Post on 08-Aug-2018
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CHAPTER 7
Chapter 9-
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Contents of Todays Lecture
Introduction to phase change processes. Phase diagram.
Chapter 9-
conditions of solubilities.
Lever Rule.
Fe-C phase diagram.
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Introduction to phase diagrams
Most of the engineering materials are alloys. In a poly-phase material, the overall properties
depend upon Number of hases resent
Chapter 9-
Relative amount of each phase Composition and microstructure of each phase
Size and distribution of the phases in the microstructure.
In this topic we are going to develop theunderstanding of composition-structure-property relationship of materials.
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About Phase diagram
The phase diagram or Equilibrium diagram is the
graphical representation of number of phases that arepresent, their compositions and the relative amount ofeach phase as the functions of temperature and theoverall composition of the material.
Chapter 9-
The term equilibrium denotes a state of rest whichimplies that, for a given composition and temperature,there shall not be any change in the constituents withtime.
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Solid solution.
Solid Solution: When two elements dissolvein the solid state, the resulting phase iscalled as solid solution.
Chapter 9-
There are following possibilities The metals are completely soluble in solid
state.
The metals are completely insoluble in solidstate.
The metals are partially soluble in solid
state.
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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 Vocabulary
Chapter 9-
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 courseprimarily deals with
Ternary System A system that has three components
Quaternary System A system that has four components
A, B, C Generic names of componentsL, , , Generic names of phases
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Material Science & Engineering
Processing Structure Properties Performance
Chapter 9-
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What is materials science and
engineering?
Materials science is the investigation of therelationships that exist between the
structure and ro erties of materials.
Chapter 9-
Materials engineering uses the structure-
property relationships of materials to link
processing withperformance.
Processing Structure Properties Performance
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Whats meant by the structure of a
material?
Subatomic- Interactions of electrons with anucleus
Atomic- Arrangement of atoms relative to
Chapter 9-
each other Microscopic- Organization of large groups
of atoms (can be seen with a microscope)
Macroscopic- Structure that can beobserved with the naked eye.
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Example: Snow.
Chapter 9-
Individualmolecules arearranged into
crystals
Individualcrystals form
a solidstructure
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.is a lot like metal
Chapter 9-
Individualatoms are
arranged intograins
Individualgrains form
a solidstructure
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TerminologyTerminologyTerminologyTerminology
Chapter 9-
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SYSTEM
SYSTEM
Chapter 9-
SURROUNDING
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Components (C)Components (C)Components (C)Components (C)No. of Elements or Compounds thatNo. of Elements or Compounds thatNo. of Elements or Compounds thatNo. of Elements or Compounds that
constitute a systemconstitute a systemconstitute a systemconstitute a system
1-C
Chapter 9-
-
3-C
4-C
Multi-C
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PhasePhasePhasePhase Physically distinct,
Mechanically Separable &
Chemically homogeneous
Chapter 9-
Region of a system is called as phase.
Homogeneous portion of a system that has
uniform physical and chemical characteristics is
called as a PHASE
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Solid
Various phases [e.g. crystal structures (diamond; graphite)
Alloys (sometimes its difficult to tell this - microscopic
examination may be necessary {dispersions uniform onmacroscopic scale}) Miscible one phase (P=1)
Chapter 9-
Liquid Miscible liquids are one phase
Immiscible liquids are multiple phases (P>1)
Gas
Systems consisting of gases can have only one phase
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Definitions
Heterogeneous and homogeneous systems
Systems with one phase are homogeneous
Systems with more than one phase are heterogeneous
Constituent- a chemical species (ion or molecule which ispresent
Component (C) - chemically independent constituents of a
Chapter 9-
C = #of independent chemical constituents - # ofdistinct chemical reactions #of independent chemical constituents = total # of constituents
minus the number of any restrictive conditions (chargeneutrality, material balance etc.)
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(lighterphase)
Solid PhaseSolid PhaseSolid PhaseSolid PhaseCOMPONENTS AND PHASES
Chapter 9- 33
AlAlAlAl----CuCuCuCu
AlloyAlloyAlloyAlloy
ar er
phase)
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EquilibriumEquilibriumEquilibriumEquilibrium
State of a System at specified conditionswhen the system possesses minimum free
ener
Chapter 9-
Temperature, Pressure & Composition
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PHASE EQUILIBRIUMPHASE EQUILIBRIUMPHASE EQUILIBRIUMPHASE EQUILIBRIUM
Constancy with time in physicalcharacteristics
Chapter 9-
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Gibbs Phase RuleGibbs Phase RuleGibbs Phase RuleGibbs Phase Rule For a solid solution, the phase rule is
{P + F = C + N
}
P No. of Phases
Chapter 9-
F DOF
CNo. of Components
N Non-compositional variables
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Degree of Freedom (DOF)Degree of Freedom (DOF)Degree of Freedom (DOF)Degree of Freedom (DOF)
The number of independent variables
required to describe the state of a system is
called as the DOF
Chapter 9-
Externally controlled variables
(Temp, Pressure, Composition)
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Gibbs Phase RuleGibbs Phase RuleGibbs Phase RuleGibbs Phase Rule Ex. Ice + Water, heating at constant pressure
{P + F = C + N
}
P No. of PhasesP + F = 1 + 1
Chapter 9-
F DOF
CNo. of Components
N Non-compositional variables
F = 2 - P
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One Component Systems
Phase rule says that you can have at most 3 phasesF = C- P +2; C=1 so F=3-P
If P=3, F=0 system is invariant Specified by temperature and pressure and occurs at 1 point
(called the triple point)
If one phase is present, F = 2 that is P and T can be varied
Chapter 9-
n epen en y
This defines an area in a P,T diagram which only onephase is present
If two phases are present, F = 1 so only P or T can bevaried independently.
This defines a line in a P, T diagram
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Solubility LimitSolubility LimitSolubility LimitSolubility Limit
The elements or compounds which are
mixed
Chapter 9-
Solvent SoluteAt some specific temperature there is a maximum concentration
of solute atoms that may dissolve in the solvent to form a solid
solution this is called solubility limit
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erature
(C)
Lli uid solution
SolubilityLimit L
(liquid)+60
80
100
THE SOLUBILITY LIMIT
Chapter 9- 2
Pure
Sugar
Temp
0 20 40 60 80 100Co=Composition (wt% sugar)
i.e., syrup)
(solidsugar)
65
20
Pure
Water
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Changing T can change # of phases: path A to B.
Changing Co can change # of phases: path B to D.
)
B(100,70)1 phase
100
D(100,90)2 phases
EFFECT OF T & COMPOSITION (Co)
Chapter 9-
70 80 1006040200
Tem
perature(
Co=Composition (wt% sugar)
L(liquid solution
i.e., syrup)
A(70,20)2 phases
20
40
60
0
(liquid)+S
(solidsugar)
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PhasePhasePhasePhase----EquilibriumEquilibriumEquilibriumEquilibrium
Chapter 9-
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Phase DiagramsPhase DiagramsPhase DiagramsPhase Diagrams
1-Component
2-Components
3-Components
Chapter 9-
Unary P.D. (Binary P.D.) (Ternary P.D.)
Much of the information about the control of microstructure or
phase structure of a particular alloy system is conveniently and
concisely displayed in what is called a phase diagram, also
often termed as equilibrium or constitutional diagram.
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Unary Phase Diagram (Fe)
GAS
LIQUID
3000
1535
P + F = C + N
P + F = 1 + 2
F = 3 - P
Chapter 9-Pressure (GPa)
Temp (oC)
FCC ()
HCP ()
BCC ()
BCC ()
1410
910
For s ngle P,F = 2
For two P,
F = 1
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BINARY ISOMORPHOUS DIAGRAMBINARY ISOMORPHOUS DIAGRAMBINARY ISOMORPHOUS DIAGRAMBINARY ISOMORPHOUS DIAGRAM
Cu + NiCu + NiCu + NiCu + Ni
Chapter 9-
100 % Liquid solubility and100 % Liquid solubility and100 % Liquid solubility and100 % Liquid solubility and100 % Solid solubility100 % Solid solubility100 % Solid solubility100 % Solid solubility
PHASE DIAGRAM f C Ni
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1400
1500
1600
T(C)
L (liquid)
qu
idus
PHASE DIAGRAM for Cu-Ni
1453 C
Chapter 9- 5
20 40 60 80 10001000
1100
1200
(FCC solidsolution)
L
solidu
(Cu) (Ni)
1085 C
COMPOSITION WT %
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InterpretationInterpretationInterpretationInterpretationof Phase Diagramsof Phase Diagramsof Phase Diagramsof Phase Diagrams
1. Phases Present
Chapter 9-
2. Composition of Phases
3. Weight Fraction of Phases
T(C) Phases PresentPhases PresentPhases PresentPhases Present
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1400
1500
1600T(C)
L (liquid)
liquidu
s
solidus
1250,35)
Phases PresentPhases PresentPhases PresentPhases Present
Chapter 9- 6
wt% Ni20 40 60 80 1000
1000
1100
1200(FCC solidsolution)
L
A(1100,60)
B
composition of phasescomposition of phasescomposition of phasescomposition of phases
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1300
T(C)
L (liquid)liq
uidus
olidu
s
TAA
B
tie line
L+
composition of phasescomposition of phasescomposition of phasescomposition of phases
1280 C
1320C
Chapter 9- 7
wt% Ni
20
1200
(solid)L+
30 40 50
DTD
433532
CoCL C
weight fractions of phases
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1300
T(C)
L (liquid) liquid
us
solid
us
TA A
TBB
tie line
L+
weight fractions of phases
Chapter 9- 8
wt% Ni
20
1200
(solid)L+
30 40 50
DTD
433532C
oC
LC
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CoR S
CL C
THE LEVER RULE
Chapter 9- 9
WWL
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WL= S/(R+S) WL= (C-C0)/(C-CL)
Chapter 9-
W = (C0-CL)/(C-CL)
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Volume Fraction of Phases
Chapter 9-
Relation in between
Volume and Weight Fraction
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Equilibrium COOLING IN A Cu-Ni
Chapter 9-
COOLING IN A Cu Ni BINARY
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COOLING IN A Cu-Ni BINARY
Equilibrium Cooling
System is:Binaryi.e., 2 components:
Chapter 9-
u an .
Isomorphousi.e., complete solubility of one
component in another; phase
field extends from 0 to 100wt% Ni.
Extreme slow cooling of alloy
EX: COOLING IN A Cu-Ni BINARY
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1300
L (liquid)
L+
T(C)
A
D
B
L: 35wt%Ni
: 46wt%Ni
C
L: 35wt%Ni
4643
32
24
35
L: 32wt%Ni
EX: COOLING IN A Cu Ni BINARY
Chapter 9-10wt% Ni20
1200
30 40 501100
(solid)
L+
35Co
E : 43wt%NiL: 24wt%Ni
: 36wt%Ni
COOLING IN A Cu-Ni BINARY
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COOLING IN A Cu-Ni BINARY
Non-Equilibrium Cooling
System is:Binary
Chapter 9-
.e., componen s:
Cu and Ni.
Isomorphousi.e., complete solubility of one
component in another; phasefield extends from 0 to 100wt% Ni.
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Non-Equilibrium COOLING IN A
-
Chapter 9-
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Chapter 9-
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NonNonNonNon----Equilibrium CoolingEquilibrium CoolingEquilibrium CoolingEquilibrium Cooling
Consequences of Non-Equilibrium cooling
Chapter 9-
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C changes as we solidify.
Cu-Ni case:
Fast rate of cooling:Cored structure
Slow rate of cooling:Equilibrium structure
First to solidify has C = 46wt%Ni.Last to solidify has C = 35wt%Ni.
Uniform C:
CORED VS EQUILIBRIUM PHASES
Chapter 9-
46wt%Ni
35wt%Ni
Last to solidfy:
< 35wt%Ni
MECHANICAL PROPERTIES: Cu-Ni System
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Effect of solid solution strengthening
on:--Tensile strength (TS) --Ductility (%EL,%AR)
MECHANICAL PROPERTIES: Cu-Ni System
on(%EL)
50
60
%EL forpure Ni
%EL for pure Cu
ngth(MP
a)
400
TS for
Chapter 9-
Elong
at
Com osition, wt%Ni
Cu Ni0 20 40 60 80 100
20
30
TensileSt
re
Composition, wt%Ni
Cu Ni0 20 40 60 80 100
200
300pure
TS for pure Cu
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Binary Eutectic SystemsBinary Eutectic SystemsBinary Eutectic SystemsBinary Eutectic Systems
Chapter 9-
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Binary Eutectic System
Apply Modified Gibbs Phase Rule Phases present: L, and (P=3)
Components: Pb and Sn (C=2)
Chapter 9-
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)
T(C)BINARY-EUTECTIC SYSTEMS
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L (liquid)
L + L+
1200( )
600
800
1000
TE 8.0 71.9 91.2779C
A
B E G
Solidus
line F
Chapter 9-13
+
Co, wt% Ag20 40 60 80 1000
200
400
CE
C
o vus ne
H
EX: Pb-Sn EUTECTIC SYSTEM
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L + L+ 200
T(C)
300
L (liquid)
represents a solid solution of tin in lead
For tin is a solvent and lead is a solute
Chapter 9-14
+
18.3
Co, wt% Sn
20 40 60 80 1000Co
100
61.9 97.8150
Wh d l k k ?
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What we wd like to know?
Microstructure Com osition
Chapter 9-
Weight Fraction
EX: Pb-Sn EUTECTIC SYSTEM
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L + L+ 200
T(C)
300
L (liquid)
183C
Chapter 9-15
+
18.3
Co, wt% Sn
20 40 60 80 1000Co
100
61.9 97.8150
11 99
R S
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Amounts of Phases at different temperatures
QP
PW
QP
QW
L+
=
+=
At Teutectic + T
( )
QP
PW
QP
QW
L
cproeutecti
+=
+=
Chapter 9-
eutectic -
( )
RQP
PW
RQP
RQW
total
++
=
++
+=
( ) ( ) ( )cproeutectitotaleutectic
WWW =
MICROSTRUCTURES IN EUTECTIC SYSTEMS
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L +
T(C)
300 L
L: Co
wt%Sn
L
400
solidus Liquidus
Chapter 9-16
Co, wt% Sn10
2
200Co
100
30
: Co
wt%Sn
+
(room T solubility limit)
TE-
System)
MICROSTRUCTURES IN EUTECTIC SYSTEMS
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2wt%Sn < Co < 18.3wt%Sn
Result:-- polycrystal with fine
crystals.
L +
T(C)
300
L
L: Cowt%Sn
400
L
d
Chapter 9-17
o
200
Co, wt% Sn10
18.3
200Co
100
30
+
(sol. limit at TE)
TE
2(sol. limit at Troom)
solvus
f
g
MICROSTRUCTURES
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T(C)
300
L: Cowt%Sn
Micrograph of Pb-Sneutecticmicrostructure
Co = CE Result: Eutectic microstructure
--alternating layers of and crystals.
IN EUTECTIC SYSTEMS
Chapter 9-18
L + 200
Co
, wt% Sn
20 400
100
60
+
TE
: 18.3wt%Sn
080 100
L +
CE18.3 97.8
61.9
183C
: 97.8wt%Sn 160m
Pb-Sn
system
MICROSTRUCTURES
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T(C)
300 L
L: Cowt%Sn
L
L
18.3wt%Sn < Co < 61.9wt%Sn
Result: crystals and a eutectic microstructure
Just above TE:C= 18.3wt%Sn
CL = 61.9wt%Sn
IN EUTECTIC SYSTEMS
Chapter 9-
L +
200
Co, wt% Sn
20 400
100
60
+
TE
080 100
L +
Co18.3 61.9
primary
97.8
S
S
R
R
eutectic eutectic
19
-
system WL= (1-W) =50wt%R+ S
W = =50wt%
Just below TE:
C = 18.3wt%Sn
C= 97.8wt%SnS
R+ SW = =73wt%
W= 27wt%
HYPOEUTECTIC & HYPEREUTECTIC
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T(C)
(Pb-Sn
System)
L + 200
Co, wt% Sn20 400
300
100
L
60
+
TE
080 100
L +
Cohypoeutectic
Cohypereutectic
HYPOEUTECTIC & HYPEREUTECTIC
Chapter 9-20
18.3
61.9
97.8eutectic
hypereutectic: (illustration only)
160m
eutectic: Co=61.9wt%Sn
175m
hypoeutectic: Co=50wt%Sn
eutectic micro-constituent
IRON-CARBON (Fe-C) PHASE DIAGRAM
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ite)
1600
1400
1200
L
(austenite)
+L L+Fe3C
1148C A
SR
Chapter 9-21
Fe3C
(ceme
n1000
800
600
4000 1 2 3 4 5 6 6.7
+Fe3C
+Fe3C
+
(Fe) C wt% C0.77 4.30
727C = TeutectoidB
R S
Important Points of to study Fe-C Diagram
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1. Pure Iron (0% C)
2. Cementite (Fe3C) (6.70% of C)
3. Alpha Ferrite4. Austenite
Chapter 9-
.
6. Cementite7. Reactions (Eutectic and Eutectoid)
8. Ferrous alloy
9. Eutectoid Alloy
10. Hypo-Eutectoid Alloy
11. Hyper-Eutectoid Alloy
IRON-CARBON (Fe-C) PHASE DIAGRAM
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2 importantpoints
-Eutectic (A):
-Eutectoid (B):
L +Fe3C
+Fe3C
ementite)
1600
1400
1200
1000
L
(austenite)
+L
+Fe3C
L+Fe3C
1148C
T(C)
A
SR
IRON-CARBON (Fe-C) PHASE DIAGRAM
Chapter 9-21
Result: Pearlite =
alternating layers of and Fe3C phases.
120m
Fe3C
(c
600
4000 1 2 3 4 5 6 6.7
+Fe3C
(Fe) Co, wt% C0.77 4.30
= eutectoid
R S
Fe3C (cementite-hard)
(ferrite-soft)
Ceutec
toid
Iron-Carbon System
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Reactions on
cooling
Peritectic
L +
Chapter 9-
Eutectic
L + Fe3C
Eutectoid
+ Fe3C
Steel Cast Iron
Iron-Carbon or Iron-Fe3C
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In principle, the components of the phase diagram should beiron (Fe) and carbon/graphite (C). Fe and C form an intermediate compound Fe3C, which is very stable
There isnt 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.
Chapter 9-
Ferrite iron bcc structure Austenite iron fcc structure
High temperature iron bcc structure
Cementite Fe3C
Steels have carbon contents
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Cabon ALLOYS
Chapter 9-
HYPOEUTECTOID STEEL
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HYPOEUTECTOID STEEL
Chapter 9-22
HYPEREUTECTOID STEEL
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HYPEREUTECTOID STEEL
Chapter 9-23
ALLOYING STEEL WITH MORE ELEMENTS
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tectoid(
C)
Ti
800
1000
1200
Mo
Si
W
Crtectoid(
wt%C)
Ni
0.4
0.6
0.8
Cr
Si
Teutectoid changes: Ceutectoid changes:
Chapter 9-
T
Eu
wt. % of alloying elements
Ni600
0 4 8 12
Mn
wt. % of alloying elements
C
eu
Ti
0 4 8 120
0.2 W
Mo
24
SUMMARY
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Phase diagrams are useful tools to determine:
--the number and types of phases,
--the wt% of each phase,--and the composition of each phase
for a given T and composition of the system.
Chapter 9-25
Alloying to produce a solid solution usually
--increases the tensile strength (TS)
--decreases the ductility.
Binary eutectics and binary eutectoids allow for
a range of microstructures.