IISc solidification lecture 2
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Solidification, Lecture 2 NTNU Nucleation Homogeneous/heterogeneous Grain refinement Inoculation Fragmentation Columnar to equiaxed transition Crystal morphology Facetted – non-facetted growth Growth anisotropy / growth mechanisms Modification of Al-Si and cast iron 1 1 Nucleation NTNU Spontaneous formation of new crystals Cluster formation Homogeneous nucleation Number of clusters with radius r: nr n0 exp Gr kT Gr cluster free energy n0 total number of atoms k Boltzmans constant T temperature 2 Nucleation activation energy NTNU Change in free energy solidification s/l interface 4 3 G r g 4r 2 3 Spontaneous growth 2 above radius r* s f T Activtion energy 3 16 G* 3s2f (T)2 3 Nucleation NTNU Rate B N A exp( 2) (T) Undercoooling nr n0 exp Gr kT r* 2 s f T 4 Heterogeneous nucleation NTNU Nucleation on solid substrate Reduction of nucleation barrier Wetting angle θ Ghet Ghom f () 5 Conditions for efficient nucleation NTNU • Small wetting angle, • Low surface energy between substrate and crystal • Good crystallographic match Lattice match between Al and AlB2 6 Nucleation on AlB2 substrate particles, inoculation NTNU AlB2 AlB2 addition No addition 7 Nucleation and growth in a pure metal NTNU T Recallescence Growth Tg Nucleation Tn Undercooling ahead of solidification front is needed for nucleation of new grains. Can be achieved by alloying. 8 Conditions for grain refinement •Substrate particles NTNU •Undercooling •Potent •Constitutional •Large number •Growth restriction •Well dispersed •Strongly segregating alloying elements A pure metal can not be efficiently grain refined! 9 Growth restriction in aluminium NTNU Q mC0 k 1 Element m(k-1) max C0 (wt%) Ti Si Mg Fe Cu Mn 246 6.1 3.0 2.9 2.8 0.1 0.15 12 35 1.8 33 1.9 10 Aluminium grain refiner master alloys NTNU Typical composition: Al-5%Ti-1%B Formation of insoluble TiB2 Ti/B ratio in TiB2 : 2.2/1 Small TiB2 1-3 m Large TiAl3 10-50 m 50 m 11 Grain refinement of aluminium NTNU X-ray video of Al-20%Cu Al-5%Ti-1%B type grain refiner Addition 1g / kg melt Growth from top Dendrite coherency – network formation 12 Substrate particle size, d NTNU 4 d s f T Too small particles will need high underecooling T T for for Grain Grain Initiation Initiation (K) 1 0.8 0.6 0.4 0.2 0 0 2 4 6 Particle Diameter (m) 8 13 Industrial grain refinement practice NTNU Alcoa 14 Dendrite fragmentation NTNU X-ray video of Al-20wt%Cu Growth of collumnar front Dendrite fragment by melting Formation of new grain New front established New fragments melt 15 Columnar-to-equiaxed transition; dendrite fragmentation • Fragmentation mechanism – Mechanical fracture – Melting • Transport of fragments out of mushy zone – Gravity/buoyancy – Convection - stirring • Survival and growth of dendrite fragments – Low temperature gradients – Constitutional undercooling NTNU Electromagnetic stirring of steel NTNU Stirring gives larger fraction of equiaxed grains 17 Growth NTNU Controlling phenomenon Importance Driving force Diffusion of heat Pure metals ΔTt Diffusion of solute Alloys ΔTc Curvature Nucleation Dendrites Eutectics ΔTr Interface kintetics Facetted crystals ΔTk 18 Interface morphology NTNU • Facetted • Atomically smooth • =sf /R>2 • Non-metals •Intermetallic phases • Non-facetted • Atomically rough • =sf/R<2 • metals Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998 19 Facetted crystals NTNU • • • • • Atomically smooth interface Large entropy of fusion Growth by nucleation of new atomic layers Large kinetic growth undercooling, ΔTk Large growth anisotropy 20 Growth anisotropy NTNU Cubic crystal bounded by (111) planes Growth of (100) Bounded by (110) planes Growth of (100) Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998 •Fastest growing planes disappear •Crystals bounded by slow growing planes 21 Growth anisotropy NTNU Anisotropy increases with α V K(hkl )Tk 22 Growth mechanisms NTNU Twinning or dislocation: Nucleation of new planes not necessary Screw dislocation Twinning Reproduced from:W. Kurz & D. J. Fisher: Fundamentals of Solidification Trans Tech Publications, 1998 23 Growth rate NTNU V K 2 (Tk )2 V K1Tk K4 V K 3 exp( ) Tk Reproduced from:M. C. Flemings Solidification Processing Mc Graw Hill, 1974 24 Modification of growth mechanism Eutectic silicon crystals in Al-Si NTNU Transition from coarse lamellar to fine fibrous eutectic Improves ductility Addition of small amounts (100 ppm) of Na, Sr, (Ca, Sb) Increases porosity 100 ppm Sr 25 Mechanism of modification NTNU Atoms of modifier causes growth branching 26 Modification and growth undercooling NTNU Eutectic growth temperature decreases about 10 K. Fading due to oxidation of modifier. Faster fading with Na than Sr 27 Modification of graphite in cast iron NTNU Small additions of Mg and FeSi to cast iron changes morphology of facetted graphite from flakey to nodular Effect of both nucleation and growth mechanism Grey cast iron Ductile iron 28 Summary / conclusions NTNU • Spontaneous formation of solid clusters. Homogeneous nucleation • Energy barrier due to s/l interface large at small crystal sizes. Needs undercooling • Heterogeneous nucleation on solid substrate. Lower activation energy – lower undercooling • Low wetting angle – potent substrate for nucleation – good crystallographic match between substrate / growing crystal • Undercooling ahead of growing front necessary for nucleation of new equiaxed grains. Provided by strongly segregating alloying elements • Efficient grain refinement can be achieved in aluminium alloys by inoculation of substrate particles, TiB2 and Ti for growth restriction • Substrate particles must not be too small. That will give large undercooling. 29 Summary / conclusions NTNU • Columnar to equiaxed transition – grain refinement can be achieved by fragmentation of columnar dendrites. Provided by convection. Transport out of M.Z and survival in undercooled melt at low temperature gradient. 30 Summary / conclusions NTNU • Metals have low entropies of fusion and grow in a non-facetted way with an atomically rough interface • Non-metals and intermetallic compounds have normally high fusion entropies and grow in a facetted way with a smoth interface. • Growth of facetted crystals occurs by successive nucleation of new atom planes at high kinetic undercooling • Facetted crystals show large growth anisotropy. Fast growing planes disappear while slowest growing planes bounds the crystals • Facetted crystals often provide nucleation sites for new atom planes at twin boundaries or screw dislocations • Growth rate of non-facetted crystals is proportional to kinetic undercooling. Dislocation growth shows a parabolic law and growth by two-dimensional nucleation an exponential growth law 31 Summary / conclusions NTNU • Growth mechanisms in facetted crystals can be very sensitive to impurities. Can be utilised for modification of morphology, Examples are modification of Si in Al-Si by Na or Sr and modification of graphite in cast iron eutectics by Mg. 32
