Phase diagram part 2

material science

1. PHASE DIAGRAM
(Part –2/3)
Prepared by
VISHAL MEHTA
Reference : Material Science and Engineering,
An Introduction by William D. Callister, Jr

2. CONTENTS
EutecticMixture
BinaryEutectic System
Eutectoid Reaction
PeritecticReaction
Basic Comparison
Congruent Phase Transformation
The Gibbs Phase Rule
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 2

3. EUTECTIC MIXTURE
Aeutecticmixtureisdefinedasamixtureoftwoormore
componentswhichusuallydonotinteracttoformanewchemical
compoundbut,whichatcertainratios,inhibitthecrystallization
processofoneanotherresultinginasystemhavingalowermelting
pointthaneitherofthecomponents
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 3

4. EUTECTIC MIXTURE
Aeutecticmixtureisdefinedasamixtureoftwoormore
componentswhichusuallydonotinteracttoformanewchemical
compoundbut,whichatcertainratios,inhibitthecrystallization
processofoneanotherresultinginasystemhavingalowermelting
pointthaneitherofthecomponents
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 4
Component 1
Melting Temp T
1

5. EUTECTIC MIXTURE
Aeutecticmixtureisdefinedasamixtureoftwoormore
componentswhichusuallydonotinteracttoformanewchemical
compoundbut,whichatcertainratios,inhibitthecrystallization
processofoneanotherresultinginasystemhavingalowermelting
pointthaneitherofthecomponents
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 5
Component 1
Melting Temp T
1
Component 2
Melting Temp T
2

6. EUTECTIC MIXTURE
Aeutecticmixtureisdefinedasamixtureoftwoormore
componentswhichusuallydonotinteracttoformanewchemical
compoundbut,whichatcertainratios,inhibitthecrystallization
processofoneanotherresultinginasystemhavingalowermelting
pointthaneitherofthecomponents
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 6
Component 1
Melting Temp T
1
Component 2
Melting Temp T
2
Eutectic Mixture
of component 1&2
Melting Temp T
12

7. EUTECTIC MIXTURE
Aeutecticmixtureisdefinedasamixtureoftwoormore
componentswhichusuallydonotinteracttoformanewchemical
compoundbut,whichatcertainratios,inhibitthecrystallization
processofoneanotherresultinginasystemhavingalowermelting
pointthaneitherofthecomponents
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 7
Component 1
Melting Temp T
1
Component 2
Melting Temp T
2
Eutectic Mixture
of component 1&2
Melting Temp T
12
T
12< T
1& T
12< T
2

8. BINARY EUTECTIC SYSTEM
•Tounderstandbinaryeutecticsystem,example
ofcopper-silversystemisconsidered.
•Thephasediagramofthecopper–silversystem
iscommon andrelativelysimplephase
diagramfoundforbinaryalloys.
•Thisisknownasabinaryeutecticphase
diagram.
•Anumberoffeaturesofthisphasediagramare
importantandworthnoting.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 8

9. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 9
BINARY EUTECTIC SYSTEM

10. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 10
BINARY EUTECTIC SYSTEM
Three
single-phase
regions
are
found.

11. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 11
BINARY EUTECTIC SYSTEM
Three
single-phase
regions
are
found.
&#3627409206;

12. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 12
BINARY EUTECTIC SYSTEM
Three
single-phase
regions
are
found.
&#3627409206;
&#3627409207;

13. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 13
BINARY EUTECTIC SYSTEM
Three
single-phase
regions
are
found.
&#3627409206;
&#3627409207;
??????????????????????????????&#3627408517;

14. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 14
BINARY EUTECTIC SYSTEM
The phase
is a solid
solution rich
in copper; it
has silver as
the solute
component
and an FCC
crystal
structure.

15. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 15
BINARY EUTECTIC SYSTEM
The βphase
is a solid
solution rich
in silver; it
has copper
as the solute
component
and an FCC
crystal
structure.

16. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 16
BINARY EUTECTIC SYSTEM
Pure copper
and
pure silver
are also
considered
to be and β
phases,
respectively.

17. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 17
BINARY EUTECTIC SYSTEM
Three
two-phase
regions
are
found.

18. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 18
BINARY EUTECTIC SYSTEM
Three
two-phase
regions
are
found.
&#3627409206;+??????

19. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 19
BINARY EUTECTIC SYSTEM
Three
two-phase
regions
are
found.
&#3627409206;+??????
&#3627409207;+??????

20. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 20
BINARY EUTECTIC SYSTEM
Three
two-phase
regions
are
found.
&#3627409206;+??????
&#3627409207;+??????
&#3627409206;+&#3627409207;

21. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 21
BINARY EUTECTIC SYSTEM
•Thesolidsolubility
limitlineseparating
singlesolidphase
region&twosolid
phase region is
termedasSOLVUS
LINE.
•HereCB&HGare
solvuslines.
SOLVUS LINE

22. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 22
BINARY EUTECTIC SYSTEM
•Thesolubilitylimit
lineseparatingsingle
solidphaseregion&
twophasesolid+liquid
regionistermedas
SOLIDUSLINE.
•HereBA&GFare
soliduslines.
SOLIDUS LINE

23. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 23
BINARY EUTECTIC SYSTEM
Horizontal isotherm
line BEG may also
be considered a
solidus line; it
represents the
lowest temperature
at which a liquid
phase may exist for
any copper–silver
alloy that is at
equilibrium.

24. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 24
BINARY EUTECTIC SYSTEM
•Thesolubilitylimit
lineseparatingsingle
liquidphaseregion&
twophasesolid+liquid
regionistermedas
LIQUIDUSLINE.
•HereAE&EFare
liquiduslines.
LIQUIDUS LINE

25. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 25
BINARY EUTECTIC SYSTEM
1085°C is Melting
temperature of Cu
As silver is added
to copper, the
temperature at
which the alloys
become totally
liquid decreases
along the liquidus
line, line AE;
thus, the melting
temperature
of copper is
lowered by silver
additions.

26. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 26
BINARY EUTECTIC SYSTEM
961.8°C is Melting
temperature of Ag
As copper is added
to silver, the
temperature at
which the alloys
become totally
liquid decreases
along the liquidus
line, line EF; thus,
the melting
temperature
of silver is lowered
by copper additions.

27. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 27
BINARY EUTECTIC SYSTEM
•Bothliquiduslinesmeet
atthepointEonthe
phasediagram,through
whichalsopassesthe
horizontalisothermline
BEG.PointEiscalled
aninvariantpoint,
whichisdesignatedby
thecompositionC
E&
temperatureT
E
E is invariant point

28. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 28
BINARY EUTECTIC SYSTEM
•Bothliquiduslinesmeet
atthepointEonthe
phasediagram,through
whichalsopassesthe
horizontalisothermline
BEG.PointEiscalled
aninvariantpoint,
whichisdesignatedby
thecompositionC
E&
temperatureT
E
•Forthecopper–silver
system,
•C
Eis71.9wt%
•T
Eis779°C

29. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 29
BINARY EUTECTIC SYSTEM
•For an alloyof
compositionC
E,upon
cooling,liquidphaseis
transformedintotwo
solidphases &βat
temperatureT
E
•Theoppositereaction
occursuponheating.
•Thisiscalledaeutectic
reaction (eutectic
meanseasilymelted)
•Horizontalsolidusline
atT
Eiscalledeutectic
isotherm
Eutectic isotherm

30. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 30
BINARY EUTECTIC SYSTEM
•EutecticsReaction
•T
Eis eutectic
temperature
•C
Eis eutectic
composition
•C
Eis eutectic
composition of at T
E
•C
βEis eutectic
composition of βat T
E
Eutectic isotherm

31. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 31
BINARY EUTECTIC SYSTEM
•EutecticsReactionforcopper-silversystem

32. EXAMPLE PROBLEM
•For a 40 wt% Sn–60 wt% Pballoy at 150
o
C (300F),
•(1) What phase(s) is (are) present?
•(2) What is (are) the composition(s) of the phase(s)?
•(3) Calculate the relative amount of each phase
present in terms of mass fraction and (b) volume
fraction.
•(4) Calculate the relative amount of each phase
present in terms of volume fraction.
•Take the densities of Pband Snto be 11.23 and
7.24 g/cm
3
, respectively.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 32

33. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 33
Sn-Pb
system
Obtain point
B which
represent
40 wt% Sn–
60 wt% Pb
alloy at
150
o
C (300F)

34. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 34
Sn-Pb
system
Answer (1)
Obtained
point is in
+βregion,
both & β
phases will
Coexist.

35. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 35
Answer (2)
Since two
phases are
present, it
becomes
necessary to
construct a
tie line
through
point B

36. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 36
Answer (2)
??????&#3627408476;,
??????
&#3627409148;????????????
10 wt% Sn–
90 wt% Pb
&
??????
&#3627409149;????????????
98 wt%Sn–
2 wt% Pb

37. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 37
Answer (3)
Since the
alloy consists
of two
phases, it is
necessary to
employ the
lever rule.
One can
observe
C,C
β& C
1
in diagram.

38. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 38
Answer (3)
So mass
fraction of
phase is,
??????
&#3627409148;=
??????
&#3627409149;−??????
1
??????
&#3627409149;−??????
&#3627409148;
=
98−40
98−10
=0.66

39. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 39
Answer (3)
So mass
fraction of
βphase is,
??????
&#3627409149;=
??????
1−??????
&#3627409148;
??????
&#3627409149;−??????
&#3627409148;
=
40−10
98−10
=0.34

40. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 40
Answer (4)
Volume fractions of phase & βphase are,
&#3627408509;
&#3627409206;=
&#3627408510;
&#3627409206;
??????
&#3627409206;
&#3627408510;
&#3627409206;
??????
&#3627409206;
+
&#3627408510;
&#3627409207;
??????
&#3627409207;
&#3627408509;
&#3627409207;=
&#3627408510;
&#3627409207;
??????
&#3627409207;
&#3627408510;
&#3627409206;
??????
&#3627409206;
+
&#3627408510;
&#3627409207;
??????
&#3627409207;
But we don’t have values of ??????
&#3627409206;& ??????
&#3627409207;

41. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 41
??????
&#3627409148;=
100
??????
????????????(&#3627409148;)
??????
????????????
+
??????
????????????(&#3627409148;)
??????
????????????
=
100
10
7.24??????/&#3627408464;&#3627408474;
3
+
90
11.23??????/&#3627408464;&#3627408474;
3
=10.64??????/&#3627408464;&#3627408474;
3
??????
&#3627409149;=
100
??????
????????????(&#3627409149;)
??????
????????????
+
??????
????????????(&#3627409149;)
??????
????????????
=
100
98
7.24??????/&#3627408464;&#3627408474;
3
+
2
11.23??????/&#3627408464;&#3627408474;
3
=7.29??????/&#3627408464;&#3627408474;
3
(values of ??????
??????&#3627408475;& ??????
??????&#3627408463;are given in question)
Answer (4)

42. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 42
Answer (4)
&#3627408509;
&#3627409206;=
&#3627408510;
&#3627409206;
??????
&#3627409206;
&#3627408510;
&#3627409206;
??????
&#3627409206;
+
&#3627408510;
&#3627409207;
??????
&#3627409207;
=
&#3627409358;.&#3627409364;&#3627409364;
&#3627409359;&#3627409358;.&#3627409364;&#3627409362;??????/&#3627408516;??????
&#3627409361;
&#3627409358;.&#3627409364;&#3627409364;
&#3627409359;&#3627409358;.&#3627409364;&#3627409362;??????/&#3627408516;??????
&#3627409361;
+
&#3627409358;.&#3627409361;&#3627409362;
&#3627409365;.&#3627409360;????????????/&#3627408516;??????
&#3627409361;
∴&#3627408509;
&#3627409206;=&#3627409358;.&#3627409363;&#3627409365;

43. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 43
Answer (4)
&#3627408509;
&#3627409207;=
&#3627408510;
&#3627409207;
??????
&#3627409207;
&#3627408510;
&#3627409206;
??????
&#3627409206;
+
&#3627408510;
&#3627409207;
??????
&#3627409207;
=
&#3627409358;.&#3627409361;&#3627409362;
&#3627409365;.&#3627409360;????????????/&#3627408516;??????
&#3627409361;
&#3627409358;.&#3627409364;&#3627409364;
&#3627409359;&#3627409358;.&#3627409364;&#3627409362;??????/&#3627408516;??????
&#3627409361;
+
&#3627409358;.&#3627409361;&#3627409362;
&#3627409365;.&#3627409360;????????????/&#3627408516;??????
&#3627409361;
∴&#3627408509;
&#3627409206;=&#3627409358;.&#3627409362;&#3627409361;

44. •One can also obtaineanswer (3) & (4) using following relations.
•So just find one value & other is obtained from this relation.
•One can observe the answers, which obtained previously
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 44
&#3627408510;
&#3627409206;+&#3627408510;
&#3627409207;=&#3627409359;
&#3627408509;
&#3627409206;+&#3627408509;
&#3627409207;=&#3627409359;
&#3627408510;
&#3627409206;=&#3627409358;.&#3627409364;&#3627409364;
&#3627408509;
&#3627409206;=&#3627409358;.&#3627409363;&#3627409365;
&#3627408510;
&#3627409207;=&#3627409358;.&#3627409361;&#3627409362;
&#3627408509;
&#3627409207;=&#3627409358;.&#3627409362;&#3627409361;
&#3627409358;.&#3627409364;&#3627409364;+&#3627409358;.&#3627409361;&#3627409362;=&#3627409359;
&#3627409358;.&#3627409363;&#3627409365;+&#3627409358;.&#3627409362;&#3627409361;=&#3627409359;

45. EUTECTOID REACTION
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 45
Whenthereisa
transformation
formonesolid
phase totwo
othersolidphases
orreverseis
calledEutectoid
Reaction.
Cu-Zn system

46. EUTECTOID REACTION
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 46
Insimplewords,
onecanunder
standthatUpon
cooling,asolid
phasetransforms
intotwoother
solidphases
(γandє).
Andthereverse
reactionoccurs
uponheating.
It is called
EutecticReaction
Cu-Zn system

47. EUTECTOID REACTION
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 47
Insimplewords,
onecanunder
standthatUpon
cooling,asolid
phasetransforms
intotwoother
solidphases
(γandє).
Andthereverse
reactionoccurs
uponheating.
It is called
EutecticReaction
Cu-Zn system

48. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 48
Cu-Zn system

49. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 49
Cu-Zn system

50. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 50
Cu-Zn system
Eutectoid Reaction

51. PERITECTIC REACTION
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 51
Whenthereisa
transformation
form solid&
liquidphaseto
other different
solidphaseor
reverseiscalled
Peritectic
Reaction.
Cu-Zn system

52. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 52
Insimplewords,
onecanunder
standthatUpon
cooling,a +L
phasetransforms
intotwoother
solidphaseє.
Andthereverse
reactionoccurs
uponheating.
It is called
PeritecticReaction
Cu-Zn system
PERITECTIC REACTION

53. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 53
Cu-Zn system
PERITECTIC REACTION
Insimplewords,
onecanunder
standthatUpon
cooling,a +L
phasetransforms
intotwoother
solidphaseє.
Andthereverse
reactionoccurs
uponheating.
It is called
PeritecticReaction

54. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 54
Cu-Zn system

55. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 55
Cu-Zn system

56. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 56
Cu-Zn system
PeritecticReaction

57. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 57
Which one is
Eutectic Reaction ?
What is
Eutectic Reaction?

58. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 58
Which one is
Eutectic Reaction ?
What is
Eutectic Reaction?

59. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 59
Which one is
Eutectic Reaction ?
What is
Eutectic Reaction?
Which one is
Eutectoid Reaction ?
What is
Eutectoid Reaction?
How to
identify the
Reaction ?

60. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 60
Which one is
Eutectic Reaction ?
What is
Eutectic Reaction?
Which one is
Eutectoid Reaction ?
What is
Eutectoid Reaction?
Which one is
PeritecticReaction ?
What is
PeritecticReaction?
How to
identify the
Reaction ?

61. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 61
Which one is
Eutectic Reaction ?
What is
Eutectic Reaction?
Which one is
Eutectoid Reaction ?
What is
Eutectoid Reaction?
Which one is
PeritecticReaction ?
What is
PeritecticReaction?
How to
identify the
Reaction ?

62. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 62
Which one is
Eutectic Reaction ?
What is
Eutectic Reaction?
Which one is
Eutectoid Reaction ?
What is
Eutectoid Reaction?
Which one is
PeritecticReaction ?
What is
PeritecticReaction?
How to
identify the
Reaction ?
Confused ?

63. BASIC COMPARISION
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 63
EUTECTIC REACTION EUTECTOID REACTION PERITECTIC REACTION
Liquid phase
Type-1
solid phase
Type-2
solid phase
Type-1 solid phase
Type-2
solid phase
Type-3
solid phase
Type-1
solid phase
Liquid
phase
Type-2 solid phase
Note : There is no specific meaning of type 1, 2 & 3. It is just randomly used to differentiate the solid phases.

64. CONGRUENT PHASE TRANSFORMATION
•Phasetransformationsmaybeclassifiedaccording
towhetherornotthereisanychangein
compositionforthephasesinvolved.
•Thoseforwhichtherearenocompositional
alterationsaresaidtobecongruent
transformations.
•Itmeansphasechangeswithoutanychangein
wt%composition.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 64

65. CONGRUENT PHASE TRANSFORMATION
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 65
Type –1 phase
with
composition
X wt% metal A
Y wt% metal B

66. CONGRUENT PHASE TRANSFORMATION
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 66
Type –1 phase
with
composition
X wt% metal A
Y wt% metal B
Congruent
Phase
Transformation

67. CONGRUENT PHASE TRANSFORMATION
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 67
Type –1 phase
with
composition
X wt% metal A
Y wt% metal B
Type –2 phase
with same
composition
X wt% metal A
Y wt% metal B
Congruent
Phase
Transformation

68. CONGRUENT PHASE
TRANSFORMATION
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 68
Aportionofthenickel–titanium
phasediagramonwhichis
shownacongruentmeltingpoint
fortheγ-phasesolidsolutionat
1310
O
Cand44.9wt%Ti.

69. CONGRUENT PHASE
TRANSFORMATION
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 69
Aportionofthenickel–titanium
phasediagramonwhichis
shownacongruentmeltingpoint
fortheγ-phasesolidsolutionat
1310
O
Cand44.9wt%Ti.

70. CONGRUENT PHASE
TRANSFORMATION
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 70
Aportionofthenickel–titanium
phasediagramonwhichis
shownacongruentmeltingpoint
fortheγ-phasesolidsolutionat
1310
O
Cand44.9wt%Ti.
Congruent
Phase
TransformationL γ

71. THE GIBBS PHASE RULE
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 71
Josiah Willard Gibbs
the nineteenth-century physicist

72. THE GIBBS PHASE RULE
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 72
Josiah Willard Gibbs
the nineteenth-century physicist

73. THE GIBBS PHASE RULE
P+ F= C+ N
P=numberofphasespresent
F=numberofdegreesoffreedomorthe
number ofexternallycontrolled
variables(e.g.,temperature,pressure,
composition)
C=numberofcomponentsinthesystem
N = number of noncompositional
variables (e.g., temperature and
pressure)
•Thisrulerepresentsacriterionforthe
numberofphasesthatwillcoexistwithina
systematequilibrium
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 73
Josiah Willard Gibbs
the nineteenth-century physicist

74. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 74
THE GIBBS PHASE RULE
Continue…

75. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 75
THE GIBBS PHASE RULE
Continue…
Considerthatwewant
tofindthenumberof
degreesoffreedomor
the number of
externallycontrolled
variablesforthesingle
phasefieldofCu-Ag
system

76. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 76
THE GIBBS PHASE RULE
Continue…
•NowGibbsphaseruleisP+F=C+N
•Here
•P=numberofphasespresent
•Aswehaveconsideredsinglephasefield,P=1
•F=?
•C=numberofcomponentsinsystem
•Asitisbinarysystem,C=2
•N=number ofnoncompositionalvariables(e.g.,
temperatureandpressure)
•Hereweneedtocheckthattemperature&pressureare
variableornot.
•Ifbotharevariable,N=2.Ifanyoneoftwoisvariable,N=1.

77. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 77
THE GIBBS PHASE RULE
Continue…
•Ithasbeendiscussedininitialphaseofthis
chapterthatforbinarysystemTemperatureand
compositionarevariableparameters,andpressure
isheldconstant—normally1atm.(slideno17&24ofPart-1)
•Sohereonlytemperatureisvariable,N=1.
•GibbsphaseruleisP+F=C+N
•So1+F=2+1
•F=2

78. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 78
THE GIBBS PHASE RULE
Continue…
•WhatisthemeaningofF=2?
•Thismeansthattocompletelydescribethe
characteristicsofanyalloythatexistswithinone
ofthesephasefields,wemustspecifytwo
parameters;thesearecomposition and
temperature,whichlocate,respectively,the
horizontalandverticalpositionsofthealloyonthe
phasediagram.

79. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 79
meaningofF=2
•Inotherwords,
itcanbesaid
thatonecan
vary two
parameters.
•Itmeansfor
anyvalueofT,
youmayget
morethanone
valuesofC&
viceversa.

80. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 80
THE GIBBS PHASE RULE
Continue…
•Nowforthesameexample&samesystem,
considertwophasefield(insteadofsinglephase).
•So,P=2
•GibbsphaseruleisP+F=C+N
•So2+F=2+1
•F=1

81. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 81
THE GIBBS PHASE RULE
Continue…
•WhatisthemeaningofF=1?
•F=1meansitisnecessarytospecifyeither
temperatureorthecompositionofoneofthe
phasestocompletelydefinethesystem.

82. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 82
meaningofF=1
•Numberofvariableparameter
is1
•So,ifyouknowanyonevalue
ofthree,remainingtwovalues
youcanfind.
•ForexampleifyouknowT
1,
youwillgetothertwovaluesof
C&C
β.
•OrifyouknowC,youcan
findothertwovalues.

83. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 83
meaningofF=1
•Inotherwords,itcanbe
saidthatonecanvary
onlyoneparameterand
othertwowillbechanged.
•Itmeansforanyvalueof
T
1,youwillgetonespecific
valueofC&onespecific
valueofC
β.
•(pointcanbeanywhere
ontieline/isotherm)

84. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 84
THE GIBBS PHASE RULE
Continue…
•Nowforthesameexample&samesystem,
considerthreephasefield(insteadoftwophase).
•So,P=3
•GibbsphaseruleisP+F=C+N
•So3+F=2+1
•F=0

85. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 85
THE GIBBS PHASE RULE
Continue…
•WhatisthemeaningofF=0?
•Thismeansthatthecompositionsofallthree
phasesaswellasthetemperaturearefixed.

86. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 86
meaningofF=0
•Number of
variable
parameteris0.
•Itmeansvalues
ofT,C
L,C&
C
βarefixed.

87. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 87
END OF PART –2 ….
PLEASE CHECK PART –3….