Lecture Problem 96

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Lecture Problem 96

• Presented by Paula Lipka

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Problem in Brief

• Given a phase diagram.
• Label all the phases and invariant reactions
• Find the stoichiometric formulas for certain
  phases
• For a certain composition, describe the phases
  present and at which temperatures they are when
  the mixture is slowly cooled
• For a certain composition and path of cooling,
  describe which microconstituents are present and
  their amounts

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Phase Diagram Review

• Gibbs Phase Rule
• Cross a phase line, change number of phases by 1
• A two-phase region is surrounded by each separate
  phase
• A horizontal line represents 3 phases

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Problem Information
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Labeling Phases and Invariant Reactions

• Label all phases in the one and two phase regions
  and the invariant reactions.
• a high-T Os-rich
• ? low-T Os-rich
• e Ja-rich
• ? congruently-melting intermetallic
• d - intermetallic
• Invariant Reactions take place where three
  phases are at equilibrium
• Congruently-Melting solid when heated,
  transitions directly to a liquid

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Invariant Reactions

• Point 1 Eutectic L ? ? a
• Point 2 Peritectic ? L ? d
• Point 3 Eutectoid a ? ß ?
• Point 4 Eutectic L ? d e

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Stoichiometric Formulas

• Give the stoichiometric formulas for ? and d.
• ?
• 42.9 mole Ja, 57.1 mole Os
• Mole ratio
• Formula Ja3Os4
• d
• 66.7 mole Ja, 33.3 mole Os
• Mole Ratio
• Formula Ja2Os

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Phases and Temperatures

• For a 35 Ja 65 Os mixture, describe what
  phases are present and approximately what
  temperature they appear when the mixture is
  slowly cooled from 2000C.
• 1200C - 2000C Liquid (L)
• 875C - 1200C a L
• 470C - 875C ? a
• 0C - 470C ß ?

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Microconstituents and Amounts

• For a 10Ja 90Os mixture which is slowly
  cooled from 1800C to 400C, describe (at 400C)
  what microconstituents are present and calculate
  their relative amounts.
• Phases microconstituents when you havent
  traveled through a horizontal line
• At 400C, have passed through a eutectoid
  reaction
• Have eutectoid and proeutectoid (primary) ?

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Microconstituent Amounts

• Lever Rule
• In a two-phase region, allows us to find how much
  of each phase at a certain overall composition

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Microconstituent Amounts

• Find amount of a and ? phase in the two-phase
  region right before the eutectoid reaction
• Wa 1 - W? 89.2
• Find amount of ß and ? phase right after the
  eutectoid reaction
• Wß 76.7

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Microconstituents Cont

• Composition
• Before Eutectoid Reaction
• 10.8 ?, 89.2 a
• After Eutectoid Reaction
• 23.3 ?, 76.7 ß
• In a eutectoid reaction, a eutectoid is formed
  below the 3-phase invariant
• The a and ? form an invarient
• Then, the ß is formed within the eutectoid
• Additional ? is formed not in the eutectoid
  structure called proeutectoid/primary ?

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Microconstituent Summary

• At 400C,
• Proeutectoid ? 12.5
• Eutectoid ß and ? 87.5
• Within the eutectoid
• ß 87.6
• ? 12.4

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Relevance

• Skills
• Reading a phase diagram
• Finding phases
• Finding amount of each phase present
• Figuring out stoichiometric formulas for
  intermetallic phases
• Recognizing invariant reactions
• Finding microconstituent composition
• Applications
• Phases determine properties
• Thin Films
• Design of material

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References

• http//www.sv.vt.edu/classes/MSE2094_NoteBook/96Cl
  assProj/pics/eutsteel.gif