2. Introduction
This chapter will discuss the atomic mechanisms
by which diffusion occurs, the mathematics of
diffusion, and the influence of temperature and
diffusing species on the rate of diffusion. Diffusion is
demonstrated with the use of diffusion couple which is
formed by joining bars of two faces of specific solids.
Interdiffusion or impurity diffusion is a process where
atoms of one metal diffuse into another. The diffusion
that occurs for pure metals is called self-diffusion. Self-
diffusion is the transport of atoms from high to low
concentration regions but the exchanging positions are
of the same type.
5. Diffusion Mechanisms
The conditions needed for diffusion are
(1) there must be an empty and adjacent site and
(2) the atoms must have sufficient energy to break bonds with its
neighbor atoms and then cause some lattice distortion during the
displacement.
The two models for atomic motion for metals are vacancy
diffusion and interstitial diffusion. Vacancy diffusion involves the
interchange of an atom from a normal position to an adjacent
vacant site or vacancy while Interstitial diffusion is involves
atoms to migrate from a position to a neighboring one that is
empty.
8. Steady-State diffusion
The rate of mass transfer in diffusion is
frequently express as a diffusion flux (J).
Diffusion flux is equal to mass over area of
the solid per unit of time.
J=M/At
Diffusion flux has the unit kg/m2*s or
atom/m2*s. Steady-state diffusion occurs
when the diffusion flux does not change
with time.
9. The concentration gradient is often called the driving
force in diffusion. The minus sign in the equation
means that diffusion is down the concentration
gradient.
10. Nonsteady-State Diffusion
Most of the diffusion situations are nonsteady-
state. The diffusion flux and concentration gradient are
at some particular point in a solid and vary with time. It
results to a net accumulation or depletion of diffusing
species. In many real situations the concentration
profile and the concentration gradient are changing
with time. The changes of the concentration profile can
be described in this case by a differential equation.
11. Factors that influence Diffusion
Temperature - diffusion rate increases very rapidly with
increasing temperature.
Diffusion mechanism – diffusion by interstitial mechanism
is usually faster than by vacancy mechanism.
Diffusing and host species - Do, Qd are different for every
solute, solvent pair
Microstructure - diffusion is faster in polycrystalline
materials compared to single crystals because of the
accelerated diffusion along grain boundaries
12. Example Problem 6.1
A plate of iron is exposed to a carburizing (carbon-rich)
atmosphere on oneside and a decarburizing (carbon-deficient)
atmosphere on the other side at 700C (1300F). If a condition of
steady state is achieved, calculate the diffusion flux of carbon
through the plate if the concentrations of carbon at positions of 5
and 10 mm (5 x10-3 and 10-2 m) beneath the carburizing surface
are 1.2 and 0.8 kg/m3, respectively. Assume a
diffusion coefficient of 3 x10-11 m2/s at this temperature.
13. SOLUTION
J = -D(CA - CB / XA _XB )
=(3 x10-11 m2/s)[(1.2 - 0.8) kg/m3 / (5 x 10-3 – 10-2) m
=2.4 x 10-9 kg/m2-s
Submitted by: Jason A. Rempillo
