Crystallography and Crystal Chemistry

Frontmatter

Chapter 1. Introduction

Abstract

Our knowledge of crystalline materials has evolved from the time of the Ancient Greek philosophers through that of the medieval alchemists and natural philosophers of the Enlightenment and finally to the scientists of modern times. This chapter provides a brief and humanized introduction to the history, language, and tools of crystallography. Brief biographies are included here on some of the leading historical figures in the field, including Évariste Galois, Auguste Bravais, and Max von Laue.

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Chapter 2. Crystals

Abstract

Crystals are variously defined as an infinite array of atoms in space, a lattice plus a basis, or even any solid having an essentially discrete diffraction pattern. This chapter develops these ideas and introduces the concepts of the unit cell, lattice planes, and directions.

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Chapter 3. Point Symmetry

Abstract

Symmetry may seem like a self-evident property of an object – you know it when you see it – but for the study of crystallography a rigorous definition is required, so here goes: Symmetry is that property possessed by an object when some operation (translation, rotation, reflection, and/or inversion) leaves it indistinguishable from its original position. In other words, symmetry is a demonstration of the invariance of the object to the operation. Topics such as electronic bands, phonon dispersion, vibrational spectroscopy (e.g., Raman and IR), and the properties of crystalline materials generally require a good understanding of crystal symmetry.

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Chapter 4. Crystal Systems

Abstract

The seven crystal systems include triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. Each differs by the symmetries present. A crystal’s symmetry will imply certain constraints on its basis vectors (i.e., lattice constants), and it is these constraints that are often used to determine or even define the crystal system; however, it should always be remembered that it is the symmetry, not the lattice constants, that determines the crystal system of any given crystal.

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Chapter 5. Lattice Systems

Abstract

One possible way of categorizing crystals is by the symmetry of their lattice. Where a crystal system is one of seven ways to categorize crystals based on the symmetry of the crystal (cubic, hexagonal, trigonal, tetragonal, orthorhombic, monoclinic, triclinic), a lattice system is one of seven ways to categorize crystals based on the symmetry of their lattice (cubic, hexagonal, rhombohedral, tetragonal, orthorhombic, monoclinic, triclinic).

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Chapter 6. Partial Translations

Abstract

A partial translation is smaller than a primitive lattice translation. Apart from translational symmetry itself, which defines periodicity, we have so far considered only point symmetries, none of which involve any kind of translation; however, some symmetry operations involve partial translations coupled with either reflection (glide symmetry) or rotation symmetry (screw symmetry).

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Chapter 7. Symmetry in Two Dimensions

Abstract

Here we simplify matters by considering only patterns in two dimensions, in which case there are just four planar systems, five lattice types, and 17 plane groups.

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Chapter 8. Space Groups

Abstract

Here we introduce the concept of space groups, Sohncke groups, crystal classes, Bravais classes, site symmetry, Wyckoff positions, and orbits.

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Chapter 9. Example Structures

Abstract

This chapter introduces some specific structures as well as the concepts of electrostriction, piezoelectricity, and ferroelectricity.

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Chapter 10. Other Classifications of Structures

Abstract

This chapter introduces the usage and limitations of the Pearson and Strukturbericht notations for crystal structures.

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Chapter 11. Diffraction and Reciprocal Space

Abstract

This chapter introduces the concept of diffraction as a way of linking measurable macroscopic phenomena to microscopic ones.

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Chapter 12. Symmetry Constraints on Properties

Abstract

This chapter introduces the distinction between isotropic and anisotropic properties as well as the application of coordinate transformations to solve problems involving anisotropic properties. Neumann’s Principle and the Curie Principle are also discussed.

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Chapter 13. Quantum Theory

Abstract

This chapter introduces the themes of crystal chemistry and quantum mechanics, including notations for electron states and configurations. Brief biographies of Democritus, John Dalton, Carl Linnaeus, George Johnstone Stoney, and Max Planck are also included.

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Chapter 14. Covalent, Metallic, and Secondary Bonding

Abstract

This chapter introduces the concepts of bonding, coordination, and packing fraction. We start with covalent bonding, encompassing both valence bond theory and molecular orbital theory, then move to metallic bonding, the Hume-Rothery Rules, and band theory; and we finish with Van der Waals forces and hydrogen bonding. A biographical sketch of Johannes Diderik van der Waals is also included.

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Chapter 15. Ionic Bonding

Abstract

Here we introduce the concept of ionic bonding, including electronegativity, the Madelung constant, lattice energy, the Born Haber cycle, and Pauling’s Rules. The chapter ends with the empirical application of Fajans’s Rules to estimate the ionic fraction of bonds and a comparison between ionic and covalent bond strengths. Brief biographies of Erwin Madelung, Max Born, and Linus Pauling are also included.

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Chapter 16. Point Defects

Abstract

Some of the most useful properties of crystalline materials arise from defects in their structure. This chapter introduces the concept of the order parameter as well as the thermodynamics of defect formation and migration. Several specific point defect types, including vacancy, interstitial, antisite, Schottky, Frenkel, and color centre are examined, and a brief biographical sketch of Eugene Paul “E.P.” Wigner is included.

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Chapter 17. Line Defects

Abstract

As we have already seen, some of the most useful properties of crystalline materials arise from defects in their structure. This chapter introduces the concept of line defects, including dislocations and disclinations. A brief biographical sketch of Vito Volterra is included.

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Chapter 18. The Non-Crystalline State

Abstract

This chapter discusses the non-crystalline state. In it, we make a distinction between amorphous and disordered materials, and we introduce the concept of short-range order. Models of amorphous materials based on either hard spheres or networks are explored, and polymers are specifically discussed in terms of structure, applications, and recyclability. Brief biographies of John Desmond “Des” Bernal and Georgy Theodosiyovych Voronoï are also included.

Rick Ubic

Backmatter