Materials Science

1. BME 303 – Biomaterials
Lecture-4
Phase Diagram
Prof. Dr. Md Enamul Hoque
BME, MIST

2. • A pure substance, under equilibrium conditions, may exist as either of a phase
namely vapor, liquid or solid, depending upon the conditions of temperature
and pressure.
• A phase can be defined as a homogeneous portion of a system that has uniform
physical and chemical characteristics i.e. it is a physically distinct from other
phases, chemically homogeneous and mechanically separable portion of a
system.
• Other words, a phase is a structurally homogeneous portion of matter.
It is a region that differs in it’s microstructure and composition from another
region.
For the same composition, different crystalstructures represent
different phases.
Useful Terminology

3. A solid solution has atoms mixed at atomic level thus it represents a single phase.
A single-phase system is termed as homogeneous, and systems composed of two
or more phases are termed as mixtures or heterogeneous. Most of the alloy systems
and composites are heterogeneous
It is a region that differs in it’s microstructure and composition from another
region.
For the same composition, different crystalstructures represent
different phases.
A solid solution has atoms mixed at atomic level thus it represents a single phase.
A single-phase system is termed as homogeneous, and systems composed of two
or more phases are termed as mixtures or heterogeneous. Most of the alloy systems
and composites are heterogeneous

4. System: Thermodynamically, a system is an isolated body of matter. It refers to a
specific portion of a object within specified boundaries subjected to specified
variables.
OR
This refers to any portion of objective space within specified boundaries
subject to specified variables.
An alloy system is a combinationof two or
more elements forming alloys which are considered
within a specified range of temp. , pressure and concentration.

5. Phase : It is a physically and chemically homogeneous composition of a
system, separated from other portions by surface and an interface.
• But each portion have different composition and
properties.
• In an equilibrium diagram, liquid is one phase and solid solution is another
phase.
Variable :
• A particular phase exists under various conditions of temp., pressure and
concentrations.
• These parameter are known as the variables of the phase.
Useful Terminology

6. Component – These are the substances, either chemical elements or
chemical compounds whose presence is necessary and sufficient to make a
system.
• Pure metal is a one-component system whereas an alloy of two metals
is a two-component system.
• H2O has 1 component but 3 Phases (Ice, Water and Steam)
• Cu-Ni is a 2 components system.
Useful Terminology

7. Alloy:
• It is a mixture of two or more elements having metallic properties.
• In the mixture, metal is in the large proportion and the others can be metals
or non-metals.
• The element in the largest amount is called as base metal (Parent metal) or
solvent and the other elements are called as alloying elements or solute.
Useful Terminology

8. Phase equilibrium –
• It refers to the set of conditions where more than one phase may exist.
• It can be reflected by constancy with time in the phase characteristics of a
system.
• In most metallurgical and materials systems, phase equilibrium involves just
solid phases.
Useful Terminology

9. Phase Diagram
• A phase diagram is a graphical representation of the phases that are
present in a material at various temperatures and pressures and
compositions.
• It usually describes the equilibrium conditions. Hence also known as
equilibrium diagrams
• Sometimes non-equilibrium conditions are also shown when well known.
• Ex: Melting point of tungsten is 3400 C and Aluminum 657C hence two
elements can not blend together .

10. Phase Diagram
• It indicates the melting/solidification temperatures of the constituents
•It indicates the compositions of alloys where solidification begins and the temperature
range over which it occurs.
For a pure substance, the Pressure-Temperature phase diagram simply tells which
forms (solid, liquid, gas) of the material exist under different P-T conditions.
Phase diagram for
magnesium, showing the
melting and boiling
temperatures at one
atmosphere pressure

11. Gibb’s Phase Rule
Gibb’s phase rule describes the thermodynamic state of a material.
This famous rule is used to determine the number of phases that can coexist in
equilibrium in a
given system.
It has the general form: D = C – P +λ
C is the number of components, usually elements or compounds, in the system.
D is the number of degrees of freedom, or number of variables, such as
temperature, pressure, or composition that are allowed to change independently
without changing the number of phases in equilibrium.
P is the number of phases present
The constant λ is system variable. Here, the variable is taken as “2” implies that
both temperature and pressure are allowed to change.

12. Gibb’s Phase Rule
For the triple point of water:
• One component, i.e., water.
• 3 phases present, i.e. vapor, liquid, and solid.
• D = 1 – 3 + 2 = 0, so this is an invariant point on the
diagram

13. Classification of Phase Diagram
Plot showing relation between temperature Vs composition in a phase
diagram can be classified as below:
•Unary Phase Diagram
•Binary Phase Diagram
•Ternary Phase Diagram
•Quaternary Phase Diagram

14. Unary Phase Diagram
Diagram for single Component (Water)

15. Binary Phase Diagram
When only two elements or two compounds are present in a material, a binary
phase diagram can be constructed.
They are found in number of Metallic & Ceramic structures like Cu-Ni alloy etc.

16. Liquidus/Solidus Temperatures
The liquidus temperature is the temperature above which a
material is completely liquid. The solidus temperature is the
temperature which the alloy is 100% solid.
The freezing range of the alloy is the temperature difference between the liquidus
and solidus where the two phases exists, ie., the liquid and solid.
The changes in slope of the cooling curve indicate the liquidus ab=nd solidus
tempratures.

17. Tie Line
Tie Line: is the line joining solidus
& liquidus curves.
A binary phase diagram between two
elements A and B.
When an alloy is present in a two phase
region, a tie line at the temperature of
interest fixes the composition of the two
phases.

18. Lever Rule
The Lever Rule is used to calculate the weight % of the phase in any two-
phaseregion of the Phase diagram (and only the two phase region!)
In general:
• Phase percent = opposite arm of lever x 100
total length of the tie line

19. • If we know T and C0, then we can determine:
-- the composition of each phase.

20. Phase Diagrams: Determination of phase weight fractions

21. Lever Rule
Calculate the amount of a phase and L phase present in a Cu40% Ni alloy at
1250 C In general:
• Percent a phase = (% Ni in alloy) – (% Ni in L) x 100
% Ni in L - % Ni in a

22. Phase Diagrams with Intermediate Phases and
Compounds
Many combinations of two elements produce more complicated phase
diagrams than the isomorphous systems and the simple eutectic
systems.
•Many equilibrium diagrams often show intermediate phases and
compounds when either incomplete solubility or compound
formation occurs.
•These new phases are distinguished by the labels “terminal phases”
and “intermediate phases”.
• Their phase diagrams look complex.

23. Phase Diagrams with Intermediate Phases Compounds
•The terminal solid-solution phases occur at the ends of the phase diagrams,
bordering on the pure components, e.g., the alpha phase and the beta phase
in the Pb-Sn phase diagram.
•Intermediate phases commonly have new compounds and are called
intermediate compounds or intermetallic compounds.
–An intermediate compound is made up of two or more elements that
produce a new phase with its own composition, crystal structure, and
properties.
– Intermediate compounds are almost always very hard and brittle.
– An example is Fe3C in steels.

24. 2
Iron Carbon Phase diagram

25. ALLOTROPY OF IRON
In actual practice it is very difficult to trace the cooling of iron from
1600°C to ambient temperature because particular cooling rate is
not known.
Particular curve can be traced from temperature, time and
transformation (TTT) curve.
However allotropic changes observed during cooling of pure iron are
depicted in Fig.

26. Molten-Fe (Liquid state of
iron)
Delta-Fe (Body centered)
austenit
e
structur
e

27. Transformation During Heating And Cooling Of Steel

28. Principal phases of steel and their Characteristics
Phase Crystal
structure
Characteristics
Ferrite BCC Soft, ductile, magnetic
Austenite FCC
Soft, moderate
strength, non-
magnetic
Cementite Compound of
Iron & Carbon
Fe3C
Hard &brittle

31. Five individual phases
□ α–ferrite (BCC) Fe-C solid solution
□ γ-austenite (FCC) Fe-C solid
solution
□ δ-ferrite (BCC) Fe-C solid solution
□ Fe3C (Iron Carbide) or cementite –
an inter-metallic compound
□ Liquid Fe-C solution

32. Phase vs. Microconstituents
□ A phase or a mixture of phases which has a
distinct identity in a microstructure is called a
microconstituent
□ Pearlite is not a phase.
□ It is a microconstituent and is a mixture of two
phases α- Ferrite and Fe3C.

33. α−Ferrite
□ Known as α -iron
□ Pure iron at room temperature
□ Body-centered cubic structure
□ Soft & ductile and imparts these
properties to the steel.
□ Less than 0.01% carbon will dissolve in
ferrite at room temperature
□ High temperature form is δ ferrite, but
the two forms are identical.
□ Pure ferritic steels are rare

34. Austenite
□ Known as γ -iron
□ Face-centered cubic
□ Much softer than ferrite
□ Not present at room temperatures.
□ More easily hot worked

35. Cementite
□ Iron Carbide - an intermetallic compound
□ Hard, brittle, white
□ melts at 1837 C , density of 7.4 g/cc
□ On the phase diagram, cementite
corresponds to a vertical line at 6.7% C
□ Engineers care only about compounds with less
carbon
□ Its presence in steels causes an increase in
hardness and a reduction in ductility and
toughness

36. Pearlite
□ A laminated structure formed of alternate
layers of ferrite and cementite with average
composition 0.83% carbon
□ Pearly lustre in the microscope
■ Interference of light in its regular layers
□ Most common constituent of steel
□ It combines the hardness and strength of
cementite with the ductility of ferrite and is the
key to the wide range of the properties of
steels.
□ The laminar structure also acts as a barrier to
crack movement as in composites. This gives
it toughness

37. Three invariant reactions
A horizontal line always indicates an invariant
reaction in binary phase diagrams
□ Peritectic reaction at 1495˚C and 0.18%C,
■ δ-ferrite + L↔ γ-iron (austenite)
□ Eutectic reaction at 1147˚C and 4.3 %C,
■ L ↔ γ-iron + Fe3C (cementite) [ledeburite]
□ Eutectoid reaction at 727˚C and 0.77%C,
■ γ-iron ↔ α–ferrite+Fe3C (cementite) [pearlite]

38. 01/03/1
9
PROF.MAYUR S MODI 88
SYMB
OL
TEMP.⁰
C
SIGNIFICAN
CE
A0 (curie
210
temp.)
Above temp. Cementite losses its
magnetism
A1 (LCT)
727
Above temp. perlite gets
transformed in austenite
A2 (curie
768
temp.)
Above temp. Ferrite losses its
magnetism
A3
(critical
hypo-
eutectoi
d
steeeel)
727-
910
Above temp. Free ferrite gets dissolved
to 100
% ferrite.
ACM(crit
ic al
hyper-
eutectoid
steeeel)
727-
1147
Above temp. Free cementite gets
dissolved to 100 % austenite.
A4
(
UCT)
140
0-
149
Above temp. Austenite gets transformed
into δ
– ferrite.

39. Peritectic Reaction

40. Metals
Ferrous metals Non-ferrous metals
Steels Cast Irons
Plain carbon steels Grey Iron
White Iron
Malleable & Ductile Irons
Low carbon steels
Medium carbon steels
High carbon steels
Low alloy steels
High alloy steels
Stainless & Tool
steels
Fe-C alloy classification

41. Fe-C alloy classification
□ Fe-C alloys are classified according to wt.% C
present in the alloys
■ Commercial pure irons % C < 0.008
■ Low-carbon steels
■ Medium carbon steels
■ High-carbon steels
■ Cast irons
0.008 - %C - 0.3
0.3 - %C - 0.8
0.8- %C - 2.14
2.14 < %C

42. Cast irons
□ Cast irons that were slowly cooled to room temperature
consists of cementite, look whitish
– white cast iron.
□ If it contains graphite, look grayish – gray cast iron.
□ It is heat treated to have graphite in form of
nodules – malleable cast iron.
□ If inoculants are used in liquid state to have graphite
nodules – spheroidal graphite (SG) cast iron.

44. Solidification of a Solid-Solution
Alloy
The change in structure and composition of a Cu-
40% Ni alloy during equilibrium solidification
showing that the liquidcontains 40% Ni and the
first solid contains Cu52%Ni. At 1250 C,
solidification has advanced and the phase diagram
tells us that the liquid contains 32% Ni and the
solid contains 45% Ni, which continues until just
below the solidus,
all of the solidcontains 40% Ni, which is
achieved through diffusion.

45. EUTECTIC TRANSFORMATION
1
2

47. Eutectoid Reaction
727o C
0.77
g ¾ c¾ool¾® a +
Fe3C
0.022 6.67
Pearlite
Eutectoid steel

48. HYPOEUTECTIC TRANSFORMATION
1
2
3

49. At just below point 3
The already separated pro-eutectic A remains unchanged.
% Amount pro-eutectic A = l(3E)/l(DE) ……….at point 3.
% Amount eutectic = l(D3)/l(DE) ……….at point 3.
At point 4
Total amount of metal A at point 4
=[amount of pro-eutectic A] + [amount of eutectic A]
=[amount of pro-eutectic A] + [ A in the eutectic x amount of eutectic]
=[l(3E)/l(DE)] + [l(EF)/l(DF) x l(D3)/l(DE)]

50. Hypoeutectoid steel
Proeutectoid
Ferrite
Pearlite
Microstructure of 0.38 wt% C
hypoeutectoid steel

51. HYPEREUTECTIC TRANSFORMATION
1
2
3

52. At just below point 3
The already separated pro-eutectic A remains unchanged.
% Amount pro-eutectic B = l(E3)/l(EF) ……….at
point 3.
% Amount eutectic = l(3F)/l(EF) ……….at point 3.
At point 4
Total amount of metal A at point 4
=[amount of pro-eutectic B] + [amount of eutectic B]
=[amount of pro-eutectic B] + [ B in the eutectic x amount of
eutectic]
=[l(E3)/l(EF)] + [l(DE)/l(DF) x l(3F)/l(EF)]

53. Hypereutectoid steel
Pearlite
Proeutectoid
cementite
Microstructure of 1.4 wt% C
hypereutectoid steel

56. The Austenite to ferrite / cementite transformation in
relation to Fe-C diagram

57. Eutectoid
steel
α+Fe3C
Pearlite
Hypoeutectoid
steel
α+Fe3C
Pearlite +
proeutectoid ferrite
Hypereutectoid
steel
α+Fe3C
Pearlite +
proeutectoid
cementite
Eutectoid, Hypoeutectoid and Hypereutectoid Steel

58. EXAMPLE: PHASE EQUILIBRIA
For a 99.6 wt% Fe-0.40 wt% C at a temperature just below the
eutectoid, determine the following:
a) composition of Fe3C and ferrite (α )
b) the amount of carbide (cementite) in grams that forms per 100 g of
steel
c) the amount of pearlite and proeutectoid ferrite (α )

59. 3
Fe3C = 5.7
g
α = 94.3 g
6.7 −
0.022
0.4 −
0.022
=
= x100
Fe3C α
x 100 =
5.7g
−
C
Fe C + α
C
Fe3C Co − Cα
b) the amount of carbide
(cementite) in grams that
forms per 100 g of steel
SOLUTION:
a) composition of Fe3C and ferrite
(α)
CO = 0.40 wt% C
Cα = 0.022 wt% C
CFe3C = 6.70 wt% C
Fe
3
C
(cementite)
1600
1200
1000
800
600
400
0 1 2 5 6
6.7
(austenite)
γ
γ+L
3
γ + Fe
C
L+Fe3C
δ
3 4
Co , wt% C
L
1148°C
1400
T(°C)
727°C
R S
α+ Fe3C
CF3
e
Cα CO

60. SOLUTION, CONT:
c) the amount of pearlite and proeutectoid
ferrite (α)
note: amount of pearlite = amount of γ
just above TE
Co = 0.40 wt% C
C = 0.022
wt% C
α
Cpearlite = Cγ = 0.76 wt% C
γ
γ+α Cγ−Cα
=Co −Cαx 100 =51.2 g
pearlite = 51.2 g
proeutectoid α = 48.8 g
Fe
3
C
(cementite)
1600
1400
1200
1000
400
0
1
2 5 6
6.7
(austenite)
γ
γ+L
3
γ + Fe
C
α+ Fe3C
L+Fe3C
δ
3 4
Co , wt% C
L
1148°C
T(°C)
727°C
800
RS
600
C CO
Cγ
Looking at the Pearlite:
11.1% Fe3C (.111*51.2 gm = 5.66 gm) & 88.9% α (.88α9*51.2gm = 45.5

61. Thank you