The 14 Bravais Lattices

(Drag with mouse over each object to rotate)
Cubic Lattices:
sc bcc fcc
Tetragonal Lattices:
P I
Orthorhombic Lattices:
P C I F
Hexagonal Lattices:
P (3 cells shown)
Trigonal Lattices:
R
Monoclinic Lattices:
P C
Triclinic Lattices:
P

Self-test Questions:

  1. Which of these cells are primitive cells?

  2. How many lattice points per cell?

  3. Can you see any n-fold rotation axes, where n =
    1. 3
    2. 4
    3. 2
    (Look for them by rotating the object until an n-fold axis is perpendicular to the screen: do you see the n-fold symmetry now?) How many rotation axes are there of each type? What are their Miller indices?

  4. How about mirror planes?

  5. View each of the cubic cells along a <111> direction. What is the rotational symmetry about this axis? Which structure (sc, fcc, bcc) is the most/least densely packed?

  6. Why is there no such lattice type as, e.g., ``face-centered (F) tetragonal''? ``Base-centered (C) tetragonal''?

  7. Can you see how to represent a primitive trigonal lattice in terms of the hexagonal conventional cell (i.e., a hexagonal lattice with an n-atom basis)? What is the value of n?
© 1999 R. J. Hauenstein