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Solid Solutions in Phase Diagrams: Rules and Applications

Learn key rules for solid solubility in phase diagrams, from Hume-Rothery rules to Lever Arm Rule applications. Understand phase compositions and microstructures in lead-tin alloys. Solve homework questions on Cu-Ni and Pb-Sn diagrams.

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Solid Solutions in Phase Diagrams: Rules and Applications

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  1. Class 6 CHE 333 Phase Diagrams Continued Prov08

  2. 1085C 420C

  3. Substitutional Solid Solubilty How much one element will dissolve inanother is determined by the Hume Rothery rules • Atomic radii should be within 15% of each other • Crystal structure should be the same for each element for good solubility • Electronegativities should be similar. • The valences of the atoms should be similar. Good solubility Cu –Ni, Cu-Au; Cu r=0.128A, Ni r=0.125, Au r=0.144 Crystal structure Ti- HCP, Al - FCC Poor soluility Na-Cl Na electronegativity 0.9, Cl 3.0 Valences – Zn 2+, Cu 1+ Only indicate solubility from these rules. DOES NOT APPLY TO THE ELEMENTS H,C,O,N,B THESE FORM INTERSTITIAL SOLID SOLUTIONS.

  4. Iron Carbon Phase Diagram 1538C Fe - a then g then d 912C 1394C • Steels • Eutectoid • S1 -> S2 + S3 • -> a + F e3C Peritectic S1+L -> S2 d + L -> g 3367 SUBLIMES Fe3C- cementite A compound

  5. Stainless Steel Phase Diagram Ternary phase diagram for stainless steels. In this case an isothermal section at a constant temperature is used.

  6. Lever Arm Rule Determine the AMOUNTS of each phase use the Inverse Lever Arm Rule. Amount of solid = wa-wl/ws-wl Amount of liquid = ws-wa/ws-wl Amount of solid at 1300C is therefore 53-45 / 58-45 = 8/13 = 0.615= 61.5% Amount of liquid at 1300C is therefore 58-53 / 58-45 = 5/13 = 0.385 = 38.5%

  7. Change Average Composition 50% Determine the AMOUNTS of each phase use the Inverse Lever Arm Rule. Amount of solid = wa-wl/ws-wl Amount of liquid = ws-wa/ws-wl Amount of solid at 1300C is therefore 50-45 / 58-45 = 5/13 = 0.385= 38.5% Amount of liquid at 1300C is therefore 58-50 / 58-45 = 8/13 = 0.615 = 61.5%

  8. Microstructures and Composition

  9. Lead Tin Microstructures 38.1%Pb 61.9% Sn 90 %Pb 10%Sn 70% Pb 30%Sn 50%Pb 50%Sn

  10. Lead Tin Microstructures 15%Pb 85%Sn Equiaxed Single Phase Grain Structure

  11. Homework • Using the Cu-Ni phase diagram, for a 50-50 Cu-Ni what are the compositions of the phases at 1400, 1300 and 1200 C and what phases would be present. • Using the Pb- Sn phase diagram,what are the compositions for points “a,c and e” on the diagram?

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