Unit Cells and Asymmetric Units

Unit Cell - Definition and animation Asymmetric Unit - Definition and animation 2D lattic types 3D lattice types
Unit Cells and Asymmetric Units

Unit Cell
A UNIT CELL is the smallest unit of volume that contains all of the structural and symmetry information and that by translation can reproduce a pattern in all of space. Structural information- the pattern (atoms) plus all surrounding space. Symmetry information- mirrors, glides, axes, and inversion centers. Translation- motion along a cell edge the length of the cell edge.
top
Asymmetric Unit
An ASYMMETRIC UNIT is the smallest unit of volume that contains all of the structural information and that by application of the symmetry operations can reproduce the UNIT CELL. Structural information- the pattern (atoms) plus all surrounding space. Symmetry information- mirrors, glides, axes, and inversion centers.
top
The shape of the unit cell is constrained by the collection of symmetry elements which make-up the group.
For PLANE GROUPS, four shapes are possible: parallelogram, rectangle, square and hexagal (one-third of a hexagon forms the unit cell).
top
top
top
top
For SPACE GROUPS, seven lattice types are possible: triclinic, monoclinic, orthrombic, tetragonal, hexagonal, rhombic and cubic.

Triclinic top
Monoclinic top
Orthorhombic top
Tetragonal top
Hexagonal top
Rhombic top
Cubic
top