Question

The process of carburization of steel, where carbon is diffused into the surface, is an example of

• A. steady-state diffusion
• B. non-steady-state diffusion
• C. isothermal diffusion
• D. chemical equilibrium

Hint:

For non-steady-state diffusion calculations, the depth of penetration is often estimated using the simplified relation \( x \approx \sqrt{Dt} \), showing that doubling the case depth requires quadrupling the processing time.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to classify the type of diffusion process that occurs during the industrial carburization of steel.

Step 2: Key Formula or Approach:
Steady-state diffusion is described by Fick's First Law, where the concentration profile does not change with time (\( \frac{\partial C}{\partial t} = 0 \)).
Non-steady-state diffusion is described by Fick's Second Law, where the concentration changes as a function of both position and time (\( \frac{\partial C}{\partial t} \neq 0 \)):
\[ \frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2} \]
For carburizing a semi-infinite solid with constant surface concentration \( C_s \), the solution to Fick's Second Law is:
\[ \frac{C_x - C_o}{C_s - C_o} = 1 - \text{erf}\left(\frac{x}{2\sqrt{Dt}}\right) \]
where:
\( C_x \) is the concentration at depth \( x \) at time \( t \),
\( C_o \) is the initial bulk concentration, and
erf is the Gaussian error function.

Step 3: Detailed Explanation:

• Carburization Process Characteristics: During gas or pack carburization, carbon atoms from the surrounding carbon-rich gas phase continuously dissolve into the surface of the hot steel part.
As time progresses, the carbon atoms diffuse deeper into the steel, increasing both the depth of the carbon-rich case and the carbon concentration at any given depth \( x \).
Because the concentration profile \( C(x,t) \) continuously changes with time, the process is a classic example of non-steady-state diffusion.

• Comparison with Steady-State: Steady-state diffusion only occurs when the concentration gradient remains constant over time, such as the diffusion of hydrogen gas through a thin metal membrane under constant pressure on both sides. This is not the case for surface hardening treatments.


Step 4: Final Answer:
Thus, the carburization of steel is an example of non-steady-state diffusion, corresponding to Option (B).