binary phase diagram of lead and tin.pdf

binary phase diagram of lead and tin

1. MATERIAL SCIENCE
Chapter 9:
Phase Diagram
1

2. Introduction and Basic Concepts
•Theunderstandingofphasediagramsforalloysystemsisextremelyimportantbecausethereisa
strongcorrelationbetweenmicrostructureandmechanicalproperties,andthedevelopmentof
microstructureofanalloyisrelatedtothecharacteristicsofitsphasediagram.Inaddition,phase
diagramsprovidevaluableinformationaboutmelting,casting,crystallization,andother
phenomena.
•Alloyisametallicsubstancethatiscomposedoftwoormoreelements.
•Componentsare pure metals and/or compounds of which an alloy is composed.
•Aphasemaybedefinedasahomogeneousportionofasystemthathasuniformphysicaland
chemicalcharacteristics.Everypurematerialisconsideredtobeaphase;soalsoiseverysolid,
liquid,andgaseoussolution.
•Manytimes,thephysicalpropertiesand,inparticular,themechanicalbehaviorofamaterial
dependonthemicrostructure.Microstructureissubjecttodirectmicroscopicobservation,using
opticalorelectronmicroscopes
•Sometimes, a single-phase system is termed homogeneous. Systems composed of two or more phases
are termed mixtures or heterogeneous systems. Most metallic alloys and, for that matter, ceramic,
polymeric, and composite systems are heterogeneous.
2

3. 3
Phase Equilibria: Solubility Limit
Question:What is the
solubility limit for sugar in
water 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 for
which only a single phase
solution exists.
Sugar/Water Phase Diagram
Sugar
Temperature (
°
C)
0 20 40 60 80 100
C= Composition (wt% sugar)
L
(liquid solution
i.e., syrup)
Solubility
Limit L
(liquid)
+
S
(solid
sugar)20
40
60
80
100
Water
Adapted from Fig. 9.1,
Callister & Rethwisch 9e.
• Solution–solid, liquid, or gas solutions, single phase
• Mixture–more than one phase

4. 4
• 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., αand β).
Aluminum-
Copper
Alloy
Components and Phases
α(darker
phase)
β(lighter
phase)
Adapted from chapter-
opening photograph,
Chapter 9, Callister,
Materials Science &
Engineering: An
Introduction, 3e.

5. One-Component (or Unary) Phase Diagrams
•There are three externally controllable parameters that will affect phase structure:
•temperature, pressure, and composition.
•Phase diagrams are constructed when various combinations of these parameters are plotted against
one another.
•Perhaps the simplest and easiest type of phase diagram to understand is that for a one-component
system, in which composition is held constant (i.e., the phase diagram is for a pure substance); this
means that pressure and temperature are the variables. This one-component phase diagram (or
unary phase diagram) [sometimes also called a pressure–temperature (or P–T) diagram]
5

6. Binary Phase Diagrams
•Anothertypeofextremelycommon
phasediagramisoneinwhich
temperatureandcompositionare
variableparameters,andpressureis
heldconstant—normally1atm.
•Possiblytheeasiesttypeofbinaryphase
diagramtounderstandandinterpretis
thetypethatischaracterizedbythe
copper–nickelsystem(Figure9.3a).
TemperatureisplottedalongtheY-axis,
andtheX-axisrepresentsthe
compositionofthealloy,inweight
percent(bottom)andatompercent(top)
ofnickel.Thecomposition
6
Ni and Cu are totally soluble in one another for all proportions.
Isomorphous i.e., complete solubility of one component in another; αphase field
extends from 0 to 100 wt% Ni.
• 2 phases:
L(liquid)
α(FCC solid solution)

7. Binary Phase Diagrams
Forabinarysystemofknowncompositionandtemperaturethatisatequilibrium,atleast
threekindsofinformationareavailable:(1)thephasesthatarepresent,(2)the
compositionsofthesephases,and(3)thepercentagesorfractionsofthephases.
7

8. 8
wt% Ni204060801000
1000
1100
1200
1300
1400
1500
1600
T(°C)
L(liquid)
α
(FCC solid
solution)
Cu-Ni
phase
diagram
Phase Diagrams:
Determination of phase(s) present
• Rule 1:If we know Tand Co, 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
(1250ºC,35)
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.)

9. 9
wt% Ni
20
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 Tand 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) present
C
L= C
0( = 35 wt% Ni)
At T
B
= 1250°C:
Both αand Lpresent
C
L
= Cliquidus( = 32 wt% Ni)
Cα= Csolidus( = 43 wt% Ni)
At T
D
= 1190°C:
Only Solid (α) present
Cα= C
0( = 35 wt% Ni)
Consider C
0= 35 wt% Ni
D
T
D
tie line
4
Cα
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.)
B
T
B

10. 10
• Rule 3:If we know Tand C
0, then can determine:
--the weight fraction of each phase.
• Examples:
At T
A: Only Liquid (L) present
W
L= 1.00, Wa= 0
At T
D:Only Solid (α) present
W
L= 0, W
α= 1.00
Phase Diagrams:
Determination of phase weight fractions
wt% Ni
20
1200
1300
T(°C)
L(liquid)
α
(solid)
30 40 50
Cu-Ni
system
T
A
A
35
C
0
32
C
L
B
T
B
D
T
D
tie line
4
Cα
3
RS
At T
B:Both αand L present73.0
3243
3543
=
-
-
=
= 0.27
W
L
=
S
R+S
W
α
=
R
R+S
Consider C
0= 35 wt% Ni
Fig. 9.3(b), Callister & Rethwisch9e.
(Adapted from Phase Diagrams of Binary
Nickel Alloys, P. Nash, Editor, 1991. Reprinted
by permission of ASM International, Materials
Park, OH.)

11. 11
wt% Ni
20
1200
1300
30 40 50
1100
L(liquid)
α
(solid)
T(°C)
A
35
C
0
L: 35 wt%Ni
Cu-Ni
system
• Phase diagram:
Cu-Ni system.
Adapted from Fig. 9.4,
Callister & Rethwisch 9e.
• Consider
microstuctural
changes that
accompany the
cooling 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
E
L: 24 wt% Ni
α: 36 wt% Ni
24 36
D
α: 35 wt% Ni

12. Binary Phase Diagrams
Acopper–nickelalloyofcomposition65
wt%Ni–35wt%Cuisslowlycooledfroma
temperatureof1300
o
C(2370
o
F).
(a)Atwhattemperaturedoesthefirstsolid
phase form?
(b)Whatisthecompositionofthissolid
phase?
(c)Atwhattemperaturedoescomplete
solidificationofthealloyoccur?
(d)Whatisthecompositionofthelastsolid
remainingpriortocompletesolidification?
12

13. •Letusconsiderthecopper–nickelsystem(Figure9.3a),specificallyanalloyofcomposition35
wt%Ni–65wt%Cuasitiscooledfrom1300
o
C.TheregionoftheCu–Niphasediagramin
thevicinityofthiscompositionisshowninFigure9.4.Coolingofanalloyofthis
compositioncorrespondstomovingdowntheverticaldashedline.At1300
o
C,pointa,the
alloyiscompletelyliquid(ofcomposition35wt%Ni–65wt%Cu)andhasthemicrostructure
representedbythecircleinsetinthefigure.Ascoolingbegins,nomicrostructuralor
compositionalchangeswillberealizeduntilwereachtheliquidusline(pointb,~1260
o
C).At
thispoint,thefirstsolidαbeginstoform,whichhasacompositiondictatedbythetieline
drawnatthistemperature[i.e.,46wt%Ni–54wt%Cu,notedas(46Ni)];thecompositionof
liquidisstillapproximately35wt%Ni–65wt%Cu[L(35Ni)],whichisdifferentfromthatof
thesolidα.Withcontinuedcooling,bothcompositionsandrelativeamountsofeachofthe
phaseswillchange.Thecompositionsoftheliquidandαphaseswillfollowtheliquidus
andsoliduslines,respectively.Furthermore,thefractionoftheαphasewillincreasewith
continuedcooling.Notethattheoverallalloycomposition(35wt%Ni–65wt%Cu)remains
unchangedduringcoolingeventhoughthereisaredistributionofcopperandnickel
betweenthephases.
•At1250C,pointcinFigure9.4,thecompositionsoftheliquidandαphasesare32wt%
Ni–68wt%Cu[L(32Ni)]and43wt%Ni–57wt%Cu[α(43Ni)],respectively.
13

14. Given here are the solidus and liquidustemperatures for the germanium (Ge) –silicon (Si) system. Construct
the phase diagram for this system and label each region,
Problem
Composition Solidus Liquidus
(wt% Si)
Temperature
(C)
Temperature
(C)
0 938 938
10 1005 1147
20 1065 1226
30 1123 1278
40 1178 1315
50 1232 1346
60 1282 1367
70 1326 1385
80 1359 1397
90 1390 1408
100 1414 1414
700
800
900
1000
1100
1200
1300
1400
1500
0 20 40 60 80 100
Temperature

C
wt% Si
14

15. 15
A copper–nickel alloy of
composition 70 wt%
Ni–30 wt% Cu is slowly heated to a
temperature of 1300C (2370F).
(a) At what temperature does the
first liquid phase form?
(b) What is the composition of this
liquid phase?
(c) At what temperature does
complete melting of the alloy
occur?
(d) What is the composition of the
last solid remaining prior to
complete melting?
Problem