When atomic arrangement changes from short range order to long range order via nucleation and growth of grains.
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Describe homogeneous nucleation
Crystal are formed on nucleation sites from the liquid phase. (hard to achieve)
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Describe heterogeneous nucleation
Crystals formed from foreign nucleation sites.(easier to achieve)
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How does Homogeneous nucleation work?
When the new interface forms there is an increase in surface energy and thus free gibbs energy. this is the energy barrier that needs to be overcomed.
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What does the cluster stability depend on?
The cluster stability depends on the competition between energies driving and opposing the cluster growth.
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What is the energy driving the cluster growth?
V_cluster*ΔG_v ^(L-->s) ] decrease in G as the liquid turns into the solid cluster. {4/3 *πr^3*ΔG_v^(L-->s)} --> cluster grows spherically
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What is the energy opposing the cluster growth?
The new interface that from liquid to solid --. A_cluster *γ_SL = 4π*r^2*γ_SL
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What is the relationship between the cluster growth and ΔG?
As the cluster grows in size ΔG increases.
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Why can we model the cluster to grow spherically?
We assume that the interfacial energy is isotropic.
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How is the interface created?
When the solid is formed an interface is created. Increase of solid volume increases the interface area and thus the interface energy
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Give the equation for the free energy change of forming homogeneous clusters and its significance.
ΔG_cluster = 4/3 *πr^3*ΔG_v^(L-->s) + 4π*r^2*γ_SL ] at a certain point the volume becomes the more dominant as r^3>r^2.
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What is the critical radius and give an equation?
It is the value where ΔG begins to decrease. r* = -2*γ_SL/ΔG_v
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What is G*?
The energy barrier for nucleation. The energy barrier needs to be overcomed for nucleus to form and for the cluster to grow.
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What happens above the critical radius?
Growth of cluster as free energy is reduced. (nucleus)
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What happens below the critical radius?
There is a shrinkage of the cluster as the free energy is reduced. (embryo)
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How does r* change with undercooling?
The critical radius decreases with greater undercooling.(lower temperature)
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How does G* change with undercooling?
The energy barrier decreases strongly with greater undercooling.
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Give an equation that links G* and temperature
G* = 16/3 π (γ^3T^2_eq)/ΔH_v^(L-->S) (1/T^2)
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What are the effects of slow cooling the substance?
Slow cooling = small undercooling = increase in G* which makes it more difficult for nucleation to occur and thus large grains are formed.
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What are the effects of fast cooling the substance?
Fast cooling = large/greater cooling = decrease in G* which makes it easier for nucleation to occur thus small grains form
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Why is heterogeneous nucleation more favourable than homogeneous nucleation?
Less undercooling is required to achieve critical size during heterogeneous nucleation.
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How does heterogeneous nucleation work?
Nuclei form at special sites (mould walls, added particles). The energy barrier is reduced at special sites. Cluster forms on a planar surface as a spherical cap (assuming interfacial energy)
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Where do large grains form? ( heterogeneous)
Nucleation at mould walls.
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Where do small grains form? ( heterogeneous)
grains refining particles (which are added) [small as more grains can nucleate]
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What is the shape of the nucleus defined by/dependent on? (heterogeneous)
The wetting angle (θ).
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Why does an energy change occur? (heterogeneous)
A new interface is formed. The original interface of Mould-Liquid is destroyed by the creation of solid-mould. It is the release of the energy associated with the destroyed interface(M-L) that reduces the energy barrier for nucleation.
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Why is the cluster stable? (heterogeneous)
The surface tensions are balanced.
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What is the equation for ΔG_(het) ?
ΔG_(het) =ΔG_(hom) *S(θ) ] where S(θ) is the 'shape factor'; S(θ)<1 (always) so ΔG_(het)<ΔG_(hom).
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Give a similarity and a difference in heterogeneous and homogeneous nucleation
The critical value is the same for heterogeneous and homogeneous nucleation BUT there is a significant difference between the energy barriers between the two process.
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State the equation that links the energy barriers for het and hom.
G*(het) =G*(hom) 。 S(θ) ] G*_het <G*_hom for all wetting angles<180
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What is a difference between the clusters made from het and hom nucleation/
The critical volume can be different. Which implies that fewer atoms are required to form heterogeneous nucleus than a homogeneous nucleus.
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Other cards in this set
Card 2
Front
Describe homogeneous nucleation
Back
Crystal are formed on nucleation sites from the liquid phase. (hard to achieve)
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