Chap06

C h a p t e r 6 / Diffusion









Photograph of a steel gear that
has been ‘‘case hardened.’’ The outer surface layer was selectively
hardened by a high-temperature heat treatment during which carbon from the surrounding atmosphere diffused into the surface. The ‘‘case’’appears as the dark outer rim of that segment of the gear that has been sectioned. Actual size. (Photograph courtesy of Surface Division
Midland-Ross.)
























Why Study Diffusion?


Materials of all types are often heat treated to im- prove their properties. The phenomena that occur during a heat treatment almost alwaysinvolve atomic diffusion. Often an enhancement of diffusion rate is desired; on occasion measures are taken to reduce it. Heat-treating temperatures and times, and/or cooling rates are often predictable using the

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mathematics of diffusion and appropriate diffusion constants. The steel gear shown on this page has been case hardened (Section 9.14); that is, its hard- ness and resistanceto failure by fatigue have been enhanced by diffusing excess carbon or nitrogen into the outer surface layer.


L e a r n i n g O b j e c t i v e s
After studying this chapter you should be able to do the following:
1. Name and describe the two atomic mechanisms of diffusion.
2. Distinguish between steady-state and nonsteady- state diffusion.
3. (a) Write Fick’s first andsecond laws in equa- tion form, and define all parameters.
(b) Note the kind of diffusion for which each of these equations is normally applied.
4. Write the solution to Fick’s second law for diffu- sion into a semi-infinite solid when the concen- tration of diffusing species at the surface is held constant. Define all parameters in this equation.
5. Calculate the diffusioncoefficient for some mate- rial at a specified temperature, given the appro- priate diffusion constants.
6. Note one difference in diffusion mechanisms for metals and ionic solids.





6.1 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 amicroscopic level) or from 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 dif- fusion.
The phenomenon ofdiffusion 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 contact between the two faces; this is illustrated for copper and nickel in Figure 6.1, which includes schematic representations of atom positions and composition across the interface. This couple is heated for an extendedperiod at an elevated temperature (but below the melting temperature of both metals), and cooled to room temperature. Chemical analysis will reveal a condition similar to that represented in Figure 6.2, namely, pure copper and nickel at the two extremit- ies of the couple, separated by an alloyed region. Concentrations of both metals vary with position as shown in Figure 6.2c. Thisresult indicates that copper atoms have migrated or diffused into the nickel, and that nickel has diffused into copper. This process, whereby atoms of one metal diffuse into another, is termed interdiffu- sion, or impurity diffusion.
Interdiffusion may be discerned from a macroscopic perspective by changes in concentration which occur over time, as in the example for...