Transcript Crystal Lattices

Crystal Lattices
• To describe crystals, three-dimensional views
must be used.
• The repeating unit of the lattice is called the unit
cell.
• There are a number of different types of unit cell;
hexagonal, rhombic, cubic, etc.
• The three types of cubic unit cells are: simple
cubic, body-centered cubic (bcc), face-centered
cubic (fcc).
Cubic Unit Cells
The unit cell is
a cube in each
case.
Whole atoms
shown for
clarity.
Close Packing in Three
Dimensions
Third layer directly
above first layer: HCP
Two layers, stacked,
give two different
locations for the
third layer …
Third layer over the octahedral
holes in the second layer: CCP
Ionic Crystal Structures
• Ionic crystals have two different types of structural
units—cations and anions.
• The cations and anions ordinarily are different sizes.
• Smaller cations can fill the voids between the larger
anions.
• Where the cations go depends on the size of the
cations and on the size of the voids.
• The smallest voids are the tetrahedral holes, then the
octahedral holes, and finally the holes in a cubic
structure. Therefore …
Ionic Crystal Structures
• Tetrahedral hole filling occurs when the
cations are small; when the radii ratio is:
0.225 < rc/ra < 0.414
• Octahedral filling occurs with larger cations,
when the radii ratio is:
0.414 < rc/ra < 0.732
• The arrangement is cubic if rc/ra > 0.732.
Unit Cell of Cesium Chloride
How many cesium
ions are inside this
unit cell? How many
chloride ions?
Unit Cell of Sodium Chloride
How many sodium
ions are inside this
unit cell? How many
chloride ions?