Transcript Chapter 9 Phase Diagrams 1

Chapter 9
Phase Diagrams
1
Phase Diagram Vocabulary
System
•
The universe or any part of it.
Phase
•
A region in the system that has a distinct structure and/or
composition
Structure
•
How the atoms or molecules of the components are physically
arranged in space
Composition
•
The relative amounts of different components
Components
•
Chemically distinct species, generally pure elements or
compounds
Phase Diagram
•
A graphical representation of the influence of various factors,
such as temperature, pressure, and composition on the phases
that exist in a system.
Unary System
•
A system that has only one component
Binary System
•
A system that has two components – what this course
primarily deals with
Ternary System
•
A system that has three components
Quaternary System
•
A system that has four components
A, B, C …
•
Generic names of components
L, α, β,  …
•
Generic names of phases
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Unary Phase Diagrams – H2O
1 atmosphere
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Unary Phase Diagram – Pure Fe
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Gibbs Phase Rule (Section 9.17)
• Tells us how many phases can exist under a given set of
circumstances.
P+F=C+2
• P = number of phases
• F = number of degrees of freedom – number of variables that can
be changed independently of all other variables in the system
• C=number of components
• The number two indicates the ability to change temperature and
pressure; these are non-compositional variables that affect the
phases.
• Modified Gibbs phase rule
• Most engineering systems function at a pressure of 1 atmosphere,
i.e. we have picked the pressure as one of our degrees of freedom.
Therefore,
P+F = C+1
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Binary Isomorphous System
• Two components are completely soluble in each other in
both solid and liquid phases
• Hume-Rothery’s Rules (Section 4.3 text 7th edition)
–
–
–
–
Atomic size difference not greater than 15%
Crystal structure is the same for both components
Similar electronegativity (i.e. no ionic bonding)
Elements have a similar valance
• Example: Cu-Ni System
–
–
–
–
rCu = 0.128 nm rNi = 0.125 nm
Both have a face centered cubic (fcc) structure
Electronegativity Cu = 0.19; Ni = 0.18
Valance – Cu+ and Cu++; Ni++
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Cooling Curves during Solidification
Solidification occurs at constant temperature while latent
heat of fusion is released
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Cooling curves for a binary
isomorphous alloy
Features:
•Solidus – locus of temperatures below which all compositions are solid
•Start of solidification during cooling
•Liquidus – locus of temperatures above which all compositions are liquid
•Start of melting during heating
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Modified Gibbs Phase Rule
• In the liquid or solid phase:
–
–
–
–
P=1, C=2
P+F=C+1
F=2
Both composition and
temperature can be varied
while remaining in the liquid
or solid phase
• In the L+a region
–
–
–
–
P=2, C=2
P+F=C+1
F=1
If we pick a temperature,
then compositions of L and
a are fixed
– If we pick a composition,
liquidus and solidus
temperatures are fixed
TL
TS
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Tie Line and Lever Rule
• At point B both
liquid and a are
present
• WL×R = WS×S
WL
WS
R
S
S
RS
R
WS 
RS
WL 
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Equilibrium Cooling
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• Non-equilibrium cooling
results in
– Cored structure
– Composition variations
in the solid phase as
layers of decreasing Ni
concentration are
deposited on previously
formed a phase
– Solidification point is
depressed
– Melting point on reheat
is lowered
• Homogenization or
reheating for extended
times at temperature
below e’
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Effect on Mechanical Properties
Due to solid solution strengthening, alloys tend to be stronger and less
ductile than the pure components.
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Binary Eutectic System
•
•
•
The two components
have limited solid
solubility in each other
Solubility varies with
temperature
For an alloy with the
Eutectic composition
the liquid solidifies into
two solid phases
Eutectic temperature
Liquid
61.9% Sn
Cooling
183ºC
α (solid solution) + β (solid solution)
18.3% Sn
97.8% Sn
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Binary Eutectic System
• Apply Modified Gibbs Phase Rule
Phases present: L, a and b (P=3)
Components: Pb and Sn (C=2)
P+F=C+1
F=0  no degrees of freedom
Therefore, three phases can coexist in a binary
system only at a unique temperature and for unique
compositions of the three phases
– Upon cooling, there is a temperature arrest during the
solidification process (eutectic reaction)
–
–
–
–
–
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Microstructures in the Eutectic System
Depending on the system, eutectic solidification can
result in:
•Lamellar structure – alternating plates
•Rod-like
•Particulate
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Microstructures in the Eutectic System
Solvus Line
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Microstructures in the Eutectic System
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Amounts of Phases at different temperatures
At Teutectic + DT
•
Wa proeutectic 
Q
PQ
P
WL 
PQ
Wa 
WL 
•
Q
PQ
P
PQ
At Teutectic - DT
QR
PQ R
P
Wb 
PQ R
Wa total 
Wa eutectic  Wa total  Wa proeutectic
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Other Reactions in the Binary System
• Upon Cooling the following reactions are
also possible
– Peritectic L + a  b
– Monotectic L1  L2 + a
– Eutectoid a  b + 
– Peritectoid a + b  
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Copper-Zinc System
• Terminal
phases
• Intermediate
phases
• Several
peritectics
• Eutectoid
• Two phase
regions
between any
two single
phase regions
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Mg-Pb System
• Intermediate
Compound
Mg2Pb
• Congruently
melting
Mg2Pb

L
heating
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Portion of the Ni-Ti System
• Congruently
melting
intermediate
phase 

 L
heating
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Iron-Carbon System
• Reactions on
cooling
• Peritectic
L+d
• Eutectic
L   + Fe3C
• Eutectoid
  a  Fe3C
Steel
Cast Iron
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Iron-Carbon or Iron-Fe3C
• In principle, the components of the phase diagram
should be iron (Fe) and carbon/graphite (C).
– Fe and C form an intermediate compound Fe3C, which is very
stable
– There isn’t anything of interest at carbon contents greater than
25 at.% or 6.7 wt.% C.
– Fe3C is considered to be a component, and the binary phase
diagram is drawn using Fe and Fe3C.
• Names of phases:
–
–
–
–
Ferrite  a iron – bcc structure
Austenite –  iron – fcc structure
High temperature d iron – bcc structure
Cementite – Fe3C
• Steels have carbon contents <2%, usually <1.2%
• Cast irons have carbon contents >2%
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Phase Transformations in Steels
Eutectoid Composition – 0.76wt% C
Pearlite
Alternating plates
(lamellae) of Fe
and Fe3C
Austenite
0.76wt.%C

Ferrite + Cementite (at 727ºC upon cooling)
0.022wt.%C
6.7wt.% C
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Phase Transformations in Steels
• Hypoeutectoid
composition <0.76 wt% C
• Proeutectoid ferrite
nucleates and spreads
along austenite grain
boundaries at T>727ºC
• Remaining austenite
converts to pearlite during
eutectoid transformation
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Phase Transformations in Steels
• Hypereutectoid
composition >0.76 wt% C
• Proeutectoid cementite
nucleates and spreads
along austenite grain
boundaries at T>727ºC
• Remaining austenite
converts to pearlite during
eutectoid transformation
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Phase Transformations in Steels
Hypoeutectoid
Hypereutectoid
Proeutectoid ferrite
Pearlite
Proeutectoid cementite
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Effect of Alloying Elements
•Addition of an alloying element increases the number of components in Gibbs
Phase Rule.
•The additional degree of freedom allows changes in the eutectoid temperature
or eutectoid Carbon concentration
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