JIC MME 323 Materials Science Teaching Slide Week 4

1. MME 323: MATERIALS SCIENCE
WEEK 4 :
STRUCTURE OF CRYSTALLINE SOLIDS*
Adhi Primartomo, PhD
Email: primartomo_a@jic.edu.sa
Office: Room 191 – JIC Academic Building
* Source: Materials Science and Engineering; 9th Edition; W.D.Callister;
Wiley; 2011
https://sites.google.com/site/primartomo/file-cabinet

2. ~ LECTURE OUTLINE ~
Chapter 4: The Structure of Crystalline Solids
(page 73 - 109)*
• Why Study the Structure of Crystalline Solids?
• Metallic Crystal Structures (FCC, BCC, SC &
HCP),
• Polymorphism and Allotropy,
• Linear and Planar Densities,
• X-Ray Diffraction.
2

3. ~ Week 4 Learning Objective ~
After studying this chapter, you should be able to:
• Define the actual number of atoms, coordination
number and atomic packing factors of BCC, FCC, SC
and HCP crystal structures,
• Define the density computation of metals,
• Describe the Polymorphism and Allotropy,
• Describe and calculate the Linear and Planar
Densities,
• Describe X-Ray Diffraction & Bragg’s Law,
• Calculate the Interplanar spacing, diffraction angle
and lattice parameter.
3

4. WHY STUDY THE STRUCTURE OF CRYSTALLINE
SOLIDS? (page 74)
Some of the properties of materials explained by their
crystal structures:
4
Magnesium (Mg):silvery white color,
light weight metal,
highly flammable
when powdered.
Gold (Au): yellow color, very dense metal,
most malleable of all metals.

5. METALLIC CRYSTAL STRUCTURES
(page 74)
5
Table 4.1.: Crystal Structures of 16 Metals with their Atomic Radii

6. METALLIC CRYSTAL STRUCTURES
(page 74)
6
• FCC Crystal Structure: (page 75)
Fig.4.1: FCC Crystal Structure
a. Hard-sphere unit cell,
b. Reduce-sphere unit cell,
c. Lattice (space lattice)
a = 2R 2

7. METALLIC CRYSTAL STRUCTURES
(page 74-81)
7
• BCC Crystal Structure: (page 76)
Fig.4.2: BCC Crystal Structure
a. Hard-sphere unit cell,
b. Reduce-sphere unit cell,
c. Lattice (space lattice)
a =
4R
3

8. METALLIC CRYSTAL STRUCTURES
(page 74-81)
8
• SC Crystal Structure: (page 77)
Fig.4.3: SC Crystal Structure
a. Hard-sphere unit cell,
b. Reduce-sphere unit cell,
c. Lattice (space lattice)
a = 2R

9. METALLIC CRYSTAL STRUCTURES
(page 74-81)
9
• HCP Crystal Structure: (page 77-78)
Fig.4.4: HCP Crystal Structure
a. Hard-sphere unit cell,
b. Reduce-sphere unit cell,
c. Lattice (space lattice)
a = 2R

10. METALLIC CRYSTAL STRUCTURES
(page 75-76)
10
• Actual Number of Atoms:
 Number of atoms associated with each unit cell,
 Some fractions of the atoms which assigned to a specific
cell,
 Atoms completely within the interior belongs to that unit
cell.
• Coordination Number:
 Numbers of nearest neighbor or touching atoms in a unit
cell.
• Atomic Packing Factors (APF):
 Sum of sphere volumes of all atoms divided by the unit cell
volume.

11. METALLIC CRYSTAL STRUCTURES
(page 75-76)
11
Coordination Number
• FCC: • SC:

12. METALLIC CRYSTAL STRUCTURES
(page 75-76)
12
Coordination Number
• HCP:

13. METALLIC CRYSTAL STRUCTURES
(page 75-81)
13
BCC FCC HCP SC
Actual no. of atom: 2 4 6 1
Unit cell length (a): a = (4/√3)R a = (2√2)R a = 2R a = 2R
Volume of unit cell (V): V=12.31R3 V=22.6R3 V=33.84R3 V=8R3
Coordination Number 8 12 12 6
APF: 0.68 0.74 0.74 0.52
Example Problem 4.1 & 4.2: (page 79)
??

14. METALLIC CRYSTAL STRUCTURES
(page 74-81)
14
• Density Computations-Metals: (page 80-81)
• Example Problem 4.4: (page 81)
??

15. POLYMORPHISM & ALLOTROPHY
(page 97)
15
Carbon: (diamond & graphite) Iron:
Tin: (white tin & grey tin)

16. LINEAR & PLANAR DENSITIES
(page 97-100)
16
• Linear Density:
??

17. LINEAR & PLANAR DENSITIES
(page 97-100)
17
• Planar Density:
??

18. X-RAY DIFFRACTION and BRAGG’S LAW
(page 103-109)
18
• Diffraction: (page 103)
A consequence of specific phase relationships established between
two or more waves that have been scattered by the obstacle.

19. X-RAY DIFFRACTION and BRAGG’S LAW
(page 103-109)
19
• Diffraction occurs when: (page 103)
A wave encounters a series of regularly spaced obstacles that:
 Are capable of scattering the wave,
 Have spacing comparable in magnitude to the wavelength.
• Effects after scattering (page 104)
Constructively Interfere

20. X-RAY DIFFRACTION and BRAGG’S LAW
(page 103-109)
20
• Effects after scattering (page 104)
Destructively Interfere

21. X-RAY DIFFRACTION and BRAGG’S LAW
(page 103-109)
21
• X-Ray Diffraction: (page 105)
X-rays:
??
Information about crystal structure of a material, i.e. Interplanar
spacing, lattice parameters, crystal structure; can be obtained
using X-Ray Diffraction.

22. X-RAY DIFFRACTION and BRAGG’S LAW
(page 103-109)
22
X-Ray Diffraction: (page 105)
nl = 2dhkl sinq Bragg’s Law  Interplanar
Spacing

23. X-RAY DIFFRACTION and BRAGG’S LAW
(page 103-109)
23
X-Ray Diffraction Rules and Reflection Indices for BCC, FCC and
SC: (page 106)

24. X-RAY DIFFRACTION and BRAGG’S LAW
24
• Diffraction Techniques: (page 106-107)

25. X-RAY DIFFRACTION and BRAGG’S LAW
(page 103-109)
25
• Example Problems 4.9 & 4.10: (page 108-109)