MSE 3300-Lecture Note 14-Chapter 09 Phase Diagrams
Transcript of MSE 3300-Lecture Note 14-Chapter 09 Phase Diagrams
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MSE 3300 / 5300 UTA Spring 2015 Lecture 14 -
Lecture 14. Phase Diagrams (1)
Learning Objectives After this lecture, you should be able to do the following:
1. Understand terminology associated with phase diagrams and
interpretate phase diagrams.
2. Sketch isomorphous phase diagrams and label the various regions
and liquidus, solidus, and solvus lines.3. Given a binary phase diagram, the composition of an alloy, and its
temperature, determine what phases are present, the compositions of
the phases, and the mass fractions of the phases.
Reading• Chapter 9: Phase Diagrams (9.1–9.10)
Multimedia
• Virtual Materials Science & Engineering (VMSE):
http://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/
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1. Definitions and Basic Concepts
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• Components: pure metals and/or compounds of which an alloy is composed
(e.g., in a copper–zinc brass, Cu and Zn).
• Solute and solvent
• System: (1) a specific body of material under consideration and (2) the series
of possible alloys consisting of the same components, but without regard to
alloy composition (e.g., the iron–carbon system).
• Solubility limit: maximum
concentration of solute
atoms that may dissolve in
the solvent to form a solid
solution.
Figure 9.1: The solubility of
sugar in a sugar–water syrup.
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Phases
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• Phase: a homogeneous portion of a system that has uniform physical and
chemical characteristics (e.g., phase 1: sugar–water syrup solution; phase 2:solid sugar).
• Single-phase system: homogeneous system
• Systems with two or more phases: mixtures or heterogeneous systems
• Equilibrium: The free energy of a
system is at a minimum undersome specified combination of
temperature, pressure, and
composition; the characteristics of
the system do not change (or the
system is stable).
• Phase equilibrium: a constancy
with time in the phase
characteristics of a system (sugar–
water syrup in contact with solid
sugar at 20 °C).
• Metastable state (Non-equilibrium)
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Phase Equilibria: Solubility Limit
Question: What is the
solubility limit for sugar inwater at 20°C?
Answer: 65 wt% sugar . At 20°C, if C < 65 wt% sugar: syrup
At 20°C, if C > 65 wt% sugar: syrup + sugar
65
• Solubility Limit:Maximum concentration forwhich only a single phase
solution exists.
Sugar/Water Phase Diagram
S
u g a r
T e m
p e r a t u r e ( ° C )
0 20 40 60 80 100 C = Composition (wt% sugar)
L(liquid solution
i.e., syrup)
SolubilityLimit L
(liquid)
+S
(solidsugar)20
4 0
6 0
8 0
10 0
W
a t e r
Adapted from Fig. 9.1,
Callister & Rethwisch 9e.
• Solution – solid, liquid, or gas solutions, single phase• Mixture – more than one phase
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• Components:
The elements or compounds which are present in the alloy(e.g., Al and Cu)
• Phases:The physically and chemically distinct material regions
that form (e.g., α and β).
Aluminum-
Copper
Alloy
Components and Phases
α
(darkerphase)
β (lighter
phase)
Adapted from chapter-
opening photograph,
Chapter 9, Callister,
Materials Science &
Engineering: An
Introduction, 3e.
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70 80 1006040200
T e m p e r a t u r e ( ° C
)
C = Composition (wt% sugar)
L(liquid solution
i.e., syrup)
20
100
40
60
80
0
L (liquid)+S
(solidsugar)
Effect of Temperature & Composition
• Altering T can change # of phases: path A to B.
• Altering C can change # of phases: path B to D.
water-
sugar
system
Fig. 9.1, Callister &
Rethwisch 9e.
D (100°C,C = 90)2 phases
B (100°C,C = 70)1 phase
A (20°C,C = 70)2 phases
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2. One-component (or Unary)
Phase Diagrams
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3. Binary Isomorphous Systems
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• Binary Isomorphous Systems: copper–nickel system
• Isomorphous: the complete liquid and solid solubility of the two components
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Criteria for Solid Solubility
CrystalStructure
electroneg r (nm)
Ni FCC 1.9 0.1246
Cu FCC 1.8 0.1278
• Both have the same crystal structure (FCC) and havesimilar electronegativities and atomic radii (W. Hume –
Rothery rules) suggesting high mutual solubility.
Simple system (e.g., Ni-Cu solution)
• Ni and Cu are totally soluble in one another for all proportions.
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Phase Diagrams
• Indicate phases as a function of T , C , and P .
• For this course: - binary systems: just 2 components.
- independent variables: T and C (P = 1 atm is almost always used).
PhaseDiagram
for Cu-Ni
system
• 2 phases:
L (liquid) α (FCC solid solution)
• 3 different phase fields:
L
L + α α
L (liquid)
α
(FCC solidsolution)
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Cu-Ni
phase
diagram
Isomorphous Binary Phase Diagram
• Phase diagram:
Cu-Ni system.
• System is:
Fig. 9.3(a), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary
Nickel Alloys, P. Nash, Editor, 1991. Reprinted
by permission of ASM International, Materials
Park, OH.)
-- binaryi.e., 2 components:
Cu and Ni.
-- isomorphousi.e., complete
solubility of one
component in
another; α phase
field extends from0 to 100 wt% Ni.
wt% Ni20 40 60 80 10001000
1100
1200
1300
1400
1500
1600
T (°C)
L (liquid)
α
(FCC solidsolution)
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wt% Ni20 40 60 80 10001000
1100
1200
1300
1400
1500
1600T (°C)
L (liquid)
α (FCC solid
solution)
Cu-Ni
phase
diagram
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Phase Diagrams:Determination of phase(s) present
• Rule 1: If we know T and C o, then we know:-- which phase(s) is (are) present.
• Examples:
A(1100°C, 60 wt% Ni):
1 phase: α B (1250°C, 35 wt% Ni):
2 phases: L + α
B
( 1 2 5 0 º C , 3
5 )
A(1100ºC,60) Fig. 9.3(a), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary
Nickel Alloys, P. Nash, Editor, 1991. Reprinted
by permission of ASM International, Materials
Park, OH.)
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Determination of Phase
Composition
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1. A tie line is constructed
across the two-phase
region at the temperature of
the alloy.
2. The intersections of the tie
line and the phaseboundaries on either side
are noted.
3. Perpendiculars are dropped
from these intersections to
the horizontal compositionaxis, from which the
composition of each of the
respective phases is read.
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wt% Ni20
1200
1300
T (°C)
L (liquid)
α
(solid)
30 40 50
Cu-Ni
system
Phase Diagrams:Determination of phase compositions
• Rule 2: If we know T and C 0, then we can determine:-- the composition of each phase.
• Examples: T A
A
35 C 0 32 C L
At T A = 1320°C:
Only Liquid (L) presentC L = C 0 ( = 35 wt% Ni)
At T B = 1250°C:
Both α and L present
C L = C liquidus ( = 32 wt% Ni)
C α = Csolidus ( = 43 wt% Ni)
At T D = 1190°C:
Only Solid (α ) present
C α = C 0 ( = 35 wt% Ni)
Consider C 0 = 35 wt% Ni
DT D
tie line
4 C α 3
Fig. 9.3(b), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary
Nickel Alloys, P. Nash, Editor, 1991. Reprinted
by permission of ASM International, Materials
Park, OH.)
BT B
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Determination of Phase Amounts:
Lever Rule
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• Rule 3: If we know T and C 0, then can determine:
-- the weight fraction of each phase.
• Examples:
At T A : Only Liquid (L) present
W L = 1.00, W α = 0 At T D : Only Solid (α ) present
W L = 0, Wα = 1.00
Phase Diagrams:Determination of phase weight fractions
wt% Ni
20
1200
1300
T (°C)
L (liquid)
α
(solid)
3 0 4 0 5 0
Cu-Ni
system
T A A
35 C 0
32 C L
BT B
DT D
tie line
4 C α 3
R S
At T B : Both α and L present
= 0.27
W L = S R +S
W α = R
R +S
Consider C 0 = 35 wt% Ni
Fig. 9.3(b), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary
Nickel Alloys, P. Nash, Editor, 1991. Reprinted
by permission of ASM International, Materials
Park, OH.)
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• Tie line – connects the phases in equilibrium with
each other – also sometimes called an isotherm
The Lever Rule
What fraction of each phase?
Think of the tie line as a lever
(teeter-totter)
M L M α
R S
wt% Ni
20
1200
1300
T (°C)
L (liquid)
α
(solid)
3 0 4 0 5 0
BTB
tie line
C 0 C L C α
S R
Adapted from Fig. 9.3(b),
Callister & Rethwisch 9e.
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Equilibrium Colling
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wt% Ni20
120 0
130 0
3 0 4 0 5 0110 0
L (liquid)
α
(solid)
T (°C)
A
35 C 0
L: 35 wt%Ni
Cu-Nisystem
• Phase diagram:
Cu-Ni system.
Adapted from Fig. 9.4,
Callister & Rethwisch 9e.
• Consider
microstuctural
changes that
accompany thecooling of a
C 0 = 35 wt% Ni alloy
Ex: Cooling of a Cu-Ni Alloy
46 35
43 32
α : 43 wt% Ni
L: 32 wt% Ni
Bα : 46 wt% Ni L: 35 wt% Ni
C
EL: 24 wt% Ni
α : 36 wt% Ni
24 36 D
α : 35 wt% Ni
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Nonequilibrium Colling
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Equilibrium Nonequilibrium
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• Slow rate of cooling: Equilibrium structure
• Fast rate of cooling: Cored structure
First α to solidify: 46 wt% Ni
Last α to solidify:
< 35 wt% Ni
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• C α changes as we solidify.
• Cu-Ni case: First α to solidify has C α = 46 wt% Ni.Last α to solidify has C α = 35 wt% Ni.
Equilibrium vs Cored Structures
Uniform C α : 35 wt% Ni
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Summary
1. Definitions and basic concepts: phases, phase
equilibrium, phase diagrams
2. One-component phase diagrams
3. Phase diagrams: Binary isomorphous systems
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