Page 195 - Materials Science and Engineering An Introduction

Questions and Problems • 167

absolute temperature and are given by the follow- Fick’s Second Law—Nonsteady-State Diffusion
ing expressions: 5.D3 The wear resistance of a steel shaft is to be im-
27,800 J>mol proved by hardening its surface by increasing the
3 (5.16a)
C H = 2.5 * 10 1p H 2 expa - b nitrogen content within an outer surface layer as a
RT
result of nitrogen diffusion into the steel; the nitro-
37,600 J>mol
3 (5.16b) gen is to be supplied from an external nitrogen-rich
C N = 2.75 * 10 1p N 2 expa - b
RT gas at an elevated and constant temperature. The
initial nitrogen content of the steel is 0.0025 wt%,
Furthermore, the diffusion coefficients for the dif- whereas the surface concentration is to be main-
fusion of these gases in this metal are functions of tained at 0.45 wt%. For this treatment to be effective,
the absolute temperature, as follows:
a nitrogen content of 0.12 wt% must be established at
13,400 J>mol a position 0.45 mm below the surface. Specify an ap-
2
-7
D H (m >s) = 1.4 * 10 expa - b (5.17a) propriate heat treatment in terms of temperature and
RT
time for a temperature between 475 C and 625 C.
76,150 J>mol
2 -7 The preexponential and activation energy for the dif-
D N (m >s) = 3.0 * 10 expa - b (5.17b)
7
2
RT fusion of nitrogen in iron are 5 10 m /s and 77,000
J/mol, respectively, over this temperature range.
Is it possible to purify hydrogen gas in this manner?
If so, specify a temperature at which the process 5.D4 The wear resistance of a steel gear is to be im-
may be carried out, and also the thickness of metal proved by hardening its surface, as described in
sheet that would be required. If this procedure is Design Example 5.1. However, in this case, the
not possible, then state the reason(s) why. initial carbon content of the steel is 0.15 wt%, and a
carbon content of 0.75 wt% is to be established at a
5.D2 A gas mixture is found to contain two diatomic
A and B species (A 2 and B 2 ), the partial pressures position 0.65 mm below the surface. Furthermore,
of both of which are 0.1013 MPa (1 atm). This the surface concentration is to be maintained con-
mixture is to be enriched in the partial pressure stant, but may be varied between 1.2 and 1.4 wt%
of the A species by passing both gases through a C. Specify an appropriate heat treatment in terms
thin sheet of some metal at an elevated tempera- of surface carbon concentration and time, and for a
ture. The resulting enriched mixture is to have a temperature between 1000 C and 1200 C.
partial pressure of 0.051 MPa (0.5 atm) for gas A
and 0.0203 MPa (0.2 atm) for gas B. The concen- Diffusion in Semiconducting Materials
3
and C B , in mol/m ) are 5.D5 One integrated circuit design calls for the diffusion
trations of A and B (C A
, in of aluminum into silicon wafers; the background
functions of gas partial pressures (p A 2 and p B 2
3
MPa) and absolute temperature according to the concentration of Al in Si is 1.75 10 19 atoms/m .
following expressions: The predeposition heat treatment is to be con-
ducted at 975 C for 1.25 h, with a constant surface
20,000 J>mol 26 3
3 (5.18a) concentration of 4 10 Al atoms/m . At a drive-in
C A = 1.5 * 10 1p A 2 expa - b
RT treatment temperature of 1050 C, determine the dif-
27,000 J>mol fusion time required for a junction depth of 1.75 m.
3 (5.18b)
RT
C B = 2.0 * 10 1p B 2 expa - b For this system, values of Q d and D 0 are 3.41 eV/atom
2
4
and 1.38 10 m /s, respectively.
Furthermore, the diffusion coefficients for the dif-
fusion of these gases in the metal are functions of FUNDAMENTALS OF ENGINEERING
the absolute temperature, as follows: QUESTIONS AND PROBLEMS
13,000 J>mol 5.1FE Atoms of which of the following elements will
2 -7
D A (m >s) = 5.0 * 10 expa - b (5.19a) diffuse most rapidly in iron?
RT
21,000 J>mol (A) Mo (B) C (C) Cr (D) W
2 -6
D B (m >s) = 3.0 * 10 expa - b (5.19b) Calculate the diffusion coefficient for copper
RT 5.2FE
in aluminum at 600 C. Preexponential and activa-
Is it possible to purify gas A in this manner? If so, tion energy values for this system are 6.5 10
5
specify a temperature at which the process may be m /s and 136,000 J/mol, respectively.
2
carried out, and also the thickness of metal sheet
2
2
2
that would be required. If this procedure is not (A) 5.7 10 m /s (C) 4.7 10 13 m /s
possible, then state the reason(s) why. (B) 9.4 10 17 m /s (D) 3.9 10 m /s
2
2
2