1. NTNU Short Course on solidification at IISc October – November 2012 Lars Arnberg, NTNU 1.Introduction – basic concepts 29/10 1.Nucleation - grain refinement 31/10 Crystal morphology 3.Interface stability5/11 Cells and dendrites 4.Three phase solidification7/11 Segregation 1

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

3. NTNU 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. NTNU 4 Microstructure Increasing concentration Increasing constitutional undercooling (  T c ) Increasing morphological instability Increasing cooling rate (G*V) Structure refinement

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

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

7. NTNU 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=Kt 1/2 Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998

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

9. NTNU 9 Structure of castings

10. NTNU 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. NTNU 11 Phase digram, solute redistribution CsCs C0C0 T0T0 C0C0 l s T ClCl TlTl TsTs Eutectic phase diagram Lower solubility of alloying elements in s than in l k=C s /C l <1 (distribution coefficient) m= dT l /dC<0 k and m constants if solidus & liquidus lines are straight C

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

13. NTNU 13 Al-Fe k=0.03 AlMg k=0.44 Al-Mn k=0.90 Al-Si k=0.14 Al phase diagrams with different partition coefficients k=C s /C l

14. NTNU 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, (C 0 ) 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. ΔT r will increase with increased curvature (small crystal radii)

15. NTNU 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. NTNU Symbols C: concentrationG: temperature gradient, dT/dx K/m k: distribution coefficient k=C s /C l Δs f : entropy of fusion, J/(m 3 K) m: liquidus slope, dT/dC σ: solid/liquid interface energy, J/m 2 V: growth rate m/sC l : liquid concentration T: temperature: KC s : solid concentration ΔT: undercooling, KC 0 : Initial alloy concentration q: heat flux W/m 2 A: area m 2 V: volume m 3 t: time, s ΔH: heat of fusion J/m 3 c: heat capacity: J/(m 3 K) f s : fraction solid ΔT f : freezing range, K 16