Chapter 9 phase diagrams 1

MSE-211-Engineering Materials 1

Phase Diagrams

Chapter reading 9

1 1

Definitions and basic concepts

Phases and microstructure

Phase equilibria

One component phase diagrams

Binary phase diagrams

The iron-carbon system (steel and cast iron)


Phase Diagrams

Background/Importance

Many material systems and alloy systems exist in more than one

phases depending on the conditions of temperature, pressure and

compositions. Each phase will have different microstructure which

is related to the mechanical properties. The development of

microstructure is related to the characteristics of phase diagrams.

Thus the knowledge and understanding of the phase diagrams is very

important for engineers . Proper knowledge and understanding of

phase diagrams will lead to design and control of heating procedures

for developing the required microstructure and properties.



Component - chemically recognizable species (Fe and C in

carbon steel, H2O and NaCl in salted water). A binary

alloy contains two components, a ternary alloy – three, etc.

The chemical elements which make up the alloy

Solvent : primary atomic species. Host atoms

Solute : the impurities. Normally the minor component

System : Specific body of material under consideration

(e.g., a ladle of molten steel)



Solubility limit: Maximum concentration of solute

atoms that may dissolve in the solvent to form a solid

solution. Example : water-sugar solution

Sugar/Water Phase Diagram

Su

gar

Tem

pera

ture

(ºC

)

0 20 40 60 80 100 C = Composition (wt% sugar)

L (liquid solution

i.e., syrup)

Solubility Limit L

(liquid)

+ S

(solid sugar) 20

4 0

6 0

8 0

10 0

Wate

r

65

What is the solubility limit for

sugar in water at 20 ºC

Ans: 65 wt% sugar

At 20ºC, if C < 65 wt% sugar: syrup

At 20ºC, if C > 65 wt% sugar:

syrup + sugar


Phase (solid, liquid, gas): a homogeneous portion of a

system that has uniform physical and chemical

characteristics.


Two distinct phases in a system have distinct physical

or chemical characteristics (e.g. water and ice) and

are separated from each other by definite phase

boundaries. A phase may contain one or more

components.

A single-phase system is called homogeneous,

Systems with two or more phases are mixtures or

heterogeneous systems.


70 80 100 60 40 20 0

Te

mp

era

ture

(ºC

)

C = Composition (wt% sugar)

L ( liquid solution

i.e., syrup)

20

100

40

60

80

0

L (liquid)

+ S

(solid sugar)

Effect of Temperature & Composition

• Altering T can change # of phases: path A to B.

• Altering C can change # of phases: path B to D.

water-

sugar

system

Adapted from Fig. 9.1,

Callister & Rethwisch 8e.

D (100ºC,C = 90)

2 phases

B (100ºC,C = 70)

1 phase

A (20ºC,C = 70)

2 phases


Phase Equilibrium

A system is at equilibrium if its free energy is at a minimum

under some specified combination of temperature, pressure,

and composition. On a macroscopic sense this means the

system is stable and its characteristics donot change over time.

Equilibrium

Under conditions of a constant temperature and pressure

and composition, the direction of any spontaneous

change is toward a lower free energy.


Metastable state: Equilibrium is the state that is achieved given sufficient

time. It is often the case in solid systems that they never achieve complete

equilibrium state because the rate to approach equilibrium is extremely

slow; such a system is said to be in a non-equilibrium or metastable state.

A system at a metastable state is trapped

in a local minimum of free energy that is

not the global one.

A metastable state or microstructure may persist

indefinitely, experiencing

only extremely slight and almost negligible changes as

time progresses. Often, metastable structures are of more

practical significance than equilibrium ones.

Phase Equilibrium


Phase Diagrams

Phase Diagram–a graphic representation showing the phase

or phases present for a given composition, temperature and

pressure. Also termed equilibrium diagrams.

A phase diagrams show what phases exist at equilibrium and

what phase transformations we can expect when we change

one of the parameters of the system (T, P, composition).

We will discuss phase diagrams for binary alloys only and

will assume pressure to be constant at one atmosphere.

Phase diagrams for materials with more than two components

are complex and difficult to represent


ONE-COMPONENT (OR UNARY)

PHASE DIAGRAMS

Example of water: Three different phases. Phase boundaries: aO, bO, cO.

The two phases on either side of the boundary are in equilibrium.

For

details

Read page

86-87


Unary Systems

Single component system

Consider 2 elemental metals separately:

Cu has melting T = 1085oC

Ni has melting T = 1453oC (at standard P = 1 atm)

What happens when Cu and Ni

are mixed?


Binary Isomorphous Systems

Isomorphous system - complete solid solubility of the

two components (both in the liquid and solid phases).

Binary: 2 components

3 different phase fields

Liquid(L)

Solid + liquid(L + α) Solid(α)

Liquidus line separates liquid

from liquid + solid

Solidus line separates solid from

liquid + solid



Example of isomorphous system: Cu-Ni


In one-component system melting occurs at a well-defined

melting temperature. In multi-component systems melting

occurs over the range of temperatures, between the solidus

and liquidus lines. Solid and liquid phases are in

equilibrium in this temperature range.

50/50 wt % composition in Cu-Ni melting begins at 1280 C





Interpretation of Phase Diagrams

From binary phase diagrams we can determine

(1) The phases that are present

(2) The composition of phases

(3) The percentage and fraction of the phases


Determination of Phases Present

wt% Ni 20 40 60 80 100 0 1000

1100

1200

1300

1400

1500

1600 T(ºC)

L (liquid)

a

Cu-Ni

phase

diagram

• Rule 1: If we know T and Co, then we know: -- which phase(s) is (are) present.

• Examples:

A(1100ºC, 60 wt% Ni): 1 phase: a

B (1250ºC, 35 wt% Ni): 2 phases: L + a

B (

1250ºC

,35)

A(1100ºC,60)


Determination of Phase Composition

Finding the composition in a two phase region:

1. Locate composition and temperature in diagram

2. In two phase region draw the tie line or isotherm

3. Note intersection with phase boundaries. Read

compositions at the intersections.

The liquid and solid phases have these compositions.


Point B: T=1250 oC ,35 wt% Ni–

65 wt% Cu

Composition of Liquid phase:

CL=31.5wt% Ni –68.5%Cu

Composition of α phase:

Cα=42.5wt% Ni‐57.5wt%Cu

Determination of Phase Composition


Determination of Phase Amounts

Phase weight fractions or %

For single phase weight fraction of a phase is 1 or 100%.

For two phase region Lever Rule

Locate composition and temperature in diagram

Construct a tie line in two phase region at alloy temperature

Fraction of a phase is determined by taking the length of the

tie line from the overall alloy composition to the phase

boundary for the other phase, and dividing by the total length

of tie line.


Determination of Phase Amounts

Mass Fraction

𝐶𝑜 = 35 𝑤𝑡.%, 𝐶𝐿 = 31.5 𝑤𝑡.% 𝐶𝛼 = 42.5𝑤𝑡.%,

𝑊𝐿 = 𝐶𝛼 − 𝐶𝑜 𝐶𝛼 − 𝐶𝐿 = 0.68

𝑊𝛼 = 𝐶𝑜 − 𝐶𝐿 𝐶𝛼 − 𝐶𝐿 = 0.32


Development of microstructure in isomorphous alloys

Equilibrium Cooling: Very slow cooling to allow phase equilibrium

to be maintained during the cooling process.



Mechanical Properties of Isomorphous Alloys

Solid solution strengthening

24

-- Tensile strength (TS) -- Ductility (%EL)

Te

nsile

Str

en

gth

(M

Pa

)

Composition, wt% Ni Cu Ni 0 20 40 60 80 100

200

300

400

TS for pure Ni

TS for pure Cu

Elo

ng

atio

n (

%E

L)

Composition, wt% Ni Cu Ni 0 20 40 60 80 100

20

30

40

50

60

%EL for pure Ni

%EL for pure Cu


Binary Eutectic Systems

Eutectic Systems

In a eutectic reaction, when a liquid solution of fixed composition, soldifies

at a constant temperature, forms a mixture of two or more solid phases

without an intermediate pasty stage. This process reverses on heating.

Systems exhibiting this behavior are known as “Eutectic systems”.

In a eutectic system there is always a specific alloy , known as eutectic

composition, that freezes at a lower temperature than all other compositions.

At ‘eutectic temperature’, two solids form simultaneously from a single

liquid phase. The eutectic temperature and composition determine a

point on the phase diagram known as ‘eutectic point’.



•Three two-phase regions (α + L, β +L, α +β)

•Solvus line separates one solid solution from a

mixture of

solid solutions. The Solvus line shows limit of

solubility

Three single phase regions

(α - solid solution of Ag in Cu

matrix,

β = solid solution of Cu in Ag

marix, L - liquid)


Eutectic or invariant point - Liquid and two solid

phases co-exist in equilibrium at the eutectic composition

CE and the eutectic temperature TE.

Eutectic isotherm - the horizontal solidus line at TE.




• TE : No liquid below TE

: Composition at

temperature TE

• CE

Ex.: Cu-Ag system

Cu-Ag

system

L (liquid)

a L + a L + b b

a + b

C , wt% Ag 20 40 60 80 100 0

200

1200 T(ºC)

400

600

800

1000

CE

TE 8.0 71.9 91.2 779ºC

Ag) wt%1.29( Ag) wt%.08( Ag) wt%9.71( b+aL cooling

heating

• Eutectic reaction

L(CE) a(CaE) + b(CbE)



General Rules

Eutectic reaction – transition between liquid and mixture of

two solid phases, α + β at eutectic concentration CE.

• The melting point of the eutectic alloy is lower than that

of the components (eutectic = easy to melt in Greek).

• At most two phases can be in equilibrium within a phase

field.

• Three phases (L, α, β) may be in equilibrium only at a few

points along the eutectic isotherm.

• Single-phase regions are separated by 2-phase regions.



On occasion, low-melting-temperature alloys are prepared having

near-eutectic compositions. A familiar example is the 60–40 solder,

containing 60 wt% Sn and 40 wt% Pb. Completely melted at 185 C.

Attractive as low temperature solder.


Compositions and relative amounts of phases are determined from

the same tie lines and lever rule, as for isomorphous alloys.



For a 40 wt% Sn-60 wt% Pb alloy at 150ºC, determine:

-- the phases present

the phase compositions


• Eutectoid – one solid phase transforms to two other

solid phases

S2 S1+S3

a + Fe3C (For Fe-C, 727ºC, 0.76 wt% C)

intermetallic compound - cementite

cool

heat

• Eutectic - liquid transforms to two solid phases

L a + b (For Pb-Sn, 183ºC, 61.9 wt% Sn)

cool

heat

cool

heat

• Peritectic - liquid and one solid phase transform to a

second solid phase

S1 + L S2

+ L (For Fe-C, 1493ºC, 0.16 wt% C)

Eutectic, Eutectoid and Pertectic Reactions


Eutectoid & Peritectic

Cu-Zn Phase diagram

Adapted from Fig. 9.21,

Callister & Rethwisch 8e.

Eutectoid transformation +

Peritectic transformation + L


Iron-Iron Carbide Phase Diagram


Phases in Fe–Fe3C Phase Diagram

α-ferrite - solid solution of C in BCC Fe

• Stable form of iron at room temperature.

• The maximum solubility of C is 0.022 wt% at 727 °C

• Transforms to FCC γ-austenite at 912 °C

γ-austenite - solid solution of C in FCC Fe

• The maximum solubility of C is 2.14 wt % at 1147 °C .

• Transforms to BCC δ-ferrite at 1395 °C

• Is not stable below the eutectic temperature

(727 ° C) unless cooled rapidly


δ-ferrite solid solution of C in BCC Fe

• The same structure as α-ferrite

• Stable only at high T, above 1394 °C

• Melts at 1538 °C

Fe3C (iron carbide or cementite)

Interstitial solution of Fe in C with maximum solubility

of 6.67 wt% C. It is satble at room temperature.

Crystalline structure is orthorhombic.

Phases in Fe–Fe3C Phase Diagram

Fe-C liquid solution


A few comments on Fe–Fe3C system

C is an interstitial impurity in Fe. It forms a solid solution

with α, γ, δ phases of iron

Maximum solubility in BCC α-ferrite is limited (max.

0.022 wt% at 727 °C) - BCC has relatively small interstitial

positions

Maximum solubility in FCC austenite is 2.14 wt% at 1147

°C - FCC has larger interstitial positions.

Mechanical properties: Cementite is very hard and brittle

-can strengthen steels. Ferrite and austenite are relatively

soft phases.

Magnetic properties: α -ferrite is magnetic below 768

°C, austenite is non-magnetic.


Classification. Three types of ferrous alloys:

• Iron: less than 0.008 wt % C in α−ferrite at room T

• Steels: 0.008 - 2.14 wt % C (usually < 1 wt % )

α-ferrite + Fe3C at room T

• Cast iron: 2.14 - 6.7 wt % (usually < 4.5 wt %)



Development of Microstructure in

Iron - Carbon alloys

Microstructure depends on composition (carbon

content) and heat treatment. Here we consider slow cooling in

which equilibrium is maintained

Microstructure of eutectoid

steel


Development of Microstructure in

Iron - Carbon alloys

Microstructure of eutectoid steel

When alloy of eutectoid composition (0.76 wt % C) is cooled

slowly it forms perlite, a lamellar or layered structure of two

phases: α-ferrite and cementite (Fe3C).

Mechanically, pearlite has properties intermediate to soft,

ductile ferrite and hard, brittle cementite

In the micrograph, the dark areas are

Fe3C layers, the light phase is α-

ferrite


At room temperature steel is Ferrite with patches of Pearlite.

Technology

Chapter 9 phase diagrams 1