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# How to Calculate and Solve for Fick’s Second Law of Diffusion | Diffusion in Alloying

Last Updated on January 12, 2023

The image above represents fick’s second law of diffusion.

To compute for fick’s second law of diffusion, two essential parameters are needed and these parameters are Diffusion Coefficient (D) and Diffusion Gradient (d²C/dx²).

The formula for calculating fick’s second law of diffusion:

dC/dt = D(d²C/dx²)

Where:

dC/dt = Fick’s Second Law of Diffusion
D = Diffusion Coefficient
d²C/dx²  = Diffusion Gradient

Let’s solve an example;
Find the fick’s seond law of diffusion when the diffusion coefficient is 4 and the diffusion coefficient is 28.

This implies that;

D = Diffusion Coefficient = 4
d²C/dx²  = Diffusion Gradient = 28

dC/dt = D(d²C/dx²)
dC/dt = (4)(28)
dC/dt = 112

Therefore, the fick’s second law of diffusion is 112mol m-2 s-1.

Calculating the Diffusion Coefficient when the Fick’s Second Law of Diffusion and the Diffusion Gradient is Given.

D = dC/dtd²C/dx²

Where:

D = Diffusion Coefficient
dC/dt = Fick’s Second Law of Diffusion
d²C/dx² = Diffusion Gradient

Given an example;
Find the diffusion coefficient when the fick’s second law of diffusion is 40 and the diffusion coefficient is 5.

This implies that;

dC/dt = Fick’s Second Law of Diffusion = 40
dC/dx = Diffusion Gradient = 5

D = dC/dtd²C/dx²
D = 40 / 5
D = 8

Therefore, the diffusion coefficient is 8.

Calculating the Diffusion Gradient when the Fick’s Second Law of Diffusion and the Diffusion Coefficient is Given.

d²C/dx² = dC/dt / D

Where:

d²C/dx² = Diffusion Gradient
dC/dt = Fick’s Second Law of Diffusion
D = Diffusion Coefficient

Let’s solve an example;
Find the diffusion coefficient when the fick’s second law of diffusion is 35 and the diffusion coefficient is 7.

This implies that;

dC/dt = Fick’s Second Law of Diffusion = 35
D = Diffusion Coefficient = 7

d²C/dx² = dC/dt / D
d²C/dx² = 35 / 7
d²C/dx² = 5

Therefore, the diffusion gradient is 5.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the fick’s second law of diffusion.

To get the answer and workings of the fick’s second law of diffusion using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

To get access to the professional version via web, you need to register and subscribe to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.

Now, Click on Diffusion In Alloying under Materials and Metallurgical

Now, Click on Fick’s Second Law of Diffusion under Diffusion In Alloying

The screenshot below displays the page or activity to enter your values, to get the answer for the fick’s second law of diffusion according to the respective parameter which is the Diffusion Coefficient (D) and Diffusion Gradient (d²C/dx²).

Now, enter the values appropriately and accordingly for the parameters as required by the Diffusion Coefficient (D) is 4 and Diffusion Gradient (d²C/dx²) is 28.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the fick’s second law of diffusion and presents the formula, workings and steps too.