Chapter 5: Diffusion Flashcards
What is Fourier’s law of heat flux and what does it describe?
j_q = -κ (dT/dx) (1D)
κ is the thermal conductivity.
The law shows that heat flows from hot to cold regions
What is Fick’s first law and what does it describe?
J = -D (dc/dx) (1D)
It describes the flow of particles from high to low concentrations
What is the D in Fick’s first law?
The diffusion coefficient
What does the J in Fick’s first law represent?
The number/moles of particles crossing a unit area per unit time
What can the negative particle gradient in Fick’s first law be considered to be?
As the driving force of the particle flux
When is Fick’s first law valid?
During steady state diffusion, when the concentration does not change with time
How is the flux density of a species i defined?
j_i = c_i v_i
c_i is the concentration, v_i is the average net drift velocity
How is the drift velocity defined?
v_i = B_i F_i
B_i is the mobility, F_i is the driving force
What can the force acting on defects be?
Electrical or chemical potential (gradient)
How is the chemical potential defined?
μ = μ_i + kT ln(a_i)
What is the Nernst-Einstein relation?
D = kTB
or
D_i/kT = σ_i/(q_i^2 c_i)
How can we express the jump rate, Γ?
Γ = n/t
It is the number of jumps (n) per time
How is the random diffusion summed up, with regards to 1, 2 and 3D?
- 1D: 2 directions
- 2D: 4 directions
- 3D: 6 directions
What is Fick’s second law of diffusion?
∂c/∂t = D ∂^2c/∂x^2 (if the diffusion coefficient is independent of c)
What are the two most important diffusion mechanisms?
Vacancy and interstitial
What is the mechanism behind interstitialcy movement?
An interstitial atom will push another atom out of its lattice site and then occupy that site, moving the original site-atom into an interstitial position
What is the difference between a collinear and non-collinear jump? (interstitialcy mechanism)
A collinear jump will move the pushed atom in the same direction as the pushing atom, a non-collinear jump moves the pushed atom in a different direction than the pushin’ one
What sort of diffusion mechanisms are protons subjected to?
- Free transport mechanism (Grotthuss)
- Vehicle mechanism
What is the free transport mechanism?
A proton jumping between oxide ions
What is the vehicle mechanism?
A proton being transported on an oxide ion as a passenger
