Solidification Flashcards
What do grain boundaries do to material strength?
Increase strength at low temperatures, decrease strength at high temps (as they deform first)
What is the driving force for nucleation and how is it calculated?
Free energy reduction caused by solidification, calculated by the difference between liquid and solidus lines
ΔGv = ΔHv.ΔT/Tm
Gv = Gibbs energy per volume, Hv 0 enthalpy per volume
Only true for pure alloys (used as estimate for others)
What is undercooling?
When a substance is cooled below a transformation temperature without transforming (in a meta-stable state)
What’s the free energy change caused by nucleation?
ΔGr = Vs.ΔGv + A.Ysl Gr = free energy change, Vs = nucleus volume, Gv = free energy difference of solidification per volume, A = area, Ysl = solid/liquid interface energy
What is meant by the critical radius?
On a ΔG vs r curve, VsΔGv and A.Ysl are plotted, product of them plotted, r* = peak of this product = when increasing nucleated particle is energetically favourable
Below r* energetically favourable p decrease nucleation, above r* energetically favourable to increase nucleation
Define the energy barrier
This is the minimum energy required to nucleate, this is the corresponding G value for r* on the ΔG vs r graph
How is the probability of clusters forming with a certain radius calculated?
P(r) = e^(-ΔGr/KT) Gr = free energy change upon nucleation, k = Boltzmann constant,T = temp, P(r) is the probability of clusters forming with radius r
What is the maximum cluster size?
r* is the maximum cluster size because smaller radii are more likely to spontaneously form (require less atoms to collide)
Explain critical undercooling
Nucleation barrier drops with increased undercooling which means probability of getting nuclei with a critical radius is 0 until a critical degree of undercooling has occurred
What is heterogenous nucleation?
An already existing interface acts as a nucleation point = lower nucleation barrier = more likely nucleation, r* is unaffected, once nucleation has occurred atoms are added like normal for the nucleation point to grow
What is the wetting angle?
Wetting angle is how much an interface reduces the nucleation barrier by, a small wetting angle = large reduction
Explain the effects of dendritic solidification
Solubility is lower in solid than in liquid = As interface moves it rejects alloying elements = enriched liquid K = Cs/Cl Partition coefficient (dictates how much solid is rejected) = comp of solid/comp of liquid
What’s the difference between global and local equilibrium?
Global - phase fractions and comp follow phase diagram, G always at minimum, no temp or comp gradients
Local - variation in comp and temp, level rule not follow, phase diagram only followed at interface
What is meant by constitutional undercooling?
Cooling of liquid below solidification temp, means dendrites form as small fluctuations at the interface result in larger driving forces = dendritic growth
When does dendritic growth occur?
Can only occur when an alloy
When cooling > diffusion
When G/V < To/Dl
G = temp gradient, V = interface velocity, To = Temp L - Temp S, Dl = diffusion in liquid
When G/V > To/Dl then planar interfacial growth occurs
