4. • Coordination # = 8
• Atoms touch each other along cube diagonals.
BODY CENTERED CUBIC STRUCTURE (BCC)
5. • Coordination # = 12
• Atoms touch each other along face diagonals.
FACE CENTERED CUBIC STRUCTURE (FCC)
6. ATOMIC PACKING FACTOR (APF)
APF =
Volume of atoms in unit cell*
Volume of unit cell
*assume hard spheres
7. close-packed directions
a
R=0.5a
contains 8 x 1/8 =
1 atom/unit cell
APF =
a3
4
3
p (0.5a) 3
1
atoms
unit cell
atom
volume
unit cell
volume
= 0.52
ATOMIC PACKING FACTOR: SCC
8. ATOMIC PACKING FACTOR: BCC
a
APF =
4
3
p ( 3a/4)3
2
atoms
unit cell atom
volume
a3
unit cell
volume
length = 4R =
Close-packed directions:
3 a
• APF for a body-centered cubic structure
a
R
a
2
a
3
= 0.68
9. ATOMIC PACKING FACTOR: FCC
maximum achievable APF
APF =
4
3
p ( 2a/4)3
4
atoms
unit cell atom
volume
a3
unit cell
volume
Close-packed directions:
length = 4R = 2 a
Unit cell contains:
6 x1/2 + 8 x1/8
= 4 atoms/unit cell
a
2 a
=0.74
11. PHASE DIAGRAM
A phase diagram shows the phases
and their compositions at any combination
of temperature and alloy composition
12. SOLUBILITY
• how much of each material or component we can combine without producing an
additional phase
• Unlimited Solubility
• When we pour a substance into another and stir, and only one phase is produced
regardless the quantity.
• Limited Solubility
• when we pour a substance into another and stir, and two phases is produced after
a certain amount.
13. CONDITIONS FOR UNLIMITED SOLID SOLUBILITY
• the Hume-Rothery rules, are as follows:
• 1. Size factor: The atoms or ions must be of similar size, with no more than a 15%
difference in atomic radius
• 2. Crystal structure: The materials must have the same crystal structure
• 3. Valence: The ions must have the same valence
• 4. Electronegativity: The atoms must have approximately the same electronegativity.
14. BINARY PHASE DIAGRAMS
• When only two elements or two compounds are present in a material, a binary
phase diagram can be constructed.
15. LIQUIDUS AND SOLIDUS CURVES
Liquidus temperature is the temperature
above which a material is completely liquid
Solidus temperature is the temperature
below which the alloy is 100% solid.
16.
17. HOW TO DETERMINE A COMPOSITION
A tie line is a horizontal line within a two-phase
region drawn at the temperature of interest
18. QUESTION 1
Determine the composition of each phase in a
Cu-40% Ni alloy at 1300°C, 1270°C, 1250°C,
and 1200°C
19. SOLUTION
1300°C: Only liquid is present
The liquid must contain 40%Ni
1270°C:Two phases are present
the liquid contains 37% Ni, and the solid contains 50% Ni.
1250°C: two phases are present.
the liquid contains 32% Ni, and the solid contains 45% Ni.
1200°C: Only solid is present, so the solid must
contain 40% Ni.
