Crystals and Crystal Structures

Richard J. D. Tilley

• Publisher: Wiley
• Year: 2020
• Print ISBN: 9781119548386
• eBook ISBN: 9781119548591
• Edition: 2
• Topic: Physical Sciences
• Subtopic: Physical & Theoretical Chemistry

An authoritative, updated text that offers an introduction to crystals and crystal structure with coverage of crystallography, and microscopy of materials

Written in a friendly, non-mathematical style, the updated second edition of Crystals and Crystal Structures offers a comprehensive exploration of the key elements of crystals and crystal structures. Starting with the basics, it includes information on multiple areas of crystallography, including modulated structures, quasicrystals and protein crystallography, and interdisciplinary applications as diverse as the relationship between physical properties and symmetry.

To enhance comprehension of the material presented, the book contains a variety of problems and exercises. The revised second edition offers new material and updates in the field including:

• An introduction to the use of high intensity X-ray analysis of protein structures
• Advances in imaging, scanning electron microscopy, and cryo-electron microscopy
• The relationship between symmetry and physical properties highlighting new findings and an introduction to tensor notation in describing these relationships in a concise fashion
• Nanoparticles as well as crystallographic aspects, defects, surface defects and the impact of these crystallographic features on properties
• Perovskite structures and their variations and the inclusion of their wide-ranging properties

Written for students ofcrystallography, chemistry, physics, materials science, biosciences and geology, Crystals and Crystal Structures, Second Edition provides an understanding of the subject and enables students to read scientific papers and articles describing a crystal structure or use crystallographic databases.

Chapter 1
Crystals and Crystal Structures

What is a crystal system?

What are unit cells?

What information is needed to specify a crystal structure?

Crystals are homogeneous solids that possess a long‐range three‐dimensional array of ordered atoms. That is, the arrangement of the atoms in one small volume of a crystal is identical (excepting localised mistakes or defects that can arise during crystal growth or that are inserted deliberately) to that in any other similar but remote part of the crystal. Crystallography is the study of crystals and describes the ways in which the component atoms are arranged in crystals and how the long‐range order is achieved. Many chemical (including biochemical) and physical properties of solids depend upon crystal structure, and knowledge of crystallography is essential if the properties of materials are to be understood and exploited.

1.1 Crystal Families and Crystal Systems

Crystallography first developed as an observational science: an adjunct to the study of minerals. Minerals were (and still are) described by their morphology or habit, the shape that a mineral specimen may exhibit, which may vary from an amorphous mass to a well‐formed gemstone. Indeed, the regular and beautiful shapes of naturally occurring crystals attracted attention from the earliest times, and the relationship between crystal shape and the disposition of crystal faces of a well‐formed crystal provides an obvious means of classification. For example, some crystals resemble cubes or octahedra, whilst others are brick‐like or form prisms with a hexagonal cross‐section (Figure 1.1).

The external shape of a well‐formed crystal reflects the internal order of the solid, especially the presence of internal symmetry. Symmetry will be developed later (especially in Chapters 3 and 4), but for the moment we can note that the most important symmetries displayed by crystals, and used in their classification, are the mirror plane, across which two parts of the crystal are related by reflection, and rotation axes. There are four different rotation axes: the diad or two‐fold, in which successive rotations by (360/2)° leave the crystal unchanged; the triad or three‐fold, in which successive rotations by (360/3)° leave the crystal unchanged; the tetrad or four‐fold, in which successive rotations by (360/4)° leave the crystal unchanged; and the hexad or six‐fold, in which successive rotations by (360/6)° leave the crystal unchanged. Careful measurement of mineral specimens using these symmetry criteria have allowed crystals to be classified in terms of six crystal families – anorthic, monoclinic, orthorhombic, tetragonal, hexagonal, and isometric or cubic – later expanded slightly by crystallographers into seven crystal systems (Table 1.1).

Figure 1.1 (a) Quartz (SiO₂) crystals, showing hexagonal morphology; (b) pyrite (FeS₂, fool’s gold) crystals showing cubic and octahedral morphology.

The crystal systems are sets of reference axes, which have a direction as well as a magnitude, and hence are vectors.¹ The allocation of a crystal to a particular system is made on the basis of the internal symmetries that are inferred from the crystal habit, which includes the apparent external symmetry. For instance, a crystal that resembled a hexagonal prism would be allocated ...

Table of contents

• Cover
• Table of Contents
• Preface
• Chapter 1: Crystals and Crystal Structures
• Chapter 2: Lattices, Planes and Directions
• Chapter 3: Two‐dimensional Patterns and Tiling
• Chapter 4: Symmetry in Three Dimensions
• Chapter 5: Symmetry and Physical Properties
• Chapter 6: Building Crystal Structures from Lattices and Space Groups
• Chapter 7: Diffraction and Crystal Structure Determination
• Chapter 8: The Depiction of Crystal Structures
• Chapter 9: Defects, Modulated Structures and Quasicrystals
• Appendix A: Vector Addition and Subtraction
• Appendix B: Crystallographic Data for Some Inorganic Crystal Structures
• Appendix C: Schoenflies Symbols
• Appendix D: The 230 Space Groups
• Appendix E: Complex Numbers
• Appendix F: Complex Amplitudes
• Answers to Problems and Exercises
• Bibliography
• Index
• End User License Agreement