Download - DIFFUSION IN SOLIDS
‘’DIFFUSION IN SOLIDS’’
IE-114 Materials Science and General Chemistry
Lecture-5
Diffusion
The mechanism by which matter is transported through matter. It is related
to internal atomic movement.
Atomic movement; Gases > Liquids > Solids
Atomic-scale motion (diffusion) in liquids and gases is rapid and easy to visualize
Gases Liquids
Diffusion in solids
The slower diffusion rate in the solid state than in the liquid state.
Heat Treatment of Metals
Case hardening of steel (carbon diffusion in steel)
Oxidation of metals
Thin film electronics (doping of semiconductors)
Sintering (fusion of powder particles at solid state)
EXAMPLE : CASE HARDENING OF STEEL
Methods used: Carburizing, Nitriding
Fe + 2CO Fe(c) + CO2
Types of diffusion in Solids
Self-diffusion Interdiffusion (Impurity diffusion)
Origin of Diffusion
Thermal energy
Concentration gradient (effective in diffusion of impurities)
In solids, atomic movements are restricted to equilibrium positions due to bondings. If energy is
provided to the solids, it can cause the thermal vibrations of atoms about their equilibrium
position and at sufficient energy vibration may be strong enough to break the bonding and make
the atom move
1) Self-diffusion
Label some atoms After some time
A
B
C
D
Diffusion in pure metals
All atoms exchanging positions are of the same type
HEAT
100%
Concentration Profiles0
HEATING
Upon heating, diffusion of atoms from high concentration to low
concentration takes place
2) Impurity-diffusion (Interdiffusion)
The process, whereby atoms of one metal diffuse into another
metal
Initially After some time
COPPER NICKEL
Diffusion Mechanisms
In atomic point of view diffusion is stepwise migration of
atoms from lattice site to lattice site
For an atom to make such a move;
a) there must be an empty adjacent site
b) atom that is moving should have enough energy to break bonds with the neighboring atoms and cause some distortion. The energy is vibrational in nature.
1) Vacancy diffusion
2) Interstitial Diffusion
There are two types of diffusion mechanisms:
Vacancy (substitutional) Diffusion
a) Self-diffusion (pure metals) b) Impurity Diffusion
Interstitial Diffusion
a) Self-diffusion (pure metals) b) Impurity Diffusion
1) Vacancy (substitutional) Diffusion
A host or substitutional atom exchanges places with a vacancy
(Both vacancies and required activation energy is provided by thermal energy which results in vibrations of
atoms and impurities)
Activation energy = Act. Ener. (to form a vacancy) + Act. Ener. (to move the atom to the vacancy)
Activation energy (Q) as melting temp.
(Stronger bonds exist in higher-melting-temperature metals)
Rate of diffusion depends on;
Number of vacancies
Activation energy to migrate
• jumping of a smaller atom (black) from one interstitial
site to another in a BCC structure.
e.g. Interstitial diffusion of carbon in iron Rcarbon=0.071 nm RFe= 0.124 nm
2) Interstitial Diffusion:
Atoms move from an interstitial position to another one closeby.
Migrating atoms should be small in size such as N, C, H and O.
Interstitial diffusion occurs much more rapidly than diffusion by
the vacancy mode, since interstitial atoms are smaller, and thus
mobile.
Conditions for atom migration:
- empty adjacent site
- atom must have enough energy to break bonds and cause lattice distortion
during displacement.
Diffusive motion influenced by atom vibrational energies (kBT)
Activation Energy for Diffusion
1) Steady-State diffusion:
Diffusion is a time dependent process; the quatity of an element
that is transported within another is a function of time.
The rate of mass transfer is explained by diffusion flux (J): the
mass of (or, number of atoms) M diffusing through and perpendicular to a unit cross-
sectional area per unit of time
mass
crosssectional area
time
In differential form:
UNIT: kg/m2s or atoms/m2s
Diffusion Modeling
Steady state condition exists when the diffusion flux does not
change with time
Concentrations(pressures) of two species are held constant, PA and PB and PA>PB
The steady-state diffusion in one (x) direction :
FICK’S FIRST LAW
Concentration gradient (dC/dx) is the driving force in diffusion reactions.
The steeper the concentration gradient, the greater will be the diffusion or
the mass transfer
D: diffusivity or diffusion coefficient (m2/sec or cm2/sec).
The negative sign indicates that the direction of diffusion is
down the concentration gradient.
2)Nonsteady state diffusion:
The diffusion flux and concentration gradient at a selected point vary
with time causing a net accumulation or depletion.
For nonsteady state diffusion Fick’s first law is not valid.
FICK’S SECOND LAW
Semi-finite solid in which the surface concentration is held constant.
Assume:
a) before diffusion, diffusing solute concentration is uniform, Co.
b) the value of x is zero at the surface and increases with distance into the solid.
c) the time is zero at the instant before the diffusion begins.
Depending on the selected boundary conditions there may be different
solutions for Fick’s second law.
Surface concentration is held constant
Cx: concentration at depth x after time t.
Cs: concentration at surface
Co: initial concentration
Gaussian error function
Factors affecting diffusion:
Different materials have different diffusion coefficient (Do),
which is also the indication of the diffusion rate.
4) Temperature: Diffusion is thermally activated process
Temperature dependence can be expressed as follows:
2) Crystal structure (BCC, FCC, ..)
3) Imperfection (grain boundary, dislocation, vacancy, lattice)
1) Diffusing species:
Diffusion coefficient vs 1/T
10-24
10-22
10-20
10-18
10-16
10-14
10-12
10-10
0.6 0.8 1 1.2 1.4 1.6
Fe in bcc FeFe in fcc FeC in bcc FeC in fcc FeMn in fcc Fe
D, m
2/s
1000/T(K)
1200°C 900°C 400°C600°C