Page 190 - Materials Science and Engineering An Introduction

162 • Chapter 5 / Diffusion

Important Terms and Concepts

activation energy diffusion flux nonsteady-state diffusion
carburizing driving force self-diffusion
concentration gradient Fick’s first law steady-state diffusion
concentration profile Fick’s second law vacancy diffusion
diffusion interdiffusion (impurity diffusion)
diffusion coefficient interstitial diffusion

REFERENCES
Carslaw, H. S., and J. C. Jaeger, Conduction of Heat in Solids, Glicksman, M., Diffusion in Solids, Wiley-Interscience, New
2nd edition, Oxford University Press, Oxford, 1986. York, 2000.
Crank, J., The Mathematics of Diffusion, Oxford University Shewmon, P. G., Diffusion in Solids, 2nd edition, The Minerals,
Press, Oxford, 1980. Metals and Materials Society, Warrendale, PA, 1989.
Gale, W. F., and T. C. Totemeier (Editors), Smithells Metals
Reference Book, 8th edition, Elsevier Butterworth-
Heinemann, Oxford, 2004.

QUESTIONS AND PROBLEMS
Problem available (at instructor’s discretion) in WileyPLUS
Introduction 5.7 (a) Briefly explain the concept of a driving force.
5.1 Briefly explain the difference between self- (b) What is the driving force for steady-state
diffusion and interdiffusion. diffusion?
5.2 Self-diffusion involves the motion of atoms that 5.8 The purification of hydrogen gas by diffusion
are all of the same type; therefore, it is not subject through a palladium sheet was discussed in Section
to observation by compositional changes, as with 5.3. Compute the number of kilograms of hydro-
interdiffusion. Suggest one way in which self- gen that pass per hour through a 6-mm thick sheet
diffusion may be monitored. of palladium having an area of 0.25 m at 600 C.
2
2
8
Assume a diffusion coefficient of 1.7 10 m /s,
Diffusion Mechanisms that the respective concentrations at the high- and
5.3 (a) Compare interstitial and vacancy atomic low-pressure sides of the plate are 2.0 and 0.4 kg
mechanisms for diffusion. of hydrogen per cubic meter of palladium, and
(b) Cite two reasons why interstitial diffusion is that steady-state conditions have been attained.
normally more rapid than vacancy diffusion. 5.9 A sheet of steel 2.5-mm thick has nitrogen atmos-
5.4 Carbon diffuses in iron via an interstitial pheres on both sides at 900 C and is permitted to
mechanism—for FCC iron from one octahedral achieve a steady-state diffusion condition. The
site to an adjacent one. In Section 4.3 (Figure diffusion coefficient for nitrogen in steel at this
2
4.3a), we note that two general sets of point coor- temperature is 1.85 10 10 m /s, and the diffusion
7
2
dinates for this site are 0 1 and . Specify the flux is found to be 1.0 10 kg/m # s. Also, it is
1 1 1
1
2
2 2 2
family of crystallographic directions in which this known that the concentration of nitrogen in the
3
diffusion of carbon in FCC iron takes place. steel at the high-pressure surface is 2 kg/m . How
far into the sheet from this high-pressure side will
5.5 Carbon diffuses in iron via an interstitial mecha- 3
nism—for BCC iron from one tetrahedral site to the concentration be 0.5 kg/m ? Assume a linear
an adjacent one. In Section 4.3 (Figure 4.3b) we concentration profile.
note that a general set of point coordinates for 5.10 A sheet of BCC iron 2-mm thick was exposed
1 1
this site are 1 . Specify the family of crystal- to a carburizing gas atmosphere on one side and
2 4
lographic directions in which this diffusion of a decarburizing atmosphere on the other side at
carbon in BCC iron takes place. 675 C. After reaching steady state, the iron was
quickly cooled to room temperature. The carbon
Fick’s First Law concentrations at the two surfaces of the sheet
5.6 Briefly explain the concept of steady state as it ap- were determined to be 0.015 and 0.0068 wt%,
plies to diffusion. respectively. Compute the diffusion coefficient if