Phase diagram

1

Devesh agrawal

Chapter 3: The Structure of Crystalline Solids 2


A solid solution forms when, as the solute atoms are added to the host materials, the crystal structure is maintained, and no new structures are formed.





Hume-Rothery (1899-1968) was a metallurgist who studied the alloying of metals. His research was conducted at Oxford University where in 1958, he was appointed to the first chair in metallurgy.

His research led to some simple and useful rules on the extent to which an element might dissolve in a metal . The rules that he derived are paraphrased here. The rules are still used widely. For example, the miscibility gap in Au-Ni is correlated with the fact that the lattice parameter of Au is 1.15 times that of Ni, thus acting maximally according to Hume-Rothery .







Chapter 09: Phase Diagram 15

Introduction

Phase Diagrams are road maps


Component: Pure metals/compounds of which an alloy is

composed

System: Alloy system, e.g., Iron-Carbon alloy system,

copper-nickel alloy system

Solid solutions

- Substitutional

- Interstitial


Solubility Limit: Max concentration of solute atoms that

may dissolve in the solvent to form a solid solution.

-The solubility limit of sugar in water depends on the

temperature of water. At 20degree C, maximum solubility

of sugar in water is 65%.

Phases: Homogenous portion of a system that has uniform

physical and chemical properties.

-Every pure material is considered to be a phase, e.g.

solid, liquid and gas phase


If more than one phase is present in a given system, each will have its own distinct properties and boundary separating the phases will exist across which there will be discontinuous and abrupt change in physical and chemical characteristicsSubstance can exist in two or more polymorphic forms (having FCC and BCC structure) each have separate phase and different properties. Sugar water example, sugar water syrup solution is one phase and solid sugar is another


Source: William Callister 7th edition, chapter 09, page 254, figure 9.1


Each phase has different phase physical properties

Microstructure

•Characterized by number of phases, proportions and the

manner of distribution of phases.

•Depends on: Alloying elements, concentrations, heat

treatment (temp, heating/cooling rate etc.)


Free energy : It is function of the internal energy of a system

and also the randomness of atoms/molecules

Equilibrium : A system is at equlibrium,if its free energy is

at a minimum under some specified combination of Temp,

Pressure and Composition

Phase equilibrium : Phase is equilibrium if it is constant

with time in the phase characteristics of a systems. It refers,

when more than one phase are present in system.

Isomorphous: Complete solubility in both liquid and solid

states.


Non-equilibrium state/Metastable: State of equilibrium

is never reached since the rate of approach to equilibrium

is very slow. This state may persist indefinitely,

experiencing only slight and almost imperceptible

changes as time progresses

Equilibrium phase diagram

•Represents the relationships between temperature and

compositions, and the quantities of phases in equilibrium

Chapter 3: The

Structure of Crystalline

Solids23

Gibbs Phase Rule

Chapter 3: The


Solids24

Chapter 3: The


Solids25

Unary Phase Diagram (Pressure-temperature diagram for Water)

The simplest phase diagrams are pressure-temperature diagrams of a single simple substance, such as water. The axes correspond to the pressure and temperature. The phase diagram shows, in pressure-temperature space, the lines of equilibrium or phase boundaries between the three phases of solid, liquid, and gas.

Chapter 3: The


Solids26

Chapter 3: The


Solids27

Chapter 3: The


Solids28


Binary Isomorphous Systems

Source: William Callister 7th edition, chapter 09, page 259, figure 9.3 a&b


Three kinds of infomation:

•What Phases are present at particular temp and comp.

•Determination of phase compositions( in term of

concentration of compoents) Using Tie Line or Isotherm.

To determine the composition (in wt% Ni and Cu) for

both the alpha and liquid phase for 35wt%Ni-65 wt%Cu at

1250 C. Composition of liquid phase is 32 wt% Ni and

composition of alpha phase is 43 wt%Ni.

•percentages/fractions of phases (Phase Amount) at

equilibrium.


73%0.7332433543W

L

27%0.2732433235W

Where, WL: weight/mass fraction of liquid

At 1250°C and Co=35% Ni


Lever Rule (Inverse lever rule)

1.Draw tie-line across the two phase region

2.Locate the overall composition (e.g., Co=35%Ni)

3.To compute the fraction of one phase, take the length of

the tie-line from the overall composition to the opposite

phase boundary and divide by the total tie line length

4.Repeat above procedure for the other phase.


•When two phases are present,Sum of their mass fractions must be Equal to unity.---- (1)

•Mass of one of the component (CuOr Ni) that is present in both phasesMust be equal to the mass of that Component in the total alloy- (2)

Where, Cs and C both are same


Lever Rule


Development of microstructures


Development of microstructures(Non Equilibrium Cooling)(


Development of Microstructures

The compositions readjust with changes in temperature.

These changes occur through the process of diffusion.

Because diffusion is time-dependent, much more time is

required, at each temperature for compositional

adjustments. Diffusion rates decrease with temperature. In

reality, cooling rates are so fast that there is little time to

enable equilibrium cooling. Diffusion rate in liquid is

faster than solid


•Because of fast cooling, there is a

non-uniform distribution of the two

elements for isomorphous alloys

“Segregation”

In the centre of each grain, the high

melting element solidifies first. At the

periphery, the low melting element

solidifies.

Non-Equilibrium Solidification


Coring

Cored Structure: Concentration contours

•Undesirable less than optimal properties due to

inhomogeneity.

•Coring is eliminated by a homogenization Heat

treatment. At a temperature below the solidus point for the

composition; atomic diffusion causes homogenization.


Mechanical Properties of Isomorphous Alloys



•Solid solution hardening or an increase in strength and

hardness by the addition of the other component

•At an intermediate composition, the curve (TS Vs Comp)

passes through a maximum

Mechanical Properties of Isomorphous Alloys


Binary eutectic systems


Binary eutectic systems Continue …..

:Solid Solution of Ag in Cu-Rich solvent

:Solid solution of Cu in Ag-Rich solvent

Technically, : Pure Cu

: Pure Ag

Below BEG, only limited solid solubility takes place


CEA: (solid) solubility limit for Ag in – phase (Cu-Rich)

HGF: Solubility limit for Cu in -phase (Ag-Rich)

CBA is between /(+) and /(+L) phase regions

•Max. at 7.9% Ag (780°C)


•Decrease to zero at 1085°C (Melting point of pure Cu)


For –phase CB: solvus line: /(+)

AB: Solidus line: /(+L)

General Rule: Single phase regions are always separated

from each other by a two phase region that consists of two

single phases that it separtes.



Prepare similar notes for -phase region

HGF is between

For -phase

HG: Solvus line and GF: Solidus line



Three two-phase regions: +L, +L and +

E: Eutectic invariant point

CE: 71.9 wt% Ag

Cu-Ag system: TE: 780°C



Binary Eutectic systems Continue …..

Eutectic Reaction:

Liquid Solid 1 + Solid 2

L +

L(CE) (C E) + (C E)

At E,



For Cu-Ag system,

L(71.9 wt% Ag) (7.9 wt% Ag) + (91.2 wt% Ag)



Solidus line at 780°C: Eutectic isotherm

Phase volume fractions represent proportions seen in the

microstructure; so they can be estimated from

microstructures, and the mechanical properties can be

estimated as well.














62

Temperature Dependence of Transformation Rate

For the recrystallization of Cu, since

rate = 1/t0.5

rate increases with increasing temperature

• Rate often so slow that attainment of equilibrium state not possible!

Adapted from Fig. 11.11, Callister & Rethwisch 3e.(Fig. 11.11 adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 188, 1950, p. 888.)

135C 119C 113C 102C 88C 43C

1 10 102 104

63

Transformations & Undercooling

• For transf. to occur, must cool to below 727°C (i.e., must “undercool”)

• Eutectoid transf. (Fe-Fe3C system): + Fe3C0.76 wt% C

0.022 wt% C6.7 wt% C

Fe 3

C (

cem

entit

e)

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6.7

L

(austenite)

+L

+Fe3C

+Fe3C

L+Fe3C

(Fe) C, wt%C

1148°C

T(°C)

ferrite

727°C

Eutectoid:Equil. Cooling: Ttransf. = 727ºC

T

Undercooling by Ttransf. < 727C

0.7

6

0.0

22

Adapted from Fig. 10.28,Callister & Rethwisch 3e. (Fig. 10.28 adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990.)

64

The Fe-Fe3C Eutectoid Transformation

Coarse pearlite formed at higher temperatures – relatively soft

Fine pearlite formed at lower temperatures – relatively hard

• Transformation of austenite to pearlite:

Adapted from Fig. 10.15, Callister & Rethwisch 3e.

pearlite growth direction

Austenite ()grain boundary

cementite (Fe3C)

Ferrite ()

• For this transformation, rate increases with [Teutectoid – T ] (i.e., T).


675°C (T smaller)

0

50

y (%

pea

rlite

)600°C

(T larger)650°C

100

Diffusion of C during transformation

Carbon diffusion

65

Adapted from Fig. 11.13,Callister & Rethwisch 3e. (Fig. 11.13 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1977, p. 369.)

Generation of Isothermal Transformation Diagrams

• The Fe-Fe3C system, for Co = 0.76 wt% C• A transformation temperature of 675°C.

100

50

01 102 104

T = 675°C

y,

% tr

ansf

orm

ed

time (s)

400

500

600

700

1 10 102 103 104 105

0%pearlite

100%

50%

Austenite (stable) TE (727C)Austenite (unstable)

Pearlite

T(°C)

time (s)

isothermal transformation at 675°C

Consider:

66

• Eutectoid composition, C0 = 0.76 wt% C• Begin at T > 727°C• Rapidly cool to 625°C• Hold T (625°C) constant (isothermal treatment)

Adapted from Fig. 11.14,Callister & Rethwisch 3e. (Fig. 11.14 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.)

Austenite-to-Pearlite Isothermal Transformation

400

500

600

700

0%pearlite

100%

50%

Austenite (stable)TE (727C)

Austenite (unstable)

Pearlite

T(°C)

1 10 102 103 104 105

time (s)

67

10 103 105

time (s)10-1

400

600

800

T(°C)Austenite (stable)

200

P

B

TE

0%

100%

50%

A

A

Bainite: Another Fe-Fe3C Transformation Product • Bainite: -- elongated Fe3C particles in -ferrite matrix -- diffusion controlled • Isothermal Transf. Diagram,

C0 = 0.76 wt% C


Adapted from Fig. 11.17, Callister & Rethwisch 3e. (Fig. 11.17 from Metals Handbook, 8th ed., Vol. 8, Metallography, Structures, and Phase Diagrams, American Society for Metals, Materials Park, OH, 1973.)

Fe3C(cementite)

5 m

(ferrite)

100% bainite

100% pearlite

68

• Spheroidite: -- Fe3C particles within an -ferrite matrix -- formation requires diffusion -- heat bainite or pearlite at temperature

just below eutectoid for long times -- driving force – reduction

of -ferrite/Fe3C interfacial area

Spheroidite: Another Microstructure for the Fe-

Fe3C System

Adapted from Fig. 11.19, Callister & Rethwisch 3e. (Fig. 11.19 copyright United States Steel Corporation, 1971.)

60 m

(ferrite)

(cementite)

Fe3C

69

• Martensite: -- (FCC) to Martensite (BCT)

Adapted from Fig. 11.22, Callister & Rethwisch 3e. (Fig. 11.22 courtesy United States Steel Corporation.)


Martensite: A Nonequilibrium Transformation Product

Martensite needlesAustenite

60

m

xx x

xx

xpotential C atom sites

Fe atom sites


• Isothermal Transf. Diagram

• to martensite (M) transformation.. -- is rapid! (diffusionless) -- % transf. depends only on T to

which rapidly cooled

10 103 105 time (s)10-1

400

600

800

T(°C)Austenite (stable)

200

P

B

TE

0%

100%50%

A

A

M + AM + A

M + A

0%50%90%

70

(FCC) (BCC) + Fe3C

Martensite Formationslow cooling

tempering

quench

M (BCT)

Martensite (M) – single phase

– has body centered tetragonal (BCT) crystal structure

Diffusionless transformation BCT if C0 > 0.15 wt% C

BCT few slip planes hard, brittle

Austenite Ferrite + Cementite = Pearlite

Tempered Martensite

71

Phase Transformations of AlloysEffect of adding other

elementsChange transition temp.

Cr, Ni, Mo, Si, Mn

retard + Fe3C

reaction (and formation of

pearlite, bainite)




Problem:

For Pb-Sn system at 150°C, calculate relative amounts of

each phase by (a) Mass fraction (b) Volume fraction

0.6711994099

CC

CCW

n(a)Solutio

gm/cm 7.3:ρgm/cm 11.2:ρ

:Given

αβ

1βα

3β

3α


Problem: Continue ….

33

33

αβ

α1β

cm 4.52gm/cm 7.3

gm 33)(

v

cm 5.98gm/cm 11.2

gm 67)(

v

Fraction Volume (b) Solution

0.3311991140

CC

CCW

1-0.67=0.33


0.434.525.98

4.52vv

vV

0.574.525.98

5.98vv

vV

Fraction Volume

βα

ββ

βα

αα

Problem: Continue ….

Vα is volume fraction of the alpha phase, Vα and Vβ denote the volumes of the respective phases in the alloy.

Engineering

Phase diagram