|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|
subvalent, aliovalent, supervalent, conduction band, valence band, semiconductor, silicon, dopant, thermal excitation, n-type, p-type, acceptor level, charge carrier, p-n junction
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|| |
silicon (Si), boron (B), diamond (C)
glass, obsidian, quartz, calcite, tin (Sn), basalt, beryl, fluorite, gold (Au), aluminum (Al), copper (Cu), platinum (Pt), methane ice (CH4), rock salt (NaCl)
transistors, diodes, current rectification
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)
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.
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
|[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|
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))
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.
|[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
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]
Niels Steensen (Nicolaus Steno)
Other OCW and OER Content
|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.|