1. Unit Cell of Crystal Structure
AL Chemistry
Unit Cell of Crystal Structure
# Definition of “Unit Cell”:
A unit cell is the smallest basic portion of the crystal lattice that, repeatedly stacked together in three dimensions , can generate the entire crystal structure.
[2003 Paper I, Q.4(b)]
p. 1

2. Common Types of Unit Cell
AL Chemistry
Common Types of Unit Cell
# 2 common types for Ionic Crystals …
Face-centered Cubic closed packed (fcc)
Simple Cubic closed packed (sc)
p. 2

3. Counting Ions in a Unit Cell
AL Chemistry
Counting Ions in a Unit Cell
FCC SC
general principle:
at corners = 1/8
along edges = 1/4
in faces = 1/2
at cubic centre = 1
at corners = 8(1/8) = 1
along edges = 0
in faces = 6(1/2) = 3
at cubic centre = 0
at corners = 8(1/8) = 1
along edges = 0
in faces = 0
at cubic centre = 0
total no. = 4
total no. = 1
p. 3

4. Generating of entire Lattice
AL Chemistry
Generating of entire Lattice
p. 4

5. Ionic Crystals ** General Bonding considerations
AL Chemistry
Ionic Crystals
 the 3-dimensional arrangement of ions.
** General Bonding considerations
The bonding forces should be maximized
by packing as many cations around each anion, and
as many cations around each anion as is possible.
but it depends on the relative size of cation and anion.
p. 5

6. How do the anion and cation pack together?
AL Chemistry
How do the anion and cation pack together?
To visualize the structures in terms of a closed packed arrangement of the larger anions (FCC or SC),
with the cations occupying the vacant sites between the close packed layers.
The number of nearest neighbor ions of opposite charge is called the coordination number.
p. 6

7. if the cation is not small
AL Chemistry
Closed packed of Anions & Cation:
if the cation is small
if the cation is not small
anions are packed in form of “FCC”
anions are packed in form of “SC”
cations fill into “tetrahedral holes”
cations fill into the “cubic centre site”
cations fill into “octahedral holes”
governed by the “radius ratio” of cation and anion !
p. 7

8. AL Chemistry
Types of “cation site” (holes) available in closed packed anions arrays:
Stacking of two closed packed anion layers produces
2 types of “holes”.
(a) octahedral hole ---- coordinated by 6 anions
(b) tetrahedral hole ---- coordinated by 4 anions
p. 8

9. FCC (for small cations)
AL Chemistry
“Stuffing” the holes by Cations:
Octahedral or Tetrahedral hole?
► determined by the radius ratio (= rcation / ranion)
[radius ratio rule] SC
FCC (for small cations)
p. 9

10. Stable Bonding Configuration :
AL Chemistry
Stable Bonding Configuration :
For a stable coordination, the bonded cation and anion must be in contact with each other.
# If the cation is larger than the ideal radius ratio …
► the cation and anion remain in contact, but the cation forces the anion apart.  STABLE!
p. 10

11. # If the cation is too small …
AL Chemistry
# If the cation is too small …
► cation would not be in contact with the surrounding anion.  repulsion between anions  UNSTABLE!
p. 11

12. Holes available in “FCC” unit cell closed packed of anions:
AL Chemistry
Holes available in “FCC” unit cell closed packed of anions:
# “O” – octahedral hole : The unit cell has 4 octahedral sites.
# “T” – tetrahedral hole : The unit cell has 8 tetrahedral sites.
p. 12

13. Example 1: Sodium Chloride (NaCl)
AL Chemistry
Example 1: Sodium Chloride (NaCl)
radius: Na+ = 1.02nm, Cl- = 1.81nm
radius ratio =  FCC
4 Cl- packed in FCC, Na+ will fit into the octahedral hole of the anion arrays.
Since stiochiometry of cation and anion = 1:1, 4 Na+ ions fit into the cell. i.e. all the octahedral sites are occupied!
6:6 coordination !
Cl-
Na+
Cl-
Na+
p. 13

14. Example 2: Zinc Blende (ZnS)
AL Chemistry
Example 2: Zinc Blende (ZnS)
radius: Zn2+ = 0.60nm, S2- = 1.84nm
radius ratio =  FCC
4 S2- packed in FCC, Zn2+ will fit into the tetrahedral hole of the anion arrays.
Since stiochiometry of cation and anion = 1:1, 4 Zn2+ ions fit into the cell. i.e. half the tetrahedral sites are occupied!
S2-
Zn2+
4:4 coordination !
# (Cations fills in the diagonally opposite sites to minimize repulsion.)
p. 14

15. Example 3: Cesium Chloride (CsCl)
AL Chemistry
Example 3: Cesium Chloride (CsCl)
radius: Cs+ = 1.74nm, Cl- = 1.81nm
radius ratio =  SC
► Anions occupy the corners of a unit cell,
the centre of the cube is larger than the tetrahedral and octahedral sites,
therefore the large Cs+ ion can fit in.
p. 15

16. 8:8 coordination ! Simple Cubic closed packed (SC) Cl- Cs+
AL Chemistry
Simple Cubic closed packed (SC)
Each unit cell has 8 anions and 8 cubic centre sites.
Since stiochiometry of cation and anion = 1:1, 8 Cs+ ions will fit into the cell. i.e. all the cubic center sites are occupied!
Cl-
Cs+
8:8 coordination !
p. 16

17. Two Inter-penetrating Lattices in CsCl:
AL Chemistry
Two Inter-penetrating Lattices in CsCl:
unit cell of CsCl
Cl-
Cs+
p. 17

18. Practice: Calcium Fluoride (CaF2)
AL Chemistry
Practice: Calcium Fluoride (CaF2)
radius: Ca2+ = 1.12nm, F- = 1.31nm
radius ratio = 0.850
Simple Cubic (SC) closed packed
Each unit cell has 8 anions and 8 cubic centre sites.
Since stiochiometry of cation and anion = 1:2, only 4 Ca2+ ions will fit into the cell. i.e. half the cubic center sites are occupied!
p. 18

19. AL Chemistry
(CaF2)
Coordination no.: each Ca2+ surrounded by 8 F-, each F- surrounded by 4 Ca2+.
p. 19

20. Conclusion ….. Closed packed of Anions & Cation:
AL Chemistry
Conclusion …..
anions are packed in form of “FCC”
Closed packed of Anions & Cation:
if the cation is small
if the cation is not small
anions are packed in form of “SC”
cations fill into “octahedral holes”
cations fill into “tetrahedral holes”
cations fill into the “cubic centre site”
e.g. ZnS
e.g. CsCl, CaF2
e.g. NaCl
p. 20