W A T K I N S - J O H N S O N C O M P A N Y Semiconductor Equipment Group

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Engineering 45
PhaseDiagrams (1)
Bruce Mayer, PE Registered Electrical
Mechanical EngineerBMayer_at_ChabotCollege.edu
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Learning Goals Phase Diagrams

• When Two Elements Are Combined, Determine the
  Resulting MicroStructural Equilibrium State
• For Example
• Specify
• a composition (e.g., wtCu - wtNi), and
• a temperature (T)
• a pressure (P)
• almost ALWAYS assume ROOM Pressure
• Determine Structure

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Learning Goals.2 Phase Dia.

• Cont Determine Structure
• HOW MANY phases Result
• The COMPOSITION of each phase
• Relative QUANTITY of each phase

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Definitions Phase Systems

• Component ? Pure Constituent of a Compound
• Typcially an ATOM, but can also be a Molecular
  Unit
• Solvent/Solute
• Solvent ? Majority Component in a Mixture
• Solute ? Minority Component in a Mixture
• System ? Possible Alloys Formed by Specific
  Components (e.g. C-Fe Sys)

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The Solid Solubility Limit

• Solubility Limit ? Max Concentration of Solute
  that will actually DISSOLVE in a Solvent to form
  a SOLUTION

• Example Water-Sugar
• Add Sugar (Solute) to Water (Solvent)

• Initially ALL the Sugar Dissolves
• But after a Certain Amount, SOLID Sugar Starts to
  Collect on the bottom of the Vessel

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The Solid Solubility Limit cont.

• Sol-Sol Quantitative Example
• At What wt Sugar does the Sugar NO Longer
  Dissolve for
• 20 C
• 80 C
• For 20 C

75
63
Sugar

• Cast Right from 20C
• Find Solid Sugar in Vessel at C0 63 wt

• For 80C, Again Cast Rt
• Find Solid Sugar in Vessel at C0 75 wt

• INcreased Temp INcreases Sol-Sol Limit

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Components Phases

• Components ? The elements or compounds which are
  mixed initially (e.g., Al and Cu)
• Phases ? The PHYSICALLY and CHEMICALLY DISTINCT
  material regions that result from mixing
  (e.g., a and b below)

• AluminumCopperAlloy

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Effect of T Composition (C0)

• Changing T can change No. of phases path A to B.
  
• Changing C0 can change No. of phases path B to D

• WaterSugarSystem

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Phase Equilibria

• Consider the Cu-Ni Alloy System

Crystal Structure electroneg r (nm)
Ni FCC 1.9 0.1246
Cu FCC 1.8 0.1278

• Both have the same crystal structure (FCC) and
  have similar electronegativities and atomic radii
  (c.f. Hume Rothery rules) suggesting high
  mutual solubility.
• Copper and Nickel are, in fact, totally miscible
  in all Proportions

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Phase Diagrams

• Describes Phase Formation as a Function of T, C0,
  P
• This Course Considers
• binary systems 2 components
• independent variables T C0 (P 1atm in all
  Cases)

• The Cu-Ni Phase Diagram

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Phase Dia.s Phase No.s Types

• Rule-1 Given T C0 (for P 1 atm) then Find
• NUMBER TYPES of Phases Present

• Examples
• Pt-A (1100C, 60wt-)
• 1 Phase ? a the FCC Solid Solution
• Pt-B (1250,35)
• 2 Phases ? La

• Cu-Ni PhaseDiagram

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Phase Dia.s Phase Composition

• Rule-2 Given T C0 (for P 1 atm) then Find
• The COMPOSITION (wt or at) for EACH Phase

• Example C0 35 wt Ni
• At TA
• Only Liquid
• CL CO 35 wt Ni

• Cu-Ni PhaseDiagram

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Phase Dia.s Phase Comp. cont.

• Example C0 35 wt Ni
• At TD
• Only Solid (a-FCC)
• Ca C0 35 wt Ni
• At TB
• BOTH a and L
• Ca Csolidus
• 43 wt Ni
• CL Cliquidus
• 32 wt Ni

• Cu-Ni PhaseDiagram

• Note the Use of the IsoThermal Tie Line at TB
  to Find CL Ca

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Phase Dia.s Phase Wt Fractions

• Rule-3 Given T C0 (for P 1 atm) then Find
• The AMOUNT of EACH Phase in Wt-Fraction

• Example C0 35 wt Ni
• At TA
• Only Liquid
• WL 1.00 Wa 0.00 (wt Fracs)
• At TD
• Only Solid
• WL 0.00 Wa 1.00 (Fracs)

• Cu-Ni PhaseDiagram

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Phase Dia.s Wt Fractions cont.

• Example C0 35 wt Ni
• At TB
• BOTH a and L
• Calc Wa,B WL,B Using the INVERSE LEVER RULE

• Cu-Ni PhaseDiagram

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Lever Rule Proof

• Sum of weight fractions

• Conservation of mass (Ni)

• Combine These Two Equations for WL Wa

• A Geometric Interpretation

Balance massXdist at Tip-Pt
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Cooling Cu-Ni Binary Phase-Sys

• Phase Diagram for Cu-Ni System ?

• System Characteristics
• BINARY ? 2 components Cu Ni
• ISOMORPHOUS ? Complete Solubility of one
  Component in Another
• At least One Solid Phase-Field Extends from 0 to
  100 wt Ni

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Ex Cu-Ni Binary Cooling

• Consider 35 wt Ni Cooled 1300 C ? Rm-Temp

• Pt-A
• 1.00 Liquid
• 35 wt Ni
• Pt-B on Liquidus
• Tiny Amount of solid-a in Liq. Suspension
• Liq ? 35 wt Ni
• a ? 46 wt Ni

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Ex Cu-Ni Binary Cooling cont.

• Pt-C in 2-Ph Region
• (43-35)/(43-32) 0.727 Liquid
• Liq ? 32 wt Ni
• a ? 43 wt Ni
• Pt-D on Solidus
• Small Liq Pockets in Solid Suspension
• Liq ? 24 wt Ni
• a ? 36 wt Ni
• Pt E
• 1.00 a, _at_ C0

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NonEquilibrium Cooling

• Phases Diagrams are Constructed Under the
  Assumption of ThermoDynamic Equilibrium
• i.e., All Phases have Formed Sufficiently Slowly
  to allow for HOMOGENOUS (same) Concentrations
  WITHIN ALL Phases
• In the Previous Example The Solid STARTS at 46
  wt-Ni (pt-B) and ENDS at 35 wt-Ni (Pt-E)
• Thus Solid particles that WERE 46Ni Had to CHANGE
  to 35Ni by SOLID STATE DIFFUSION
• But Solid-State Diffusion Proceeds Slowly
• Rapid Cooling Can result in NonUniform Comp.

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NonEquil Cool ? Cored Structure

• Ca Changes Composition Upon Cooling
• First a to solidify has Ca 46 wtNi
• Last a to solidify has Ca 35 wtNi

• Fast Cool Rate ? Cored structure

• Slow Cool Rate ? Equil. Structure

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Mech Props ? Cu-Ni System

• Recall Solid-Solution Strengthening

• Tensile Strength, TS

• Ductility (EL,AR)

• Max As Fcn of C0

• Min as Fcn of C0

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WhiteBoard PPT Work

• Problems 9.5,6
• The Affect of PRESSURE on Phase Diagrams
• Water Ice, Has at Least TEN, yes 10, Distinct
  Structural Phases
• Phases form in Response to the PRESSURE Above
  The Ice

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Ice is Nice Problem 9.5

• Given Ice-I at -15C 10atm ? Find MELTING and
  SUBLIMATION PRESSURES

• Note Typo in Book
• Temperature needs to be 15 C for this to work

Starting Point
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Ice is Nice P9.5a Melt Temp

• At -15C Cast UPward to the Solid-LIQUID Phase
  Boundary

• Find that Ice-I, when held at -15C, MELTS at
  about 1000 atm (15000 psi, 100 Mpa)

1000
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Ice is Nice P9.5b Sublime Temp

• At -15C Cast DOWNward to the Solid-VAPOR Phase
  Boundary

• Find that Ice-I, when held at -15C, VAPORIZES at
  about 0.003 atm (0.0002 psi, 20 Pa)

0.003
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Ice is Nice P9.6 ? P 0.1 Atm

• At 0.1 Atm Cast RIGHTward to intercept the
  Sol-Liq and Liq-Vap Phase-Boundaries

• Ice-I MELTS at ?2 C
• Water BOILS at ?75 C
• i.e., the VAPOR PRESSURE of Water at 75 C
  is?10 of Atm

2.0
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