Determining the Diffusion Coefficients for Carbon in Nickel

To determine the diffusion coefficients for carbon in nickel, we need to find two parameters: D₀ (the pre-exponential factor) and Q_d (the activation energy for diffusion). These parameters can be determined using the Arrhenius equation, which describes how the diffusion coefficient varies with temperature:

D = D₀ * e^{(-Q_d / RT)}

Where:

• D = diffusion coefficient
• R = universal gas constant (8.314 J/mol·K)
• T = temperature in Kelvin

In order to find D₀ and Q_d, you typically need diffusion coefficient values at two different temperatures. If you’ve provided those values, you can set up two equations based on the Arrhenius equation:

D₁ = D₀ * e^{(-Q_d / (R * T₁))}

D₂ = D₀ * e^{(-Q_d / (R * T₂))}

By taking the natural logarithm of both equations, you can eliminate D₀ and solve for Q_d.

Once you have D₀ and Q_d, you can find the diffusion coefficient at 875°C (which is 1148 K) using the Arrhenius equation again:

D(875) = D₀ * e^{(-Q_d / (R * 1148))}

Remember to convert the temperature to Kelvin (K) by adding 273.15 to the Celsius temperature. With all of these calculations, you should be able to determine the values of D₀ and D at 875°C.