This textbook presents an extensive manual of crystallography, including geometric crystallography, crystallochemistry, and crystallophysics. Illustrated with a wealth of figures and diagrams, it offers a thorough introduction to crystals for undergraduate and graduate students interested in learning the essentials and advanced concepts of crystallography.
The book begins with basic concepts such as the geometry, morphology and symmetry of lattices, allowing readers to approach the subject from a mathematical point of view, abstracting it from its material content. In turn, the second part focuses on crystallochemistry and explains the differences between ideal and real crystals, and between static and dynamic ones. The third part of the textbook concerns crystallophysics and addresses the electrical, magnetic, mechanical, elastic and optical properties of crystals, as well as the fundamental laws and methods of X-ray diffraction.
Author(s): Celia Marcos
Series: Springer Textbooks in Earth Sciences, Geography and Environment
Publisher: Springer
Year: 2022
Language: English
Pages: 526
City: Cham
Preface
Acknowledgements
Contents
Part I Geometric Crystallography
1 Introduction to Crystallography
Abstract
1.1 Introduction
1.2 Crystallography and Mineralogy
1.3 Historical Background
1.4 Crystalline State
1.5 Crystal, Monocrystal, and Crystalline Aggregate
1.6 Crystalline Structure
References
2 Periodicity, Crystalline Lattices, Symbols, and Notations
Abstract
2.1 Crystal Lattice
2.2 Translation
2.3 Plane Lattices
2.4 Space Lattices
2.5 Lattice Origin
2.6 Elemental Cell
2.7 Unit Cell
2.8 Cell Parameters
2.9 Cell Volume
2.10 Properties of Crystal Lattice
2.11 The Crystal as Interpenetrated Parallel Lattices
2.12 Lattice Elements
2.12.1 Node
2.12.2 Lattice Row
2.12.3 Lattice Plane
2.13 Lattice Spacing
2.14 Tautozonal Planes
2.15 Reticular Density
2.16 Crystal Face
2.17 Crystal Edge
2.18 Reciprocal Lattice
2.19 Relations Between the Direct and Reciprocal Lattices
References
3 Symmetry and Lattices
Abstract
3.1 Concept of Symmetry
3.2 Symmetry Contained in the Lattices
3.3 Symmetry Operation
3.4 Element of Symmetry
3.5 Translation
3.6 Symmetry Proper Operations
3.6.1 Rotations
3.7 Symmetry Proper Operations
3.7.1 Rotation-Inversion
3.7.2 Reflection-Translation (Glide)
3.7.3 Rotation-Translation
4 Point Symmetry
Abstract
4.1 Introduction
4.2 Point Group Definition
4.3 Rules that Condition the Presence of Several Symmetry Elements in the Same Point Group
4.4 Crystalline System
4.5 Point Group Symbol
4.6 Symmetry Operations of Point Groups
4.7 Point Groups and Crystal Classes
4.8 Two-Dimensional Point Groups and Point Groups of the Plane Lattices
4.9 Three-Dimensional Point Groups and Three-Dimensional Lattices Point Groups
4.10 Crystalline Forms
4.11 Zone and Zone Axis
4.12 Bundle of Normals to Faces
4.13 Crystalographic Projections
4.13.1 Spherical Projection
4.13.2 Stereographic Projection
4.14 Crystallographic Calculations
References
5 Space Groups
Abstract
5.1 Space Groups Definitions
5.2 Space Group Symmetry Operations
5.3 Derivation of Space Groups
5.4 Space Group Symbol
5.5 Plane Space Groups and Symbol
5.6 Equivalent Positions
5.7 Graphic Description of Space Groups
References
Part II Crystallochemistry
6 Crystal Structures, Compact Packing, Coordination
Abstract
6.1 Introduction
6.2 Crystalline Structures
6.3 Bonds in Crystalline Structures
6.4 Ionic Crystals
6.5 Covalent Crystals
6.6 Metal Crystals
6.7 Compact Packing
6.8 Size of Atoms
6.9 Coordination, Pauling Rules
6.10 Positions in Compact Packaged Structures
References
7 Crystal Structures
Abstract
7.1 Introduction
7.2 Compact Cubic Structures
7.2.1 Gold Structure
7.3 Compact Hexagonal Structures
7.3.1 Magnesium Structure
7.4 Body-Centered Cubic Structures
7.4.1 Iron Structure
7.5 Structures Derived from Compact Cubic Packing
7.5.1 Halita (NaCl)
7.5.2 Fluorite-Type Structures (CaF2)
7.5.3 Sphalerite—Type Structures (ZnS)
7.5.4 Diamond
7.6 Structures Derived from Compact Hexagonal Packing
7.6.1 Nickelite Structure (NiAs)
7.6.2 Wurtzite Structure (ZnS)
7.7 Other Structural Types
7.7.1 CsCl Type Structure
7.7.2 Calcite Structure (CaCO3)
7.7.3 Spinel Structure (AB2O4)
7.8 Silicate Structures
References
8 Defects
Abstract
8.1 Introduction
8.2 Order and Disorder
8.3 Crystalline Defects
8.4 Point Defects
8.4.1 Point Defects and Solid-State Diffusion
8.4.2 Point Defects and Color in Crystals and Minerals
8.4.3 Point Defects and Chemical Composition
8.5 Linear Defects
8.6 Two-Dimensional Defects
8.7 Three-Dimensional Defects
References
9 Polymorphism and Polymorphic Transformations Transformation Order—Disorder
Abstract
9.1 Introduction
9.2 Stability and Equilibrium
9.3 Polymorphism and Polymorphic Transformations of Crystals and Minerals
9.4 Thermodynamic Aspect of Polymorphic Transformations
9.5 Mechanisms of Polymorphism
References
Part III Crystallophysics
10 Relationship Between Symmetry and Physical Properties
Abstract
10.1 Physical Property
10.2 Scalar Properties
10.2.1 Density
10.2.2 Specific Gravity
10.2.3 Specific Heat or Specific Heat Capacity
10.3 Tensor Properties
11 Interaction of Electromagnetic Waves with Crystals and Minerals
Abstract
11.1 Electromagnetic Waves and Maxwell Equations
11.2 Electromagnetic Wave Propagation
11.3 Propagation of Light in a Transparent Crystal
11.4 Electrical Polarization, Local Electric Field, and Velocity of Light in a Crystal
11.5 Electromagnetic Spectrum
11.6 Isotropic Crystals and Minerals
11.7 Anisotropic Crystals and Minerals
11.7.1 Uniaxial Crystals and Minerals
11.7.2 Orthorhombic, Monoclinic and Triclinic Crystals and Minerals
11.8 Dispersion
References
12 Representation Surfaces of Optical Properties of Crystals
Abstract
12.1 Introduction–Representation Surfaces of Optical Properties of Crystals
12.2 Ellipsoid of the Indices or Optical Indicatrix of the Transparent Crystals
12.2.1 Ellipsoid of the Indices and Indicatrix Surface of Reflectance of the Isotropic Crystals and Minerals
12.2.2 Ellipsoid of the Indices and Indicatrix Surface of Reflectance of the Anisotropic Crystals and Minerals
12.3 Surface Indicatrix of Reflectance of the Absorbent (Opaque) Crystals and Minerals
12.3.1 Surface Indicatrix of Reflectance of the Isotropic Crystals and Minerals
12.3.2 Surface Indicatrix of Reflectance of the Anisotropic Crystals and Minerals
Reference
13 The Polarizing Microscope
Abstract
13.1 Polarizing Transmission Microscope
13.2 Reflection Polarizing Microscope
13.3 Illumination Types
13.4 Sample Preparation
14 Optical Properties of Transparent Crystals and Minerals
Abstract
14.1 Orthoscopic Arrangement of the Microscope
14.1.1 Observations with Plane Polarized Light
14.1.2 Observations with Polarized and Analyzed Light
14.2 Conoscopic Microscope Arrangement
14.3 Optical Activity
14.4 Dispersion
Reference
15 Optical Properties of Opaque Crystals
Abstract
15.1 Orthoscopic Arrangement of the Microscope
15.1.1 Observations with Polarized Light
15.2 Observations with Crossed Polarizers (Polarized and Analyzed Light)
15.3 Conoscopic Arrangement of the Microscope
15.3.1 Observations with Polarized Light
15.4 Dispersion
15.4.1 Color and Dispersion Effects
15.4.2 Anisotropic Effects Between Crossed Polarizers
15.4.3 Dispersion in the Polarization Figures
16 Electrical, Magnetic, Mechanical, and Elastic Properties
Abstract
16.1 Electrical Properties
16.1.1 Pyroelectricity
16.1.2 Piezoelectricity
16.2 Magnetic Properties
16.2.1 Introduction
16.2.2 Types of Minerals According to Magnetic Properties
16.3 Mechanical Properties
16.3.1 Cleavage
16.3.2 Tenacity
16.3.3 Hardness
16.4 Elastic Properties
16.4.1 Homogeneous Deformation
16.4.2 Thermal Expansion or Expansion
16.4.3 Compressibility
17 Methods and Applications of X-ray Diffraction in Crystallography and Mineralogy
Abstract
17.1 Nature of X-rays
17.2 X-ray Production, X-ray Tube
17.3 Spectra Emitted by X-ray Tube
17.4 X-ray Diffraction Theory
17.5 Laue Equations
17.6 Bragg’s Law and X-ray Reflection
17.7 Ewald Sphere or Reflection Sphere
17.8 X-ray Intensity, Atomic Scattering Factor, Structure Factor
17.9 Symmetry of Diffraction Effects, Laue Classes
17.10 Application of X-ray Diffraction in Crystals and Minerals
17.11 X-ray Diffraction Methods
17.11.1 Laue Method
17.11.2 Oscillation Method
17.11.3 Weissenberg Method
17.11.4 Precession Method
17.11.5 Powder Diffractometry Method
17.11.6 Goniometric Methods: 4-circle Diffractometer
17.11.7 Synchrotron Radiation-Based Methods
Appendix I Correspond to Chapter 4
Appendix II Correspond to Chapter 4
Appendix III Correspond to Chapter 9
Appendix IV
Appendix V
Appendix VI
Appendix VII
