10.phase Diagrams PDF [PDF]

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Phase Diagrams Reading: Callister Ch. 10 • What is a phase? • What Wh t iis th the equilibrium ilib i state t t when h diff differentt elements l t are mixed? • What phase diagrams tell us. • How phases evolve with temperature and composition (microstructures). β (lighter phase)



α (darker phase)



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© 2007, 2008 Moonsub Shim, University of Illinois



MSE280



Phases Phase: A homogeneous portion of a system that has uniform physical and chemical characteristics. 1 Diff 1. Differentt physical h i l states: t t vapor, liliquid, id solid lid e.g. water



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© 2007, 2008 Moonsub Shim, University of Illinois



MSE280



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Phases 2. Different chemical compositions



e.g. sugar water • Solubility Limit: Max concentration for which only a solution occurs. • Solubility limit increases with T: e.g., if T = 100C, solubility limit = 80wt% sugar.



Question: What is the solubility limit at 20C? Answer: 65wt% sugar. If Co < 65wt% sugar: syrup 3 If Co > 65wt% sugar: syrup + sugar.



© 2007, 2008 Moonsub Shim, University of Illinois



MSE280



• Components: elements or compounds which are mixed initially (e.g., Al and Cu)



• Phases: physically p ys ca y and a d chemically c e ca y d distinct s c regions eg o s that a result esu (e.g., α and β). AluminumCopper Alloy



β (lighter phase) α (darker phase)



Plain carbon steel



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© 2007, 2008 Moonsub Shim, University of Illinois



MSE280



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Temperature and composition B



C



A



A: 2 phases present (liquid solution and solid sugar) B: Single phase C: back to 2 phases but at different composition Note: this is an equilibrium phase diagram (What does it mean to have phase equilibrium?) 5



© 2007, 2008 Moonsub Shim, University of Illinois



MSE280



Phase Equilibrium Equilibrium: minimum energy state for a given T, P, and composition (i (i.e. e equilibrium state will persist indefinitely for a fixed T, P and composition). An equilibrium phase will stay constant over time. Phase diagrams tell us about equilibrium phases as a function of T, P and composition (here, we’ll always keep P constant for simplicity) simplicity).



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© 2007, 2008 Moonsub Shim, University of Illinois



MSE280



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Unary Systems Single component system Consider 2 elemental metals separately: Cu has melting T = 1085oC Ni has melting T = 1453oC



(at standard P = 1 atm) T



T



liquid liquid



1453oC



1085oC



solid



solid Ni 7 What happens when Cu and Ni are mixed? © 2007, 2008 Moonsub Shim, University of Illinois MSE280 Cu



Binary Isomorphous Systems 2 components



Complete liquid and solid solubility



Expect Tm of solution to lie in between Tm of two pure components T



T



liquid liquid



L 1453oC



1085oC solid



S



0 Cu wt% Ni © 2007, 2008 Moonsub Shim, University of Illinois



solid



100 Ni



For a pure component, complete melting occurs before T increases (sharp phase transition). transition) But for multicomponent systems, there is usually a coexistence of L and S. 8



MSE280



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Binary Isomorphous Systems What can we learn from this phase diagram? 1. Phase(s) present. A: solid (α) only B: solid and liquid



2. Composition of those phases A: 60 wt% Ni B: 35 wt% Ni overall (how about in L and S separately?)



Solid-liquid coexistence region



3. Amount of the phases. A: 100% α phase B: % solid and % liquid? 9



© 2007, 2008 Moonsub Shim, University of Illinois



MSE280



Determining phase composition in 2-phase region: 1. Draw the tie line. 2. Note where the tie line intersects the liquidus and solidus lines (i.e. where the tie line crosses the phase boundaries). 3. Read off the composition at the boundaries: Liquid is composed of CL amount of Ni (31 (31.5 5 wt% Ni) Ni). Solid is composed of Cα amount of Ni (42.5 wt% Ni).



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© 2007, 2008 Moonsub Shim, University of Illinois



MSE280



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Lever Rule Determining phase amount in the 2phase region: 1. Draw the tie line. 2 Determine 2. D t i th the “di “distance t ffrom th the point of interest (B) to each of the phase boundaries. R = Co – CL S = Cα - Co 3. Mass fractions (wt%) of each phase:



C − Co S 42.5 − 35 = α = = 0.68 R + S Cα − C L 42.5 − 31.5 C − CL R 35 − 31.5 Solid: Wα = = o = = 0.32 R + S Cα − C L 42.5 − 31.5



Liquid: WL =



i.e. 68% of the mass is liquid and 32% of the mass is solid. © 2007, 2008 Moonsub Shim, University of Illinois



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MSE280



Lever Rule: Derivation Since we have only 2 phases:



WL + Wα = 1



(1)



Conservation of mass requires that: Amount of Ni in α-phase + amount of Ni in liquid phase = total amount of Ni or Wα Cα + WL C L = Co (2) From 1st condition, we have: Sub-in to (2):



Wα = 1 − WL



(1 − WL )Cα + WL C L = Co



Solving for WL and Wα gives :



WL =



Cα − Co Cα − C L



© 2007, 2008 Moonsub Shim, University of Illinois



Wα =



Co − C L Cα − C L



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Lever Rule: Derivation • A geometric interpretation: Co CL Cα R S



WL



Wα



moment equilibrium:



WLR = WαS 1 − Wα solving gives Lever Rule



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© 2007, 2008 Moonsub Shim, University of Illinois



MSE280



Microstructures in Isomorphous Alloys Microstructures will vary on the cooling rate (i.e. processing conditions) 1. Equilibrium Cooling: Very slow cooling to allow phase equilibrium to be maintained during the cooling process.



a (T>1260oC): start as homogeneous liquid solution.



b (T ~ 1260oC): liquidus line reached. α phase begins to nucleate. Cα = 46 wt% Ni; CL = 35 wt% Ni c (T= 1250oC): calculate composition and mass fraction of each phase.



d (T~ 1220oC): solidus line reached. Nearly complete solidification. Cα = 35 wt% Ni; CL = 24 wt% Ni



e (T> diffusion rate in solid Cooling rate 1260oC): start as



homogeneous liquid solution.



b’ (T ~ 1260oC): liquidus line



phase begins g to nucleate. reached. α p Cα = 46 wt% Ni; CL = 35 wt% Ni



c’ (T= 1250oC): solids that formed at pt b’ remain with same composition (46wt%) and new solids with 42 wt% Ni form around the existing solids (Why around them?).



d’ (T~ 1220oC): solidus line reached. Nearly complete solidification. •Previously solidified regions maintain original composition and further solidification occurs at 35 wt% Ni.



e (T