

Table 3.5 The formation enthalpy of Frenkel defects.

Table 3.6 The Kröger–Vink notation for defects in crystals.

a

Chapter 4

Table 4.1 Allotropic structures of some metals.

Table 4.2 A summary of silicate structures.

Table 4.3 Some silicate glasses.

Table 4.4 Glass viscosity.

Table 4.5 Addition polymers.

Table 4.6 Typical Portland cement constituents.

Chapter 5

Table 5.1 Solutions of the diffusion equation.

Table 5.2 Values of the error function.

a

Table 5.3 Some representative values for self‐diffusion coefficients.

a

Table 5.4 Approximate enthalpy values for the formation and movement of defec...

Table 5.5 Correlation factors for self‐diffusion.

Chapter 7

Table 7.1 Standard reduction potentials at 25 °C.

Chapter 8

Table 8.1 Representative values of Young's modulus and Poisson's ratio.

Chapter 9

Table 9.1 The relative permittivity and refractive index of some crystals.

Table 9.2 Ferroelectrics and antiferroelectrics.

Chapter 10

Table 10.1 Calculated and observed magnetic dipole moments for the lanthanoid...

Table 10.2 The magnetic properties of the 3d‐transition metal ions.

Table 10.3 Ferromagnetic and antiferromagnetic compounds.

Table 10.4 Magnetic moments and electron configurations of the ferromagnetic ...

Chapter 11

Table 11.1 Approximate values for the band gap of some semiconductors.

Table 11.2 Some cuprate superconducting oxides.

Table 11.3 Homologous series of cuprate superconductors.

Chapter 12

Table 12.1 The visible spectrum.

Table 12.2 Luminescence.

Table 12.3 Refractive indices.

Table 12.4 Refractive coefficients for some oxides.

a

Table 12.5 The colour of a thin film in white light.

Chapter 13

Table 13.1 The Debye temperature and room temperature heat capacity of some e...

Table 13.2 Coefficients of thermal conductivity and thermal expansion.

Chapter 14

Table 14.1 Nuclides and particles in nuclear reactions.

Table 14.2 Periodic Table group seven elements.

Table 14.3 Half‐lives of some radioisotopes.

List of Illustrations

Chapter 1

Figure 1.1 Electron energy levels of the H atom.

Figure 1.2 Schematic energy level diagram for a light, hydrogen‐like atom.

Figure 1.3 The probability of finding an s electron at a distance

r

from the...

Figure 1.4 The boundary surfaces of the p orbitals: (a) p

x

; (b) p

y

; (c) p

z

....

Figure 1.5 The boundary surfaces of the d orbitals: (a) d

xy

; (b) d

xz

; (c) d

y

...

Figure 1.6 The evolution of the electron energy levels of an atom with a 3d

2

Figure 1.7 Ionic radii, nm. Cation radii apply to ions octahedrally coordina...

Figure 1.8 The total potential energy between two monovalent ions as a funct...

Figure 1.9 Covalent bond formation: (a) two H atoms with opposed electron sp...

Figure 1.10 Covalent bonding: (a) σ bonding via overlap of s and p orbitals;...

Figure 1.11 (a) The 2s and 2p orbitals on C; (b) four sp

3

hybrid orbitals; (...

Figure 1.12 The formation of molecular orbitals in an H

2

molecule.

Figure 1.13 Schematic molecular orbital energy level diagram for homonuclear...

Figure 1.14 Molecular orbitals formed by a more metallic atom A and a less m...

Figure 1.15 The schematic development of energy bands from delocalised molec...

Figure 1.16 Schematic development of energy bands from atomic orbitals for m...

Figure 1.17 The energy levels and allowed wavelengths of an electron wave co...

Figure 1.18 The relationship between energy,

E

and wavenumber,

k

, for an ele...

Figure 1.19 The Fermi function,

P

(

E

).

Figure 1.20 (a) The one‐dimensional free‐electron

E

vs.

k

curve broken into ...

Figure 1.21 The bonding in a molecule, M

2

, and a solid metal.

Figure 1.22 Schematic development of energy bands from isolated atoms for so...

Figure 1.23 Schematic development of energy bands from isolated atoms for ge...

Figure 1.24 The boiling points of the alkanes, C

n

H

2

n

 + 2

, pl...

Figure 1.25 The Lennard‐Jones potential between two atoms separated by a dis...

Chapter 2

Figure 2.1 The cubic unit cells of (a) tungsten; (b) copper.

Figure 2.2 Silicate glasses, schematic: (a) structure of an SiO

4

tetrahedron...

Figure 2.3 Polythene: chemical formula representation of (a) linear polythen...

Figure 2.4 Sheet‐like nanomaterials: (a) graphene; (b) a single boron nitrid...

Figure 2.5 (a) C nanotube; (b) double tube arrangement, schematic.

Figure 2.6 Nanoparticles: (a) C

60

buckyball; (b) Au core nanoparticle with N...

Figure 2.7 Electronic semiconductor nanostructures: (a) a quantum well; (b) ...

Figure 2.8 Polycrystalline solids: (a) granite; mica (black), quartz and fel...

Figure 2.9 The generalised form of a one‐component phase diagram.

Figure 2.10 The phase diagram for water, schematic.

Figure 2.11 (a) The cooling curve generated as a sample of water is slowly c...

Figure 2.12 The copper (Cu)–nickel (Ni) phase diagram at 1 atm pressure.

Figure 2.13 Composition determination when two phases are present.

Figure 2.14 The lead (Pb)–tin (Sn) phase diagram at 1 atm pressure.

Figure 2.15 Composition determination in the Pb–Sn system.

Figure 2.16 The CaSiO

3

(wollastonite)–CaAl

2

O

4

phase diagram at 1 atm pressur...

Figure 2.17 The V

2

O

5

–MgO phase diagram at 1 atm pressure.

Figure 2.18 The iron‐rich region of the iron–carbon existence diagram. (The ...

Figure 2.19 (a) The general form of an isobaric ternary phase diagram; (b) R...

Figure 2.20 The simplified WO

3

–WO

2

–ZrO

2

phase diagram; (b) determination of ...

Figure 2.21 The FeO–Fe

2

O

3

–TiO

2

system at: (a) approximately 500 °C; (b) appr...

Figure 2.22 Approximate phase diagram for the MgO–Al

2

O

3

–SiO

2

system.

Chapter 3

Figure 3.1 The reference axes used to characterise the crystal systems.

Figure 3.2 The 14 Bravais lattices. (Note that the lattice points are exagge...

Figure 3.3 (a) A regular TiO

6

octahedron. (b) A regular SiO

4

tetrahedron.

Figure 3.4 The positions of an atom in a unit cell, specified as fractions o...

Figure 3.5 The face‐centred cubic (fcc, A1) structure.

Figure 3.6 The body‐centred cubic (bcc, A2) structure.

Figure 3.7 The hexagonal close‐packed (hcp, A3) structure.

Figure 3.8 The structure of diamond: (a) unit cell; (b) cell viewed approxim...

Figure 3.9 The structure of graphite: (a) unit cell; (b) projection down the...

Figure 3.10 The halite (NaCl) structure: (a) perspective view; (b) projectio...

Figure 3.11 The cubic perovskite structure SrTiO

3

.

Figure 3.12 The MgAl

2

O

4

normal spinel structure: (a) projected down the

c

‐ax...

Figure 3.13 Vegard's law, relating unit cell lattice parameters to compositi...

Figure 3.14 Miller indices of crystal planes: (a) (100); (b) (200); (c) (300...

Figure 3.15 Miller indices of crystals planes: (a) (110); (b) (101); (c) (01...

Figure 3.16 Miller indices of crystal planes: (a) (110) and (

10); (b) (1

0)...

Figure 3.17 Miller indices of crystal planes: (a) (111); (b) (1

1).

Figure 3.18 Determination of Miller indices: (a), (b), (320); (c), (d), (3

0...

Figure 3.19 Miller indices in hexagonal crystals.

Figure 3.20 (a) Directions in a lattice; (b) parallel directions have the sa...

Figure 3.21 Directions in the (001) plane of a hexagonal crystal.

Figure 3.22 Hexagonal close‐packing (hcp) of spheres: (a) single layer; (b) ...

Figure 3.23 Hexagonal close‐packing unit cell: (a) basal layer; (b) perspect...

Figure 3.24 Cubic close‐packing (ccp) of spheres. The layers follow the sequ...

Figure 3.25 The cubic close‐packing (ccp) unit cell: (a) layers A and B; (b)...

Figure 3.26 Sites between close‐packed layers of spheres: (a), (b) tetrahedr...

Figure 3.27 Representations of tetrahedra: (a), (b) perspective view; (c), (...

Figure 3.28 Representations of octahedra: (a), (b) perspective view; (c), (d...

Figure 3.29 The structure of α‐quartz (SiO

2

) projected down the

c

‐axis. The ...

Figure 3.30 (a) The cubic ReO

3

structure represented as corner‐shared ReO

6

o...

Figure 3.31 Idealised point defects in a pure monatomic crystal: (a) vacancy...

Figure 3.32 The Gibbs energy of a pure crystal as a function of the number o...

Figure 3.33 Impurity or dopant point defects in a crystal, schematic: (a) su...

Figure 3.34 Point defects in an ionic crystal, formula MX, schematic: (a) Sc...

Figure 3.35 The structure of calcia‐stabilised zirconia, schematic. The unit...

Figure 3.36 The layered structure of TiS

2

, schematic: (a) without and (b) co...

Figure 3.37 (a) an edge dislocation in a metal crystal: (b), (c) a circuit a...

Figure 3.38 Screw dislocations: (a), (b) screw dislocation formed by displac...

Figure 3.39 Formation of dislocation loops: (a) the aggregation of vacancies...

Figure 3.40 Planar defects in crystals: (a) grain boundary; (b) twin plane; ...

Figure 3.41 A precipitate formed by the clustering of impurity atoms in a cr...

Chapter 4

Figure 4.1 The crystal structures and unit cell parameters (nm) of the metal...

Figure 4.2 Metallic radii, for 12‐coordination.

Figure 4.3 The crystal structure of: (a) disordered CuAu; (b) ordered Cu

3

Au;...

Figure 4.4 Octahedral (a) and tetrahedral (b) sites in the face‐centred cubi...

Figure 4.5 Octahedral (a) and tetrahedral (b) sites in the hexagonal close‐p...

Figure 4.6 Octahedral (a) and tetrahedral (b) sites in the body‐centred cubi...

Figure 4.7 The glass forming region in the (Fe

1−

x

Cr

x

Mo

y

)

75

C

15

B

10

phase...

Figure 4.8 Electron diffraction pattern from the quasicrystalline alloy Al

72

Figure 4.9 Icosahedra: (a) icosahedral geometry; (b) part of the As

3

Co skutt...

Figure 4.10 Icosahedra, arranged with the same orientation, but not on a lat...

Figure 4.11 Linked [SiO

4

] units found in ionic silicates: (a) isolated (SiO

4

Figure 4.12 (a) Single (SiO

3

) and (b) double (Si

4

O

11

) chains.

Figure 4.13 (a) Single sheet of corner‐linked (SiO

4

) tetrahedra; (b) the sam...

Figure 4.14 The structure of clays and related minerals: (a) single layer of...

Figure 4.15 The structures of some clay‐ and mica‐related minerals formed fr...

Figure 4.16 (a) Truncated octahedron; (b) sodalite unit, with oxygen atoms o...

Figure 4.17 The structure of alumina, Al

2

O

3

: (a) projected close to [001]; (...

Figure 4.18 Cubic calcia‐stabilised zirconia: (a) unit cell; (b) the structu...

Figure 4.19 The random network model of corner‐linked (SiO

4

) tetrahedra in a...

Figure 4.20 Specific volume vs. temperature curves: (a) crystalline solid wi...

Figure 4.21 Viscosity of a soda‐lime glass: (a) viscosity vs. temperature; (...

Figure 4.22 Angel plot of fragility. The curves are for silica and soda‐lime...

Figure 4.23 Crystal nucleation (a) and growth (b, c) in a glass ceramic, sch...

Figure 4.24 The polymerisation of ethylene, schematic: (a) a single monomer ...

Figure 4.25 (a, b) The structure of a tetrahedral CH

2

unit in a polymer chai...

Figure 4.26 The formation of the polyester PET, schematic.

Figure 4.27 Formation of nylon, schematic: (a) nylon 66; (b) nylon 6. The ca...

Figure 4.28 Epoxy resins: (a) epoxide group; (b) a small diepoxy molecule; (...

Figure 4.29 Reaction of molecules to give cross‐linked polymers.

Figure 4.30 Molar mass of a polymer. (a) Idealised distribution:

M

n

, number ...

Figure 4.31 Polymer chain geometries, schematic: (a) linear; (b) branched; (...

Figure 4.32 (a) Polymer chains in polyethylene, schematic; (b) folded chains...

Figure 4.33 Schematic structure of a spherulite in a polymer such as polythe...

Figure 4.34 Polymer chains: (a) perspective view of an isotactic polymer cha...

Figure 4.35 Schematic polymer geometry: (a) alternating copolymer; (b) rando...

Figure 4.36 Elastomer, schematic: (a) unstretched; and (b) stretched.

Figure 4.37 Rubber: (a) isoprene; (b) bond redistribution and polymerisation...

Figure 4.38 The formation of cross‐links between molecules as a result of vu...

Figure 4.39 Synthetic elastomers: (a) neoprene; and (b) nitrile rubber.

Figure 4.40 Polymerisation mechanisms: (a) step growth; (b) chain growth, A*...

Figure 4.41 The generation of free radicals (*) by bond breaking: (a) an azi...

Figure 4.42 Chain termination: (a) two chains meeting; (b) disproportionatio...

Figure 4.43 Metallocene catalysis: (a) the C atom framework of [C

5

H

5

]

−

Figure 4.44 MOFs: (a) schematic structure, consisting of metal nodes and org...

Figure 4.45 Covalent organic frameworks: (a) DBA; (b) HHTP; (c) MOF‐5; (d) D...

Figure 4.46 The basic tetrahedral unit found in zeolitic imidazolate framewo...

Figure 4.47 Fibre‐reinforced composites: (a) aligned fibres; (b) random orie...

Figure 4.48 The approximate relative strengths of the components of Portland...

Chapter 5

Figure 5.1 Self‐diffusion of atoms in a solid: (a) initial state; (b) after ...

Figure 5.2 Diffusion couple formed by two MgO crystals separated by a film o...

Figure 5.3 Diffusion profiles: (a), (b), (c), gradually increasing heating t...

Figure 5.4 The straight‐line graph of ln 

c

vs.

x

2

from a diffusion experimen...

Figure 5.5 Geometries for non‐steady‐state diffusion: (a), (b), the concentr...

Figure 5.6 Steady‐state diffusion: (a) gas diffusing through a porous solid;...

Figure 5.7 Arrhenius plot of ln 

D

vs. 1/

T

.

Figure 5.8 A form of the Arrhenius equation found for crystals with lower (l...

Figure 5.9 Computed random walk in three‐dimensions.

Figure 5.10 One‐dimensional random walks of 100 steps of length

a

. The total...

Figure 5.11 The probability of a diffusing atom arriving at a point

ma

after...

Figure 5.12 Self‐diffusion mechanisms: v, vacancy; i, interstitial; iy, inte...

Figure 5.13 Impurity diffusion mechanisms; v, vacancy; e, exchange; r, ring;...

Figure 5.14 Diffusion mechanisms: (a) a crystal containing Schottky defects;...

Figure 5.15 (a) Atom diffusion from one stable position to another; (b) The ...

Figure 5.16 Two adjacent planes in a crystal, containing

n

1

and

n

2

diffusing...

Figure 5.17 The variation of Arrhenius plots with impurity content.

D

, diffu...

Figure 5.18 Correlated motion during vacancy diffusion: (a) a vacancy can ju...

Figure 5.19 Energy barriers to be surmounted by an ion during ionic conducti...

Figure 5.20 Arrhenius plot of ln (σ

T

) vs. 1/

T

for ionic conductivity in an a...

Figure 5.21 The structure of α‐AgI: (a) body‐centred cubic arrangement of I

−

...

Figure 5.22 (a) Idealised β‐alumina structure projected down [110] drawn as ...

Figure 5.23 Possible correlated jumps to move an Na

+

pair in (a) to that...

Figure 5.24 The fluorite structure: (a) projection of the structure down the...

Figure 5.25 The tunnel framework in NASICON phases.

Chapter 6

Figure 6.1 Initial stages in sintering: (a) Initial compact of slightly unev...

Figure 6.2 Sintering via vapour transport (a, b) does not cause shrinkage. S...

Figure 6.3 (a) Material transfers from hills to valleys during vapour‐phase ...

Figure 6.4 Definitions of (a) neck radius,

x

, and (b) sphere radius,

r

, used...

Figure 6.5 First‐order transitions: (a) variation of molar Gibbs energy with...

Figure 6.6 Second‐order transitions: (a) variation of molar Gibbs energy wit...

Figure 6.7 Displacive transitions, schematic: (a) undistorted octahedra; (b)...

Figure 6.8 Displacive transition in La

2

CuO

4

: (a) The idealised structure of ...

Figure 6.9 Displacive transition in CaTiO

3

: (a) room temperature structure; ...

Figure 6.10 A reconstructive transition, in which components are rearranged ...

Figure 6.11 A topotactic reconstructive transformation in which the …ABAB… p...

Figure 6.12 The idealised structure of (a) TiS

2

; (b) phases with composition...

Figure 6.13 Orientational transformations: (a, b) alternative orientations o...

Figure 6.14 (a) Two unit cells of the cubic face‐centred cubic structure, th...

Figure 6.15 Schematic crystallographic changes occurring during the formatio...

Figure 6.16 (a) The unconstrained transformation of austenite (γ phase) to m...

Figure 6.17 The shape‐change caused by deformation (a, b) can be minimised b...

Figure 6.18 Hysteresis (schematic) between martensite start and finish tempe...

Figure 6.19 The structural relationship between the forms of zirconia.

Figure 6.20 Part of the phase diagram of the Ti–Ni system.

Figure 6.21 The CsCl structure of the high‐temperature form of TiNi: (a) cub...

Figure 6.22 (a) A stack of unit cells of TiNi projected down [110]. Shear di...

Figure 6.23 The sequence of events taking place during deformation and shape...

Figure 6.24 (a–e) The progressive recovery of the original shape of a deform...

Figure 6.25 Cooling a sample of composition

c

in the Cu–Ni system: (a) liqui...

Figure 6.26 Microstructures of a solidified Cu–Ni allot: (a) slow cooling; (...

Figure 6.27 The microstructure of solidified Pb–Sn alloys: (a) the Pb–Sn pha...

Figure 6.28 The microstructure of solidified Pb–Sn alloys: (a) the Pb–Sn pha...

Figure 6.29 The microstructure of solidified Pb–Sn alloys: (a) the Pb–Sn pha...

Figure 6.30 (a) The existence diagram of the Fe–C system. (b) Microstructure...

Figure 6.31 (a) The existence diagram of the Fe–C system. (b) Microstructure...

Figure 6.32 (a) The existence diagram of the Fe–C system. (b) Microstructure...

Figure 6.33 Oxide formation on a metal surface, schematic: (a) physical abso...

Figure 6.34 Growth of an oxide film on a metal surface: (a) diffusion of met...

Figure 6.35 Mechanisms of spinel formation: (a) initial state; (b) diffusion...

Figure 6.36 Markers used to determine the mechanism of MgAl

2

O

4

formation: (a...

Figure 6.37 Photoresists, schematic: (a) negative photoresist; (b) positive ...

Figure 6.38 C

120

dimers produced by milling C

60

monomers.

Chapter 7

Figure 7.1 The components of a galvanic cell.

Figure 7.2 Daniell cell, schematic.

Figure 7.3 (a) A glass electrode for the measurement of pH. (b) Practical ar...

Figure 7.4 Arrangement of an ion selective electrode, schematic. (b) Practic...

Figure 7.5 The ‘rocking chair’ operation of a secondary battery, schematic: ...

Figure 7.6 Section through a zinc‐carbon battery, schematic.

Figure 7.7 Section through an alkaline battery, schematic.

Figure 7.8 Section through a lithium coin cell primary battery, schematic.

Figure 7.9 Li‐air battery, schematic

Figure 7.10 Fuel cells, schematic: AFC, alkaline fuel cell; PEMFC, proton ex...

Figure 7.11 Solid oxide fuel cells: (a) planar‐design; (b) tubular design; (...

Figure 7.12 A single cell in a lead‐acid battery, schematic.

Figure 7.13 The original configuration of a Li‐ion cell in discharge operati...

Figure 7.14 Li‐ion cell electrode reactions: (a, b) anode: the C layer stack...

Figure 7.15 The advance and retreat operation of a dual‐ion secondary batter...

Figure 7.16 Dissimilar metal corrosion of a steel rivet in contact with copp...

Figure 7.17 Protective galvanizing: (a) a perforation in the zinc coating ca...

Figure 7.18 Differential aeration leading to pitting in steel: (a) initial s...

Figure 7.19 Crevice corrosion due to differential aeration: (a) initial situ...

Figure 7.20 The components of an electrolytic cell.

Figure 7.21 Nickel electroplating: the nickel anode is dissolved and transpo...

Figure 7.22 The FCC Cambridge cell for the production of titanium, schematic...

Figure 7.23 Pourbaix diagram showing the stability field of water.

Figure 7.24 Pourbaix diagram showing the stable species in the iron–water–ox...

Figure 7.25 Generalised Pourbaix diagram showing the stable species in a sys...

Figure 7.26 Simplified version of a Pourbaix diagram showing the range of co...

Chapter 8

Figure 8.1 Mechanical loading of solids: (a) tension; (b) compression; (c) s...

Figure 8.2 A rod in tension: (a) initial state; (b) final state.

Figure 8.3 Three‐point bend testy for ceramic samples: (a) sideways view; (b...

Figure 8.4 Engineering stress‐strain curves, schematic: (a) brittle and slig...

Figure 8.5 (a) Young's modulus; (b) secant modulus; (c) tangent modulus.

Figure 8.6 Toughness of a solid: curve C represents the toughest solid.

Figure 8.7 Engineering stress–strain curve, schematic, for a Nitinol shape‐m...

Figure 8.8 Hardness indenters.

Figure 8.9 Schematic relationship between Vickers hardness and shear modulus...

Figure 8.10 Elastic moduli: (a) initial dimensions; (b) specimen after appli...

Figure 8.11 (a) The lattice potential energy

U

as a function of the atomic s...

Figure 8.12 Elastic moduli: (a) initial state; (b) after application of shea...

Figure 8.13 Waves in solids, schematic: (a) longitudinal waves; (b) transver...

Figure 8.14 The pulse‐echo technique for the determination of elastic moduli...

Figure 8.15 Fracture surfaces: (a) cleavage fracture of single crystal silic...

Figure 8.16 Stress in a solid at: (a) an elliptical pore; (b) an elliptical ...

Figure 8.17 Plastic deformation: (a) the permanent distortion of the materia...

Figure 8.18 Slip: (a, b) slip following the application of a shear stress; (...

Figure 8.19 Application of shear stress to a crystal containing an edge disl...

Figure 8.20 (a) The (111) plane in a crystal of a metal with the face‐centre...

Figure 8.21 A (110) slip‐plane in the halite (NaCl) structure.

Figure 8.22 Schematic engineering stress‐strain curve for a carbon steel.

Figure 8.23 Deformation of a semi‐crystalline polymer: (a) unstressed state;...

Figure 8.24 Metal ductility: (a) schematic engineering stress vs. engineerin...

Figure 8.25 (a) A fractured semi‐ductile steel tensile test specimen showing...

Figure 8.26 Polymer elongation: (a) schematic engineering stress vs. enginee...

Figure 8.27 Dislocation multiplication at a Frank–Read source: a dislocation...

Figure 8.28 Stress cycles: (a) irregular; (b) positive sinusoidal cycle; (c)...

Figure 8.29 Stress amplitude plotted against log (number of cycles to failur...

Figure 8.30 Fatigue failure: (a) stage 1, initial crack formation; (b) stage...

Figure 8.31 A normal creep curve for a solid subjected to constant load at a...

Figure 8.32 The effect of temperature on creep.

Figure 8.33 Creep mechanisms: (a) Coble creep: atoms diffuse along grain bou...

Figure 8.34 The structures of solid lubricants: (a) graphite; (b) graphite f...

Figure 8.35 An auxetic network in which the links between elements of the st...

Figure 8.36 A solid composed of rigid blocks of crystal linked by bonds of c...

Figure 8.37 Auxetic β‐brass: (a) the CsCl structure of β‐brass; strong bonds...

Figure 8.38 Nanoindentation: (a) indentation of a thin film; (b) schematic u...

Figure 8.39 Aligned fibre composites: (a) longitudinal load; (b) transverse ...

Figure 8.40 Layered materials: (a) longitudinal (parallel) tension; (b) tran...

Figure 8.41 Young's modulus of a composite, schematic: (a) configuration of ...

Chapter 9

Figure 9.1 The range of electronic conductivity in solids.

Figure 9.2 Capacitors: (a) charges will accumulate on metal plates due to an...

Figure 9.3 In an applied electric field,

E

0

, an insulator gains a surface ch...

Figure 9.4 Polarisation: (a) electronic; (b) ionic; (c) orientational. Dipol...

Figure 9.5 The contribution of dipoles, ions and electrons to the polarisabi...

Figure 9.6 Schematic relationship between insulating solids:

E

is an applied...

Figure 9.7 The relationship between point‐group symmetry and piezoelectric a...

Figure 9.8 The structure of hexagonal ZnS (wurtzite): (a) a ZnS

4

tetrahedron...

Figure 9.9 Piezoelectricity: (a) a force applied to a tetrahedron along a bo...

Figure 9.10 Piezoelectricity in quartz: (a) Part of the structure of room‐te...

Figure 9.11 Quartz crystals: (a) section through a crystal normal to the

c

‐a...

Figure 9.12 (a) dipoles present in a tetrahedral unit of PVF, poly(vinyl flu...

Figure 9.13 The electric dipoles present in (a) chains of nylon 6; (b) chain...

Figure 9.14 The crystal structures, schematic, of two forms of PVF

2

viewed d...

Figure 9.15 The α‐helix, schematic: (a) the succession of carbon and nitroge...

Figure 9.16 Ferroelectric crystal formation, schematic: (a) a cation‐centred...

Figure 9.17 Variation of potential energy vs. position for cation displaceme...

Figure 9.18 Two domains formed by differing alignment of electric dipoles in...

Figure 9.19 Antiparallel arrangement of electric dipoles in an antiferromagn...

Figure 9.20 Hysteresis behaviour of the polarisation,

P

, vs. applied electri...

Figure 9.21 Domain growth in ferroelectric BiFeO

3

: (a) (001) single domain s...

Figure 9.22 Ferroelectric behaviour near to the Curie temperature: (a) first...

Figure 9.23 The Curie–Weiss behaviour of a ferroelectric above the Curie tem...

Figure 9.24 Hydrogen bonds (dashed) in ferroelectrics: (a, b) below the Curi...

Figure 9.25 Ferroelectric KH

2

PO

4

: (a) skeleton of the room temperature struc...

Figure 9.26 Ferroelectricity in sodium nitrite, NaNO

2

: (a) the planar nitrit...

Figure 9.27 The barium titanate, BaTiO

3

, structure: (a) cubic paraelectric h...

Figure 9.28 The phase diagram of the PbZrO

3

–PbTiO

3

(PZT) system. The space g...

Figure 9.29 Relaxor ferroelectric properties, schematic: (a) variation of re...

Figure 9.30 A ferroelectric superlattice composed of

m

 = 2 unit cells of SrT...

Figure 9.31 The flexoelectric effect: (a) evolution of the potential energy ...

Chapter 10

Figure 10.1 Magnetic materials in a Gouy balance: (a) electromagnet off; (b)...

Figure 10.2 Weak magnetic materials in an external field: (a) no solid prese...

Figure 10.3 Behaviour of a diamagnetic solid (a) in no field; (b) in an appl...

Figure 10.4 (a, b) Behaviour of a paramagnetic solid in an applied magnetic ...

Figure 10.5 (a) Magnetic dipole ordering in a ferromagnetic solid; (b) tempe...

Figure 10.6 (a) Magnetic dipole ordering in an antiferromagnetic solid; (b) ...

Figure 10.7 (a) Magnetic dipole ordering in a ferrimagnetic solid; (b) tempe...

Figure 10.8 Ordered arrays of magnetic dipoles arranged on a cubic lattice: ...

Figure 10.9 Cations in (a) an anion octahedron; (b) an anion tetrahedron.

Figure 10.10 The crystal field splitting, Δ (tet) or 10 Dq (tet) and Δ (oct)...

Figure 10.11 The electron configurations possible for d

n

cations in an octah...

Figure 10.12 Splitting of atomic energy levels in a magnetic field.

Figure 10.13 The density of states for electrons in a metal: (a) in the abse...

Figure 10.14 Variation of the relative spontaneous magnetisation

M

/

M

s

as a f...

Figure 10.15 The Bethe

–

Slater curve for the magnitude of the exchange ...

Figure 10.16 Schematic diagram of energy band overlap of 3d, 4s, and 4p orbi...

Figure 10.17 Ferromagnetic domains: (a) Weiss domains, schematic; (b) domain...

Figure 10.18 A domain (Bloch) wall between two magnetic domains, schematic....

Figure 10.19 The

B

–

H

(hysteresis) loop of a ferromagnetic solid.

Figure 10.20 Schematic

B

–

H

loops for soft and hard magnetic solids.

Figure 10.21 (a) The room temperature face‐centred cubic structure of Mn

3

Pt;...

Figure 10.22 Superexchange between Ni

2+

and O

2−

(schematic) leadin...

Figure 10.23 Schematic representation of the magnetic spin arrangement in Ba...

Figure 10.24 Double exchange (electron transfer) between Fe

2+

and Fe

3+

...

Figure 10.25 (a) Films less than a domain wide have magnetic dipoles aligned...

Figure 10.26 A single sheet of the CrX

3

structure (X = Cr, Br, I).

Figure 10.27 Part of an

m

 = 

n

 = 3 magnetic LaMnO

3

/LaNiO

3

superlattice in a (...

Figure 10.28 Photoinduced spin crossover in transition metal cations: (a) pr...

Figure 10.29 Bound magnetic polarons, schematic: (a) one bound magnetic pola...

Figure 10.30 Possible electron spin configurations for Co

3+

(3d

6

) cation...

Figure 10.31 Double exchange between Mn

3+

and Mn

4+

high spin (HS) ca...

Figure 10.32 Electron configurations possible for Mn cations in an octahedra...

Chapter 11

Figure 11.1 Schematic energy band representations of materials: (a) insulato...

Figure 11.2 Free electrons in a one‐dimensional metal: (a) energy vs. wave v...

Figure 11.3 The circular Fermi surface of a two‐dimensional metal, dots repr...

Figure 11.4 The variation of the resistivity of a metal with temperature, sc...

Figure 11.5 The variation of the resistivity of alloys with concentration of...

Figure 11.6 The variation of resistivity vs. temperature for an intrinsic se...

Figure 11.7 Impurities in a crystal of silicon: (a) donor (P) atoms; (b) don...

Figure 11.8 The position of the Fermi energy,

E

F

, in semiconductors: (a) int...

Figure 11.9 The position of the Fermi energy,

E

F

, in a semiconductor at ordi...

Figure 11.10 The temperature variation of the position of the Fermi energy,

Figure 11.11 Arrangement of the four‐point probe method of measurement of re...

Figure 11.12 Measurement of the Hall effect, schematic: (a) reference axes; ...

Figure 11.13 The p‐n junction schematic: (a) energy bands of separate p‐type...

Figure 11.14 Band structure across a p–n junction: (a) under forward bias; (...

Figure 11.15 Ideal current–voltage curve for a p–n junction.

Figure 11.16 The currents flowing across a p–n junction under forward bias....

Figure 11.17 Weakly interacting atoms: (a) ground state with one localised e...

Figure 11.18 The (slightly idealised) structure of Ca

2

RuO

4

projected down [0...

Figure 11.19 Part of a conjugated hydrocarbon molecule (schematic) in which ...

Figure 11.20 The structures of polyacetylenes, schematic: (a) acetylene (eth...

Figure 11.21 Conjugated polymers: (a) a chain of isolated half‐occupied p or...

Figure 11.22 Distortion of a polymer chain: (a) delocalized orbitals lead to...

Figure 11.23 Variation of the conductivity of polyacetylene with iodine dopa...

Figure 11.24 Variation of the conductivity of polyacetylene doped with iodin...

Figure 11.25 A soliton in

trans

‐polyacetylene, schematic. The shaded ellipse...

Figure 11.26 Superconducting transition temperatures.

Figure 11.27 The Meissner effect: (a) normal metal or superconducting metal ...

Figure 11.28 The variation of superconductivity with external magnetic field...

Figure 11.29 A Type II superconductor in the mixed state.

Figure 11.30 The temperature–current–magnetic field phase space delimiting s...

Figure 11.31 Cooper pairs: (a) a single electron passing through a supercond...

Figure 11.32 A dc SQUID: (a) the circuit consists of a loop of superconducto...

Figure 11.33 The crystal structure of La

2

CuO

4

. The

c

‐axis is vertical.

Figure 11.34 The phase region supporting superconductivity for La

2−

x

Sr

Figure 11.35 Comparison of the structures of (a) LaCuO

4

and (b) Nd

2

CuO

4

.

Figure 11.36 The crystal structures of: (a) YBa

2

Cu

3

O

7

; (b) YBa

2

Cu

3

O

6

.

Figure 11.37 The variation of the superconducting transition temperature

T

c

...

Figure 11.38 Superconducting sheets found in cuprate superconductors: (a) a ...

Figure 11.39 Doping into the charge reservoir layers of a cuprate supercondu...

Figure 11.40 Idealised structures of the cuprate superconductors: (a) Bi

2

Sr

2

Figure 11.41 Quantum wells: (a) a single quantum well in gallium arsenide, G...

Figure 11.42 The first three energy levels for an electron trapped in a one‐...

Chapter 12

Figure 12.1 The electromagnetic spectrum; the visible portion extends from a...

Figure 12.2 The electric field of a light wave represented as a sinusoidal w...

Figure 12.3 The interference of light waves: (a, b) two waves in step add to...

Figure 12.4 Absorption and emission of radiation: (a) light absorption; (b) ...

Figure 12.5 Black body emission spectra.

Figure 12.6 Fluorescent lamps: electrons from the cathode collide with mercu...

Figure 12.7 The principle of LED operation. Electrons and holes combine in t...

Figure 12.8 Photon absorption and emission in direct (a, b) and indirect (c,...

Figure 12.9 Principle of an organic electroluminescent device (OLED); (a) th...

Figure 12.10 An MEH‐PPV OLED: (a) energy level diagram for the anode, emitti...

Figure 12.11 The energy levels involved in the ruby laser: (a) spin‐allowed ...

Figure 12.12 The main transitions in four‐level laser operation.

Figure 12.13 The energy levels of most importance in the neodymium laser.

Figure 12.14 Semiconductor laser, schematic.

Figure 12.15 Refraction of a light beam on entering a transparent solid.

Figure 12.16 The effect of refractive index on the wavelength of light.

Figure 12.17 Total internal reflection of a beam of light: (a), (b)

θ

l...

Figure 12.19 Phase change on reflection at a surface of higher refractive in...

Figure 12.18 The reflection of light from a surface: (a) angles of incidence...

Figure 12.20 Multiple reflections at the upper and lower surfaces of a thin ...

Figure 12.21 The sinusoidal variation of the reflectivity of a thin film.

Figure 12.22 Reflection at a thin film in air: (a) perpendicular incidence (...

Figure 12.23 The approximate colour of a thin film when viewed from directly...

Figure 12.24 A quarter‐wave stack of alternating layers of high and low refr...

Figure 12.25 Interference filters: (a) shortpass; (b) longpass; (c) bandpass...

Figure 12.26 Scattering: (a) Rayleigh scattering; (b) Mie scattering from re...

Figure 12.27 The diffraction pattern from a thin slit.

Figure 12.28 Diffraction gratings: (a) transmission; (b) reflection.

Figure 12.29 (a) Diffraction of X‐rays by a crystal; (b) diffraction of ligh...

Figure 12.30 A one‐dimensional photonic crystal.

Figure 12.31 Rainbow hologram: (a–c) a security hologram viewed at slightly ...

Figure 12.32 The structure of a silica glass optical fibre.

Figure 12.33 Alternative paths that light beams can take in the core of an o...

Figure 12.34 Types of optical fibre: (a) stepped index; (b) graded index; (c...

Figure 12.35 Signal amplification: an incoming weak signal is amplified on p...

Figure 12.36 Solar cells: (a) a photon incident upon a p–n junction generate...

Figure 12.37 Dye‐sensitised solar cell, schematic: (a) reactions taking plac...

Figure 12.38 The structure of (CH

3

NH

3

)PbCl

3

(MAPbCl

3

). In the layers precedi...

Figure 12.39 Perovskite solar cells, schematic: (a) dye‐sensitised solar cel...

Figure 12.40 Interband transitions (schematic) between electron (upper) and ...

Figure 12.41 Green‐emitting single quantum well (SQW) active layer LED.

Figure 12.42 Photoluminescent colours emitted by CdS quantum dots.

Figure 12.43 Quantum dot colours: (a) the change in energy level structure o...

Figure 12.44 A QLED screen (EL QD LED screen) schematic.

Figure 12.45 A ‘moth‐eye’ surface structure.

Chapter 13

Figure 13.1 The variation of heat capacity of a solid with temperature: (a) ...

Figure 13.2 Variation of the heat capacity of a solid at a phase transition:...

Figure 13.3 Thermal conductivity: (a) the temperature gradient across a homo...

Figure 13.4 The variation of thermal conductivity with temperature of some c...

Figure 13.5 Thermal expansion: the mean coefficient of thermal expansion, [α

Figure 13.6 The variation of expansivity with temperature for tungsten, magn...

Figure 13.7 Interatomic potentials, schematic: (a) variation of potential wi...

Figure 13.8 The thermal expansion/contraction of water close to 0 °C.

Figure 13.9 The thermal expansion of the

c

‐axis and contraction of the

a

‐ an...

Figure 13.10 Thermal contraction due to the removal of octahedral distortion...

Figure 13.11 Thermal contraction due to ‘rocking’ (rotation) of octahedra.

Figure 13.12 Thermal contraction brought about by silicon‐oxygen ‘hinges’ co...

Figure 13.13 Thermoelectric effects: (a) the Seebeck effect; (b) the Peltier...

Figure 13.14 The Seebeck effect in a single phase.

Figure 13.15 Thermocouple temperature measurement.

Figure 13.16 A thermopile: thermocouples connected in series.

Figure 13.17 Use of the Peltier effect for (a) thermoelectric heating; (b) t...

Figure 13.18 Adiabatic cooling: the initial state is regenerated by the cool...

Figure 13.19 The giant magnetocaloric effect: the initial paramagnetic multi...

Figure 13.20 Liquid crystal thermometer display.

Figure 13.21 The cholesteric chiral nematic liquid crystal structure, schema...

Figure 13.22 The rutile structure of metallic VO

2

above 68 °C.

Figure 13.23 VO

2

thermochromic coating, schematic: (a) below the transition ...

Chapter 14

Figure 14.1 The uranium‐238 decay series.

Figure 14.2 The thorium‐232 decay series.

Figure 14.3 The actinium‐227 (uranium‐235) decay series.

Figure 14.4 The plutonium‐241 decay series.

Figure 14.5 The band of stability of the elements.

Figure 14.6 The exponential rate of radioactive decay.

Figure 14.7 Plot of isotope ratios

87

Sr/

86

Sr vs.

87

Rb/

86

Sr, schematic.

Figure 14.8 The isotopic binding energy per nucleon.

Figure 14.9 A fission chain reaction, schematic. In the chain illustrated, e...

Figure 14.10 A pressurised water nuclear reactor for power generation, schem...

Guide

Cover Page

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Understanding Solids

The Science of Materials

Richard J. D. Tilley

University of Cardiff

United Kingdom

Third Edition

This edition first published 2021

© 2021 John Wiley & Sons Ltd

Edition History

Richard J. D. Tilley, Understanding Solids, 1st edition (978‐0‐470‐85275‐0 Cloth, 978‐0‐470‐85276‐7 Paper)

Richard J. D. Tilley, Understanding Solids, 2nd edition (978‐1‐118‐42328‐8 Cloth, 978‐1‐118‐42346‐2 Paper)

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Library of Congress Cataloging‐in‐Publication Data

Name: Tilley, R. J. D., author.

Title: Understanding solids : the science of materials / Richard J. D.

  Tilley, Professor Emeritus, University of Cardiff, United Kingdom.

Description: Third edition. | Chichester, West Sussex, United Kingdom :

  John Wiley & Sons Ltd., 2021. | Includes bibliographical references and

  index.

Identifiers: LCCN 2021005722 (print) | LCCN 2021005723 (ebook) | ISBN

  9781119716501 (hardback) | ISBN 9781119716549 (adobe pdf) | ISBN

  9781119716556 (epub)

Subjects: LCSH: Materials science. | Solids. | BISAC: TECHNOLOGY &

  ENGINEERING / Material Science.

Classification: LCC TA403 .T63 2021 (print) | LCC TA403 (ebook) | DDC

  620.1/1–dc23

LC record available at https://lccn.loc.gov/2021005722

LC ebook record available at https://lccn.loc.gov/2021005723

Cover Design: Wiley

Cover Image: © phochi/iStock/Getty Images

Preface

As with the previous editions, this new edition is aimed at introducing undergraduate students in sciences, engineering, and technology to the properties of solids and how these arise. The Chapters 1–4 cover basics such as atomic structure, chemical bonding, crystallography, and phase relationships, so as to provide a foundation for Chapters 5–14, which are concerned with describing the chemical and physical properties of solids in more detail.

All of the chapters in the second edition have been completely revised for this edition. The first five chapters in the earlier version have been condensed into three so as to present the material in a more coherent fashion, better suited to current requirements, without losing the overall aims of the previous edition: that of summarising basic properties essential to the understanding of the chemical and physical behaviours described in later chapters.

Since the previous edition, the scientific literature has been dominated by research on batteries and fuel cells, perovskite solar cells, lighting and displays, and solids with small dimensions: nanoparticles, whiskers, and sheets. All of these areas are introduced within the overall scheme of this book. The sections concerned with batteries and fuel cells have been updated, particularly with respect to lithium‐ion and lithium‐air cells. Sections concerned with organic framework structures, superionic conductors, mechanochemistry, bi‐layer graphene, hologram formation and recording, perovskite solar cells, the optics of nanoparticle arrays, and thermochromic materials have been added.

New problems have been added throughout where helpful to the assimilation of newer material. In addition, to assist in making progress in these areas, the Further Reading sections at the end of each chapter include reference to a reasonable number of recent review articles on these topics. These, together with the other references, are designed to expand the material presented and provide a starting point for further exploration of the topics covered.

It is a pleasure to record help from the staff at John Wiley, including Emma Strickland, Jenny Cossham, and Dr. M. A. Preuss, and the staff of the Trevithick library in Cardiff University for the continuing help with current literature. Finally, I must acknowledge my wife Anne, who has continually supported my efforts, and without whose help this revision would not have been possible.

R.J.D. Tilley

October 2020

About the Companion Website

This book is accompanied by a companion website for professors and instructors

www.wiley.com/go/tilley/understandingsolids3e

The website includes:

answers to problems

exercises

Part IStates of Aggregation

1Atoms and Bonding

What is an atomic term symbol?

How are ionic radii determined?

What are energy bands?

1.1 The Electron Structure of Atoms

An atom is made up of a small massive nucleus, in which almost all of the mass resides, surrounded by an electron cloud. Each element is differentiated from all others by the amount of positive charge on the nucleus, called the proton number or atomic number, Z. In a neutral atom, the nuclear charge is exactly balanced by Z electrons in the outer electron cloud, each of which carries one unit of negative charge. Variants of atoms that have slightly more or less electrons than are required for charge neutrality are called ions; those that have lost electrons have an overall positive charge and are called cations, while those that have gained electrons have an overall negative charge and are called anions. Many of the physical and chemical properties of solids described in later chapters are controlled by the outer electron structure of the component atoms.

1.1.1 Hydrogen

Hydrogen is the simplest atom and consists of a nucleus consisting of a single proton carrying one unit of positive charge together with a single bound electron carrying one unit of negative charge. The quantum mechanics of the hydrogen atom allows the probability of the location of the electron and its energy, defined in terms of wavefunctions, to be completely specified. The region of space defining the most probable location of the electron is termed an orbital. The wavefunctions are described by three quantum numbers: n, the principal quantum number; l, the orbital angular momentum quantum number; and ml, the magnetic quantum number. The principal quantum number, n, defines the energy of the electron. It can take integral values 1, 2, 3, … to infinity. The energy of the electron is lowest for n = 1 and this represents the most stable or ground state of the hydrogen atom. The next lowest energy is given by n = 2, then by n = 3, and so on.

The energy of each state is given by the formula:

where A is a constant equal to 2.179 × 10−18 J (13.6 eV)1 and E is the energy of the level with principal quantum number n. The negative sign in the equation indicates that the energy of the electron is chosen as zero when n is infinite, that is to say, when the electron is no longer bound to the nucleus.

There is only one wavefunction and orbital associated with the lowest energy, n = 1, state. The states of higher energy each have n2 different wavefunctions, corresponding to n2 different orbitals, all of which have the same energy. There are four different wavefunctions and orbitals corresponding to n = 2, nine different wavefunctions and orbitals for n = 3, and so on. These are differentiated from each other by different values of the quantum numbers l and ml, as explained in the following text. Wavefunctions with the same energy are said to be degenerate.

It is often convenient to represent the energy associated with each value of the principal quantum number, n, as a series of steps or energy levels (Figure 1.1). When an electron gains energy, it jumps from an energy level with a lower value of n to a level with a higher value of n. When an electron loses energy, it drops from an energy level with a higher value of n to an energy level with a lower value. The discrete packets of energy given out or taken up in this way are photons of electromagnetic radiation. The energy of a photon needed to excite an electron from energy E1, corresponding to an energy level n1 to energy E2, corresponding to an energy level n2 is given by:

Figure 1.1 Electron energy levels of the H atom.

The energy of the photon emitted when the electron falls back from E2 to E1 is the same as that required for the excitation. The frequency ν (or the equivalent wavelength, λ) of the photons that are either emitted or absorbed during these energy changes is given by the equation:

where h is the Planck constant. (Note that this equation applies to the transition between any two energy levels on any atom, not just between energy levels on hydrogen.) The energy needed to free the electron completely from the proton, which is called the ionisation energy of the hydrogen atom, is given by putting n1 = 1 and n2 = ∞ in the equation. The ionisation energy is 13.6 eV (2.179 × 10−18 J).

In the case of a single electron attracted to a nucleus of charge +Ze, the energy levels are given by: