Diffusion

Question 1

What are the two main kinds of atomic movement in diffusion?

Answer 1

Vacancy diffusion and interstitial diffusion

Question 2

What is the critical radius for nucleation, how does it differ between homogenous and heterogenous nucleation?

Answer 2

Homogenous Critical Radius: r*=2γ/ΔGv
γ: surface free energy
ΔGv: volume free energy

Heterogenous Critical Radius: r*=2γsl/ΔGv
γsl: solid liquid interface energy
ΔGv: volume free energy

Question 3

What is the activation free energy of nucleation formula and how does it change for homogenous and heterogenous nucleation?

Answer 3

Homogenous: ΔG*=(16πγ^3)/(3ΔGv^2)

Heterogenous: ΔG*=((16πγsl^3)/(3ΔGv^2))S(θ)
γ to γsl and add S(θ), which is for shape of nucleus (I think it’s the wetting angle)

Question 4

What is spinodal decomposition?

Answer 4

Spinodal decomposition is the spontaneous (without nucleation) separation of a solid solution into two distinct phases
It is characterized by nested curves on a phase diagram and a sinusoidal Gibb’s free energy curve, with the middle section concave down

Question 5

How does the melting temperature of nanoparticles compare to that of the bulk material, why?

Answer 5

Nanomaterials have significantly lower melting temperatures than their bulk counterparts due to to the extreme surface area to volume ratio, and the interfacial energy drives the phase transformation, it is called melting point depression

Question 6

What is mean field theory and how does it relate to diffusion?

Answer 6

Mean field theory is a way to study random (stochastic is the descriptor for random chance models) movement dictated by certain degrees of freedom
In diffusion it is used to simplify and study study particle movement, and it assumes that it is surrounded by a mean concentration instead of an actual distribution

Question 7

What is the Kirkendall effect?

Answer 7

The Kirkendall effect is the movement of an interface between two metals due to differing diffusion rates

Question 8

What is the Avrami equation?

Answer 8

The Avrami equation describes phase transformation and crystallization at constant temperature
Assumes that nucleation occurs randomly and homogenously, growth rate is independent of transformed volume and is isotropic

Question 9

What is a GP zone?

Answer 9

A Guinier-Preston zone is an area with a high concentration of fine particles formed upon cooling a supersaturated material
The solute atoms accumulate into precipitates and harden the area

Question 10

What happens when an alloy is cooled such that the behavior is not the same as if it were cooled infinitely slowly?

Answer 10

Nucleation will occur in areas rich in the component with a higher melting temperature, the concentration gradient going out from the nuclei will have increasing concentration of the component with the lower melting temperature

Question 11

What is a dendrite? What conditions cause their growth?

Answer 11

A dendrite is a tree like formation caused by undercooling and influenced by the anisotropic preferred growth directions of the material
Conditions: supersaturation, undercooling, rapid solidification (often rapid cooling), anisotropic crystal growth, limited diffusion (restricting new nucleation)

Question 12

What is undercooling? How does it affect a sample?

Answer 12

Undercooling is when a sample is cooled below its melting temperature without causing a phase transformation
A higher degree of undercooling leads to more driving force for solidification and nucleation, more undercooling leads to more nucleation and a finer grain structure, this is why quenching is used to create metastable states like martensite as well as strengthening through grain size reduction

Question 13

What are the differences between low angle and high angle grain boundaries?

Answer 13

Low and high angle grain boundaries are split at 10°-15°
Low angle grain boundaries can be described as a series of edge dislocations, having low interface energy and allowing dislocations to travel between grains with some effort
High angle grain boundaries have significant disorder, high energy, and prevent dislocation movement

Question 14

What is Fick’s first law? When is it used? Derive it

Answer 14

Describes steady-state diffusion in one direction:
J = -D dC/dx
D: diffusion coefficient

Question 15

What is Fick’s second law? When is it used? Derive it

Answer 15

Describes non-steady state diffusion in one direction, D must be independent of composition
dC/dt = D d2C/dx2
(d means delta)

Question 16

What is flux and what is the equation that describes it?

Answer 16

Flux is the movement of atoms across some interface and is described by the following formula
J = N/At
J: Flux (kg/m^2s)
N: number of atoms
A: Area
t: Time

Question 17

What formula describes changing concentration in a semi-infinite solid? What assumptions are made for this formula?

Answer 17

(Cx-C0)/(Cs-C0) = 1 - erf(x/2sqrt(Dt))
erf(z) = (2/sqrt(π)) Integral(e^-y^2 dy)

At time t=0 there is a uniform concentration of solute atoms through the sample
At t>0; C=Cs at the surface and C=C0 at the infinite end

Question 18

Why is a TTT diagram shaped like that?

Answer 18

TTT diagrams are c shaped due to the competition between undercooling (the driving force of solidification) and diffusion (the ability to grow nuclei)
At high T, diffusion is good but nucleation is limited, large grains of even composition, thermodynamically stable
At low T, plenty of nucleation but diffusion is limited and grains will be small, can form metastable states

Question 19

How does the diffusion constant change with temperature?

Answer 19

D = D0 exp(-Qd/RT)
D0: temperature dependent preexponential
Qd: activation energy for diffusion

Question 20

What is the free energy change of solidification?

Answer 20

ΔG = 4/3 πr^3ΔGv + 4πr^2 γ
ΔGv: volume free energy (will be negative)
γ: surface energy
has two terms: volume term and surface energy term
take the derivative of this and set to zero to derive critical radius

Question 21

What is the grain growth equation?

Answer 21

d^2-d0^2=kt
k=k0exp(-Q/RT)