Definition and description of different diffusion terms
Before proceeding further, it is necessary to introduce different terms frequently used
in diffusion studies.
Many terms will be introduced, which are not necessarily discussed in general books.
Till now we discussed diffusion without classifying the type.
For example, diffusion can be classified in mainly two categories: interstitial and
substitutional. We will not discuss about another, not so common, interstitialcy diffusion.
Host atoms occupy the lattice points. Interstitial atoms, such as C, H, O occupy the
interstitial voids in metals, for example in Fe.
When interstitial atoms jump from one interstitial void to another it is called interstitial
diffusion.
When host atoms jump to another lattice position it is called substitutional
diffusion.
It must be clear from the figure in the previous slide that substitutional diffusion is
possible only when a vacant site or vacancy is available on the next lattice position.
Further, it should be noticed that atoms cannot jump easily. In general the void
through which the atom should jump is smaller than its size.
So first it should push away the neighboring atoms and then jump.
Diffusion will be possible, only when it gains enough energy to push neighboring
atoms.
This is called the activation barrier. The energy required is called the activation
energy for migration.
If no particular interstitial atom is smaller than the other, it needs less energy for
migration and diffusion rate is higher.
As we have seen already, the presence of vacancy is important for
substitutional diffusion.
Formation of vacancy has its own activation energy barrier.
So there are two contributions in activation energy barrier, one from migration
and another from vacancy formation.
This is also the reason that the interstitial diffusion rate is higher than the
substitutional diffusion.
Further, we know that there can be many types of defects which are present in
the structure.
Impurities and vacancies are the common point defects.
Dislocations are the common line defects.
Pipe diffusion: When diffusion occurs via edge dislocation, it is called pipe diffusion.
Since it feels like movement of atoms through a pipe.
Note that both interstitial and substitutional diffusion can occur via dislocations.
Even impurities are attracted by the dislocations because of availability of more
space and chance to release stress.
This is also the reason (more open space) that it has lower activation barrier
and diffusion rate through dislocation is higher than the diffusion through lattice.
Diffusion occurs via grain boundaries even easily and it is called grain
boundary diffusion.
Since grain boundaries are relatively more open structure compared to
atomic structure inside the grains, the barrier for diffusion through grain
boundary is much less and the diffusion rate is higher.
Rate of diffusion increases with the increase in misorientations.
Surface diffusion: When diffusion occurs over a surface, it is called surface
diffusion.
Here activation energy for diffusion is the lowest since there are no atoms
above the atom of interest, which exchanges position with the vacancy. So
diffusion rate is the highest compared to other diffusion mechanisms.
Diffusion coefficient
surface
Grain
boundary
lattice
Surface diffusion
1/T
Note that both interstitial and substitutional diffusion can happen through,
lattice, dislocations, grain boundaries and surface.
Slope of the diffusion coefficient vs. 1/T gives the activation barrier for
diffusion. Activation barrier is the lowest and diffusion rate is the highest for the
surface diffusion. Activation barrier is the highest and diffusion rate is the
lowest for lattice diffusion.
Diffusion couple: When two blocks with different compositions are joined
(coupled) together and annealed to allow diffusion between them, it is called
diffusion couple.
Interdiffusion (chemical diffusion): Since elements in the diffusion couple
interdiffuse to each other, it is called interdiffusion.
The diffusion coefficient is in general called as interdiffusion coefficient and if
sometimes any new compound forms during the diffusion at the interface,
occasionally, it is called chemical diffusion coefficient.
Note that actually elements A and B diffuse. Diffusion of these elements are
called intrinsic diffusion of elements.
Intrinsic and interdiffusion flux: The flux of elements A and B, denoted by JA and
JB, respectively, are called the intrinsic flux of elements A and B, respectively ,
Interdiffusion flux ( ~
J ) is kind of average of these two fluxes.
Similarly, DA and DB are the intrinsic diffusion coefficients of the species A and B.
~
Interdiffusion coefficient ( D ) is related with the intrinsic diffusion coefficients as
~
D = C AVA DB + C BVB DA ≈ N A DB + N B DA
for VA=VB=Vm
These relations will be derived in following lectures
Self diffusion: When diffusion occurs without any presence of driving force, it is
called self diffusion.
Atoms vibrate at their positions and because of some violent jumps, it can cross
the activation barrier to make the jump successful.
Since there is no driving force to direct the jump of atoms to a particular
direction, self diffusion is truly random in nature.
This indicates that when a pure metal is kept at elevated temperature jump of
atoms is always happening.
In low melting point metals, like In or Sn, even at room temperature, atoms
exchange their position.
However, since these are very small in size, we cannot follow a particular atom
jump.
We shall see that the jump can be many orders of magnitude in one second. This
makes it even difficult to follow the jump of atoms.
To obviate this problem, concept of tracer diffusion is introduced.
Tracer diffusion: Radio isotopes are used in tracer method so that the movement
of atoms can be traced and diffusion coefficient can be measured.
It has only one or two neutron mass difference.
Diffusion rate of these tracer atoms are called tracer diffusion coefficient.
Note: Self diffusion coefficient (Ds) is not necessarily equal to the tracer
diffusion coefficient (D*). These two are related as
D* = f D s
f is the correlation factor (f = 1 for interstitial diffusion)
This method will be explained in detail.
When tracer diffusion coefficient of element B in pure material A is measured, it
is called impurity diffusion coefficient.