Quiz 4 Chap 5

Diffusion

Mass transport by atomic motion relative to neighbors

Gasses & liquids

random (Brownian) diffusion

Solids

vacancy diffusion & interstitial diffusion

Interdiffusion

Migration of atoms from one material to another

Self-diffusion

atomic migration within a pure material

• random (Brownian)

• thermally driven

doping defined

Diffusion of very small concentrations of impurity atoms (ex. P) into the semiconductor silicon

process of doping

1. deposit P-rich layers on surface

2. heat treat the sample to drive in P

3. Result is P-doped semiconductor silicon

Case hardening of iron alloy

• Outer surface selectively hardened by diffusing carbon atoms into surface

• Improves wear resistance of gear

• Improves resistance to fatigue failure

Vacancy diffusion

atoms & vacancies exchange position

In vacancy diffusion, the diffusion rate depends on (2 things)

• activation energy to exchange

• number of vacancies

Interdiffusion happens IF

within solubility limit

In interdiffusion, atoms tend to migrate from regions of ____ to regions of _____

high concentration, low concentration

Interstitial diffusion defined

small, interstitial atom move from one interstitial position to an adjacent one

Interstitial diffusion depends on _____ to move to adjacent site

activation energy

Interstitial diffusion is _____ than vacancy diffusion

more rapid

kinetics

how fast underlying processes occur

driving force

provides direction, compels a reaction or process forward

Activation energy, Q

energy required for an atom to break bonds and jump

• value depends on material

• given element and situation, Q doesn’t depend on T

“jumping” in atoms

when an atom moves from one lattice site to another

Thermal energy available (kT) depends on

Temperature, T

ratio between Q and kT part of

what determines how frequently atoms dump

Diffusion coefficient increases with _____

increasing T

D = D₀e^-Q/RT

• D = diffusion coefficient (m²/s)

• D₀ = pre-exponential (m²/s)

• Q_d = activation energy (J/mol or eV/atom)

• R = gas constant = 8.314 J/mol*K or k(8.62×10^-5 eV/atom*K)

• T = absolute temp (K)

Diffusion Coefficient, D

Indication of how fast atoms move in given conditions

• related to # of jumps / second

_______ and _______ can contribute to how fast an atom can move, and is reflected in ___

• Crystal structure

• electronic configuration

• pre-exponential, D₀

Activation energy, Q and the pre-exponential, D₀ do NOT depend on

Temperature, T

If Q/kT ratio is high

lower jump rate

Relationship between diffusion coefficient, D, and Temperature, T

D has an exponential dependence on T

concentration gradient

driving force for diffusion

• Assumes T and stress are uniform throughout sample

• assumes diffusing species is soluble in host

If concentration (high or low) is uniform throughout a sample

no net transport

random motion in a sample means ___ and results in ______

• spread

• net transport from high to low concentration region

Diffusion is a ______ process

time-dependent

rate of diffusion (diffusion flux, J): J = M/At

• M = mass of diffused species

• A = area

• t = time

• Units: kg/m²s

FIck first law of diffusion

Flux (J) is proportional to concentration gradient

J = -D(dC/dx)

• dC/dx = concentration gradient

Steady state diffusion

Concentration of an atom does not change at a given location over time

In Steady state diffusion, flux must be ________

constant over entire length of piece

In steady state diffusion, flux (J) is independent of

time

Non-steady state diffusion

• Concentration of diffusing species is a function of both time and position C = C(x, t)

• seek solutions to Fick’s 2^nd law — assume D is independent of concentration

kinetics — how fast atoms jump

Increasing T → Increasing TE & T → activation energy is reached more frequently → increasing vacancy concentration