Question

Answer the following questions related to diffusion. Quantitatively describe the boundary conditions for the well-known assumption of a semi-infinite solid. Why is Qd for diffusion of Fe into gamma-iron greater than Qd for diffusion of C into gamma -iron? If the temperature was increased to 1100 degree C, how would you expect the carburizing time to change? What accounts for this change at the atomic level and how does it affect D, Do, and Qd?

Answer 1

a) Semi-infinite solids is visualized as very thick walls with one side exposed to some fluid. The other side, since the wall is very thick, remains unaffected by the fluid temperature. The condition at the exposed side of the wall is called the boundary condition.

One possible condition for the wall surface is a constant temperature. In this case, the temperature inside the wall at time t, at distance x from the surface, is given by

Θ /θi = Tx,t – T surface /Ti – T surface = erf(x/2 )

Here T Surface is the constant wall temperature and α is the thermal diffusivity of the wall.

c) Qd for diffusion of Fe in ϒ iron is greater than Qd of diffusion of C in ϒ Iron

D_ϒ for Iron (2.3 x 10^-5 m2/s) exp [-148,000 J/mol/(8.31 J/mol- K)(1273 K)] = 1.93 x 10^-11 m2/s

D_ϒ for Carbon = (2.3 x 10^-5 m2/s) exp [-148,000 J/mol/(8.31 J/mol- K)(1173 K)] = 5.86 x 10^-12 m2/s

Carbon diffuses at lower temperature than Fe; So Qd for diffusion of Fe in ϒ iron is greater than Qd of diffusion of C in ϒ Iron.

d) Temperature is increased 1100ºC (1373 K)

Diffusion and Temperature

• Diffusion coefficient increases with increasing T.

D = D^o exp (Qd/RT)

D= pre-exponential [m2/s]

D⁰= diffusion coefficient [m2/s]

Qd = activation energy J/mol

R = gas constant [8.314 J/mol-K]

T = absolute temperature [K]

D = (2.2 x 10^-5 m2/s) exp [- 252,400J/mol (8.31 J/mol- K)(1373 K)] = 5.4 x 10^-15 m2/s