University of California Berkeley MSE 200A Fall 2017 Binary Phase Diagrams

University of california berkeley mse 200a fall 2017

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University of California, Berkeley MSE 200A Fall, 2017 Binary Phase Diagrams; Three Pieces of Information for Given (T,x) 1. Phases present From phase field 2. Compositions of phases Only needed for two-phase fields x α and x β from intersection of isothermal line with boundaries 3. Phase fractions From the lever rule f α = x β x x β x α f β = 1 f α = x x α x β x α
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Complex Diagrams: Read in the Same Way 1. Phases from phase field 2. Compositions from isotherm 3. Fractions from lever rule Al-Cu Phase Diagram
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 The Solid Solution Diagram To form a solid solution at all compositions Pure A and pure B must have the same crystal structure A and B must have chemical affinity The ( α +L) region appears near the melting points Generated as the L and α curves pass through one another Often (but not always) between T A and T B L L + α å A B T x T A T B
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Solidifying a Solid Solution Let the solution have the composition shown First solid to form is very rich in B As T decreases : Fraction of α increases Composition of α (x α ) evolves toward x Final α has the average composition of the solution (x α = x)
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Application: Purification (Zone Melting) To purify an impure (AB) liquid to pure B Cool until first solid forms ( rich in B ) Extract, re-melt and repeat ( richer in B ) Repeat as often as needed to create as pure B as desired Zone melting : A continuous process that accomplishes this Was the enabling technology for the transistor Very pure starting materials are necessary to create doped semiconductors
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 The Simple Eutectic Phase Diagram Eutectic diagram : Simplest diagram when α and β have different structures Named for eutectic reaction : L α + β at T E Source: As T rises, L free energy curve cuts through α , β common tangent Note T E is the lowest melting point
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Eutectic Diagram: Characteristic Equilibrium Microstructure at x 1 Let L at composition x 1 be cooled slowly L freezes gradually as T drops into α region Likely into polygranular microstructure shown On further cooling β precipitates from α Likely into microstructure shown β precipitates on grain boundaries and/or in grain interiors
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Eutectic Diagram: Characteristic Equilibrium Microstructure at x 3 Let L at composition x 3 be cooled slowly Solidification occurs sharply at T E Eutectic reaction: L α + β Microstructure resembles that shown (the eutectic microstructure ) α and β grow as plates
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  • Fall '08
  • Staff
  • Thermodynamics, University of California, Phase transition, J.W. Morris

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