4.7: Summary

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The focus of this package is the difference between single crystals, polycrystals and amorphous solids. This is explained in terms of the atomic scale periodicity: single crystals are periodic across their entire volume; polycrystals are periodic across individual grains; amorphous solids have little to no periodicity at all.

The different atomic structures can have effects on the macroscopic properties. A single crystal may exhibit anisotropy - we have seen mechanical anisotropy of gypsum, and optical anisotrpy of quartz. Polycrystals may also be anisotropic within each grain, as seen when the polycrystalline quartz-feldspar mix was placed between the crossed polarisers. Amorphous solids do not have anisotropic mechanical or optical properties, since they are isotropic on the atomic scale.

Defects may exist in all structures, even single crystals. They include vacancies and grain boundaries, where the regular repeating structure is disrupted.

Going further

Most 'introductory' materials science textbooks will cover the basic material in this package. The following resources cover the subjects in more detail than this teaching and learning package, and may prove useful to the interested student.

Books

Introduction to Mineral Sciences by Putnis (Cambridge University Press, 1992)
Provides a mineral-based treatment of many of the topics introduced in this package. Of particular interest:
Chapter 1 on Periodicity and Symmetry
Chapter 2 on Anisotropy and Optical Properties, including the phenomenon of birefringence
Chapter 5 on Crystal Structures
Chapter 7 on Defects in Minerals

The Structure of Materials by Allen and Thomas (Wiley, 1999)
Gives a thorough mathematical treatment of the noncrystalline and crystalline states (chapters 2 and 3).

Websites

Steffen Weber's homepage
Contains java-based applets that allow the structure of common polyhedra and crystals to be explored.
Crystallography and Minerals Arranged by Crystal Form
A library of 'crystal forms' - the shapes adopted by natural crystals. Contains Java applets.
Molecular Expressions: Optical Birefringence
An excellent tutorial on birefringence. Contains Java applets.

Other resources

The MATTER Project's 'Materials Science on CD-ROM' includes modules on:
Introduction to Crystallography (including Miller Indices etc.)
Introduction to Point Defects
Dislocations
See the MATTER website for details of availability.