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Crystals and Crystal Structures

  • ID: 2325069
  • Book
  • 270 Pages
  • John Wiley and Sons Ltd
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Crystallography plays an important part in a wide range of disciplines, including biology, chemistry, materials science and technology, mineralogy, physics, and engineering. Crystals and Crystal Structures is an introductory text for students and others who need to enable students to read scientific papers and articles describing a crystal structure or use enable stude3nts to read scientific papers and articles describing a crystal structure or use crystallographic databases with confidence and understanding.

reflecting the interdisciplinary nature of the subject, the book includes a variety of applications as diverse as the relationship between physical properties and symmetry, and molecular and protein crystallography. As well as covering the basics the book contains an introduction to areas of crystallography, such as modulated structures and quasicrystals, and protein crystallography, which are the subject of important and active research.


  • A non–mathematical introduction to the key elements o the subject
  • Contains numerous applications across a variety of disciplines
  • Includes a range of problems and exercises

Written by an author with many years teaching and research experience Crystals and Crystal Structures will prove invaluable to students taking an introductory course in crystallography in departments of chemistry, physics, materials science, biosciences and geology.

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1. Crystals and crystal structures.

1.1   Crystal families and crystal systems.

1.2   Morphology and crystal classes.

1.3   The determination of crystal structures.

1.4   The description of crystal structures.

1.5   The cubic close–packed (A1) structure of copper.

1.6   The body–centred cubic (A2) structure of tungsten.

1.7   The hexagonal (A3) structure of magnesium.

1.8   The halite structure.

1.9   The rutile structure.

1.10   The fluorite structure.

1.11   The structure of urea.

1.12   The density of a crystal.

Answers to introductory questions.

Problems and Exercises.

2. Lattices, planes and directions.

2.1   Two–dimensional lattices.

2.2   Unit cells.

2.3   The reciprocal lattice in two dimensions.

2.4   Three–dimensional lattices.

2.5   Alternative unit cells.

2.6   The reciprocal lattice in three dimensions.

2.7   Lattice planes and Miller indices.

2.8   Hexagonal lattices and Miller–Bravais indices.

2.9   Miller indices and planes in crystals.

2.10   Directions in lattices.

2.11   Lattice geometry.

Answers to introductory questions.

Problems and Exercises.

3. Two–dimensional patterns and tiling.

3.1   The symmetry of an isolated shape: point symmetry.

3.2   Rotation symmetry of a plane lattice.

3.3   The symmetry of the plane lattices.

3.4   The ten plane crystallographic point symmetry groups.

3.5   The symmetry of patterns: the 17 plane groups.

3.6   Two–dimensional crystal structures .

3.7   General and special positions.

3.8   Tesselations.

Answers to introductory questions.

Problems and Exercises.

4. Symmetry in three dimensions.       

4.1   The symmetry of an object: point symmetry.

4.2   Axes of inversion: rotoinversion.

4.3   Axes of inversion: rotoreflection.

4.4   The Hermann–Mauguin symbols for point groups.

4.5   The symmetry of the Bravais lattices.

4.6   The crystallographic point groups.

4.7   Point groups and physical properties.

4.8   Dielectric properties.

4.9   Refractive index.

4.10  Optical activity.

4.11  Chiral molecules.

4.12  Second harmonic generation (SHG).

4.13  Magnetic point groups.

Answers to introductory questions.

Problems and Exercises.

5. Building crystal structures from lattices and space groups.

5.1   Symmetry of three–dimensional patterns: space groups.

5.2   The crystallographic space groups.

5.3   Space group symmetry symbols.

5.4   The graphical representation of the space groups.

5.5   Building a structure from a space group.

5.6   The structure of diopside, MgCaSi2O6.

5.7   The structure of alanine, C3H7NO2 .

6.  Diffraction and crystal structures.

6.1   The position of diffracted beams: Bragg s law.

6.2   The geometry of the diffraction pattern.

6.3   Particle size.

6.4   The intensities of diffracted beams.

6.5   The atomic scattering factor.

6.6   The structure factor.

6.7   Structure factors and intensities.

6.8   Numerical evaluation of structure factors.

6.9   Symmetry and reflection intensities.

6.10  The temperature factor.

6.11  Powder X–ray diffraction.

6.12  Electron microscopy and structure images.

6.13  Structure determination using X–ray diffraction.

6.14  Neutron diffraction.

6.15  Protein crystallography.

6.16  Solving the phase problem.

6.17  Photonic crystals.

Answers to introductory questions.

Problems and Exercises.

7. The depiction of crystal structures.

7.1   The size of atoms.

7.2   Sphere packing.

7.3   Metallic radii.

7.4   Ionic radii.

7.5   Covalent radii.

7.6   Van der Waals radii.

7.7   Ionic structures and structure building rules.

7.8   The bond valence model.

7.9   Structures in terms of non–metal (anion) packing.

7.10  Structures in terms of metal (cation) packing.

7.11  Cation–centred polyhedral representations of crystals.

7.12  Anion–centred polyhedral representations of crystals and cation diffusion paths.

7.13  Structures as nets.

7.14  The depiction of organic structures.

7.15  The representation of protein structures.

Answers to introductory questions.

Problems and Exercises.

8. Defects, modulated structures and quasicrystals.

8.1   Defects and occupancy factors.

8.2   Defects and unit cell parameters.

8.3   Defects and density.

8.4   Modular structures.

8.5   Polytypes.

8.6   Crystallographic shear phases.

8.7   Planar intergrowths and polysomes.

8.8   Incommensurately modulated structures.

8.9   Quasicrystals.

Answers to introductory questions.

Problems and Exercises.


Appendix 1   Vector addition and subtraction.

Appendix 2   Data for some inorganic crystal structures.

Appendix 3   Schoenflies symbols.

Appendix 4   The 230 space groups.

Appendix 5    Complex numbers.

Appendix 6    Complex amplitudes.

Answers to problems and exercises.



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Richard J. D. Tilley
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