Crystallography: Introduction to the Study of Minerals (Springer Textbooks in Earth Sciences, Geography and Environment)

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. 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