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Short Course on solidification at IISc October – November 2012 Lars Arnberg, NTNU

Short Course on solidification at IISc October – November 2012 Lars Arnberg, NTNU. Introduction – basic concepts 29/10 Nucleation - grain refinement 31/10 Crystal morphology Interface stability 5/11 Cells and dendrites Three phase solidification 7/11 Segregation.

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Short Course on solidification at IISc October – November 2012 Lars Arnberg, NTNU

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  1. Short Course on solidification at IISc October – November 2012Lars Arnberg, NTNU • Introduction – basic concepts 29/10 • Nucleation - grain refinement 31/10 Crystal morphology • Interface stability 5/11 Cells and dendrites • Three phase solidification 7/11 Segregation

  2. Solidification, Lecture 1 Introduction / Basic concepts Simple heat flow during solidification Mushy Zone Columnar / equiaxed solidification Curvature effects Phase diagrams – solute redistribution

  3. Microstructure Solidification of metals is a crystallisation process Microstructure development Microstructure Crystal types, phases Crystal morphology Crystal size Chemical composition Depends on Composition (constitution) Concentration, C Phase diagram, k, m Casting conditions Growth rate, V Temperature gradient, G Cooling rate, G*V

  4. Increasing concentration Increasing constitutional undercooling (Tc) Increasing morphological instability Microstructure Increasing cooling rate (G*V) Structure refinement

  5. Heat flow Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998

  6. Mushy zone Alloys will solidify over a temperature Interval, ΔTf M. Z. is where solidification occurs Depending on freezing range and temp gradient a

  7. Controlled solidification a: Bridgman furnace Independent control of G & V. G & V constant b: Directional chill casting G & V time dependant dT/dt = GV s=Kt1/2 Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998

  8. Growth modesmorphology & temperature distribution Directional Growth of columnar crystals Free growth of equiaxed crystals Pure metal Alloy Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998 Positive G Negative G

  9. Structure of castings

  10. Capillary effects; solid/liquid interface • Undercooling • Curvature 2/r for sphere • Gibbs Thomson ~ 10-7 Km • Solidification microstructures • given by competition between: • Curvature : tends to maximise scale • Diffusion: tends to minimise scale Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998

  11. T l C0 Tl T0 Ts Cl Cs C0 s Phase digram, solute redistribution • Eutectic phase diagram • Lower solubility • of alloying elements • in s than in l • k=Cs/Cl<1 (distribution coefficient) • m= dTl/dC<0 • k and m constants if solidus • & liquidus lines are straight C

  12. Al-Fe Al-Mg Eutectic Al phase diagrams for important alloying elements Al-Si Al-Mn

  13. Al-Fe k=0.03 AlMg k=0.44 Al phase diagrams with different partition coefficients k=Cs/Cl Al-Mn k=0.90 Al-Si k=0.14

  14. Summary/ Conclusions • Solidification is accomplished by external cooling of a melt. Needed for decreasing the temperature and removing latent heat of fusion • Metals solidify at a distinct freezing point, alloys have a solidification interval (freezing range) • Solidification microstructure will depend on both composition, (C0) constitution (k, m) and process (G, V) • Control of V and G will differ between casting processes • Solidification will occur in mushy zone. Extent of MZ will depend on temperature gradient and freezing range • Crystal may grow directionally as columnar grains (G>0) or freely from an undercooled melt as equiaxed grains (G<0) • Creation of s/l interface will require undercooling. ΔTr will increase with increased curvature (small crystal radii)

  15. Summary/ Conclusions • Scale of solidification microstructure will be determined by diffusion (decreasing) and curvature (increasing) • Solidification of alloys means redistribution of solute between s and l. Determined by distribution coefficient, k.

  16. Symbols C: concentration G: temperature gradient, dT/dx K/m k: distribution coefficient k=Cs/Cl Δsf: entropy of fusion, J/(m3K) m: liquidus slope, dT/dC σ: solid/liquid interface energy, J/m2 V: growth rate m/s Cl: liquid concentration T: temperature: K Cs: solid concentration ΔT: undercooling, K C0: Initial alloy concentration q: heat flux W/m2 A: area m2 V: volume m3 t: time, s ΔH: heat of fusion J/m3 c: heat capacity: J/(m3K) fs: fraction solid ΔTf: freezing range, K

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