Crystals

1
Crystals

• Crystal consist of the periodic arrangement of
  building blocks
• Each building block, called a basis, is an atom,
  a molecule, or a group of atoms or molecules
• Such a periodic arrangement must have
  translational symmetry such that if you move a
  building block by a distance
• then it falls on another identical building
  block with the same orientation.
• If we remove the building blocks and replace them
  with points, then we have a point lattice or
  Bravais lattice.

2
Crystal Symmetry

• These Bravais lattices have several symmetry
  operations (these are operations on the lattice
  which leave it looking identical to the original
  lattice).
• Translational (as weve already seen)
• Rotation about an axis (1, 2, 3, 4, or 6 fold)
• Reflection through a mirror plane
• Inversion through a point
• Combination of two of the above
• Glide ( reflection translation)
• Screw ( rotation translation)

3
Point and Space Groups
32 point groups link
Any group constructed by reducing the symmetry of
an object characterized by a particular crystal
system continues to belong to that system until
the symmetry has been reduced so far that all of
the remaining symmetry operations of the object
are also found in a less symmetrical crystal
system when this happens the symmetry group of
the object is assigned to the less symmetrical
system. Thus the crystal system of a
crystallographic point group is that of the least
symmetric of the seven Bravais lattice point
groups containing every symmetry operation of the
crystallographic group.