Chapter 13 Diffusion

diffusion

the movement of atoms/ions/molecules within a material; integral to many important treatments used in the processing of materials (heat treatment, ceramics manufacture)

glass capillary tube

this is filled with water, and at time t = 0, add a drop of ink to one end. The diffusion distance, x, varies over time as the ink molecules move through the water molecules.

diffusion occurs in…

solids, liquids, and gases. Pure materials (self-diffusion). Impure materials (impurity diffusion, interdiffusion)

diffusion in solids, liquids, and gases

for solids, atoms not moving much → things can more at relatively high temperature

for liquids, depends on viscosity

for gases, molecules fairly far apart, so diffusion occurs rapidly

concentration gradient

before diffusion occurs, this is equal to infinity. Diffusion is very slow compared to convection, and as the material diffuses into the other, this becomes smaller.

interdiffusion

a process of diffusional exchange of atoms across two materials that are in contact

self-diffusion

Atoms move from one lattice position to another in pure solid crystalline materials by ____________ (detectable using radioactive tracers).

isotopes

Identify atoms differing only as ______ will diffuse into pure material. Some of these are radioactive and can be used as markers to track diffusion

Vacancy Diffusion

Atoms jump into adjacent vacancy sites. Vacancy concentration is strongly temperature-dependent, and so is the atomic jump rate.

Happens for substitutional atoms + point defects in crystal.

Interstitial Diffusion

Small interstitial atoms can move from site to site without vacancies. More rapid.

Interstitial sites between atoms in crystals - smaller atoms can’t typically fit in these sites. Faster → smaller atoms can squeeze + moves around without distorting the crystal

opposite direction

for vacancy diffusion, only adjacent atoms can move into a vacancy, and it moves in _________ of atomic motion. 

rate of vacancy diffusion

Depends on concentration of vacancies and energy of atom-vacancy exchange (frequency of jumping)

small atoms

interstitial diffusion is generally limited to __________ (eg. H, B, C, N)

They can move into any adjacent empty interstitial position

rate of interstitial diffusion

depends on concentration of interstitial atoms and energy of migration.

interdiffusion

Diffusion of copper atoms into nickel. Eventually, the copper atoms are randomly distributed throughout the nickel.

high to low

Generally, atoms migrate from regions of ______ concentration to regions of _____ concentration.

case hardening of steel gear

Diffuse carbon atoms into the host steel (iron) at the surface. The resulting C-enriched surface (the “case”) is in compression and is strong and hard. Diffusion causes significant changes in properties. 

gear teeth

want to prevent wear on these; want high hardness and strength

body of gear

more tough, make it more difficult for dislocations to move by diffusing carbon atoms into the surface, so the teeth can be strengthening while this part is not

activation energy

Energy is required for an atom to squeeze past its neighbors from one low-energy site to the next. This barrier must be overcome, and heat supplies this energy. When Q is small, diffusion is easy.

increasing diffusion rate

increasing temperature does this because more molecules are at a sufficiently high energy to overcome the activation energy barrier

flux

The rate of diffusion is measured by the ______, J, which is the number of atoms passing through a plane of unit area per unit time

Fick’s First Law

J = -D dc/dx

J = flux (atoms/m²/s)

D = diffusivity (diffusion coefficient) (m²/s)

dc/dx = concentration gradient (atoms/m³/m)

this equation applies everywhere *assuming molecules randomly jump

flux during diffusion

defined as the number of atoms passing through a plane of unit area per unit time

concentration gradient

change in concentration with distance (slope of concentration vs. distance curve). For a given T, the flux is constant only if this is also constant.

reduced with time

This is not true in typical cases where the gradient is __________, and therefore the flux decreases with time. → transient

steeper; higher

The ______ the concentration profile, the _______ the flux.

steady-state diffusion

takes place at a constant rate - that is, once the process starts the number of atoms (or moles) crossing a given interface (the flux) is constant with time.

Units of J: kg/(m²s)

purify a gas

Thin metal plate separates two regions of different pressures, and the diffusion of gaseous species allows you to do this.

mobile

atoms are _____. They may jump into a vacancy, across a grain boundary, etc. How often or how fast is dependent on temperature

thermally activated

atom mobility is _______; diffusion increases as temperature increases

Arrhenius equation

kinetics of atom jumps are described by this

Rate = c₀ exp[-Q/(RT)]

c₀ = constant; e is base of natural log; R is gas constant,; T is absolute temp (K); Q is activation energy to move the atom

plotting ln(Rate) vs 1/T

slope of curve is -Q/R

ln(c₀) is intercept when 1/T is zero

this graph can be used to determine activation energy required for a reaction

temperature and diffusion coefficient

D = D₀ exp[-Q/(RT)]

D₀ is a constant for a given system (hypothetical diffusion at infinite temperature)

increases

as temperature _______, so does D and diffusion flux

insignificant

at low temperature, diffusion may be ________ from a practical point of view

steep slope

of a diffusion coefficient D as a function of 1/T graph, this denotes a high activation energy

characteristic diffusion distance

for a time t, given by x = √(Dt)

For a case of mixing atoms between two materials with different concentrations, this distance is the depth to which the concentration has changed by one-half of the difference in concentrations between the two materials

time required

the diffusion distance formula can also be used to estimate this to achieve a desired depth of diffusion