### Unit Cells and Holes

```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
Types of Holes
109.50
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
SF6
OCT AHEDRAL
CUBIC
Cube –
Octahedron – 8 identical
triangles
SIMPLE CUBIC PACKING
HOLES
CUBIC
C
C
CUBIC CLOSEST PACKING – FACE CENTERED CUBIC
HOLES
T
T
T
O
T
O
T
O
tetrahedral
octahedral
Unit Cell
Packing Eff
Coord #
Holes
≈ Hole Size
(r=1),
Simple
Cubic
0.52
6
cubic
0.732-1.00
Face
centered
0.74
12
4
Octahedral
Tetrahedral
0.414-0.732
0.225-.0.414
O
z
Example: NaCl (Jmol)
• What type of unit cell is defined by the Cl- ions?
x
y
z=1
Top face
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
A
Z=1
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 MxNy.
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
2. Barium Chloride
3. Rhenium oxide
Examples from Chemtube3D
4. Based on Clalone, what type of
unit cell is this?
What type of “hole”
is occupied by Cu+?
```