Transcript Slide 1

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Phase Diagram (1)
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Pearlite in a plain-carbon steel,
0.05mm
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Phase Diagrams
Phase: A region of material that has uniform physical and
chemical properties and the same composition.
Represents phases present in metal at different
conditions (Temperature, pressure and
composition).
Indicates equilibrium solid solubility of one element
in another.
Indicates temperature range under which
solidification occurs.
Indicates temperature at which different phases
start to melt.
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Phase Diagram of Pure Substances
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Pure substance exist as solid, liquid and vapor.
Phases are separated by phase boundaries.
Example : Water, Pure Iron.
• Different phases coexist at triple point.
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After W. G. Moffatt, et al., “The Structure and Properties of Materials,” vol I: “Structure,” Wiley, 1965, p.151
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Gibbs Phase Rule
P = number of phases that coexist in a system
C = Number of components
F = Degrees of freedom
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P+F = C+2
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For pure water, at triple point, 3 phases coexist.
There is one component (water) in the system.
Therefore 3 + F = 1 + 2
F = 0.
Degrees of freedom indicate number of variables that
can be changed without changing number of phases.
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Multi-component Phase-Diagram
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Terminologies
Alloy: A mixture of a metal with other metals or nonmetals (the “alloying elements”). Ceramics, too, can
be mixed to form alloys.
Alloy System: All the alloys you can make with a given
set of components.
Components: The chemical elements which make up
the alloy.
Concentrations: Weight ( or atom, or mol) % of
component in an alloy
WA = [( weight of component A)/( weights of all components)]  100%
XA = [( number of atoms of component A)/(number of atoms of all
components)]  100%
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Equilibrium Constitution of an Alloy: At a given,
constant temperature T and pressure P, there is no
further tendency for the constitution to change with
time. This constitution is the stable one.
State Variables (or independent constitution
variables): T, P, and composition.
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Terminologies
Constitution of an Alloy:
1) The overall composition
2) The number of phases
3) The composition of each phase
4) The proportion by weight of each phase
Phase Diagram ( or Equilibrium Diagram, or
Equilibrium-Constitution Diagram): Diagram that
summarizes the equilibrium constitution of the alloy
system.
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Constitution Point: A point defined by the state
variables. If this point is given, then the equilibrium
number of phases can be read off. So, too, can their
composition and the quantity of each phase. (The
diagram tells you the entire constitution of any given
alloy, at equilibrium.)
Fields: Regions in which the number of phases is
constant.
Phase Boundaries: The Boundaries between fields.
When a phase boundary is crossed, a phase change
starts, or finishes, or both.
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Phase Analysis in Lead-Tin System
Pb + 50at%Sn
• Liquid
• Reaction: Liquid Liquid + Pb
(3) Liquid+ Pb
(4) Reaction: Liquid  Sn + Pb
(5) Sn + Pb
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Composition of the Phases
Rule 1:
When the constitution point lies in a single-phase region,
the alloy consists of a single, homogeneous, phase. Its
composition must be that of the alloy. The phase
composition and the alloy composition coincide in
single-phase fields.
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Composition of the Phases
Rule 2:
When the constitution point for an alloy lies in the twophase field the alloy breaks up into a mixture of two
phases. The composition of each phase is obtained by
constructing the tie line (the isotherm spanning the twophase region, terminating at the nearest phase boundary
on either side). The composition of each phase is
defined by the end of the tie line.
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Lever Rule
Wt fraction of solid phase
= Xs = w0 – w1
ws – w1
Wt fraction of liquid phase
= Xl = ws – w0
ws – w1
W0 is the weight percentage of the alloy.
Ws is the weight percentage within the solid
phase
Wl is the weight percentage in the liquid
phase
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Example
Pb-20Sn
At 150C
•Phase 1: Sn-2Pb;
•Phase 2: Pb–10Sn
•Wphase1 = 11%;
•Wphase2 = 89%
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Phase Diagram Measurements
1. Cooling Curves
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Phase Diagram Measurements
1. Cooling
Curves (Cont’d.)
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Cooling Curves
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Used to determine phase transition temperature.
• Temperature and time data of cooling molten metal is
recorded and plotted.
Pure Metal
Iron
• Thermal arrest : heat lost = heat supplied by solidifying
metal
• Alloys solidify over a range of temperature (no thermal
arrest)
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Phase Diagram Measurements
2. DTA (Differential Thermal Analysis)
A sample with the same
thermal mass as the test
sample, but showing no
phase transformation, is
cooled (or heated) sideby-side with the test
sample, and the
difference T between the
cooling (or heating)
curves is plotted.
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Summary
– Alloy, Component,
Concentrations, Phase, Constitution of the
Alloy, Equilibrium Constitution of the Alloy,
State Variables, Alloy System, Phase
Diagram, Constitution Points, Fields, Phase
Boundaries, etc.
1. Terminologies
2. Nature of Phase Diagrams, Fields in Phase
Diagrams, Single-phase field, two-phase field, etc.
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Summary
3. Composition of Phases
(1) Rule 1: Single-phase fields: Composition of
alloy is the same as Composition of the phase
(2) Rule 2: Tie line decide the composition of each
phase in two-phase field
(3) Lever Rule
4. Gibbs’ Phase Rule
F=C–P+2
If pressure keep constant
F=C–P+1
5. Measurement of Phase Diagram: Cooling Curve,
DTA
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