Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY T1: PBU Printer: Yet to Come
GTBL042-06 GTBL042-Callister-v2 July 31, 2007 16:31

184 • Chapter 6 / Diffusion

preexponential and activation energy for the

diffusion of Ni in Cu are 2.7× 10 −^4 m^2 /s and

236,000 J/mol, respectively.

6.16The outer surface of a steel gear is to be hard-

ened by increasing its carbon content; the car-

bon is to be supplied from an external carbon-

rich atmosphere that is maintained at an

elevated temperature. A diffusion heat treat-

ment at 600◦C (873 K) for 100 min increases

the carbon concentration to 0.75 wt% at a po-

sition 0.5 mm below the surface. Estimate the

diffusion time required at 900◦C (1173 K) to

achieve this same concentration also at a 0.5-

mm position. Assume that the surface carbon

content is the same for both heat treatments,

which is maintained constant. Use the diffu-

sion data in Table 6.2 for C diffusion inα-Fe.

Diffusion in Polymeric Materials

6.17Consider the diffusion of oxygen through a

low density polyethylene (LDPE) sheet 15

mm thick. The pressures of oxygen at the two

faces are 2000 kPa and 150 kPa, which are

maintained constant. Assuming conditions of

steady state, what is the diffusion flux [in (cm^3

STP)/cm^2 -s] at 298 K?

6.18The permeability coefficient for a type of small

gas molecule in a polymer is dependent on ab-

solute temperature according to the following

equation:

PM=PM 0 exp

(

−

Qp

RT

)

wherePM 0 andQpare constants for a given

gas-polymer pair. Consider the diffusion of

water through a polystyrene sheet 30 mm

thick. The water vapor pressures at the two

faces are 20 kPa and 1 kPa, which are main-

tained constant. Compute the diffusion flux [in

(cm^3 STP)/cm^2 –s] at 350 K? For this diffusion

system

PM 0 = 9. 0 × 10 −^5 (cm^3 STP)(cm)/cm^2 -s-Pa

QP= 42 .3kJ/mol

Also, assume a condition of steady-state diffu-

sion.

DESIGN PROBLEMS

Steady-State Diffusion

(Factors That Influence Diffusion)

6.D1A gas mixture is found to contain two di-

atomic A and B species (A 2 and B 2 ) for which

the partial pressures of both are 0.1013 MPa

(1 atm). This mixture is to be enriched in the

partial pressure of the A species by passing

both gases through a thin sheet of some metal

at an elevated temperature. The resulting en-

riched mixture is to have a partial pressure

of 0.051 MPa (0.5 atm) for gas A and 0.0203

MPa (0.2 atm) for gas B. The concentrations

of A and B (CAandCB, in mol/m^3 ) are func-

tions of gas partial pressures (pA 2 andpB 2 ,in

MPa) and absolute temperature according to

the following expressions:

CA= 1. 5 × 103

√

pA 2 exp

(

−

20 .0kJ/mol

RT

)

(6.17a)

CB= 2. 0 × 103

√

pB 2 exp

(

−

27 .0kJ/mol

RT

)

(6.17b)

Furthermore, the diffusion coefficients for the

diffusion of these gases in the metal are func-

tions of the absolute temperature as follows:

DA(m^2 /s)= 5. 0 × 10 −^7 exp

(

−

13 .0kJ/mol

RT

)

(6.18a)

DB(m^2 /s)= 3. 0 × 10 −^6 exp

(

−

21 .0kJ/mol

RT

)

(6.18b)

Is it possible to purify the A gas in this man-

ner? If so, specify a temperature at which the

process may be carried out, and also the thick-

ness of metal sheet that would be required. If

this procedure is not possible, then state the

reason(s) why.

Nonsteady-State Diffusion

(Factors That Influence Diffusion)

6.D2The wear resistance of a steel gear is to be im-

proved by hardening its surface, as described

in Design Example 6.1. However, in this case