Material Science

1. MME 195
Lecture-2
Crystal Structure
Course Tutor:
Moniruzzaman Jamal
Assistant Professor
Dept. of MME, BUET

2. 1
Crystalline materials...
• atoms pack in periodic, 3D
arrays -metals
-many
ceramics
-some
polymers
Noncrystalline materials...
• atoms have no periodic
packing -complex
structures
-rapid cooling
"Amorphous" =
Noncrystalline
noncrystalline
SiO2
Adapted from Fig. 3.22(b),
Callister 7e.
Materials and
Packing
S
i
crystalline SiO2
Adapted from Fig. 3.22(a),
Callister 7e.
Oxyge
n
• typical
of:
• occurs
for:

3. Lattice - An array of atoms arranged in a 3-D grid like pattern.
Unit cell - The smallest representative structural unit of lattice
that can describe the crystal structure. Repetition of the unit
cell generates the entire crystal.
Unit cells are stacked together endlessly to form the lattice (with
no empty
spaces between cells).
Crystal
Systems

4. 3
Crystal
Systems
14 crystal
lattices
Fig. 3.4,
Callister 7e.
Unit cell: smallest repetitive volume which
contains the complete lattice pattern of a
crystal.
a, b, and
c
α, β and γ
˃ Lattice
Constants

5. Crystal
Systems

6. Crystal
Systems

7. Cubic Systems
Orthorhombic
Systems

8. Tetragonal Systems
Monoclinic Systems

9. 6
Metallic Crystal
Structures
• Tend to be densely packed.
• Reasons for dense packing:
-Typically, only one element is present (as in pure
metal), so all atomic radii are the identical. Alloy
contains another atomic species added to metal, but
the material still remains crystalline
We will examine ....
•Simple Cubic (SC)
•body-centered cubic (BCC)
•face-centered cubic (FCC)
•hexagonal close-packed (HCP).

10. 7
Simple Cubic Structure
(SC)
Crystal structure formed by
periodic
• Rare due to low packing denisty
• Close-packed directions are cube edges.
The coordination
number, CN = the
number of closest
neighbors to which
an atom is bonded
= number of
touching atoms
A simple cubic (SC) unit cell
(Courtesy P.M. Anderson)
Number of atoms per
unit cell, n = 1
8 corner atoms shared
by
eight cells: 8 x 1/8 = 1

11. 8
• APF for a simple cubic structure =
0.52
APF =
a 3
4
3
π
(0.5a)
3
1
atom
s
unit
cell
ato
m
volum
e
unit
cell
volum
e
Atomic Packing Factor
(APF)
APF =
Volume of atoms in unit
cell
Volume of unit cell
a
R=0.5
a
close-packed
directions contains
8 x 1/8 =
1 atom/unit

12. 9
Adapted from Fig.
3.2,
Callister 7e.
Body Centered Cubic Structure
(BCC)
• Atoms touch each other along cube diagonals.
--Note: All atoms are identical; the center atom is
shaded differently only for ease of viewing.
ex: Cr,W, Fe (α), Tantalum, Molybdenum
• Coordination # = 8
2 atoms/unit cell: 1 center + 8 corners x
1/8
A body-centred cubic (BCC) unit
cell (Courtesy P.M.
Anderson)
Crystal structure formed by
periodic

13. Atomic Packing Factor:
BCC
4
3
π ( 3 a/4 )
3
2
unit cell
APF =
ato
m
volum
e
a 3
unit
cell
volume
3
a
a
R
Adapted from
Fig. 3.2(a),
Callister 7e.
atoms
2 a
Close-packed
directions:
length = 4R =
• APF for a body-centered cubic structure = 0.68
3 a
a

14. Face Centered Cubic Structure
(FCC)
•Atoms touch each other along face diagonals.
--Note: All atoms are identical; the face-centered atoms are
shaded
differently only for ease of viewing.
ex: Al, Cu, Au, Pb, Ni,
Pt, Ag
• Coordination # = 12
A face-centred cubic (FCC) unit
cell (Courtesy P.M.
Anderson)
Adapted from Fig. 3.1, Callister 7e.
4 atoms/unit cell: 6 face x 1/2 + 8 corners
x 1/8

15. 12
Atomic Packing Factor:
FCC
• APF for a face-centered cubic structure = 0.74
maximum achievable
APF
4
π
( 2 a/4
3
)
3
4
atom
s
unit cell
APF =
atom
volum
e
a 3
unit
cell
volume
Close-packed
directions: length
= 4R =
2
a
Unit cell
contains: 6 x
1/2 + 8 x 1/8
= 4
atoms/unit cell
a
2
a
Adapted
from Fig.
3.1(a),
Callister 7e.

16. Hexagonal Close-Packed Crysta
Structure
• HCP is one more common structure of metallic crystals
• Six atoms form regular hexagon, surrounding one atom in c
Another plane is situated halfway up unit cell (c-axis),
additional atoms situated at interstices of hexagonal (close-p
planes
• Cd, Mg, Zn, Ti have this crystal structure

17. Hexagonal Close-Packed Crystal
Structure
• Unit cell has two lattice parameters a and c. Ideal ratio c/a = 1.633
• The coordination number, CN = 12 (same as in FCC)
• Number of atoms per unit cell, n = 6.
• 3 mid-plane atoms shared by no other cells: 3 x 1 = 3
• 12 hexagonal corner atoms shared by 6 cells: 12 x 1/6 = 2
• 2 top/bottom plane center atoms shared by 2 cells: 2 x 1/2 = 1
• Atomic packing factor, APF = 0.74 (same as in FCC)
• All atoms are equivalent

18. Principles of Atomic
Packing
Structures based on the square net
Simple cubic
Body centred cubic
Structures based on the close-packed net
Face centred cubic
Hexagonal close-packed

19. A
sites
Cubic Stacking
Sequence
A

20. A
sites
B
A
B
sites
C
sites
HCP Stacking
Sequence
C
B
C
B
C
B
ABAB... Stacking
Sequence

21. 16
A
sites
FCC Stacking
Sequence
ABCABC... Stacking Sequence-2D Projection (TOP VIEW)
B
B
B
B
B. site
s
C. site
s
C
B
C
B
C
B
A

22. 17
A
sites
• FCC Unit
Cell
FCC Stacking
Sequence
B
B
B. site
s
C. site
s
• ABCABC... Stacking Sequence
• 2D Projection
B
C
C
B
C
B
A
B
C

24. • Coordination # =
12
• APF = 0.74
Adapted from Fig.
3.3(a),
Callister 7e.
Hexagonal Close-Packed
Structure (HCP)
6 atoms/unit
cell
ex: Cd, Mg,Ti,
Zn
•c/a =
1.633
c
a
A
sites
Bottom
layer
B sites Middle layer
• ABAB... Stacking Sequence
• 3D Projection • 2D Projection
A sites Top layer

26. VOIDS
Tetrahedral Octahedral OV
TV
Interstitial sites [Voids] in
crystals
❑ The size and distribution of voids in materials plays a role in determining aspects of
material behaviour
❑ Tetrahedral: 4 atoms surround the hole
❑ Octahedral: 6 atoms surround the hole
❑ Cubic : 8 atoms surround the hole