Unit Cell of Crystal Structure

1
Unit Cell of Crystal Structure
Definition of Unit Cell
A unit cell is the smallest basic portion of the
crystal lattice that, repeatedly stacked
togetherin three dimensions , can generate the
entire crystal structure.
2003 Paper I, Q.4(b)
p. 1
2
Common Types of Unit Cell
2 common types for Ionic Crystals
Face-centered Cubicclosed packed (fcc)
Simple Cubicclosed packed (sc)
p. 2
3
Counting Ions in a Unit Cell
SC
FCC
general principle
total no. 1
total no. 4
p. 3
4
Generating of entire Lattice
p. 4
5
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 cationpack 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
Closed packed of Anions Cation
anions are packed in form of SC
anions are packed in form of FCC
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
Types of cation site (holes) availablein
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
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
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
? 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
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)
radius Na 1.02nm, Cl- 1.81nm
radius ratio 0.563 ? FCC
4 Cl- packed in FCC,Na will fit into the
octahedral hole of the anion arrays.
Since stiochiometry ofcation and anion 11,4
Na ions fit into the cell.i.e. all the
octahedral sites are occupied!
66 coordination !
p. 13
14
Example 2 Zinc Blende (ZnS)
radius Zn2 0.60nm, S2- 1.84nm
radius ratio 0.330 ? FCC
Since stiochiometry ofcation and anion 11,4
Zn2 ions fit into the cell.i.e. half the
tetrahedral sites are occupied!
4 S2- packed in FCC,Zn2 will fit into the
tetrahedral hole of the anion arrays.
44 coordination !
(Cations fills in the diagonally opposite sites
to minimize repulsion.)
p. 14
15
Example 3 Cesium Chloride (CsCl)
radius Cs 1.74nm, Cl- 1.81nm
radius ratio 0.960 ? 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
Simple Cubic closed packed (SC)
Each unit cell has 8 anionsand 8 cubic centre
sites.
Since stiochiometry of cation and anion 11,8
Cs ions will fit into the cell.i.e. all the
cubic center sites are occupied!
88 coordination !
p. 16
17
Two Inter-penetrating Lattices in CsCl
p. 17
18
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 anionsand 8 cubic centre
sites.
Since stiochiometry of cation and anion
12,only 4 Ca2 ions will fit into the
cell.i.e. half the cubic center sites are
occupied!
p. 18
19
(CaF2)
Coordination no. each Ca2 surrounded by 8
F-, each F- surrounded by 4 Ca2.
p. 19
20
Conclusion ..
e.g. ZnS
e.g. CsCl, CaF2
e.g. NaCl
p. 20