Packing of more than one type of sphere into unit cells:
Packing of ions in salts
Which is usually larger, negative (anions) or positive
(cations) ions?
Construct binary salts in lattice with anions usually occupying positions in unit cell and cations in holes in cell
How do you describe salts with more than one atom type? By unit cells and holes
NaCl
Space fill

109.5
0 Types of Holes Ion in hole
3 atoms e clouds in plane
TETRAHEDRAL
Tetrahedron – 4 identical equilateral triangles
• What's a tetrahedron
• What's an octahedron
• Holes : Chemtube3D
• Cubic close packed /
• Face-centred cubic (ccp/fcc)
• CCP and holes
5 atoms/ e clouds in plane
OCT AHEDRAL
SF
6
Octahedron – 8 identical triangles
CUBIC
Cube –

SIMPLE CUBIC PACKING
HOLES
CUBIC
C
C
CUBIC CLOSEST PACKING – FACE CENTERED CUBIC
HOLES
T T
T T
T
O
O
O
O tetrahedral octahedral
Unit Cell
Simple
Cubic
Face centered
Packing Eff Coord #
0.52
0.74
6
12
4
Holes cubic
≈ Hole Size
(r=1),
0.732-1.00
Octahedral
Tetrahedral
0.414-0.732
0.225-.0.414

• What type of unit cell is defined by the Cl ions?
Example: NaCl (Jmol) z=1 y
Top face z x z=0.5
z=0
Bottom face
Tetrahedral Holes
• How many tetrahedral holes are there in the fcc unit cell?
• Are there any Na + ions occupying the holes?
Octahedral Holes
• How many octahedral holes are there in one fcc unit cell?
• In what type of holes are Na + ions in edges throughout the whole lattice?

Hexagonal Closest Packing
Z=1 A
Arsenide
Nickel
Z=0.75
B
Z=0.5
Example: Nickel Arsenide
(this Jmol link shows lattice based on Ni as in workbook pg 49, #4 )
• In what type of hole is Ni found in the structure above
• How many As are in the unit cell to the right? How many Ni?
• What is the formula for nickel arsenide?
• Locate a tetrahedral hole? Are there any Ni ions there?
Z=0.25
Z=0 A
Unit cell: hexagonal closest packing
Of Arsenide with Ni in what holes?

Determining the empirical formula from unit cell data:
A salt must be electrically neutral. If you know the charge on the cations and anions, you can determine M x
N y
.
Alternatively, you can use crystal data to determine the structure of the unit cell and hence the empirical formula. Determine the number of each different ion in the following unit cells. Does it correspond to the formula from charge balance?
1.
Copper (I) chloride
Cl
Cu
4. Based on Cl alone, what type of unit cell is this?
What type of “hole” is occupied by Cu + ?
2. Barium Chloride
3. Rhenium oxide
Examples from Chemtube3D