Ch 10

Chapter 10. Phase Diagrams

MAE 2321

The Solubility of Sugar

MAE 2321

EFFECT OF T & COMPOSITION • Changing T can change # of phases: path A to B. • Changing Co can change # of phases: path B to D. B(70,97) D(90,97) 1 phase

• watersugar system

Temperature (°C)

100

L

80 60 40 20 0

0

2 phases

(liquid)

L (liquid solution i.e., syrup)

+ S (solid sugar)

A(70,20) 2 phases

20 40 60 70 80 100 Co=Composition (wt% sugar) MAE 2321

COMPONENTS AND PHASES • Components: The elements or compounds which are mixed initially (e.g., Al and Cu)

• Phases: The physically and chemically distinct material regions. AluminumCopper Alloy

β (lighter phase) α (darker phase)

MAE 2321

3

Interpretation of Phase Diagrams

From the phase diagram, we know 1. The phases that are present. 2. The compositions of these phases. 3. The percentages of the phases.

MAE 2321

Cu-Ni Phase Diagram

• Tell us about phases as function of T, Co, P. • For this course: --binary systems: just 2 components. --independent variables: T and Co (P = 1atm is always used).

MAE 2321

Complete Solid Solution: Isomorphous Alloys

MAE 2321

Interpretation of Phase Diagrams

• Phases present. • Determination of phase compositions. • Determination of phase amounts.

MAE 2321

Cu-Ni Phase Diagram

MAE 2321

The Lever Rule: A Proof WL + Wα = 1 Co = WL CL + Wα Cα • Conservation of mass (Ni): • Sum of weight fractions:

• Combine above equations: Cα − Co = S = WL Cα − CL R + S • A geometric interpretation: Co CL Cα R S

WL

Wα

Co − CL = R Wα = Cα − CL R + S

moment equilibrium:

WLR = WαS 1− Wα solving gives Lever Rule MAE 2321

Concept Check 10.2

MAE 2321

Development of Microstructure during Equilibrium Solidification • Phase diagram: Cu-Ni system. • System is: --binary i.e., 2 components: Cu and Ni. --isomorphous i.e., complete solubility of one component in another; a phase field extends from 0 to 100wt% Ni. Overall alloy composition remains unchanged during cooling even though there is a redistribution of Cu and Ni between the phases. MAE 2321

Development of Microstructure during Nonequilibrium Solidification

• Diffusion • Cooling Rate • Segregation • Cored Structure

MAE 2321

CORED VS EQUILIBRIUM PHASES • Cα changes as we solidify. • Cu-Ni case: First a to solidify has Cα = 46wt%Ni. Last a to solidify has Cα = 35wt%Ni.

• Fast rate of cooling: Cored structure

• Slow rate of cooling: Equilibrium structure

First α to solidfy: 46wt%Ni Last α to solidfy: < 35wt%Ni

Uniform Cα: 35wt%Ni

MAE 2321

Mechanical Properties of Isomorphous Alloys

MAE 2321

Solid-Solution Strengthening

Fig. 8.17

Fig. 8.18

Dislocation movement is restricted. MAE 2321

BINARY-EUTECTIC SYSTEMS 2 components

Low melting point

Ex.: Cu-Ag system

• 3 single phase regions (L, α, β) • Limited solubility: α: mostly Cu β: mostly Ag • T E: No liquid below T E • CE: Min. melting T composition

Limited solubility

MAE 2321

Cu-Ag Phase Diagram

Invariant Point (Eutectic Point)

Eutectic Isotherm (parallel to the composition axis, Extends between the maximum solubility positions)

MAE 2321

Eutectic Reaction L(CE)

α(CαE) + β(CβE)

• The eutectic reaction, upon cooling, proceeds to completion at a constant temperature, or isothermally, at TE (similar to solidification for pure material). • Along the eutectic isotherm, three phases (α,β, and L) are in equilibrium.

MAE 2321

Lead-Tin Eutectic System

MAE 2321

H2O-NaCl Phase Diagram

MAE 2321

Microstructure in Eutectic Alloys

MAE 2321

Microstructure in Eutectic Alloys

MAE 2321

Microstructure in Eutectic Alloys

MAE 2321

Microstructure in Eutectic Alloys

MAE 2321

Microstructure in Eutectic Alloys

MAE 2321

Microstructure in Eutectic Alloys

Lead-Tin alloy with composition of 50wt% Sn MAE 2321

Relative Amount of Each Phase Fraction of eutectic microconstituent We Fraction of eutectic liquid WL Fraction of primary α, Wα’ Fraction of total α, Wα Fraction of total β, Wβ

We = WL = P/(P+Q) Wα’ = Q/(P+Q) Wα = Q+R/(P+Q+R) Wβ = P/(P+Q+R)

MAE 2321

Intermediate Phases Intermediate Phases

Terminal Phase Terminal Phase

MAE 2321

The magnesium-Lead Phase Diagram

Intermetallic Compound

Two eutectic systems joined back to back MAE 2321

Eutectoid Reaction

δ

cooling heating

γ+ε

• The eutectoid reaction, upon cooling, proceeds to completion at a constant temperature. • Along the eutectoid isotherm, three phases (δ,γ, and ε) are in equilibrium.

MAE 2321

Peritectic Reaction

δ+L

cooling heating

ε

• The peritectic reaction, upon heating, proceeds to completion at a constant temperature. • Along the peritectic isotherm, three phases (δ,L, and ε) are in equilibrium.

MAE 2321

Congruent and Incongruent Transformations

Congruent melting point

Congruent transformation: no compositional alterations Example: melting of pure metals MAE 2321

Concept Check 10.6

β+L HfV2 + L

Two eutectics, one eutectoid, one congruent melting MAE 2321

Al3+ and Cr3+ have the same charge and similar radii. MAE 2321

There are two eutectics. MAE 2321

One eutectic and two eutectoid reactions. MAE 2321

MAE 2321

Ternary Phase Diagrams

MAE 2321

The Gibbs Phase Rule

P+F=C+N P: The number of phases F: The number of degree of freedom or The number of externally controllable variables (T, P, composition) C: The number of components N: The number of available noncompositional variables (T and P)

MAE 2321

The Gibbs Phase Rule (example) P+F=C+N

MAE 2321

The Iron-Iron Carbide Phase Diagram

MAE 2321

Classification of Ferrous Alloys

Iron (0-0.008 wt% C)

Steel (0.008-2.14 wt% C)

Cast Iron (2.14-6.70 wt% C)

Hypoeutectoid steel Hypereutectoid steel MAE 2321

Pearlite

MAE 2321

Hypoeutectoid Alloy

0.38 wt% C steel

MAE 2321

Hypereutectoid Alloy

1.4 wt% C steel

MAE 2321

The Influence of Other Alloying Elements

MAE 2321