Solidification Flashcards
What are the assumptions made for solidification in a mould?
1 The mould is of infinite thickness ie neglect any heat transfer at the outer-surface of the mould
2 There is no superheat in the liquid ie the liquid is at the solidification temperature
3 There is no thermal resistance at the mould/metal interface ie perfect thermal contact
4 The temperature of the solid remains constant and equal to the melting point of the material
5 We are considering a single melting point material ie a pure metal or eutectic alloys
6 We are considering unidirectional solidification ie an infinitely long slab
For the linear profile method what is assumed?
The temperature profile is linear
Rate of heat absorption by wall = heat transfer through wall
Rate of heat accumulated by wall = area x density x conductance per increment of time
For the parabolic integral profile method what is used?
A parabolic temperature gradient
Dimensionless terms T* X*
Heat stored in the mould wall
For the analytical solution what is assumed?
The penetration depth is less than the mould wall thickness
What is the method for determining the solution when there is a thermal gradient in both mould wall and solid?
1 find the temperature gradient at the wall
2 find the temperature gradient in the solid
3 equate using the equation with kw and ks
4 sub into the equation for heat flow in solidified metal
When a pure metal grows into a superheated liquid what is the nature of the interface?
The SL interface growth rate increases when the solid temperature gradient increases or the liquid temperature gradient decreases
When a small perturbation occurs the solid isotherms are further apart while in the liquid they are closer so the heat flux into the solid decreases and the perturbation heats up faster and melts back
Planar front is stable, perturbation is unstable
When a pure metal grows into a supercooled liquid what is the nature of the interface?
The SL interface growth rate increases when the solid and liquid temperature gradient increases
When a small perturbation occurs the latent heat flows away from the SL interface more rapidly thus the perturbation will grow outwards
Planar front is unstable, perturbation is stable
How do pure metal crystals grow at low R?
As cells with low curvature
How do pure metal crystals grow at high R?
The SL interface breaks down into dendrites with larger curvature and a paraboloid tip shape
What is the velocity of the dendrite related to?
Undercooling
What are the components of undercooling?
The diffusion of latent heat from the interface, the radius of curvature of the tip, the atomic attachment kinetics
What kind of growth is dendritic and which component is largest in the undercooling?
Nonfaceted, diffusion limited undercooling
What is the chill zone?
Narrow band of equipped crystals randomly orientated adjacent to the mould wall
What is the columnar zone?
Outer region of larger crystals elongated parallel to the direction of heat flow
What are the 3 main factors limiting growth of pure metals
Diffusion of heat from the interface
Curvature of the interface
attachment kinetics of atoms at the interface
What are additional factors affecting growth of alloys?
Solute is partitioned between the solid and liquid
This rejected solute must be diffused away in the liquid (in addition to heat)
The equilibrium interface temperature depends on the liquid composition at the interface CL*
What is the definition of nucleation?
Initiation of the certain centres (the creation of a new SL interface)
What is the definition of growth?
The propagation of SL interfaces form these centres
What is the overall transformation rate?
The nucleation rate x growth rate
The microstructure formed is a competition between…
Interface curvature
Diffusion of heat and solute from the interface
When is a planar interface stable?
When the thermal gradient in the liquid is steeper than the gradient in the liquidus temperature at the SL interface
When do planar, cells or dendrites grow?
Planar - high G low R, high G/r low c
Cells - intermediate G R, intermediate G/R c
Dendrites - low G high R, low G/R high c
What is the effect of decreasing the thermal gradient in the liquid on the SL interface?
Increase maximum constitutional supercooling
Increase distance constitutionally supercooled
What is the effect of increasing the growth rate on the SL interface?
Less time for solute to diffuse, concentration gradient steeper
What is the effect of increasing the bulk alloy composition on the SL interface?
More solution rejection at the interface, increase the maximum constitutional supercooling, increase the distance that is constitutionally supercooled
What is solute undercooling?
The amount by which the temperature must be reduced in order to have that amount of solute at the SL interface
What is curvature undercooling?
How curvature alters the equilibrium between solid and liquid
What is kinetic undercooling?
The undercooling due to attachment kinetics (faceted or non faceted)
How does cell growth depend on undercooling?
Cell growth for small supercooling, the shape allows solute to be rejected laterally and grooves develop between the cells assisting the transport of solute and the solute undercooling decreases significantly. The shape requires some curvature undercooling. As growth rate increases, the cells develop increasing curvature in order to enhance solute transport and decrease total growth undercooling with increasing velocity
How does dendritic growth depend on undercooling?
Dendritic growth for high supercooling, the shape maximises diffusion of solute away from the dendrite tip and creates a large amount of curvature, the curvature undercooling is significant. Shape is a balance to minimise the interface energy and maximise solute diffusion from the interface. As dendrite grows faster their spacing becomes smaller and their average curvature increases, and there is less time for solute diffusion in the liquid. Total growth undercooling increases with increasing dendrite growth rate.
What is the central zone?
Region ahead of columnar zone where nucleation occurs due to constitutional supercooling equal or exceeds required, growth will be dendritic
What additional factors can promote the central equiaxed zone?
Turbulent flow
Fragmentation
Potent heterogeneous nuclei will reduce the nucleation undercooling
Why do we want a small-equiaxed grains?
A small grain size increases yield strength (Hall Patch)
GB retard cracks, improve toughness
Small primary crystals tend to reduce the size of secondary phases and disperse them more evenly
Equiaxed grains produce uniform properties
easier to forge/roll/extrude
What are applications of eutectic alloys?
Casting alloys, soldering, functional alloys
What is a eutectic reaction?
Binary eutectic is an invariant three-phase equilibrium, no degrees of freedom due to Gibbs phase rule
L -> alpha + beta
What are the factors affecting eutectic microstructure?
1 Freezing behaviour (faceted or non faceted)
2 relative volume fractions of the two phases
3 the solid-liquid and solid-solid interfacial energies
4 impurities or deviation from eutectic composition
5 crystallographic orientation of the phases relative to each other and to the growth direction
6 solidification conditions
What is a barrier to steady-state planar growth of eutectics?
Solute undercooling (immiscibility model)
What is a more efficient method of solute transport?
Lateral diffusion and solute mixing ahead of the alpha-L and beta-L interfaces
How do real eutectics grow?
Alternating layers/sheets
Numerous rods/fibres of one phase in a matrix of the other phase
What does the morphology of the eutectic phase depend on?
The volume fraction of the phases
Faceted or non-faceted
For isotropic interfacial energy…
the lowest energy structure minimises the total interface area
For constant spacing…
the total interface area for lamellar does not depend on the volume fraction
the total interface area for rod increases as the volume fraction increase to 50:50
What are the two possible arrangements of the minor phase?
Square or hexagonal array
Why might lamellae form even below 28%?
alpha and beta are crystals and have some degree of anisotropy, generally when one of the phases is faceted
When do lamellar or rods grow?
When both phases are non-faceted
What are the morphologies formed when beta is faceted?
Irregular rods - low fraction of the faceted phase
Irregular lamellae - similar fractions of faceted and nonfaceted
What are examples of faceted SL interface?
Si, C graphite, water
What are examples of nonfaceted SL interfaces?
Fe, Ti, Al, Mg
Which key factors are linked by the Jackson-Hunt equation?
Eutectic growth temperature
Growth rate
Interphase spacing
What do the terms in the Jackson-Hunt equation relate to?
Solute undercooling - proportional to amount of solute rejected, inversely proportional to the diffusion coefficient, proportional to lamda, V
Curvature cooling - inversely proportional to lamda, proportional to K2 depends on interfacial energy and angle
What is the critical spacing related to?
Scales with V^-0.5
Which interface does jackson-hunt fit best?
nf-nf eutectic eg Sn-Cu6Sn5
What are the types of primary phase growth?
Planar, cells, dendrites
How do cells grow?
Cells transport solute laterally, solute content at the tip is lower than the planar front, decreases solute undercooling and a small curvature undercooling is required.
What are the assumptions used for finding analytical solutions to dendrite growth?
The tip shape is paraboloid of revolution
The tip grows in a shape-preserving manner
The tip grows at constant velocity into an infinite undercooled melt
What does the LGK model depend on?
R tip, V
What does the LGK model consider?
An isolated dendrite tip
with paraboloid shape
growing at constant velocity
into an infinite undercooled melt
What does the LGK model predict?
V, Rtip, Undercooling growth, C0 (fix two and find out other two)
What is the undercooling-velocity relationship for dendrites?
As dendrites grow faster the curvature increases, less time for solute diffusion in the liquid, total growth undercooling increases, with increasing dendrite growth rate
Why do dendrites grow along specific directions?
SL interfacial energy varies with crystallographic orientation, dendrites grow along max interfacial energy
What is the eutectic coupled zone?
100% eutectic will grow preferentially vs primary phases growth for a range of composition near the eutectic point.
For nf-nf the zone is pretty symmetrical, and becomes wider for increasing growth rate
What are examples of nf-nf systems?
Fe-graphite, Fe-Fe3C, Al-Si
When the system is nf-f what happens to the coupled zone?
We must account for kinetic undercooling, the growth undercooling increases with growth rate more rapidly, the eutectic front becomes non isothermal, so the eutectic growth is dependent on the thermal gradient
Which three microstructures can grow in a hyper eutectic composition?
Primary alpha Al ahead of eutectic
100% primary eutectic
Primary Si ahead of eutectic
Which two microstructures can grow in a hypo eutectic composition?
Primary alpha Al ahead of eutectic
100% eutectic at very low growth rate
What is the influence of the temperature gradient on the coupled zone?
Gl affects the low velocity part of the single-phase growth curve, steeper Gl promotes eutectic formation at higher growth rate
What happens to the coupled zone when the temperature gradient is negative?
A planar front is very stable, primary phase growth is only dendritic, at higher T the eutectic does not grow over the primary phase at low growth rates, alpha Al is selected at all growth rates
What is microstructure selection due to?
Competitive growth and competitive nucleation.
What is the role of nucleation in microstructure selection?
It is necessary for a phase to nucleate before it can participate in competitive growth
How does solute rejection affect nucleation undercooling?
Growth of Pb dendrites will reject Sn solute into liquid moving liquidus composition into the Sn-rich end, increasing the driving force for beta Sn nucleation
What is the competition between droplet microstructure vs nucleation undercooling for beta Sn?
1 As the liquidus cools wrt the beta Sn liquidus, at some point the temperature drops below the Pb liquidus line -> primary Pb nucleates and grows
2 The growth of primary Pb enriches the liquid in the Sn solute
3 When beta eutectic nucleates, in the coupled zone -> fully eutectic growth
4 Eutectic growth in undercooled melt -> latent heat releases causes recalescence
5 At some point leave coupled zone -> get beta Sn dendrites ahead of eutectic front
What is a metastable phase?
A phase that is structurally stable but has higher Gibbs energy than the lowest gibbs energy line
Why does metastable eutectics win at higher growth rates?
Due to kinetic undercooling
What are industrial shape casting alloys?
Cast-irons - ductile cast iron, grey cast iron, white cast iron
Al-Si based alloys - Al-7Si-0.3Mg, Al-9Si-4Cu
Mg-Al based alloys - Mg-9Al-07Zn, Mg-6Al-0.1Mn
How can we increase the nucleation rate?
Add numerous heterogeneous nucleating substrates that reduce the barrier to nucleation
What are intentional additions to Al-Si alloys?
Mn Mg Ti B Sr
What are impurities in Al-Si?
Fe P H
What are the assumption made for equilibrium solidification and scheil solidification?
No nucleation barrier
Local interfacial equilibrium
Complete diffusion in the solid
Completely mixed liquid
Scheil (No diffusion in the solid)
What are the requirements for heterogeneous nucleation?
We want a substrate of low wetting angle
