Crystal Lattices

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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).

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Cubic Unit Cells
The unit cell is a cube in each case.
Whole atoms shown for clarity.
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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
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Ionic Crystal Structures

• Ionic crystals have two different types of
  structural unitscations 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

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Ionic Crystal Structures

• Tetrahedral hole filling occurs when the cations
  are small when the radii ratio is
• 0.225 lt rc/ra lt 0.414
• Octahedral filling occurs with larger cations,
  when the radii ratio is
• 0.414 lt rc/ra lt 0.732
• The arrangement is cubic if rc/ra gt 0.732.

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Unit Cell of Cesium Chloride
How many cesium ions are inside this unit cell?
How many chloride ions?
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Unit Cell of Sodium Chloride
How many sodium ions are inside this unit cell?
How many chloride ions?