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Anthony Kelly. Crystallography and Crystal Defects
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Crystallography and Crystal Defects
Copyright
Preface to the Third Edition
Companion Website
1 Lattice Geometry
1.1 The Unit Cell
1.2 Lattice Planes and Directions
1.3 The Weiss Zone Law
1.4 Symmetry Operators6
1.4.1 Translational Symmetry
1.4.2 Rotational Symmetry
1.4.3 Centre of Symmetry
1.4.4 Reflection Symmetry
1.5 Restrictions on Symmetry Operations
1.6 Possible Combinations of Rotational Symmetries
1.7 Crystal Systems
1.8 Space Lattices (Bravais12 Lattices)
Problems
Suggestions for Further Reading
References
Notes
2 Point Groups and Space Groups
2.1 Macroscopic Symmetry Elements
2.2 Orthorhombic System
2.3 Tetragonal System
2.4 Cubic System
2.5 Hexagonal System
2.6 Trigonal System
2.7 Monoclinic System
2.8 Triclinic System
2.9 Special Forms in the Crystal Classes
2.10 Enantiomorphous Crystal Classes
2.11 Laue Groups
2.12 Space Groups
2.12.1 Screw Axes
2.12.2 Glide Planes
2.12.3 Combinations of Symmetry Operations to Form Space Groups
2.12.4 The Relationship Between the Space Group Symbol and the Point Group Symmetry for a Crystal
2.13 The 17 Two‐Dimensional Space Groups
2.14 Nomenclature for Point Groups and Space Groups
2.15 Groups, Subgroups, and Supergroups
2.16 An Example of a Three‐Dimensional Space Group
2.17 Frequency of Space Groups in Inorganic Crystals and Minerals
2.18 Magnetic Groups
Problems
Suggestions for Further Reading
References
Notes
3 Crystal Structures. 3.1 Introduction
3.2 Common Metallic Structures
3.2.1 Cubic Close‐Packed (Fmm)
3.2.2 Hexagonal Close‐Packed (P63/mmc)
3.2.3 Double Hexagonal Close‐Packed (P63/mmc)
3.2.4 Body‐Centred Cubic (Imm)
3.3 Related Metallic Structures
3.3.1 Indium (I4/mmm)
3.3.2 Mercury (Rm)
3.3.3 β‐Sn (I41/amd)
3.4 Other Elements and Related Compounds. 3.4.1 Diamond (Fdm)
3.4.2 Graphite (P63/mmc)
3.4.3 Hexagonal Boron Nitride (P63/mmc)
3.4.4 Arsenic, Antimony, and Bismuth (Rm)
3.5 Simple MX and MX2 Compounds
3.5.1 Sodium Chloride, NaCl (Fmm)
3.5.2 Caesium Chloride, CsCl (Pmm)
3.5.3 Sphalerite, α‐ZnS (F3m)
3.5.4 Wurtzite, β‐ZnS (P63mc)
3.5.5 Nickel Arsenide, NiAs (P63/mmc)
3.5.6 Calcium Fluoride, CaF2 (Fmm)
3.5.7 Rutile, TiO2 (P42/mnm)
3.6 Other Inorganic Compounds
3.6.1 Perovskite (Pmm)
3.6.2 α‐Al2O3 (Rc), FeTiO3 (R) and LiNbO3 (R3c)
3.6.3 Spinel (Fdm), Inverse Spinel and Related Structures
3.6.4 Garnet (Iad)
3.6.5 Calcite, CaCO3 (Rc)
3.7 Interatomic Distances
3.8 Solid Solutions
3.9 Polymers
3.10 Additional Crystal Structures and their Designation
Problems
Suggestions for Further Reading
References
Notes
4 Amorphous Materials and Special Types of Crystal–Solid Aggregates. 4.1 Introduction
4.2 Amorphous Materials
4.3 Liquid Crystals
4.3.1 Nematic Phases
4.3.2 Cholesteric Phases
4.3.3 Smectic Phases
4.4 Geometry of Polyhedra
4.5 Icosahedral Packing
4.6 Quasicrystals
4.6.1 A Little Recent History and a New Definition
4.7 Incommensurate Structures
4.8 Foams, Porous Materials, and Cellular Materials
Problems
Suggestions for Further Reading
References
5 Tensors
5.1 Nature of a Tensor
5.2 Transformation of Components of a Vector
5.3 Dummy Suffix Notation
5.4 Transformation of Components of a Second‐Rank Tensor
5.5 Definition of a Tensor of the Second Rank
5.6 Tensor of the Second Rank Referred to Principal Axes
5.7 Limitations Imposed by Crystal Symmetry for Second‐Rank Tensors
5.8 Representation Quadric
5.9 Radius–Normal Property of the Representation Quadric
5.10 Third‐ and Fourth‐Rank Tensors
Problems
Suggestions for Further Reading
References
Notes
6 Strain, Stress, Piezoelectricity and Elasticity
6.1 Strain: Introduction
6.2 Infinitesimal Strain
6.3 Stress
6.4 Piezoelectricity
6.4.1 Class 2
6.4.2 Class 222
6.4.3 Class 23
6.4.4 Class 432
6.4.5 The Converse Effect
6.5 Elasticity of Crystals
6.5.1 Class
6.5.2 Class 2
6.5.3 Class 222
6.5.4 Class 23
6.5.5 Reduction in the Number of Independent cij and sij for Other Crystal Classes
6.5.6 Isotropic Media
6.6 Elasticity of Cubic Crystals
6.6.1 Transformation of the Stiffness and Compliance Tensors for Cubic Materials
6.6.2 Shear Stiffnesses and Compliances on the (111) Plane of Cubic Crystals
Problems
Suggestions for Further Reading
References
Notes
7 Glide
7.1 Translation Glide
7.2 Glide Elements
7.3 Independent Slip Systems
7.4 Large Strains of Single Crystals: The Choice of Glide System
7.5 Large Strains: The Change in the Orientation of the Lattice During Glide
Problems
Suggestions for Further Reading
References
Notes
8 Dislocations
8.1 Introduction
8.2 Dislocation Motion
8.3 The Force on a Dislocation
8.4 The Distortion in a Dislocated Crystal
8.5 Atom Positions Close to a Dislocation
8.6 The Interaction of Dislocations with One Another
Problems
Suggestions for Further Reading
References
Notes
9 Dislocations in Crystals
9.1 The Strain Energy of a Dislocation
9.2 Stacking Faults and Partial Dislocations
9.3 Dislocations in C.C.P. Metals
9.4 Dislocations in the Rock Salt Structure
9.5 Dislocations in Hexagonal Metals
9.6 Dislocations in B.C.C. Crystals
9.7 Dislocations in Some Covalent Solids
9.8 Dislocations in Low Symmetry Crystal Structures
9.9 Dislocations in Other Crystal Structures
Problems
Suggestions for Further Reading
References
Notes
10 Point Defects
10.1 Introduction
10.2 Point Defects in Ionic Crystals
10.3 Point Defect Aggregates
10.4 Point Defect Configurations
10.5 Experiments on Point Defects in Equilibrium
10.6 Experiments on Quenched Metals
10.7 Radiation Damage
10.8 Anelasticity and Point Defect Symmetry
Problems
Suggestions for Further Reading
References
Note
11 Twinning
11.1 Introduction
11.2 Description of Deformation Twinning
11.3 Examples of Twin Structures. 11.3.1 C.C.P. Metals
11.3.2 B.C.C. Metals
11.3.3 Sphalerite (Zinc Blende)
11.3.4 Calcite
11.3.5 Hexagonal Metals
11.3.6 Graphite
11.4 Twinning Elements
11.5 The Morphology of Deformation Twinning
11.6 Friedel's Classification of (Growth) Twinning
11.6.1 Twinning by Merohedry
11.6.2 Twinning by Reticular Merohedry
11.6.3 Twinning by Pseudomerohedry
11.6.4 Twinning By Reticular Pseudomerohedry
11.7 Atomistic Modelling of Twin Boundaries
Problems
Suggestions for Further Reading
References
Notes
12 Martensitic Transformations. 12.1 Introduction
12.2 General Crystallographic Features
12.3 Transformation in Cobalt
12.4 Transformation in Zirconium
12.5 Transformation in Indium–Thallium Alloys
12.6 Transformations in Steels
12.7 Transformations in Copper Alloys
12.8 Transformations in Ni–Ti‐Based Alloys
12.9 Magnetic Shape Memory Alloys
12.10 Transformations in Non‐metals
12.11 Crystallographic Aspects of Nucleation and Growth
12.12 The Shape Memory Effect and Superelasticity
12.12.1 The One‐Way Shape Memory Effect
12.12.2 The Two‐Way Shape Memory Effect
12.12.3 Superelasticity
12.13 Modern Theories of Martensitic Transformations
12.13.1 The Topological Model
12.13.2 Non‐linear Elasticity Model
Problems
Suggestions for Further Reading
References
Notes
13 Grain Boundaries. 13.1 The Structure of Surfaces and Surface Free Energy
13.2 Structure and Energy of Grain Boundaries
13.3 Equivalent Geometrical Descriptions of High‐Angle Grain Boundaries
13.4 Interface Junctions
13.5 The Shapes of Crystals and Grains
Problems
Suggestions for Further Reading
References
14 Interphase Boundaries
14.1 Boundaries Between Different Phases
14.2 Interphase Boundaries Between C.C.P. and B.C.C. Phases
14.3 Strained Layer Epitaxy of Semiconductors
Problems
Suggestions for Further Reading
References
Note
15 Texture. 15.1 Texture
15.2 Euler Angles
15.3 Microtexture
15.3.1 Rodrigues Vectors and Rodrigues Space
Problems
Suggestions for Further Reading
References
Note
Appendix 1 Crystallographic Calculations
A1.1. Vector Algebra
A1.1.1 The Scalar Product
A1.1.2 The Vector Product
A1.2. The Reciprocal Lattice
A1.3. Matrices
A1.4. Rotation Matrices and Unit Quaternions
References
Notes
Appendix 2 The Stereographic Projection. A2.1 Principles
A2.2 Constructions
A2.2.1 To Construct a Small Circle. A2.2.1.1 About the Centre of the Primitive
A2.2.1.2 About a Pole within the Primitive – say about P (Figure A2.7)
A2.2.1.3 About a Pole on the Primitive – say about P (Figure A2.8)
A2.2.2 To Find the Opposite of a Pole
A2.2.3 To Draw a Great Circle through Two Poles
A2.2.4 To Find the Pole of a Great Circle
A2.2.5 To Measure the Angle Between Two Poles on an Inclined Great Circle
A2.3 Constructions with the Wulff Net
A2.3.1 Two‐Surface Analysis
A2.4 Proof of the Properties of the Stereographic Projection
References
Notes
Appendix 3 Interplanar Spacings and Interplanar Angles. A3.1. Interplanar Spacings
A3.1.1 Triclinic
A3.1.2 Monoclinic
A3.1.3 Orthorhombic
A3.1.4 Trigonal
A3.1.5 Tetragonal
A3.1.6 Hexagonal
A3.1.7 Cubic
A3.2. Interplanar Angles
A3.2.1 Orthorhombic
A3.2.2 Hexagonal
A3.2.3 Cubic
Appendix 4 Transformation of Indices Following a Change of Unit Cell
A4.1. Change of Indices of Directions
A4.2. Change of Indices of Planes
A4.3. Example 1: Interchange of Hexagonal and Orthorhombic Indices for Hexagonal Crystals
A4.4. Example 2: Interchange of Rhombohedral and Hexagonal Indices
Appendix 5 Slip Systems in C.C.P. and B.C.C. Crystals
A5.1. Independent Glide Systems in C.C.P. Metals
A5.1.1 Example: Slip Along on the (111) Slip Plane
A5.1.2 Number of Independent Glide Systems
A5.2. Diehl's Rule and the OILS Rule
A5.2.1 Use of Diehl's Rule for Slip (such as C.C.P. Metals)
A5.2.2 Use of Diehl's Rule for Slip (such as B.C.C. Metals)
A5.2.3 The OILS Rule
A5.3. Proof of Diehl's Rule and the OILS Rule
References
Appendix 6 Homogeneous Strain
A6.1 Simple Extension
A6.2 Simple Shear
A6.3 Pure Shear
A6.4 The Relationship Between Pure Shear and Simple Shear
Appendix 7 Crystal Structure Data. A7.1 Crystal Structures of the Elements, Interatomic Distances and Six‐Fold Coordination‐Number Ionic Radii
A7.2 Crystals with the Sodium Chloride Structure
A7.3 Crystals with the Caesium Chloride Structure
A7.4 Crystals with the Sphalerite Structure
A7.5 Crystals with the Wurtzite Structure
A7.6 Crystals with the Nickel Arsenide Structure
A7.7 Crystals with the Fluorite Structure
A7.8 Crystals with the Rutile Structure
Appendix 8 Further Resources. A8.1 Useful Web Sites
A8.2 Educational and Information Resources
A8.3 Computer Software Packages
Brief Solutions to Selected Problems1. Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Note
Index
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