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Phase Diagrams

a Review

Topic 2

Review of

Phase Transformation

Diagrams

Example: Solubility of salt in water

There exists a maximum amount of salt that can be

completely dissolved in water; excess of salt stays as solid. This maximum amount is the solubility of salt in water. The solution containing the maximum concentration of salt is a saturated solution. Cooling of saturated solution results in the formation of solid salt from the solution, indicating that solubility decreases with decreasing T. This process is called precipitation and the solid formed is a precipitate. Heating the solution will lead to the dissolving of the precipitate back into solution.

Salty water -

the solution

Solid salt - the

precipitate

The same concepts apply to solids: solid solution, saturation, solubility, precipitationIn this example there exist two phases in the system and the two phases stay in

equilibrium:

SolutionSolid

dissolvingprecipitation

Solution and Solubility

Phase diagrams are used to map out

the existence and conditions of various phases of a give system.

The phase diagram of water is a

common example. Water may stay in liquid, solid or gaseous states in different pressure-temperature regions. Boundaries of the regions express the equilibrium conditions in terms of P and T. Water is a monolithic system. For binary systems, which contains two constituents, such as binary alloys, phase diagrams are often expressed in the temperature-composition plane.

LiquidSolidGasSuper-critical

fluid

Triple

point

Critical

point

Temperature

0°C100°C374°C0 bar1 bar221 bar

Pressure

phase diagram of water

Phase Diagrams

The simplest type of binary phase

diagrams is the isomorphous system, in which the two constituents form a continuous solid solution over the entire composition range. An example is the Ni-Cu system.

Solidification of alloy C

o starts on cooing at T 1 . The first solid formed has a composition of C s1 and the liquid C o . On further cooling the solid particles grow larger in size and change their composition to C s2 and then C o following the solidus whereas the liquid decrease in volume and changes its composition from C o to C L3 following the liquidus. The solidification completes at T 3

1455°C 1085°C

Cu Ni phase (fcc) -

Solid solution

of Cu and Ni liquid phase -

Solution of

Cu and Ni

CompositionTemperature

C S 1 T 1 C L 2 C o T 2 T 3 C S 2 C o C L 3 L

Binary Phase Diagrams

The simplest type of binary phase

diagrams is the isomorphous system, in which the two constituents form a continuous solid solution over the entire composition range. An example is the Ni-Cu system.

Compositions of phases is determined

by the tie line

The relative fractions of the phases are

determined by the lever rule

W1W2L2L1

1455°C 1085°C

Cu Ni phase (fcc) -

Solid solution

of Cu and Ni liquid phase -

Solution of

Cu and Ni

CompositionTemperature

C S T*C L C o

Binary Phase Diagrams

W1W2L2L1

Weight fractions:

Lever Rule

Read from the tie line:

Liquid phase:Cu-30%Ni

α-phase: Cu-55%Ni

C L C S C o

At temperature T

1 , alloy C o is in the dual phase region, comprising the liquid phase and the α-phase. (i) Determine the compositions of the two phases; (ii) Determine the weight fractions of the two phases

50%NiCu Ni 1455°C 1085°C C

S C 0 C L T 1

55%Ni30%Ni

Example

5550

0.220%

5530
so L sL CC W CC 5030

0.880%

5530

110.20.880%

oL sL L CC W CC or WW determination of Phase diagrams T

1085°C

II (thermal arrest)

TtT2T1I

Cu Ni

T%IIIIII

1455°C 1085°C

T1T2

SolidusLiquidus

Cooling Curves

Pb-Sn phase diagram

β phase: solid

solution of Pb in tetragonal Sn

α phase: solid

solution of Sn in fcc Pb

Liquid

Pb (Fcc) Sn (Tetra)

Temperature

Wt%

The Pb-Sn system is

characteristic of a valley in the middle. Such system is known as the Eutectic system. The central point is the Eutectic point and the transformation though this point is called

Eutectic reaction: L8α+β

Pb has a fcc structure and Sn has

a tetragonal structure. The system has three phases: L, α and solvussolvussolidusLiquidusEutectic point

α + βα + LL + β

Eutectic Systems

Alloy I:

At point 1: Liquid

Solidification starts at liquidus

At point 2: L+α

The amount α ↑ with ↓ T

Solidification finishes at solidus

At point 3: α

Precipitation starts at solvus

At point 4: α+β

Further cooling leads to formation

and growth of more β precipitates whereas Sn% in α decreases following the solvus.

The cooling curve of this alloy is

similar to cooling curve I shown in slide 9.quotesdbs_dbs14.pdfusesText_20