Diffusion

Question 1

Define Diffusion

Answer 1

Diffusion is a thermally activated process which causes the random migration of atoms through a material. The concentration gradient results in the flow from regions of low to high concentration

Question 2

What are the two key parameters of random motion

Answer 2

1. Length Scale (lambda) e.g mean free path

2. Time Scale (tau) e.g time between collisions

Question 3

Outline the two bulk mechanisms of diffusion in solids and their relative speeds

Answer 3

1. Bulk interstitial diffusion: Small interstitial atoms move between interstitial spaces. Fast
2. Bulk vacancy diffusion: Substitutional atoms exchange places with a vacancy in the structure. Slow

Question 4

Outline the two short circuit mechanisms of diffusion in solids

Answer 4

1. Diffusion along a grain-boundary:
   Grain boundaries are more open allowing for faster diffusion. Fast
2. Diffusion along dislocation cores
   Atom spacing is greater around a dislocation core. Fast

Question 5

Define the Arrhenius Law

Answer 5

Process that follow an exponential relationship with temperature are said to be thermally activated.

Rate is proportional to exp(-Q/RT)
where Q is the activation energy

Question 6

How do you determine if a process obeys the Arrhenius Law

Answer 6

Measure the rate at a range of temperatures and plot on a log axis.
ln(rate) = ln(A) - Q/RT

Question 7

Give an example of a thermally activated process

Answer 7

Diffusion is an example of a thermally activated process. Specially Bulk interstitial diffusion require moving atoms from positions of minimum Gibbs free energy resulting in a an energy barrier. Note the energy per atom varies and is governed by an exponential distribution.

Question 8

What are the thermodynamic driving forces needed to clear an energy barrier

Answer 8

1. Free energy change due to phase transformation
2. Surface energy
3. Stress Field
4. Electric Field

Question 9

How does the growth rate of a solid-liquid interface vary with the degree of undercooling

Answer 9

The rate of growth increases with both temperature and undercooling. So the two effects oppose one another and the optimum rate is found at an intermediate level.

Question 10

How does there growth rate of nucleation vary with undercooling

Answer 10

Similar to the case of the liquid-solid interface the optimum rate corresponds to a balance between maximising fluctuations in atomic energy (high temperature) and undercooling to minimise the critical radius.