3.091SC | Fall 2010 | Undergraduate

Introduction to Solid State Chemistry

Crystalline Materials

15. Introduction to Crystallography

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Session Overview

Modules Electronic Materials, Crystalline Materials
Concepts p-n junction, introduction to the solid state, the 7 crystal systems, the 14 Bravais lattices, properties of cubic crystals: simple cubic, face-centered cubic, body-centered cubic, and diamond cubic

Electronic Materials

subvalent, aliovalent, supervalent, conduction band, valence band, semiconductor, silicon, dopant, thermal excitation, n-type, p-type, acceptor level, charge carrier, p-n junction

Crystalline Materials

crystal, glass, amorphous solid, ordered solid, long-range order, Bravais lattice, crystal system, point group, translation, rotation, symmetry plane, degree of symmetry, crystal basis, unit cell, face-centered cubic, simple cubic, body-centered cubic, hexagonal close-packed, rock salt structure, diamond cubic, birefringence, crystallography, nearest neighbor, Auguste Bravais, René Haüy, Robert Hooke, Christiaan Huygens, Nicolaus Steno

Chemical Substances

Electronic Materials

silicon (Si), boron (B), diamond (C)

Crystalline Materials

glass, obsidian, quartz, calcite, tin (Sn), basalt, beryl, fluorite, gold (Au), aluminum (Al), copper (Cu), platinum (Pt), methane ice (CH4), rock salt (NaCl)


Electronic Materials

transistors, diodes, current rectification

Crystalline Materials

cannonball stacking, tiling of 2D surfaces, fiber optics coupling, optical beam-splitter, colored gold


Before starting this session, you should be familiar with:

  • Semiconductor properties and behavior (Session 14)
  • Basic geometry in 2D and 3D
  • Bond angles and lengths in molecules (Session 11)

Looking Ahead

This session introduces the cubic unit cells, a key framework for discussing atomic-level processes in solids throughout this module and in later topics, such as Diffusion (Session 24) and Solid Solutions (Session 33 onwards). The next module on Amorphous Solids (Session 21 onwards) discusses non-crystalline materials in more detail, contrasting their structure and properties with the ordered solids studied here.

Learning Objectives

After completing this session, you should be able to:

  • Classify materials as n- or p-type, and explain how simple p-n junction devices work.
  • Derive the 7 crystal systems by varying the lattice constants a, b, c and angles α, β, γ.
  • For a given repeating pattern, determine the crystal basis and Bravais lattice.
  • Sketch the simple cubic, body-centered cubic, and face-centered cubic structures, and calculate key parameters such as the lattice constant, atomic radius, and packing density.


Archived Lecture Notes #4 (PDF), Sections 1-3

Book Chapters Topics
[Saylor] 12.1, “Crystalline and Amorphous Solids.” Crystal lattice parameters; properties of crystalline and amorphous solids
[Saylor] 12.2, “The Arrangement of Atoms in Crystalline Solids.” The unit cell; packing of spheres
[JS] 3.1, “Seven Systems and Fourteen Lattices.” The unit cell and its parameters; crystal systems and crystal (Bravais) lattices
[JS] 3.2, “Metal Structures.” Body-centered cubic, face-centered cubic/cubic close-packed, and hexagonal close-packed structures; atomic packing factor; plane stacking

Lecture Video


Lecture Slides (PDF - 3.2MB)

Lecture Summary

Continuing last lecture’s explanation of extrinsic semiconductors, the Electronic Materials module ends at 13:00 with an exploration of p-type doping and an overview of the p-n junction. Prof. Sadoway moves on to introduce a classification for materials based on the degree of atomic-level order, contrasting ordered solids (crystals, e.g. quartz, calcite) with amorphous solids (glasses, e.g. obsidian). The 7 crystal systems and 14 Bravais lattices are introduced:

  • Tetragonal (e.g. tin (Sn), basalt)
  • Hexagonal (e.g. beryl)
  • Rhombohedral (e.g. calcite)
  • Cubic (e.g. fluorite, gold (Au), aluminum (Al), copper (Cu), platinum (Pt), methane (CH4(s)), rock salt (NaCl))
  • Triclinic
  • Monoclinic
  • Orthorhombic

Crystal structures are described using a basis, which may be an atom, a group of ions (e.g. rock salt (NaCl)), or a molecule (e.g. methane (CH4(s)), proteins), repeated at the points of a Bravais lattice. Since they apply to many common metals and minerals, this course focuses on the cubic crystal systems: simple, body-centered, and face-centered.


Problems (PDF)

Solutions (PDF)

Textbook Problems

[Saylor] Sections Conceptual Numerical
[Saylor] 12.2, “The Arrangement of Atoms in Crystalline Solids.” 1, 8, 9 3, 5, 9, 11
[Saylor] 12.3, “Structures of Simple Binary Compounds.” 4 none

For Further Study

Supplemental Readings

Hooke, Robert. Micrographia; or, Some Physiological Descriptions of Minute Bodies Made by Magnifying Glasses, with Observations and Inquiries. London, England: J. Martyn and J. Allestry, 1665. [View on Project Gutenberg]

Chapman, Allan. England’s Leonardo: Robert Hooke and the Seventeenth-Century Scientific Revolution. Philadelphia, PA: Institute of Physics Publishing, 2005. ISBN: 9780750309875.

Steno, Nicolaus. The Prodromus of Nicolaus Steno’s Dissertation Concerning a Solid Body Enclosed by Process of Nature within a Solid. Translated by John Garrett Winter. New York, NY: Macmillan, 1916.

Cutler, Alan. The Seashell on the Mountaintop: A Story of Science, Sainthood, and the Humble Genius Who Discovered a New History of the Earth. New York, NY: Plume, 2004. ISBN: 9780452285460.

Dijksterhuis, Fokko Jan. Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century. Boston, MA: Kluwer, 2004. ISBN: 9789048167067.


Auguste Bravais

René Just Haüy

Robert Hooke

Christiaan Huygens

Niels Steensen (Nicolaus Steno)


M. C. Escher

Georges Braque

Vallier, Dora. Braque: The Complete Graphics: Catalogue Raisonne. New York, NY: Alpine Fine Arts Collection, 1988. ISBN: 9780881680065.

Talking Heads. “Burning Down the House.” Speaking in Tongues. Sire Records, 1983.

Other OCW and OER Content

Content Provider Level Notes
Crystallography DoITPoMS Undergraduate  
Crystal Structure Connexions Undergraduate  
3.60 Symmetry, Structure, and Tensor Properties of Materials MIT OpenCourseWare Graduate A mathematical approach to crystal symmetry with connections to bulk material properties such as stress, strain, thermal conductivity, and piezoelectricity.

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Course Info

As Taught In
Fall 2010
Learning Resource Types
Course Introduction
Exams with Solutions
Lecture Notes
Lecture Videos
Problem Sets with Solutions
Recitation Videos
Problem Sets
Exam Materials