Please enable JavaScript.
Coggle requires JavaScript to display documents.
METALS 2 (Diffusional transformations (Precipitation in age-hardening…
METALS 2
-
Solidification
Nucleation
Homogeneous nucleation
Radius
- Maximum excess free energy: dΔG/dr=0
- r<r*: dissolution of solid (clusters)
- r>r*: solid growth (nuclei)
- r*=2γsl/ΔGv=(2γsl.Tm/Lv).1/ΔT
- ΔG*=(16πγsl^3.Tm^2/3Lv^2).1/(ΔT)^2
- Increasing T: decreasing G, r → Excess energy can be minimised by the choise of particle shape
- Higher ΔT: less segregation, more homogeneous structure (smaller gains), but :warning: slow diffusion in this region
- Number of spherical nucleus: nr=n0.exp(-ΔGr/kT)
with ΔGr= excess free energy (due to cluster)
- Rate: Nhom=f0.C0.exp(-ΔG*hom/kT) [nuclei.m-3.s-1]
f0 = depends on vibration frequency, the activation energy for diffusion in liquid and the surface area of the critical nuclei ~10^11
C0 ~1029 atoms m-3
Energy
- Solid nuclei from homogeneously from liquid
- ΔG = reduction in bulk free energy+increase in surface energy (+increase in strain energy)
- if no solid => G1 = (Vs + VL)Gv(L)
G2= Vs.Gv(S)+Vl.Gv(L)+Asl.γsl
- ΔG = G2- G1= -Vs ΔGv+ ASLγSL, ΔGv = Gv(L)-Gv(S)
Creation of small particles will lead to free energy increase: ΔGhom=ΔGr=-4/3.πr^3ΔGv+4πr^2γsl
- Driving force= undercooling ΔT > ΔGv = (Lv ΔT)/Tm
Recap
- Mimultaneous processes which both decrease and increase the free energy of the system:
- Release of the driving force due to the transformation > decrease free energy)
- Decrease is proportional to the driving force (undercooling) and to the volume of the new nucleus (to the factor r^3)
- Formation of a new surface between the liquid and solid phases > surface energy bound > increase free energy ( factor r^2)
- Undercooling required for homogeneous nucleation is large (ΔT/Tm= 0,2); for reaching the critical size at least 200 atoms have to join together
- Nucleation may be easier by reducing interfacial energy > not spherical > heterogeneous nucleation
Heterogeneous nucleation
Energy
- Wetting angle: θ
- Cap radius: r
- Shape factor: S(θ) = (2+ cos θ)(1- cos θ)^2/4
- ΔGhet='-4/3.πr^3ΔGv+4πr^2γsl).S(θ)
ΔGhet=ΔGhom.S(θ)
- Number of nuclei: n*=n1.exp(-ΔGhet/kT)
- Rate: Nhet=f1.C1.exp(-ΔG*het/kT) [nuclei.m-3.s-1]
Recap
- The nucleation of solid phase occurs at sites which are favourable for nucleation: crucible walls, foreign particles in the melt etc.
- The energy needed for nucleation (driving force) depends on the contact angle between the nucleus and the substrate
- The contact angle depends on eventual coherency between the substrate and nucleus, chemical interactions, substrate topography
- Heterogeneous nucleation becomes clearly more favourable with decreasing contact (wetting) angle
- Undercooling required for heterogeneous nucleation is only a few degrees
To enhace nucleation
- Add nucleation agents or inoculant:
- insoluble in the melt, a small contact angle or will react with the liquid to form a nucleation catalyst
- Interface between low-index planes of the substrate and nucleus must be coherent or near coherent
- γML > γSL
- Small value of θ > γSM is low > the atoms in the liquid readily form a solid nucleus on the surface of the substrate, also need for ΔT small
- Choosing a nucleating agent with a low value of γSL
- The value of (γML-γSM) will determine the effectiveness of the
heterogeneous nucleating agent → high γML or low γSM
- Seeding rain-bearing clouds → AgCI or NaCl → nucleation of ice crystals
- Ni (FCC, a = 3.52 Å) is used a heterogeneous nucleating agent in the production of artificial diamonds (FCC, a = 3.57 Å) from graphite
Growth of pure solid
Interfaces
- Smooth or sharp: similar to solid/vapour interface, transition from liquid to solid occurs overs a narrow transition zone
- Diffuse: transition over several atom layers
- Jacson theory predicts: transition when Lf/Tm ~4R (critical value), above flat below diffuse
- Most metals round R →rough surface
- Si, Ge, Sb and most non-metallic materials high Lf/Tm => flat close packed surfaces
- γSL ~0.45Lf/Na :red_flag: Does not take into account entropy
Lateral growth
- Slide 5.46
- Smooth and rough interface
- Many non-metals
- High entropy of melting > minimal number of "broken bonds"
- Probability of growth highest at jobs and ledges (non eq. features)
- Rem:
- Addition of a single atom ont a flat interface increase by 4 the number of broken bonds
- Addition to a ledge increase by 2 the number of broken bonds
- Meschanism:
- Repeated surface nucleation, v ∞ exp (-k2ΔTi )
- Spiral growth > screw dislocation v=k3(ΔTi)^2
- From twin boundaries
Continuous growth
- Most mtals
- Free energy: analogy to grain boundary migration from grain to another
- ΔG=L/Tm.ΔT
-> Solidification diffusion-controlled, v=k1.ΔTi
- Rem:
- Pure metals solidification: rate controlled by heat conduction
- Alloy solidification: rate is controlled by solute diffusion
Heat conduction for metals, Dentrite
- Solidification controlled by the rate at which the latent heat of solidification can be conducted away from the solid/liquid interface
- Heat cond. into solid > protusions, when mold walls cooler than the melt
- Heat cond. into liquid > the interface unstable, initial stages of solidification
- Superheated liquid: protrusion will diappear, plane-front solidification (unstable)
- Supercooled liquid: protrusion will grow, stable dentrites
- Dentrites dire.: irection in cubic (100) and in hexagonal (1100)
- Max volume:
T’s = 0 (solid isothermal) + KsT’s = KLT’L + vLv = >
v = - (KLT’L)/ Lv ≈ (KL/Lv)(ΔT/r)
v ≈ (KL/Lv) (1/r)(1-r/r) > Vmax r= 2r
- :warning: But undercooling not dependent of ΔT
Alloy solidification
Observations and basis
- Slide 5.63
- Single phase alloys
- Constant composition in liquid phase
- Increasing concentration in solid phase, from kC0 to Cs
- Equilibrium solidification (extremely slow solidification)
- Partition coefficient k= Xs/XL
No diffusion in solid, perfect mixing in liquid
- (XL-XS)dfS = (1- fS)dXL and k= Xs/XL
with dfS = volume fraction solidified
- Boundary conditions XS =kX0 when fS= 0
=> XS=k.X0(1-fS)^(k-1) and XL=X0.fL^(k-1)
= > non equilibrium lever rule (Scheil eq.)
No diffusion in solid, diffusional mixing in liquid
- Solute diffuses down the gradient: DC’L= v(CL-CS)
- Rate of solute rejection: C’L=dCL/dx
- Concentration profile: XL=X0.[1+(1-k)/k.exp(-x/(D/v))]
- D/v is width of concentration profile (diffusivity/solidification rate)
- Even when solidification is not unidirectional the previous can be applied at microscopic level
Commercially
- Production of creep resistant directionally solidified turbine blades
- Zone refining in the production of pure metals
Planar solidification
- Planar solidification is difficult for alloys having with a large solidification range and high rate of solidification
- If temperature gradient ahead of planar interphase is gradually reduced below the critical value
- The 1st stage is the formation of a cellular structure, protrusion lower (solidification T, solute rejection, composition between cells may reach eutectic compo.)
- Critical gradient =(T1-T3)/(D/v)
=> stable planar interphase T’L>(T1-T3)/(D/v)
Eutectic
- Time of cooling arrest proportional to composition
- Slide 5.80: Interdiffusion in the liquid ahead of the eutectic front
- Lamelar structure