Page 169 - Materials Science and Engineering An Introduction

WHY STUDY Diffusion?

Materials of all types are often heat-treated to improve can often be predicted by using the mathematics of
their properties. The phenomena that occur during a diffusion and appropriate diffusion constants. The steel
heat treatment almost always involve atomic diffusion. gear shown on page 140 (top) has been case hardened
Often, an enhancement of diffusion rate is desired; (Section 8.10)—that is, its hardness and resistance to
on occasion, measures are taken to reduce it. Heat- failure by fatigue have been enhanced by diffusing ex-
treating temperatures and times and/or cooling rates cess carbon or nitrogen into the outer surface layer.

Learning Objectives
After studying this chapter, you should be able to do the following:
1. Name and describe the two atomic mechanisms 4. Write the solution to Fick’s second law for diffu-
of diffusion. sion into a semi-infinite solid when the concen-
2. Distinguish between steady-state and nonsteady- tration of diffusing species at the surface is held
state diffusion. constant. Define all parameters in this equation.
3. (a) Write Fick’s first and second laws in equa- 5. Calculate the diffusion coefficient for a material
tion form and define all parameters. at a specified temperature, given the appropri-
(b) Note the kind of diffusion for which each of ate diffusion constants.
these equations is normally applied.

5.1 INTRODUCTION
Many reactions and processes that are important in the treatment of materials rely on the
transfer of mass either within a specific solid (ordinarily on a microscopic level) or from
diffusion a liquid, a gas, or another solid phase. This is necessarily accomplished by diffusion, the
phenomenon of material transport by atomic motion. This chapter discusses the atomic
mechanisms by which diffusion occurs, the mathematics of diffusion, and the influence of
temperature and diffusing species on the rate of diffusion.
The phenomenon of diffusion may be demonstrated with the use of a diffusion couple,
which is formed by joining bars of two different metals together so that there is intimate
Tutorial Video: contact between the two faces; this is illustrated for copper and nickel in Figure 5.1, which
Diffusion includes schematic representations of atom positions and composition across the interface.
What is Diffusion?
This couple is heated for an extended period at an elevated temperature (but below the
melting temperature of both metals) and cooled to room temperature. Chemical analysis
reveals a condition similar to that represented in Figure 5.2—namely, pure copper and

100
Concentration of Ni, Cu Cu Ni

Cu Ni
0
Position
(a) (b) (c)
Figure 5.1 (a) A copper–nickel diffusion couple before a high-temperature heat treatment. (b) Schematic repre-
sentations of Cu (red circles) and Ni (blue circles) atom locations within the diffusion couple. (c) Concentrations of
copper and nickel as a function of position across the couple.

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