CHAPTER 7
PHASE DIAGRAMS
Chapter 9-
Contents of Todays Lecture
Introduction to phase change processes. Phase diagram. Phase diagrams based on different conditions of solubilities. Lever Rule. Fe-C phase diagram.
Chapter 9-
Introduction to phase diagrams
Most of the engineering materials are alloys. In a poly-phase material, the overall properties depend upon
Number of phases present 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 the understanding of composition-structureproperty relationship of materials.
Chapter 9-
About Phase diagram
The phase diagram or Equilibrium diagram is the graphical representation of number of phases that are present, their compositions and the relative amount of each phase as the functions of temperature and the overall composition of the material. The term equilibrium denotes a state of rest which implies that, for a given composition and temperature, there shall not be any change in the constituents with time.
Chapter 9-
Solid solution.
Solid Solution: When two elements dissolve in the solid state, the resulting phase is called as solid solution. There are following possibilities
The metals are completely soluble in solid state. The metals are completely insoluble in solid state. The metals are partially soluble in solid state.
Chapter 9-
Phase Diagram Vocabulary
System Phase Structure Composition Components Phase Diagram The universe or any part of it. A region in the system that has a distinct structure and/or composition How the atoms or molecules of the components are physically arranged in space The relative amounts of different components Chemically distinct species, generally pure elements or compounds A graphical representation of the influence of various factors, such as temperature, pressure, and composition on the phases that exist in a system. A system that has only one component A system that has two components what this course primarily deals with A system that has three components A system that has four components Generic names of components Generic names of phases
Chapter 9-
Unary System Binary System Ternary System Quaternary System A, B, C L, , ,
Material Science & Engineering
Processing
Structure
Properties
Performance
Chapter 9-
What is materials science and engineering? Materials science is the investigation of the relationships that exist between the structure and properties of materials. Materials engineering uses the structureproperty relationships of materials to link processing with performance.
Processing Structure Properties Performance
Chapter 9-
Whats meant by the structure of a material? Subatomic- Interactions of electrons with a nucleus Atomic- Arrangement of atoms relative to each other Microscopic- Organization of large groups of atoms (can be seen with a microscope) Macroscopic- Structure that can be observed with the naked eye.
Chapter 9-
Example: Snow.
Individual molecules are arranged into crystals
Individual crystals form a solid structure
Chapter 9-
.is a lot like metal
Individual atoms are arranged into grains
Individual grains form a solid structure
Chapter 9-
Terminology
Chapter 9-
SYSTEM
SYSTEM
SURROUNDING
Chapter 9-
Components (C)
No. of Elements or Compounds that constitute a system
1-C 2-C 3-C 4-C Multi-C
Chapter 9-
Phase
Physically distinct, Mechanically Separable & Chemically homogeneous 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
Chapter 9-
Solid
Various phases [e.g. crystal structures (diamond; graphite)
Alloys (sometimes its difficult to tell this - microscopic examination may be necessary {dispersions uniform on macroscopic scale})
Miscible one phase (P=1) Immisible multiple phases (P>1)
Liquid
Miscible liquids are one phase Immiscible liquids are multiple phases (P>1)
Gas
Systems consisting of gases can have only one phase
Chapter 9-
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 is present Component (C) - chemically independent constituents of a system C = #of independent chemical constituents - # of distinct chemical reactions
#of independent chemical constituents = total # of constituents minus the number of any restrictive conditions (charge neutrality, material balance etc.)
Chapter 9-
Solid Phase
COMPONENTS AND PHASES
(lighter phase) (darker phase)
AlAl-Cu Alloy
Chapter 9- 3
Equilibrium
State of a System at specified conditions when the system possesses minimum free energy
Temperature, Pressure & Composition
Chapter 9-
PHASE EQUILIBRIUM
Constancy with time in physical characteristics
Chapter 9-
Gibbs Phase Rule
For a solid solution, the phase rule is
{P+F=C+N} P F C N No. of Phases DOF No. of Components Non-compositional variables
Chapter 9-
Degree of Freedom (DOF)
The number of independent variables required to describe the state of a system is called as the DOF
Externally controlled variables (Temp, Pressure, Composition)
Chapter 9-
Gibbs Phase Rule
Ex. Ice + Water, heating at constant pressure
{P+F=C+N} P F C N No. of Phases F=2-P DOF No. of Components Non-compositional variables
Chapter 9-
P+F=1+1
One Component Systems
Phase rule says that you can have at most 3 phases
F = 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 independently This defines an area in a P,T diagram which only one phase is present If two phases are present, F = 1 so only P or T can be varied independently. This defines a line in a P, T diagram
Chapter 9-
Solubility Limit
The elements or compounds which are mixed
Solvent
Solute
Chapter 9-
At 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
THE SOLUBILITY LIMIT
100 Temperature (C) 80 60 40 20 0 Solubility Limit
L
(liquid)
L
(liquid solution i.e., syrup)
+ S
(solid sugar)
Pure Sugar
Chapter 9- 2
Pure Water
20 40 6065 80 100 Co=Composition (wt% sugar)
EFFECT OF T & COMPOSITION (Co)
Changing T can change # of phases: path A to B. Changing Co can change # of phases: path B to D.
B(100,70) D(100,90) 100
Temperature (C)
1 phase 2 phases
80 60 40 20 0
0
L
(liquid)
L
(liquid solution
i.e., syrup)
+ S
(solid sugar)
A(70,20)
2 phases
20 40 60 70 80 100 Co=Composition (wt% sugar)
Chapter 9-
PhasePhase-Equilibrium & Phase Diagram
Chapter 9-
Phase Diagrams
<Components>
1-Component Unary P.D. 2-Components (Binary P.D.) 3-Components (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.
Chapter 9-
Unary Phase Diagram (Fe)
GAS
3000
P+F=C+N LIQUID P+F=1+2 F=3-P
1535 1410 910
BCC ()
FCC ()
For single P, F=2 For two P, F=1
Temp (oC)
HCP () BCC () Pressure (GPa)
Chapter 9-
BINARY ISOMORPHOUS DIAGRAM Cu + Ni 100 % Liquid solubility and 100 % Solid solubility
Chapter 9-
T(C)
1600 1500 1400 1300 1200 1100 1000 0
(Cu) 1085 C
PHASE DIAGRAM for Cu-Ni
2 phases:
L (liquid)
s u id u liq + s L lidu so
1453 C
3 phase fields:
(FCC solid solution)
60 80 100
Chapter 9- 5
20
40
COMPOSITION WT % (Ni)
Interpretation of Phase Diagrams
1. 2. 3. Phases Present Composition of Phases Weight Fraction of Phases
Chapter 9-
T(C)
1600 B(1250,35) (1250,35) 1500 1400 1300 1200 1100 1000 0 20 40
Phases Present
L (liquid)
L (FCC solid
solution)
A(1100,60) 60 80 100
s u id u s liq u id l so
wt% Ni
Chapter 9- 6
composition of phases
T(C) TA
1300
A L (liquid) B
L +
tie line dus i u q li
1320C 1280 C
+ L s
so lidu
TB
1200
TD
20
(solid)
50
Chapter 9- 7
30 32 35 4043
CLCo
C wt% Ni
T(C) TA
1300
weight fractions of phases
A L (liquid)
tie line dus i u q li
TB
1200
B R S
L +
+ L s
u d i l so
TD
20
(solid)
50
Chapter 9- 8
30 32 35 4043
CLCo
C wt% Ni
THE LEVER RULE
CL R
Co S
WL
Chapter 9- 9
WL= S/(R+S) WL= (C-C0)/(C-CL) W = R/(R+S) W = (C0-CL)/(C-CL)
Chapter 9-
Volume Fraction of Phases
Relation in between
Volume and Weight Fraction
Chapter 9-
Equilibrium COOLING IN A Cu-Ni BINARY ALLOY
Chapter 9-
COOLING IN A Cu-Ni BINARY
Equilibrium Cooling
System is:
Binary i.e., 2 components:
Cu and Ni.
Isomorphous
i.e., complete solubility of one component in another; phase field extends from 0 to 100wt% Ni.
Extreme slow cooling of alloy
Chapter 9-
EX: COOLING IN A Cu-Ni BINARY
T(C) L (liquid)
1300 L: 35wt%Ni : 46wt%Ni 32 24 1200 L: 35wt%Ni
A
35
B C D 36
+ L
46 43 L: 32wt%Ni : 43wt%Ni L: 24wt%Ni : 36wt%Ni
(solid)
1100 20 30
35 Co
40
50
wt% Ni
Chapter 9- 10
COOLING IN A Cu-Ni BINARY
Non-Equilibrium Cooling
System is:
Binary i.e., 2 components:
Cu and Ni.
Isomorphous
i.e., complete solubility of one component in another; phase field extends from 0 to 100wt% Ni.
Chapter 9-
Non-Equilibrium COOLING IN A Cu-Ni BINARY ALLOY
Chapter 9-
Chapter 9-
NonNon-Equilibrium Cooling
Consequences of Non-Equilibrium cooling
Chapter 9-
CORED VS EQUILIBRIUM PHASES
C changes as we solidify. Cu-Ni case: First to solidify has C = 46wt%Ni.
Last to solidify has C = 35wt%Ni.
Fast rate of cooling:
Cored structure
First to solidfy: 46wt%Ni Last to solidfy: < 35wt%Ni
Slow rate of cooling:
Equilibrium structure
Uniform C: 35wt%Ni
Chapter 9-
MECHANICAL PROPERTIES: Cu-Ni System
Effect of solid solution strengthening on:
--Tensile strength (TS)
Tensile Strength (MPa) Elongation (%EL)
60 50
--Ductility (%EL,%AR)
%EL for pure Cu %EL for pure Ni
400 TS for pure Ni TS for pure Cu 200 0 20 40 60 80 100 Cu Ni
300
40 30 20 0 20 40 60 80 100 Cu Ni
Composition, wt%Ni
Composition, wt%Ni
Chapter 9-
Binary Eutectic Systems Cu + Ag
Chapter 9-
Binary Eutectic System
Apply Modified Gibbs Phase Rule
Phases present: L, and (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)
Chapter 9-
1200
A
T(C) BINARY-EUTECTIC SYSTEMS
Solidus line
1000 TE 800
L (liquid)
F
L+
8.0
779C
71.9 91.2
E G
L+
B 600 Solvus Line
400 C 200 0 20
+
H
40
60 CE 80
100
Co, wt% Ag
Chapter 9- 13
EX: Pb-Sn EUTECTIC SYSTEM
T(C)
300
represents a solid solution of tin in lead For tin is a solvent and lead is a solute
L (liquid) L+
18.3 183C 61.9
200 150 100
L+
97.8
+
20 40 Co 60 80 100
Chapter 9- 14
Co, wt% Sn
What we wd like to know?
Microstructure Composition Weight Fraction
Chapter 9-
EX: Pb-Sn EUTECTIC SYSTEM
T(C)
300
L (liquid) L+
18.3 183C 61.9
200 150 100
L+
97.8
S
+
40 Co 60 80 99100
Chapter 9- 15
0 11 20
Co, wt% Sn
Amounts of Phases at different temperatures
At Teutectic + T
(W ) proeutectic =
W = Q P+Q P WL = P+Q
Q P+Q
WL =
P P+Q
At Teutectic - T
Q+R P+Q+ R P W = P+Q+ R
(W )total
(W )eutectic = (W )total (W ) proeutectic
Chapter 9-
MICROSTRUCTURES IN EUTECTIC SYSTEMS
T(C)
400 L: Cowt%Sn L 300
solidus
200 TE
L Liquidus L+ (Pb-Sn System)
: Cowt%Sn
100
0 10 20 30 Co Co, wt% 2 (room T solubility limit)
Sn
Chapter 9- 16
MICROSTRUCTURES IN EUTECTIC SYSTEMS
2wt%Sn < Co < 18.3wt%Sn Result:
-- polycrystal with fine T(C) crystals.
400 L: Cowt%Sn
L
300
d
L
L+
200 TE
: C owt%Sn
100
solvus g
+
10
30 C o Co, wt% 2 (sol. limit at Troom) 18.3 (sol. limit at TE)
20
Sn
Chapter 9- 17
MICROSTRUCTURES IN EUTECTIC SYSTEMS
C o = CE Result: Eutectic microstructure
--alternating layers of and crystals.
T(C)
L: Cowt%Sn 300
Micrograph of Pb-Sn eutectic microstructure
Pb-Sn system
200 TE
L L+
183C
L+
160m
100
: 97.8wt%Sn : 18.3wt%Sn 60 CE 61.9 80 100 97.8
0 0
20 18.3
40
Co, wt% Sn
Chapter 9- 18
MICROSTRUCTURES IN EUTECTIC SYSTEMS
18.3wt%Sn < Co < 61.9wt%Sn Result: crystals and a eutectic microstructure
T(C)
300
L: Cowt%Sn L L+
R R S S
Just above TE:
C = 18.3wt%Sn CL = 61.9wt%Sn W = S =50wt% R+S WL = (1-W) =50wt%
L L+
Pb-Sn system
200 TE
100
Just below TE:
+
20 18.3 40 Co 60 61.9 80 100 97.8
primary eutectic eutectic
C = 18.3wt%Sn C = 97.8wt%Sn W = S =73wt% R+S W = 27wt%
Chapter 9- 19
0 0
Co, wt% Sn
HYPOEUTECTIC & HYPEREUTECTIC
T(C)
300
L L+ L+ +
200 TE
(Pb-Sn System)
100
0 0
hypoeutectic hypereutectic
20 18.3 40 60 80 100 97.8
Co
Co
Co, wt% Sn
eutectic
61.9
hypoeutectic: Co=50wt%Sn
hypereutectic: (illustration only)
175m
eutectic: Co=61.9wt%Sn
160m eutectic micro-constituent
Chapter 9- 20
T(C)
1600
IRON-CARBON (Fe-C) PHASE DIAGRAM
1400
L Fe3C (cementite)
1148C
+L 1200 (austenite)
1000 800
R +Fe3C S +Fe3C
L+Fe3C S
600
toid
400 0 (Fe)
727C = Teutectoid
0.77
4.30 Co, wt% C Fe C (cementite-hard)
Chapter 9- 21
6.7
Important Points of to study Fe-C Diagram
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Pure Iron (0% C) Cementite (Fe3C) (6.70% of C) Alpha Ferrite Austenite Delta Ferrite Cementite Reactions (Eutectic and Eutectoid) Ferrous alloy Eutectoid Alloy Hypo-Eutectoid Alloy Hyper-Eutectoid Alloy
Chapter 9-
IRON-CARBON (Fe-C) PHASE DIAGRAM
2 important points -Eutectic (A):
L + Fe3C T(C)
1600
1400 1200 1000 800
-Eutectoid (B):
+ Fe3C
+Fe3C
S +Fe3C
727C = Teutectoid
600
Result: Pearlite = alternating layers of and Fe3C phases.
Ceutectoid
120m
400 0 (Fe)
0.77
4.30 Co, wt% C Fe3C (cementite-hard) (ferrite-soft)
6.7
Chapter 9- 21
Fe3C (cementite)
+L (austenite)
1148C
L+Fe3C S
Iron-Carbon System
Reactions on cooling Peritectic L+ Eutectic L + Fe3C Eutectoid + Fe3C
Steel Cast Iron
Chapter 9-
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 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.
Names of phases:
Ferrite iron bcc structure Austenite iron fcc structure High temperature iron bcc structure Cementite Fe3C
Steels have carbon contents <2%, usually <1.2% Cast irons have carbon contents >2%
Chapter 9-
Development of Microstructure in IronCabon ALLOYS
Chapter 9-
HYPOEUTECTOID STEEL
Chapter 9- 22
HYPEREUTECTOID STEEL
Chapter 9- 23
ALLOYING STEEL WITH MORE ELEMENTS
Ceutectoid (wt%C)
Teutectoid changes:
TEutectoid (C)
1200 1000 Cr 800 Mn 600 0 Ni 4 8 12 Ti Mo Si W
Ceutectoid changes:
0.8 0.6 0.4 0.2 0 0 Si Ti Mo 4 W 8 Mn Ni Cr
12
wt. % of alloying elements
wt. % of alloying elements
Chapter 9- 24
SUMMARY
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. 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.
Chapter 9- 25
