1. EME 201 Materials Science
Diffusion

2. Stability of Atoms and Ions
Atoms or ions in their actual positions in the crystal structures are not at rest.
Instead, atoms or ions will have thermal energies and will move.
For example, an atom can move from its actual crystal structure to fill a space close to it.
An atom can pass from one interstitial site to another at the same time.
Atoms or ions can cross a grain boundary.
The ability of atoms and ions to move rises as the temperature or thermal energy that atoms and ions possess increases.
The diffusion process can be exlained with the help of the diffusion couple, that is created by joining pieces of two different metals together.

3. Mechanisms for Diffusion
This pair is heated for a long time at a high temperature and then cooled to room temperature.
Chemical analysis brings to light that pure copper and nickel are separated by an alloyed region.
The concentration of both metals varies depending on the position of both materials.
This result indicates that the copper atoms migrate into nickel and the nickel atoms are dispersed into the copper.
The process at which atoms of a metal diffuse into another metal is called interdiffusion.
The high-low concentration regions have a net transport of atoms.
In void or vacancy containing materials, atoms move or skip from one lattice position to another.

4. Mechanisms for Diffusion
Figure 1. Nickel and copper diffusion pair before and after heat treatment

5. Mechanisms for Diffusion
There is a net atom motion from high concentration to low concentration regions within the alloy structure.
There are two basic mechanisms by which atoms or ions can move or diffuse.
Figure 2. Diffusion process of vacancy and interstitial atom

6. Mechanisms for Diffusion
Vacancy type of diffusion mechanism:
In diffusion involving self-propagation and substitution atoms, an atom is separated from the lattice space to fill a near void (thus creating a new void or vacancy in the original lattice position).
When the diffusion process continues, there is a countercurrent flow of atoms and vacancy, called vacancy type of diffusion.
As the temperature increases, the number of vacancy increases also.
When a small foreign or interstitial atom or ion is present in the crystal structure, the atom or ion passes from one interstitial region to another.
There is no need for vacancy type of diffusion mechanism.

7. Mechanisms for Diffusion
Vacancy type of diffusion mechanism:
In part, interstitial diffusion is much easier than vacancy type of diffusion because there are far more interstitial sites than voids or vacancy sites.
In addition, relatively small interstitial atoms can be propagated more rapidly.
For many ceramic type of material possessing ionic bonds, the structure can be regarded as close packing of anions with cations in interstitial sites.
In this type of materials, smaller cations move faster than larger anions.
The rate at which atoms or ions move or diffuse within a material can be measured by the flux (J ).

8. Rate of Diffusion (Fick’s First Law)
The diffusion flux can be defined as the number of atoms or ions passing through a plane of unit area per unit time.
Fick’s first law is used to explain the net flux of atoms or ions:
J = -D(dc/dx)
Where
-J = the flux
-D = the diffusivity or diffusion coefficient (cm2/s)
-dc/dx = the concentration gradient (atoms/cm3.cm)
Several factors will determine the flux of atoms during the diffusion process.

9. Rate of Diffusion (Fick’s First Law)
Concentration Gradient :
The concentration gradient (dc/dx) illustrates how the composition of the substance changes with the diffusion distance
The concentration gradient (dc/dx) can be established when two materials of different composition are in contact or when unstable structures are produced in a material being treated.
The flux (J) at a certain temperature is fixed only if the concentration gradient is constant.
However, in many practical situations, these compositions change as the atoms redistribute, and so the flux changes.
In general, we find that the flux is initially high and gradually decreases when the concentration gradient is reduced by diffusion.

10. REFERENCES
William D. Callister, ‘Materials Science and Engineering: An Introduction’, Seventh edition, John Wiley & Sons, Inc., U.S.A.
Brian S. Mitchell, ‘AN INTRODUCTION TO MATERIALS ENGINEERING AND SCIENCE FOR CHEMICAL AND MATERIALS ENGINEERS’, John Wiley & Sons, Inc., U.S.A,
J. W. Martin, ‘Materials for Engineering’, Third Edition, WOODHEAD PUBLISHING LIMITED, Cambridge, England.
Donald R. Askeland & Pradeep P. Fulay, ‘Essentials of Materials Science and Engineering’, Second Edition, Cengage Learning, Toronto, Canada.
G. S. Brady, H. R. Clauser, J. A. Vaccari, ‘Materials Handbook’, Fifteenth Edition, McGraw-Hill Handbooks.