1. Crystal Systems
Cubic
Orthorhombic
Rhombohedral
Tetragonal
Triclinic
Hexagonal
Monoclinic
Bravais Lattices
Primitive, FCC, BCC
Primitive, FC, BC, EC
Primitive
Primitive, BC
Primitive
Primitive
Primitive, EC

2. Layer A
Layer arrangement view

3. Layer B

4. Layer C
Layer A
Layer B
Layer C
Cubic Close Packing
(CCP)

6. Layer A
Layer arrangement view

7. Layer B

8. Layer A
Layer A
Layer B
Layer A
Hexagonal Close
Packing

9. Unit Cell shape view
Unit Cell arrangement view

10. Packing Fraction depends on:
1. Layout of each layer
2. Placement of one layer over the other

11. Two types of voids:
Octahedral
Tetrahedral
Found only in FCC & Hexagonal primitive unit cells
Octahedral void in FCC

12. Each octahedral void located at the edge center is shared by 4 unit
cells
Total contribution of edge centre voids = 312
4
1

Contribution of central void 1
Total contribution of all octahedral voids per unit cell of FCC = 4
No. of Octahedral voids per unit cell =
Rank of unit cell

13. Tetrahedral void in FCC
(0,0,0)
x-axis
y-axis
z-axis
(a/2, a/2,0)
(a/2, 0,a/2)
(0, a/2,a/2)
(a/4, a/4,a/4)

14. (0,0,0)
(a/2, a/2,0)
(a/4, a/4,a/4)
a

b

k
a
j
a
i
a
a ˆ
4
ˆ
4
ˆ
4


k
a
j
a
i
a
b ˆ
4
ˆ
4
ˆ
4












ba
ba


.
.
cos 1









16
3
16cos 2
2
1
a
a




3
1
cos 1 o
268.109

15. With each corner as origin there are 8 tetrahedral voids in FCC unit
cell
 No. of tetrahedral voids = 2  no. of Octahedral voids