Lecture

9

Phase

Diagrams

8-1

Introduction

• Phase: A region in a material that differs in structure and function from other regions.

• Phase diagrams: Represents phases present in metal at different conditions

(Temperature, pressure and composition). Indicates equilibrium solid solubility of one element in

another. Indicates temperature range under which solidification

occurs. Indicates temperature at which different phases start to

melt.

8-2

Phase Diagram of Pure Substances

• Pure substance exist as solid, liquid and vapor.

• Phases are separated by phase boundaries.

• Example : Water, Pure Iron.

• Different phases coexist at triple point.

Figure 8.1 Figure 8.2

After W. G. Moffatt, et al., “The Structure and Properties of Materials,” vol I: “Structure,” Wiley, 1965, p.151

8-3

Gibbs Phase Rule

• P+F = C+2

• For pure water, at triple point, 3 phases coexist.

• There is one component (water) in the system.

• Therefore 3 + F = 1 + 2 F = 0.

• Degrees of freedom indicate number of variables that can be changed without changing number of phases.

P = number of phases that coexist in a systemC = Number of componentsF = Degrees of freedom

8-4

Cooling Curves

• Used to determine phase transition temperature.• Temperature and time data of cooling molten metal

is recorded and plotted.

• Thermal arrest : heat lost = heat supplied by solidifying metal

• Alloys solidify over a range of temperature (no thermal arrest)

Pure Metal

Iron

Binary Isomorphous Alloy Systems

• Binary alloy

• Isomorphous system: Two elements completely soluble in each other in liquid and solid state.

• Example: Cu-Ni solution.

Mixture of two systems

Two componentsystem

Composition at liquid and solid phases at any temperature can be determined by drawinga tie line.

Figure 8.3

Adapted from “Metals Handbook,” vol. 8, 8th ed., American society of Metals, 1973, p. 294.

8-5

Phase Diagram from Cooling Curves

• Series of cooling curves at different metal composition are first constructed.

• Points of change of slope of cooling curves (thermal arrests) are noted and phase diagram is constructed.

• The greater the number of cooling curves the more accurate the phase diagram.

Figure 8.4

8-6

The Lever Rule

• The Lever rule gives the weight % of phases in any two phase regions.

Wt fraction of solid phase= Xs = w0 – w1

ws – w1

Wt fraction of liquid phase= Xl = ws – w0

ws – w1

Figure 8.5

8-7

W0 is the weight percentage of the alloy.

Ws is the weight percentage within the solid phase

Wl is the weight percentage in the liquid phase

Non Equilibrium Solidification of Alloys

• Very slow cooling (equilibrium) gives rise to cored structure as composition of melt continuously changes.

• Rapid cooling delays solidification but also leads to cored structure

. • Homogenization: Cast ingots heated to elevated temperature to eliminate cored structure.• Temperature of homogenization must be lower than lowest melting

point of any of the alloy components.

Figure 8.7 Figure 8.8

8-8

W0=30% Cu

Binary Eutectic Alloy System

• In some binary alloy systems, components have limited solid solubility.

• Eutectic composition freezes at lower temperature than all other compositions. • This lowest temperature is called eutectic temperature.

Liquid α solid solution + β solid solutionEutectic temperature

Cooling

Example : Pb-Sn alloy.

Figure 8.11

8-9

Slow Cooling of 60% Pb – 40% Sn alloy

• Liquid at 3000C.

• At about 2450C first solid forms – proeutectic solid.

• Slightly above 1830C composition of alpha follows solidus and composition of sn varies from 40% to 61.9%.

• At eutectic temperature, all the remaining liquid solidifies.

• Further cooling lowers alpha Sn content and beta Pb.•(They try to move to equilibrium)

Figure 8.13

Figure 8.12

From J. Nutting and R. G. Baker, “Microstructure of Metals,” Institute of Metals, London, 1965,p.19.

8-10

Various Eutectic Structures

• Structure depends on factors like minimization of free energy at α / β interface.

• Manner in which two phases nucleate and grow also affects structures.

Figure 8.14

After W. C. Winegard, “An Introduction to the Solidification of Metals,” Institute of Metals, London, 1964.8-11

Binary Peritectic Alloy System

• Peritectic reaction: Liquid phase reacts with a solid phase to form a new and different solid phase.

Liquid + α β

cooling

• Peritectic reaction occurs when a slowly cooled alloy of Fe-4.3 wt% Ni passes through Peritectic temperature of 1517C.• Peritectic point is invariant.

Liquid(5.4 wt% Ni) + δ (4.0 wt% Ni) γ 4.3 wt % Nicooling

Figure 8.16

8-12

Peritectic Alloy System• At 42.4 % Ag & 14000C Phases present Liquid Alpha Composition 55% Ag 7%AgAmount of Phases 42.4 –7 55-42.4 55 – 7 55 - 7 = 74% = 26%• At 42.4% Ag and 11860C – ΔT Phase Present Beta only Composition 42.4% Ag Amount of Phase 100%

• At 42.4% Ag and 11860C + ΔT Phases present Liquid Alpha Composition 66.3% Ag 10.5%AgAmount of Phases 42.4 –10.5 66.3-42.4 66.3 – 10.5 66.3–10.5 = 57% =43%

Figure 8.17

Figure 8.18

8-13

Rapid Solidification in Peritectic System

• Surrounding or Encasement: During peritectic reaction, L+ α β , the beta phase created surrounds primary alpha.

• Beta creates diffusion barrier resulting in coring.

Figure 8.20Figure 8.19

After F Rhines, “ Phase Diagrams in Metallurgy,”McGraw- Hill, 1956, p. 86.

8-14

Binary Monotectic Systems

• Monotectic Reaction: Liquid phase transforms into solid phase and another liquid.

L1 α + L2Cooling

• Two liquids are immiscible.• Example:- Copper – Lead system at 9550C and 36% Pb.

Eutectic

Eutectoid

Peritectic

Peritectoid

Monotectic

Figure 8.23

Table 8.1

Metals Handbook,” vol. 8: “Metallography Structures and Phase Diagrams,” 8 th ed., American Society of Metals, 1973, p. 296. 8-15

Intermediate Phases and Compounds

• Terminal phases: Phases occur at the end of phase diagrams.

• Intermediate phases: Phases occur in a composition range inside phase diagram.

• Examples: Cu-Zn diagram has both terminal and intermediate phases.

• Five invariant peritectic points and one eutectic point.

Figure 8.25“Metals Handbook,” vol. 8: “Metallography Structures and Phase Diagrams,” 8 th ed., American Society of Metals, 1973, p. 301

8-16

Intermediate Phases in Ceramics

• In Al2O2 – SiO2 system, an intermediate phase called Mullite is formed, which includes the compound 3Al2O3.2SiO2.

Figure 8.26

After A. G. Guy, “Essentials of Materials Science, “McGraw-Hill, 1976 8-17

Intermediate Compounds

• In some phase diagrams, intermediate compound are formed – Stoichiometric

• Percent Ionic/Covalent bond depends on electronegativeness

• Example:- Mg-Ni phase diagram contains Mg2Ni : Congruently melting compound

MgNi2 : Incongruently melting compound.

Figure 8.27

Metals Handbook,” vol. 8: American Society of Metals, 1973, p. 314. 8-18

Ternary Phase Diagrams

• Three components

• Constructed by using a equilateral triangle as base.

• Pure components at each end of triangle.• Binary alloy composition represented on edges.

Temperature can be represented as uniform throughout the Whole Diagram Isothermal section.

Figure 8.28

8-19

Ternary Phase Diagram (Cont..)

• Example:- Iron-Chromium-Nickel phase diagrams.

•Isothermal reaction at 6500C

for this system

• Composition of any metal

at any point on the phase

diagram can be found by

drawing perpendicular

from pure metal corner to

apposite side and calculating

the % length of line at that

point Figure 8.30

After “Metals Handbook,” vol. 8: American Society of Metals, 1973, p. 425.

8-20