03 - Diffusion II

Non-Steady-State Non-Steady-State Diffusion

Fick’s Second Law

 

=

  

Solution to Fick’s Second Law depends on the initial boundary conditions: •

Carburization

•

Decarburization

•

Diffusion Couple

•

Thin-Film Diffusion

•

solution to Fick’s second law (differential equation) depends on the initial boundary conditions 1. Before diffusion, any of the diffusing solute atoms in the solid are uniformly with concentration, C0 2. The value of x at the surface is zero and increases with distance into the solid 3. The time is taken to be zero the instant before the diffusion process begins

      where Cx Cs C0 D t

= = = = =

=   

concentration at depth x concentration at the surface initial concentration diffusion coefficient time

  

Callister, W. (2011). Materials Science and Engineering: An Introduction. 8 th Edition. CRC Press.

Nitrogen from a gaseous phase is to be diffused into pure iron at 675 °C. If the surface concentration is maintained at 0.2 wt% N, what will be the concentration 2 mm from the surface after 25 h? The diffusion coefficient for nitrogen in iron at 675 °C is 1.9 x 10-11 m2/s.

        0 0.20

= 1  

 2 

2  10− 

 = 1   2

  1.9  10− (25 ℎ)(3600 /ℎ) 

  0 0.20

 = 1  (0.765)

0.765  0.750 0.800  0.750

=

  0.7112 0.7421  0.7112

 =  0.765 = 0.7205

  0 0.20

 = 1  0.7205

   = 0.056 % 

The wear resistance of a steel gear is to be improved by hardening its surface. This is to be accomplished by increasing the carbon content within an outer surface layer as a result of carbon diffusion into the steel; the carbon is to be supplied from an external carbon-rich gaseous atmosphere at an elevated and constant temperature. The initial carbon content of the steel is  0.20 wt%, whereas the surface concentration is to be maintained at  1.00 wt%. For this treatment to be effective, a carbon content of   0.60 wt% must be established at a position  0.75 mm below the surface. Specify an appropriate heat treatment in terms of temperature and time for temperatures  900 °C, 950 °C, 1000 , and  1050 °C. Use the data for the diffusion of carbon in γ-iron.

C0 = 0.20 wt% C

Cx

= 0.60 wt% C

Cs = 1.00 wt% C

x

= 0.75 mm = 7.5 x 10-4 m

      

0.60  0.20 1.00  0.20

= 1  

 = 1  

 2 

7.5  10−  2 

0.5 = 

Determine z.

7.5  10−  2 

Callister, W. (2011). Materials Science and Engineering: An Introduction. 8 th Edition. CRC Press.

Determine the value of z through interpolation. z

erf(z)

0.45

0.4755

z

0.5000

0.50

0.5205

  0.45 0.50  0.45

=

0.5000  0.4755 0.5205  0.4755

 = 0.4772

7.5  10−  2 

= 0.4772

 = .   − 

Solution:  .    s    s    e    r    P    C    R    C  .    n    o    i    t    i     d    E

    h    t

   8  .    n    o    i    t    c    u     d    o    r    t    n    I    n    A   :    g    n    i    r    e    e    n    i    g    n    E     d    n    a    e    c    n    e    i    c    S    s     l    a    i    r    e    t    a    M  .     )    1    1    0    2     (  .    W  ,    r    e    t    s    i     l     l    a    C

Diffusion coefficient is dependent on temperature. From the table of values,

  = 2.3  10−  /   = 148000 /  =    −

(2.3  10

 

148000 /  /)   (8.314   )  

 = .   − 

Diffusion coefficient is dependent on temperature. From the table of values, .     = .    

Callister, W. (2011). Materials Science and Engineering: An Introduction. 8 th Edition. CRC Press.

[1] Callister, W. Materials Science and Engineering: An Introduction . 8th Edition. CRC Press, 2014. eBook. [2] Porter, David A., and K. E. Easterling. Phase Transformations in Metals and Alloys . 2nd Edition. London: Chapman and Hall, 1992. Print. [3] Smallman, R. E., and R.E Smallman. Modern Physical Metallurgy. 8th Edition. Amsterdam: Butterworth-Heinemann, 2014. eBook.