# Fick's First Law (Diffusion Problem)

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1. Jun 15, 2015

### goncalo x. r.

1. A sheet (with a thickness of 0.05 cm) of MgO lies in between layers of Ni and Ta to avoid reaction between these two metals . At 1400 ºC, ions of Ni are created and diffuse through the ceramic MgO to the Ta. Find the number of ions that go through the MgO per second, knowing that the diffusion coefficient of the nickel ions in the MgO is 9*10^(-12) (cm^2)/s, and the lattice constant of Ni at 1400 ºC is 3.6*10^(-8) cm.

2. Relevant equations
Fick's First Law: J=-D*gradient(n) , n being the concentration of the species in cause

3. The attempt at a solution
The exercise is pretty straight forward. The real issue is to calculate the gradient. With the lattice constant and Ni's type of structure (FCC) it's easy to find Ni's concentration, but I am lacking another concentration to make the gradient. Is the 'ceramic' suppose to imply some lattice constant and/or type of structure?
(All the information given is highlighted)

Thanks in advance,
Gonçalo X. R. N.

2. Jun 16, 2015

### ehild

The thickness of the MgO sheet is given. Assume that there are no Ni ions in the MgO.

Last edited: Jun 16, 2015
3. Jun 17, 2015

### goncalo x. r.

Oh ok, didn't think of that assumption.
Thank you!

Last edited: Jun 17, 2015
4. Jun 17, 2015

### insightful

If you assume there are no Ni ions in the MgO, you have an unsteady-state situation. I would assume you are looking for the steady-state diffusion rate and that the Ta reacts instantly with the Ni so that the Ni concentration at the Ta side of the MgO is zero.

5. Jun 19, 2015

### goncalo x. r.

Thank you!

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