Solidification: basics and beyond Equilibrium and nonequilibrium solidification Prof. Dmitry Eskin BCAST NETCENG, 2015 1
Types of solidification reactions Equilibrium solidification 2
Gibbs phase rule Gibbs phase rule defines the degrees of freedom F for the system as F = Components Phases + 2 or F = Components Phases + 1 in condensed systems. Josiah Willard Gibbs (1839 1903) Degrees of freedom the number of independent parameters (temperature, composition, pressure) that can change preserving the same phase state. In binary metallic alloys (condensed systems) The boundary separating regions with two phases degree of freedom is 1 (line). In a three-phase equilibrium region degree of freedom is 0 (point)
Phase equilibrium Prof. Roozeboom (Uni. Amsterdam) studied the equilibrium of multiple-phase systems. The theoretical foundations for this were laid by J. W. Gibbs with his phase rule, but Roozeboom would be the one to apply the theory and demonstrate its usefulness. He is mainly remembered for his melting phase diagrams of metal alloys. Hendrik Willem Bakhuis Roozeboom (1854-1907) Roozeboom also was the first to plot ternary phase equilibria in two-dimensional plots that were taken as vertical or horizontal slices from the three-dimensional solid diagrams. These are termed, respectively, isopleths and isotherms.
Phase diagram; alloys Partition coefficient C xs /C xl = k Solute conservation M S C xs + M L C xl = C 0 M L = 1 M S 5
Equilibrium solidification: lever rule C C M C C L S x 0 L S x x L C 1 C 1 f (1 k) 0 s 6
Phase diagram; alloys Lever rule for mass fraction C C M C C L S x 0 L S x x g S S S L M S M M Volume fraction expressed from the mass fraction S L f S 1 Tx T Liquidus(C 0) 1 k T T (A) x m Solid fraction in the two-phase solidification range 7
Partitioning of solute during solidification
L S ( ) Solidification
Types of solidification reactions in alloys L S ( ) Full solubility Ag-Au; Au-Cu; Mn-Al; Fe-V; Ni-Cu; Ni-Pt; Ni-Pd; Ni-Au; Ti-V
Types of solidification reactions in alloys L S ( ) + S ( ) EUTECTIC Al-Cu; Al-Fe; Al-Ge; Al-Li; Al-Mg; Al-Mn; Al-Ni; Al-Si; Al-Zn ;Mg-Ca; Mg-Al; Mg-La; Mg-Nd; Mg-Li; Cu-Mg; Cu-Sb; Cu-P; Fe-C; Fe-Ti; Ni-Ti
Types of solidification reactions in alloys L + S ( ) S ( ) PERITECTIC Al-Cr; Al-Ti; Al-V; Al-Zr; Mg-Sc; Mg-Mn; Mg-Zr; Cu-Fe; Cu-Zn; Cu-Sn; Fe-Al; Fe-C; Fe-Mn; Fe-Ni; Ni-Re
Types of solidification reactions in alloys L L + L" MISCIBILITY L S ( ) + L" MONOTECTIC Ag-Co; Al-Bi; Al-Cd; Al-In; Al-Pb; Al-S; Mg-V; Mg-Na; Cu-Pb; Fe-O; Fe-Sn; Ti-Y
Types of solidification reactions in alloys S ( ) L + S ( ) METATECTIC Gd-Cu; Hf-Cu; Fe-Sc; Fe-S; Fe-Zr; Y-Ti
Types of solidification reactions in alloys L + L" S ( ) SYNTECTIC K-Zn; Na-Zn; Cg-Rb; Cd-Cs
Reality is more complex
Types of solidification reactions in Al and Mg alloys
Reality is even more complex
Eutectic and peritectic reactions
Eutectic solidification L S ( ) + S ( ) MS3021 20
Main features of eutectic solidification Low temperature of solidification (and melting): last liquid to solidify Cooperative growth of at least two solid phases, each as a single crystal within the colony Coupled growth facilitated by lateral diffusion between lamellae 21
Peritectic solidification L + S ( ) S ( ) 22
Main features of peritectic solidification High temperature of solidification Controlled by diffusion though solid Does not complete at high cooling rates Offers natural solidification site for the second phase, hence grain refinement L + 23
Nonequilibrium solidification 24
Equilibrium solidification C C M C C L S x 0 L S x x L C 1 C 1 f (1 k) 0 s 25
Eq. vs Neq. solidification 26
Non-equilibrium solidification C C L 0 [1 f (1 2 k)] s k 1 1 2 k Erich Scheil Dsts L Fourier number: dimensionless diffusion time =0.5 then lever rule =0 then Gulliver-Scheil rule (no solid diffusion) C C L 0 (1 f ) s (k 1) G.H. Gulliver, J. Inst. Met., 9:120, 1913; E. Scheil, Z. Metallk., 34:70, 1942. 27
Non-equilibrium solidification 28
Nonequilibrium solidification L L+B L+AB2 L+A L+AB1 A+AB1 AB1+AB2 B+AB2 A AB1 AB2 B 29
Nonequilibrium solidification L L+B L+AB2 L+A L+AB1+AB2 A+AB1+AB2 AB1+AB2 B+AB2 A AB1 AB2 B 30
Nonequilibrium solidification L L+B L+AB2 L+A L+AB2 A+AB2 A+AB2 B+AB2 A AB1 AB2 B 31
Metastable phases Al 32
Cooling curve and its analysis 33
Cooling curve C 0 TEMPERATURE T L T Cs C L T S CONCENTRATION 34
Cooling rate: local solidification time 35
Undercooling L. Backerud, G. Chai, J. Tamminen, Solidification Characteristics of Aluminum Alloys, vol. 2, AFS/Skanaluminium, 1990. 36
Transformations T, C dt/dt, C/s t, s A.H. Ahmad, S. Naher and D. Brabazon: Key Engineering Materials, 2013, vol. 554-557, p. 582 t, s 37
Transformations C p is the heat capacity and L is the latent heat T, C A.H. Ahmad, S. Naher and D. Brabazon: Key Engineering Materials, 2013, vol. 554-557, p. 582 Fraction solid 38
Structure evolution: coherency TCc TCw H.Jiang, W.T. Kierkus, J.H. Sokolowski, AFS Trans., 1999, 99-68, pp. 169-172. 39
Microsegregation 40
Microsegregation 41
Microsegregation 42
Homogenization As-cast Homogenized 43