Chapter 7 - Chapter 7 Phase Equilibria and Phase Diagrams...

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Chapter 7 Phase Equilibria and Phase Diagrams • The one-component phase diagram – Gibbs Phase Rule • Phase equilibria in a two-component system – The isomorphous diagram –The leve r ru le – Equilibrium solidification and microstructure of isomorphous alloys • Liquidius and solidus boundaries • Deviations from ideal behavior
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Chapter 7 Phase Equilibria and Phase Diagrams, Continued • Phase equilibria in a two-component system – The eutectic phase diagram – The peritectic phase diagram – The monotectic phase diagram – Complex diagrams – Phase equilibria involving solid-to-solid reactions
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Pure Sugar Temperature (°C) 0 20 40 60 80 100 C o =Composition (wt% sugar) L (liquid solution i.e., syrup) Solubility Limit L (liquid) + S (solid sugar) 65 20 80 100 Water Two-Component Phase Diagram Sugar-Water
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Source: http://people.clarkson.edu/~rasmu/ES-260/Chapter_10.ppt Solubility Limit : Max concentration for which only a solution occurs. • Ex: Phase Diagram: Water-Sugar System Question: What is the solubility limit at 20C? Answer: 65wt% sugar . If C o < 65wt% sugar: sugar If C o > 65wt% sugar: syrup + sugar. • Solubility limit increases with T: e.g., if T = 100C, solubility limit = 80wt% sugar. Pure Sugar Temperature (°C) 0 20 40 60 80 100 C o =Composition (wt% sugar) L (liquid solution i.e., syrup) Solubility Limit L (liquid) + S (solid sugar) 65 20 80 100 Water Adapted from Fig. 9.1, Callister 6e. THE SOLUBILITY LIMIT
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One-Component Phase Diagrams F = C – P + 2 C- Components P- Number of phases F- Degrees of freedom F = 2 F = 1 F = 0 Solid
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One-Component Phase Diagrams
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One-Component Phase Diagrams
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Two-Component Phase Diagrams F = C – P + 1 F = 2 F = 1 T F: Degrees of freedom - Number of independent variables necessary to specify equilibrium In a two-phase field need to specify either the temperature or the composition of one of the phases. X s X l Isomorphous
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Two-Component Phase Diagrams In a single-phase field the composition of the phase is the composition of the alloy In a two-phase field, the amount of each phase and the composition of each phase can be determined using a tie line and the lever rule In a single-phase field the composition of the phase is the composition of the alloy X o
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Two-Component Phase Diagrams
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Two-Component Phase Diagrams Composition, X B Temperature () 1 1 1 ls ol s s s s l ss s s sl s ff XX f X f f X f X f X f f f += =+ =− + + −= = ( ) s o l s l f =
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Two-Component Phase Diagrams Composition, X B Composition, X B Temperature Composition of the liquid for each alloy Composition of the solid for each alloy Alloy 1- 0.2 Alloy 2- 0.2 Alloy 3- 0.2 Alloy 4- 0.2 Alloy 5- 0.2 Alloy 1- 0.8 Alloy 2- 0.8 Alloy 3- 0.8 Alloy 4- 0.8 Alloy 5- 0.8
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The Lever Rule in a Two-Component System
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PRS Question What is the fraction of solid, f s , in alloy 2 (X o = 0.3)? 1. 1/6 2. 2/6 3. ½ 4. 5/6
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Two-Component Phase Diagrams
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PRS Question What is the fraction of solid, f s, at T 2 ?
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This note was uploaded on 02/03/2011 for the course MSE 2001 taught by Professor Tannebaum during the Spring '08 term at Georgia Institute of Technology.

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Chapter 7 - Chapter 7 Phase Equilibria and Phase Diagrams...

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