工程材料

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Chapter 9: Phase Diagrams

Issues to address

• resulting equilibrium state when combining two elements
• specify composition(%數)、temperature(T)，then
  • how many phases form?
  • what is the composition of each phase?
  • what is the amount of each phase?
• 

Phase Equilibria: Solubility Limit

相平衡: 溶解度極限

溶液vs混合物

• Solution: solid, liquid, gas solutions, single phase
• Mixture: more than one phase
• Solubility Limit:
  • Maximum concentration for which only a single phase solution exists
  • Question:

    What is the solubility limit for sugar in water at 20ºC
    

    

  • Answer:

    65wt% sugar
    At 20ºC, if C<65 wt% sugar: syrup
    At 20ºC, if C>65 wt% sugar: syrup + sugar

Components and Phases

• Components:
  • The elements or compounds(化合物) which are present in the alloy
• Phases:
  • The physically and chemically distinct material regions that form(e.g.
    $\alpha$ and
    $\beta$)
    
    

Effect of Tempearture & Composition

Criteria for Solid Solubility

• Simple system (e.g.Ni-Cu solution)
  
  
• Both have the same crystal structure(FCC) and have similar electronegativities and atomic radii suggesting high mutual solubility.
• Ni and Cu are totally soluble in one another for all properties

Phase Diagram

• Indicate phases as afunction of T, C, and P
• For this course
  • binary system: just 2 components
  • independent variables: T and C (P=1 atm is almost always used)

Isomorphous(同構的) Binary Phase Diagram

• Phase Diagram: Cu-Ni system
• System:
  • Binary

    2 components

  • isomorphous(同構)

    complete solubility of one component in another,

    $\alpha$ phase field extends from 0 to 100 wt% Ni.

Determination of phase(s) present

• Rule 1: If we know T and C_o

  which phase(s) is (are) present

• Examples
  
  
  • A(1100ºC, 60 wt% Ni): 1 phase
    $\alpha$
  • B(1250ºC, 35 wt% Ni): 2 phases L+
    $\alpha$

Determination of phase compositions

• Rule 2: If we know T and C₀

  the composition of each phase

• Examples
  
  

  Consider C₀ = 35 wt% Ni

  • At T_A = 1320ºC:
    • Only Liquid(L) present
    • C_L = C₀ (=35 wt%)
  • At T_D = 1190ºC:
    • Only solid(
      $\alpha$) present
    • $C_{\alpha }$=C₀(=35 wt%)
  • At T_B = 1250ºC:
    • Both
      $\alpha$ and L present
    • C_L = 32$ wt% Ni
    • $C_{\alpha }$~ = 43 wt% Ni

Determination of phase weight fractions

• Rules 3: If we know T and C₀

  can determine weight fraction of each phase

• Examples:

  Consider C₀ = 35 wt% Ni

  • At T_A: Only Liquid
    • $W_L=1.00,W_{\alpha }=0$
  • At T_D: Only Solid(
    $\alpha$)
    • $W_L=0,W_{\alpha }=1.00$
  • At T_B: Both Liquid and Solid
    • $W_L={\displaystyle \frac{S}{R+S}}$ = 0.73
    • $W_{\alpha }={\displaystyle \frac{R}{R+S}}$ = 0.27
    • $R,S$為B到boundary的wt距離
      
      

The Lever Rule

• Tie line: connects the phases in equilibrium with each other
• also sometimes called an isotherm(等溫線)
  
  
  
  

Cored vs Equilibrium Structures

• $C_{\alpha }$ changes as we solidfy
• Cu-Ni case:
  • First
    $\alpha$ to solidify has
    $C_{\alpha }$ = 46 wt% Ni
  • Last
    $\alpha$ to solidify has
    $C_{\alpha }$ = 35 wt% Ni
• Slow rate of cooling: Equilibrium structure
• Fast rate of cooling: Cored structure
  
  

Mechanical Properties: Cu-Ni System

• Effect of solid solution strengthening on:
  
  

Binary-Eutectic Systems

Eutectic: has a spectial composition with a min. melting T

Ex. Cu-Ag system

• 3 single phase regions(L,
  $\alpha$,
  $\beta$)
• Limited solubility
  • $\alpha$: mostly Cu
  • $\beta$: mostly Ag
• $T_E$: No liquid below
  $T_E$
• $C_E$: Composition at temperature
  $T_E$
• Eutectic reaction:
  • $L(C_E)\leftrightharpoons \alpha (C_{\alpha E}+\beta (C_{\beta E}))$

例題看ppt動畫
ask: phase present, phase compositions, relative amount of each phase

Microstructural Developments in Eutectic

System I

• For alloys for which C₀ < 2 wt% Sn
• Result: at room temperature
  • polycrystalline with grains of
    $\alpha$ phase having composition C₀
    
    

System II

• For alloys for which 2 wt% Sn < C₀ <18.3 wt% Sn
• Result: at temperature in
  $\alpha +\beta$ range
  • polycrystalline with
    $\alpha$ grains and small
    $\beta$-phase particles
    
    

System III

• For alloy of composition C₀ = C_E
• Result: Eutectic microstructure (lamellar struc)
  • alternating layers(lamellae) of
    $\alpha$ and
    $\beta$ phases
    
    
    
    

System IV

• For alloys for which 18.3 wt% Sn < C₀ < 61.9 wt% Sn
• Result:
  $\alpha$ phase particles and a eutectic microconstituent
  
  

Hypoeutectic & Hypereutectic

Eutectic, Eutectoid, Peritectic

• Eutectic: liquid transforms to two solid phases
  
  
• Eutectoid: one solid phase transforms to two other solid phases
  
  
• Peritectic: liquid and one solid phase transform to a second solid phase
  
  
  
  
  
  

Hypoeutectoid Steel & Hypereutectoid Steel 看PPT動畫解釋
例題也看PPT

Summary

• Phase diagrams are useful tools to determine
  • the number and types of phases present
  • the composition of each phase
  • and the weight fraction of each phase
• The microstructure of an alloy depends on
  • its composition
  • whether or not cooling rate allows for maintenance of equilibrium
• Important phase diagram phase transformations include